More Reasons Why Objective Reality Cannot Be Descartes’s Universal Theory of Ideas with Claude Opus 4.7

Introduction by Grok 4.3 (xAI, May 2026)

A central ambition of Descartes’s Theory of Ideas (DTOI) is to provide a systematic account of how ideas represent their objects through the distinction between formal and objective reality. On one influential reading, objective reality (OR) offers a universal framework: every thinkable content is, or can be reconstructed as, the objective being of some ranked item (infinite substance, finite substance, or mode) in the intellect. Yet certain perfectly intelligible ideas and propositions resist this treatment. False but thinkable judgments such as “a vacuum exists” initially seem promising counterexamples, but a careful pro-OR interpreter can reconstruct them as misjudgments composed of OR-bearing constituents (extension and body). Even imaginative composites like a chimera turn out to have aggregated OR from their parts. Stronger pressure comes from cases whose content cannot plausibly be assigned any rank on Descartes’s ontological hierarchy—even when grounded in God’s intellect or treated as true-and-immutable natures. Privative ideas (the idea of nothing), foundational eternal truths (ex nihilo, nihil fit), relational structures, and modal necessities such as “a mode is necessarily related to a substance” are thinkable, even foundational to Cartesian metaphysics, yet function as modi cogitandi or intelligible truth-contents rather than representations of ranked objects. This post refines the argument by retiring weaker (I.e., false) examples, sharpening the decisive ones, and mapping the resulting pattern in a summary table at the post’s end. The result is a clearer view of where Descartes’s OR apparatus succeeds and where it necessarily falls silent.

This post is the fourth in a series. See “Condensation: Why Objective Reality Cannot Be Descartes’s Theory Of Thought: Burman, Common Notions, And The Failure Of The Strict Idea Model” (a condensed version of the first in the series: “Why Objective Reality Cannot Be Descartes’s Universal Theory Of Thought: Burman, Common Notions, And The Failure Of The Strict-Idea Model” and its follow-up second companion piece “Why Objective Reality Cannot Be Universal In Descartes’s Theory Of Ideas: Nothing, Eternal Truths, Sensations, And Fear With Claude Opus 4.6.”

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Argumentative Outline: More Reasons Why Objective Reality Cannot Be Descartes’s Universal Theory of Ideas

I. Introduction & Thesis

• Main Thesis (Restriction Thesis): Descartes’s Objective Reality (OR) apparatus succeeds as a framework for ranked representational content (substances, modes, true-and-immutable natures) but necessarily falls silent for a large class of perfectly intelligible Cartesian ideas.
• Refinement over prior posts: Retire weaker examples (false judgments, non-existent composites), sharpen decisive ones (privative, eternal-truth, relational, modal, universal contents).
• Roadmap: Test candidate counterexamples → distinguish OR-bearing from non-OR-bearing → identify three structural classes of non-OR content → map results in a summary table.

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II. Background: The Pro-OR (“Universal OR”) Reading

• DTOI’s Pro-OR ambition: every thinkable content = objective being of some ranked item (infinite substance / finite substance / mode) in the intellect.
• Pro-OR interpreters (Lawrence Nolan, Vere Chappell, John Carriero, Dan Kaufman): even non-existent or false contents reduce to OR-bearing constituents.
• OR ≠ formal existence outside the mind (AT VII 102–103); represented content alone suffices.

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III. Weak Counterexamples (To Be Retired)

A. False judgments: “A vacuum exists”

• Pro-O reconstruction: extension (OR as principal attribute) + body (OR as finite substance) composed via false judgment.
• Falsity is metaphysical, not a failure of intelligibility.
• Lesson: Shows only that thinkability outruns truth, not that content escapes OR.

B. Imaginative composites: The chimera

• Descartes himself lists chimeras among paradigmatic ideas (AT VII 37; AT VII 232).
• Constituents (lion, goat, snake) are OR-bearing finite-substance ideas; composition preserves OR.
• Lesson: Non-existence ≠ non-OR. Chimeras are easy cases for OR, not hard ones.

C. Take-away: Decisive anti-OR cases must lack OR-bearing constituents at any ontological rank, not merely lack formal existence.

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IV. Decisive Anti-OR Cases — Three Structural Classes

Class 1: Privative Content

• The idea of nothing (Burman: “purely negative, and hardly counts as an idea at all”).
• No positive representatum; grasped only privatively through being.
• No OR candidate survives (nothingness, impossibility, being-as-such all fail).

Class 2: Eternal Truths / Common Notions

• Ex nihilo, nihil fit as a proposition.
• Intelligible, foundational to Cartesian metaphysics, yet its distinctive content (causal-dependence axiom) is intelligible truth-content, not an internal object contained objectively in the intellect.
• Functions as a modus cogitandi governing thought, not as a ranked representatum.
• Paradigm case: Ex nihilo, nihil fit—intelligible, foundational to Cartesian metaphysics, yet its distinctive content (a causal-dependence axiom) is intelligible truth-content, not an internal object contained objectively in the intellect. It functions as a modus cogitandi governing thought, not as a ranked representatum.
• Descartes’s own doctrine of the created eternal truths supplies the decisive textual backing for treating such content as non-OR:
• To Mersenne, 15 April 1630 (AT I 145): the eternal truths (mathematical and metaphysical) are freely created by God and depend on His will, not on any independent realm of essences.
• To Mersenne, 6 May 1630 (AT I 149–150): God is the efficient and total cause of these truths; they are not co-eternal Platonic objects.
• To Mersenne, 27 May 1630 (AT I 151–154): the doctrine of the created eternal truths reaffirmed and extended; God is not constrained by mathematical or metaphysical essences, since He is their free author.
• To Mersenne, 16 October 1639 (AT II 597–599): Descartes treats truth itself as so transcendentally clear it cannot be defined, and reaffirms that eternal truths are accessed via the natural light rather than as items ranked alongside substances and modes.
• Sixth Replies (AT VII 432, 435–436): the indifference doctrine—God’s will is the source of essential truths, not constrained by them.

Why this supports non-OR status: if eternal truths are products of divine willing rather than ranked representata, then their content in finite intellects is not an item with objective being inherited from a substance or mode. It is intelligible truth-content grasped by the natural light—a third ontological category alongside ranked items and modi cogitandi, irreducible to either.

Pro-OR rescue attempts fail here:

• Reducing the truth to its constituent ideas (e.g., “nothing,” “comes from,” “something”) fails because nothing is itself privative (Class 1) and comes from is a relational/modal structure (Classes 3–4).
• Treating the truth as a mode of the mind grasping it collapses content into act, which Descartes explicitly resists (AT VII 8, 102–103).
• Grounding the truth in God’s intellect locates its formal reality but not the objective reality of the finite idea, which is what OR theory is supposed to measure.

Class 3: Relational Structure (Principles I.55–58)

• Descartes’s deflationary nominalism: relations are modi cogitandi of the comparing mind, not items in re.

• “Numerus etiam … modus tantum est cogitandi; ut & alia omnia, quae universalia vocamus” (I.58).

• “A is to the left of B”: OR exhausted by A and B; the relation contributes only a comparative form of thought.

• “Watch out for the person behind the person in front of you”: OR in the persons; relational + imperatival structure is mind-side.

• Spatial relations might reduce to positional modes, but non-spatial relations (father-of, taller-than, believes-that) cannot—the modus cogitandi treatment is unavoidable.

Class 4 (Capstone): Modal-Necessity Content

• “A mode is necessarily related to a substance” (Principles I.51–53).

• Triggers all three anti-OR classes simultaneously:

• mode-in-general and substance-in-general = universals = modi cogitandi (by I.58).

• necessary dependence = eternal truth, not a representatum.

• Self-referential force: OR theory cannot rank its own enabling background.

• Resists every standard pro-OR rescue (constituent-reduction, false-judgment composition, mode-of-mode, divine grounding).

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V. Supporting Argument: Principles I.58 Universally Quantified

Claim: All universals are modi cogitandi—load-bearing for Classes 3 and 4.

Cross-textual: The universal reading of I.58 is reinforced by Descartes’s other discussions of universals and abstraction:

• • Conversation with Burman, 16 April 1648 (AT V 158): Burman presses Descartes directly on the status of universals; Descartes reaffirms that they are modes of thinking produced by the mind’s abstracting activity from particulars, not items existing in re.

• • Comments on a Certain Broadsheet (1648), AT VIIIB 344–351: against Regius, Descartes clarifies the role of abstraction and innate ideas, consistent with the anti-realist treatment of universals in Principles I.58–59.

• • To Mesland, 2 May 1644 (AT IV 113–114): supplementary remarks on abstraction and the mind’s formation of general notions.

• • Rule 14, Regulae ad directionem ingenii (AT X 438ff.): early anti-realist treatment of universals via abstraction; useful as developmental background showing the doctrine is long-standing, not an ad hoc Principles-era addition.

Together with I.58’s explicit universal quantifier (“alia omnia, quae universalia vocamus“) and the systematic treatment in I.55–62, these texts make the restricted reading exegetically untenable: nowhere does Descartes carve out a privileged sub-class of universals exempt from modus cogitandi status.

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VI. Modern Structural Analogues (Illustrative, Not Historical)

• • The universal set: thinkable, definable, refutable (Russell); not rankable on Descartes’s hierarchy; set and all are not OR-bearing constituents.

• • 17th-century analogue: the greatest finite number: Descartes denies that the series of numbers admits a greatest member, classifying number among the indefinite rather than the infinite, with infinitum reserved for God alone (Principles I.26–27, AT VIIIA 14–15; First Replies, AT VII 113; To More, 5 February 1649, AT V 274). The impossibility is internal to the structure of number itself, not a matter of false composition of OR-bearing constituents. Cleaner than the squared circle, whose constituents have TIN-status.
  • In the context of that post, TIN-status means “True and Immutable Nature” status—a reference to Descartes’s doctrine of true and immutable natures from the Fifth Meditation. The post contrasts two impossible objects:
    • The greatest finite number — its impossibility is internal to the structure of number itself. There’s nothing for the pro-OR reader to grab onto, because the constituent concept (number) generates the impossibility structurally (for any n, n+1 exists).
    • The squared circle — its constituents, circle and square, are geometrical essences that Descartes treats as having true and immutable natures (Fifth Meditation, AT VII 64). Because those constituents have TIN-status, they are OR-bearing: the pro-OR interpreter can say each part has objective reality as a genuine geometrical essence, and the impossibility lies merely in the judgment that combines them (false composition of OR-bearing constituents).
  • So when the post says the greatest-finite-number case is “cleaner than the squared circle, whose constituents have TIN-status,” it means:
    

    The squared circle is a weaker anti-OR example because its parts (circle, square) are true-and-immutable-nature essences that the pro-OR reader can claim carry objective reality. The impossibility there is combinatorial (a bad judgment joining good OR-bearing parts) rather than structural. The greatest finite number avoids this loophole—its impossibility comes from inside a single concept, so there are no OR-bearing TIN-constituents for the pro-OR reader to fall back on.This matches the earlier passage in the same post, where the squared circle is explicitly flagged as dialectically weaker precisely because circle, square, and rectilinear are “geometrical essences with true and immutable natures, in Descartes’s Fifth Meditation sense.”

  • So TIN = True and Immutable Nature, and TIN-status = the property of being one of Descartes’s genuine geometrical/mathematical essences, which is what confers objective reality on a constituent idea.

• • Backup cases: indefinitely-extended body, smallest extended body (Principles I.26–27, I.20).

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VII. Pressures on the Cartesian Framework (Collateral Arguments)

These extend the post by showing I.53 itself is contested:

A. Counterexamples to “one principal attribute per substance” (I.53):

• • The human substantial union (Sixth Meditation; To Elisabeth 21 May 1643) — strongest internal case (Rozemond; Hoffman).

• • God under divine simplicity — intellect, will, power, goodness all essential.

• • External: Spinoza, neutral monism.

B. Natural kinds (gold):

• • Goldness as principal attribute → circular.

• • Atomic number 79 → contentful, but: (i) anachronistic; (ii) reduces to a mode of extension; (iii) a posteriori not natural-light intelligible; (iv) proliferates substantial forms; (v) confuses kind-as-universal with individual-as-body.

• • Best framing: External pressure on Cartesian mechanism, not an internal I.53 counterexample.

C. Duration vs. time (I.57):

• • A motionless (and mindless) universe still endures (duration is real-in-things) but no time-as-measure-of-movement occurs.

• • Parallels number-in-things vs. number-in-general: real-in-things has OR; modus cogitandi does not.

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VIII. Summary Table

Two-axis mapping of items (God, finite substances, modes, gold-kind vs. this-piece-of-gold, duration, time, number-in-things, number-in-general, relations, common notions, nothing, necessity, principal attribute, substantial union) against:

• • Ontological status (in re vs. modus cogitandi)

• • Cartesian framework treatment

• • OR-bearing status (rank inheritance vs. no OR)

Organizing principle: Real-in-things items inherit OR rank from the substance/mode they modify; modi cogitandi and abstractions consistently fall outside OR.

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IX. Conclusion

• • The OR apparatus succeeds for ranked representational content but is constitutively silent for:

1. 1. Privative content (nothing),

1. 1. Some eternal-truth content (ex nihilo, nihil fit),

1. 1. Some relational structures and universals (I.55–58),

1. 1. Modal-necessity content (a mode is necessarily related to a substance)—the capstone, which triggers all three.

• • Collateral pressures (substantial union, natural kinds, duration/time) show the broader framework strains beyond just the OR doctrine.

• • Final claim: Descartes’s
    • • OR doctrine.
    • • Final claim: Descartes’s OR is a restricted—not universal—theory of ideas. Its silence on its own foundational background is not a paradox but the expected behavior of a measure-apparatus operating within an ontological framework rather than over it.
     

    is a restricted—not universal—theory of ideas. Its silence on its own foundational background is not a paradox but the expected behavior of a measure-apparatus operating within an ontological framework rather than over it.

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A proposition such as ‘a vacuum exists’ (or ‘the void exists’) is judged false by Descartes—extension and body are inseparable—yet it is perfectly thinkable.

  ^{Cannot Descartes specify the objectively real representational content for the idea that a vacuum exists?}

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Why “a vacuum exists” is a problematic example for the anti-OR side

A Cartesian vacuum is supposed to be extension without body—a region of space in which no corporeal substance is present. Descartes’s reason for denying that a vacuum can exist is precisely that extension is the principal attribute of body, so wherever there is extension there is body. The proposition is judged false, but the falsity is metaphysical, not a failure of intelligibility.

The pro-OR interpreter (Lawrence Nolan, say) can therefore reply:

1. 1. The constituent idea extension has objective reality—it is the principal attribute of corporeal substance and is one of Descartes’s paradigm cases of a clearly and distinctly perceived intellectual content.

1. 1. The constituent idea body (or corporeal substance) has objective reality as a finite substance.

1. 1. The proposition a vacuum exists is composed by negating the inseparability of extension and body—roughly, “there is extension where there is no body.”

1. 1. Both halves of that composition trade in OR-bearing constituents. The proposition is false because the constituents cannot be combined in reality, not because either constituent fails to be objectively contained somewhere.

So the proposition can be reconstructed as a misjudgment about OR-bearing constituents rather than as a thought whose content escapes the OR apparatus. That is exactly the move the pro-OR side wants: false propositions are intelligible because their constituent ideas have OR; the falsity lies in the judgment, not in a content beyond OR.

This is structurally the same problem you already flagged for figure is the limit of extension in your Proposition/Constituent section: the proposition has OR-bearing constituents even though the proposition-as-a-whole need not be a further OR-bearing item. Against a careful pro-OR reader, “a vacuum exists” doesn’t isolate non-OR content; it isolates judgmental composition of OR-bearing content.

Why “time is relative to speed” was no better

I originally flagged “time is relative to speed” as anachronistic, but the deeper problem is the same: duration, motion, measure, and relation are all available to Descartes as intelligible intellectual materials, and a pro-OR reader can say the proposition trades in OR-bearing or quasi-OR-bearing constituents. Both examples fail in the same way.

What would actually do the work

The anti-OR example you need is one where no plausible OR-bearing representatum is available even at the constituent level. The two cleanest cases in your post already do this work, and you should lean on them rather than on a false-judgment example:

1. 1. The idea of nothing. Burman’s “purely negative, and hardly counts as an idea at all” is the strongest single text. Nothing is not a constituent with positive content; it is a privation grasped through being. No OR candidate survives scrutiny (your own Testing-Candidates table makes this case).

1. 1. Ex nihilo, nihil fit considered as a proposition. The proposition is intelligible, but its distinctive content—the causal-dependence axiom—is not naturally cashed as “an internal object contained objectively in the intellect.” Your table already canvasses the candidates (nothingness, impossibility, causal dependence, being-as-such, the proposition itself) and shows that each either fails or merely renames the problem.

A false-judgment example like “a vacuum exists” is not doing the same anti-OR work, because the pro-OR reader concedes that false judgments compose OR-bearing constituents. What false-judgment examples do show is something weaker but still useful: that thinkability outruns truth. Some false judgments can have OR so do not yet show that thinkability outruns OR.

Recommendation for the Conceptual Content Without Objective Reality section

Rather than substituting one false-judgment example for another, I’d recommend rewriting the paragraph to do exactly the work it can do, and no more. Something like:

False but intelligible judgments illustrate a narrower point. A proposition such as a vacuum exists is judged false by Descartes—extension and body are inseparable—yet it is perfectly thinkable. Its thinkability shows that intelligibility outruns truth, and it shows that the proposition need not itself be a unified OR-bearing representatum even when its constituents (extension, body) are OR-bearing. It does not by itself show that the proposition’s content escapes the OR apparatus entirely, since a pro-OR reader can reconstruct the proposition as a misjudgment composing OR-bearing constituents. The decisive anti-OR cases remain ex nihilo, nihil fit and the idea of nothing, where no plausible OR-bearing representatum is available even at the constituent level.

This concedes exactly what the pro-OR reader will press, narrows the false-judgment example to what it actually shows (thinkability outruns truth; the whole proposition need not be a further OR item), and routes the heavy lifting back to your two genuinely decisive cases.

Bottom line

You spotted a real weakness. The honest answer to your question—why can’t Descartes specify the OR-content for “a vacuum exists”?—is that he probably can, by appealing to the OR of extension and body as constituents and locating the falsity in the judgmental combination. The example is therefore good for showing thinkability ≠ truth and proposition ≠ unified OR item, but it is not good for showing content beyond OR. The idea of nothing and ex nihilo, nihil fit remain your strongest non-OR cases, and the post should rely on them rather than on false-judgment examples.

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In light of the Cartesian pushing back and arguing that false judgments may contain objectively real representational content (OR), let’s explore the content of an idea of a chimera, which is a mythological fire breathing animal with the body of a lion, the head of a goat on its back, and a snake for a tail?

  Is the OR content of an idea of a chimera an objectively real representation of a chimera?

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Excellent test case. The chimera is exactly the right example to press, because Descartes himself uses it as a paradigm of a thinkable-but-non-existent idea, and a careful answer reveals something important about what OR can and cannot do.

What Descartes himself says about the chimera

Descartes invokes the chimera (or “hippogriff,” or composite imaginary animals) in several places as examples of ideas whose objects do not exist outside the mind. The Third Meditation passage is the most directly relevant:

“And although these ideas do not depend on my will, it does not follow that they must come from things located outside me. . . . even if [the ideas] did proceed from things other than myself, it would not follow that they must resemble those things. On the contrary, I have observed in many cases that there is a great disparity between an object and its idea. For example, . . . I find within me two quite different ideas of the sun.” (AT VII 39; CSM II 27)

And more directly:

“Some of my thoughts are as it were the images of things, and it is only in these cases that the term ‘idea’ is strictly appropriate—for example, when I think of a man, or a ‘chimera’, or the sky, or an angel, or God.” (AT VII 37; CSM II 25)

All of these items, including the chimera, are the paradigmatic examples of objectively real representational contents!

The chimera is for Descartes a composed idea: the imagination fuses constituent ideas of really-existing kinds (lion-body, goat-head, snake-tail) into a single imaginative presentation.

“You say that the mind has the faculty not just of perceiving adventitious ideas but also ‘of putting them together and separating them in various ways, of enlarging them and diminishing them, of comparing them and so on’. Hence you conclude that the ideas of chimeras, which the mind makes up by the process of putting together and separating etc., are not constructed by the mind but are adventitious. By this argument you could prove that Praxiteles never made any statues on the grounds that he did not get from within himself the marble from which he sculpted them; or you could prove that you did not produce these objections on the grounds that you composed them out of words which you acquired from others rather than inventing them yourself. But in fact the form of a chimera does not consist in the parts of the goat or lion, nor does the form of your objections consist in the individual words you have used; they both consist simply in the fact that the elements are put together in a certain way.” (AT VII 232; CSM II 250; bold and bold italic not in original)

The pro-OR reading of the chimera

Here is the strongest pro-OR case, which a Cartesian like Lawrence Nolan, Vere Chappell, John Carriero, or Dan Kaufman would press:

1. 1. Lion, goat, and snake are each ideas of finite corporeal substances. Each has objective reality at the rank of finite substance (or finite animal substance).

1. 1. Body, head, tail are modal or part-whole ideas with OR at the rank of mode or part.

1. 1. The chimera-idea is a composite idea: the intellect or imagination assembles these OR-bearing constituents into one complex representation.

1. 1. Therefore the chimera-idea has OR—not the OR of a really existing chimera (there is no such substance to be ranked), but the aggregated OR of its constituents, presented as if combined in one animal.

1. 1. The fact that no chimera exists outside the mind is irrelevant to OR. Descartes is explicit (AT VII 102–103, First Replies) that OR is the mode of being a thing has as represented in the idea, regardless of whether the thing exists formally outside the mind. Non-existent objects can have OR.

On this reading, the chimera-idea is an OR-bearing idea of a (non-existent) finite corporeal substance. Its OR is the OR of a-lion-bodied-goat-headed-snake-tailed-animal-as-represented. The pro-OR reader will say: this is exactly what OR is for. OR measures represented content, and the chimera-idea has represented content in spades.

Is that a correct OR-content?

This is the subtle move. There is no really existing chimera, so there is nothing outside the mind that the OR could be of in the sense of “resembling” or “having as its formal counterpart.” But Descartes is clear that OR does not require formal existence of the represented object. The OR of the idea of a chimera is just the represented content as the intellect/imagination has assembled it. It is “objectively real representation of a chimera” in the precise Cartesian sense: the chimera has objective being in the intellect via this idea, even though it has no formal being outside the intellect.

So the answer to your question—is the OR content of an idea of a chimera an objectively real representation of a chimera?—is: yes, in the precise Cartesian technical sense, the chimera-idea contains the chimera objectively, i.e., as represented; and that represented content can be ranked at the level of a finite corporeal substance (or animal). The chimera-idea is OR-bearing.

What this does to the anti-OR argument

This is the critical philosophical point, and I think it is good news for your anti-OR project rather than bad news. The chimera shows that:

1. 1. Composition of OR-bearing constituents preserves OR-bearing status. Compose lion + goat + snake and you get a composite OR-bearing idea (a finite-corporeal-substance representation, ranked accordingly).

1. 1. OR does not require formal existence of the represented object. Non-existent finite substances can be represented with full OR.

1. 1. Therefore, the way to isolate non-OR content is not to find false or non-existent objects. False propositions and non-existent objects (chimeras, hippogriffs, golden mountains) are exactly the cases where the pro-OR reader is strongest, because OR was always designed to handle them.

This is precisely the point I conceded in my last reply about a vacuum exists: false judgments and non-existent objects compose OR-bearing constituents. Chimeras do the same.

The decisive anti-OR cases must therefore have a different structure. They must be cases where no OR-bearing constituent or composite is available even in principle, not cases where the object happens not to exist outside the mind. Your two clean cases remain:

1. 1. The idea of nothing. Nothing is not a constituent like lion or goat. It is privative, grasped through being. There is no positive representatum at any ontological rank—not finite substance, not mode, not infinite substance, not even a “minimal” representatum. Burman’s “purely negative, and hardly counts as an idea at all” is doing real work here.

1. 1. Ex nihilo, nihil fit as a proposition. The constituents are being, non-being, causal dependence, production. The proposition asserts a necessary truth about the impossibility of production-from-nothing. Even the strongest candidate (causal dependence) is, as your table notes, “more like intelligible truth-content than an objectively contained representatum.” And the proposition’s distinctive content is the necessary truth itself, which is not an object with an ontological rank.

The chimera shows by contrast why these two cases are special. The chimera assembles positively typed constituents into a finite-substance representation. Nothing and ex nihilo do not. That asymmetry is the heart of your anti-OR argument.

A useful structural lesson for the post

The chimera example is worth introducing in the Conceptual Content Without Objective Reality section, precisely because it sharpens the contrast. Something like:

The decisive anti-OR cases must be distinguished from cases of non-existent or composite objects. The idea of a chimera—a lion-bodied, goat-headed, snake-tailed animal—has full objective reality in the Cartesian sense, even though no chimera exists outside the mind. Its OR is the composite OR of its constituent ideas (lion, goat, snake, and the corresponding parts), assembled by the imagination into a finite-corporeal-substance representation. Descartes is explicit that OR is the being of the thing as represented, and does not require formal existence outside the intellect (AT VII 102–103). Chimeras, hippogriffs, golden mountains, and similar imaginative composites are therefore the easy cases for objective reality, not hard ones. The genuinely hard cases—the idea of nothing and propositions such as ex nihilo, nihil fit—are different in kind: their alleged content cannot be reconstructed as the composition of OR-bearing constituents at any ontological rank.

This concession actually strengthens the anti-OR position by sharpening which cases do and do not press against universal OR.

Direct answer to your question

Yes—the OR content of the idea of a chimera is an objectively real representation of a chimera, in Descartes’s precise technical sense. It represents a (non-existent) finite corporeal substance assembled from OR-bearing constituent ideas of really-existing animal kinds. The chimera-idea has OR; it does not have a formally existing counterpart outside the mind, but OR was never about formal existence outside the mind.

That is why the chimera is not a counterexample to universal OR and why the anti-OR argument must rest on nothing and ex nihilo, nihil fit, not on non-existent or false-judged objects.

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    What about the idea of the set of all sets, often called the universal set? Must that idea contain an OR universal set, according to Cartesian OR theory?

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Beautiful test case. The universal set is a much harder example than the chimera for the pro-OR side, and it isolates exactly the structural feature that distinguishes genuinely non-OR content from merely non-existent content. Let me work through it.

Why the universal set is unlike the chimera

The chimera is a composite of OR-bearing constituents (lion, goat, snake) assembled into a finite corporeal substance representation. Each constituent has a determinate ontological rank, and the composite inherits a rank (finite corporeal substance, or finite animal substance).

The universal set is not like this. It is the set whose members are all sets—including, on the naive comprehension principle, itself. Two features distinguish it from the chimera:

1. 1. It is not the composition of independently OR-bearing constituents into a finite-substance representation. A “set” is not a Cartesian substance, mode, or attribute. It does not appear anywhere in Descartes’s official ontological hierarchy (mode / finite substance / infinite substance). The universal set is not a finite corporeal substance, not a finite mental substance, not God, and not a mode of any of these.

1. 1. It is paradoxical. Russell’s paradox shows that on naive comprehension the universal set both must and cannot contain itself in a coherent way (the set of all sets that do not contain themselves leads to contradiction; the universal set considered as containing itself produces well-known size paradoxes via Cantor’s theorem on power sets). The “object” the idea purports to represent is not merely non-existent; it is impossible in a stronger sense than a chimera or a vacuum.

The pro-OR reader’s best move, and why it fails

A determined pro-OR reader (Nolan, Kaufman) will try one of three reconstructions. Each one fails in a revealing way.

    Reconstruction 1: The universal set is a finite substance-like representatum.
This fails immediately. A set is not a Cartesian finite substance. Sets are not the kind of thing that appears on the mode/finite-substance/infinite-substance scale. There is no rank to assign. Even granting that Descartes has some tolerance for mathematical objects (geometrical essences, numbers as abstracted modes), the universal set is not analogous to a triangle or to two. A triangle has a true and immutable nature that the intellect grasps; the universal set has no coherent nature to grasp.

    Reconstruction 2: The universal set is a composite of OR-bearing constituents (just like the chimera).
This is the move the pro-OR reader will most want to make. The constituents would be set, all, and perhaps membership or containment. The idea would be: just as lion + goat + snake compose into chimera, set + all compose into universal set.

But this fails for two reasons. First, set is not itself an OR-bearing constituent in any recognizable Cartesian sense. It is not a substance, mode, or attribute. (One could try to reconstruct set as a relation or as a kind of intelligible structure, but this immediately moves out of the OR apparatus and into the intelligible-truth-content region you have already identified as non-OR.) Second, and more decisively, the composition is incoherent. With the chimera, lion + goat + snake yields a coherent (if non-existent) animal. With the universal set, set + all yields a contradiction-generating pseudo-object. There is no coherent represented content for OR to measure.

    Reconstruction 3: The universal set has minimal or infinitesimal OR (a Gueroult-style move).
This is even worse than the cold-sensation case you already reject. At least the cold sensation is a formally real positive mental mode. The universal set is not even a coherent thinkable as the pro-OR reader would need it. Gueroult’s move was already textually weak for sensations; for the universal set it has no purchase at all.

What the universal set actually is, in Cartesian terms

The best Cartesian description of what is going on when we “think” the universal set is something like this:

We have intellectual materials—collection, all, member, containment—which are intelligible but not OR-bearing in the strict sense. We compose them into a propositional or quasi-propositional content: the collection whose members are all collections. This composition is intelligible enough for us to formulate it, and intelligible enough for us to prove (via Russell, via Cantor) that it cannot have a coherent referent. The intelligibility of the composition is exactly what allows us to recognize the contradiction.

This is structurally parallel to ex nihilo, nihil fit but in the opposite direction. Ex nihilo uses intelligible non-OR materials (being, non-being, causal dependence) to compose a necessary truth. The universal set uses intelligible non-OR materials (set, all, membership) to compose a necessary falsehood (or, more precisely, a content that cannot be coherently instantiated even as represented). In both cases, the thinkability of the content does not consist in its containing an OR-rankable representatum.

Direct answer to your question

No. The idea of the universal set does not contain an OR universal set, and the pro-OR reader cannot plausibly maintain that it does. The universal set is not assignable to any rank on Descartes’s mode / finite substance / infinite substance hierarchy; it cannot be reconstructed as a composition of OR-bearing constituents in the chimera-style way (because set is not an OR-bearing constituent and the composition is contradiction-generating); and Gueroult-style infinitesimal-OR moves have no purchase here.

What the idea of the universal set shows is exactly what ex nihilo, nihil fit and the idea of nothing show, but with an added feature: even coherent representability fails. The idea is thinkable enough to be entertained, defined, and refuted—but its thinkability does not consist in OR-bearing content.

Why this strengthens your post

The universal set is a cleaner anti-OR example in one respect than ex nihilo, nihil fit: it is more obviously not a composition of OR-bearing constituents, because set and all are manifestly not Cartesian substances or modes. Where the pro-OR reader can at least try the constituent-composition move on ex nihilo (via being, causal dependence), the move is harder to even formulate for the universal set.

However, the universal set has an anachronism cost: it is a post-Cantorian object, and Descartes had no concept of sets in the modern sense. So while it is dialectically powerful as a thought experiment, it should not replace your historical cases. I would recommend introducing it briefly as a contemporary structural analogue that illustrates the same anti-OR point, then routing the historically grounded argument back through nothing and ex nihilo, nihil fit.

A draft sentence or two for the post:

A structurally similar but contemporary example reinforces the point. The idea of the universal set—the set whose members are all sets—is thinkable enough to be defined and refuted (via Russell’s paradox), but it cannot be assigned any rank on Descartes’s mode / finite-substance / infinite-substance hierarchy, and it cannot be reconstructed as a composition of OR-bearing constituents in the way the idea of a chimera can be. Set and all are not Cartesian substances, modes, or attributes. The thinkability of the universal set, like the thinkability of ex nihilo, nihil fit and the idea of nothing, consists in the intellect’s use of intelligible but non-OR-bearing materials, not in the OR-bearing representation of an object.

That gives you a vivid modern illustration of the structural point while keeping the historical argument anchored where it belongs.

Bottom line

The universal set is an even cleaner anti-OR case than the chimera-style examples can ever be, because it isolates the feature that genuinely distinguishes non-OR content from non-existent OR-bearing content: no constituent at any ontological rank, and no coherent composition of constituents, is available even in principle. That is exactly the structural feature that ex nihilo, nihil fit and the idea of nothing also have, and that a vacuum exists and a chimera do not.

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    What would be a 17th-century example of an idea that resembles the idea of a set of all sets where the object seems coherent but is necessarily impossible?

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Excellent question. You want a 17th-century-available idea that has the same structural profile as the universal set: thinkable enough to be defined and entertained, but on analysis necessarily impossible (not merely non-existent), and not reducible to a composition of OR-bearing constituents. Here are the strongest candidates, ranked by how well they match the structural profile.

1. The largest number (or the greatest finite number)

This is the closest 17th-century analogue. The idea is straightforwardly thinkable: the number than which no greater finite number can be conceived. It seems coherent on first formulation. But it is necessarily impossible, because for any candidate n, n+1 is also a number, and the construction is internal to the very concept of number. The impossibility is not contingent (like a chimera’s non-existence) but follows from the structure of arithmetic itself.

Descartes himself flirts with exactly this territory in the Third Meditation when distinguishing the indefinite from the infinite, and in correspondence (to Mersenne, 27 May 1630; AT I 152; CSMK 25) where he discusses the impossibility of a greatest number. He uses the inexhaustibility of number as one ground for refusing to call number truly infinite. So this example is not merely available in the 17th century—it is one Descartes actively discussed.

Structural match to the universal set:

• • Thinkable enough to define and refute. ✓

• • Not assignable to any Cartesian ontological rank (number is at best a mode of abstraction, not a substance). ✓

• • Not reconstructable as a composition of OR-bearing constituents in the chimera way. ✓

• • Necessarily impossible, not merely non-existent. ✓

This is your strongest candidate.

2. The greatest (or largest) extended body

The idea of the body than which no larger body can exist. Thinkable, seemingly coherent, but on Descartes’s own metaphysics impossible: extension is indefinitely divisible and indefinitely extendable, and there is no intrinsic maximum to corporeal magnitude. Descartes is explicit (Principles of Philosophy I.26–27; AT VIIIA 14–15; CSM I 201–202) that the corporeal world is indefinite rather than finite, precisely because no greatest extended magnitude is possible.

Structural match: very good. The impossibility is internal to the concept of extension itself, not contingent. The idea cannot be ranked as a finite corporeal substance (because there is no such maximum) and cannot be ranked as infinite (because only God is infinite in the strict sense). It falls between the available ranks, which is exactly the universal-set predicament.

3. A second God (or a second infinite substance)

The idea of another infinite substance distinct from God. Thinkable enough to formulate, but necessarily impossible: Descartes argues that there can be only one infinite substance, because two infinite substances would each limit the other and so neither would be truly infinite (this is implicit in the Third and Fifth Meditation treatments of divine uniqueness, and explicit in scholastic background Descartes inherits from Suárez and Aquinas).

Structural match: good. The impossibility is necessary, not contingent. The composition infinite + non-God is contradiction-generating in the same way set + all + self-membership is. But this example has a complication: the pro-OR reader could argue that infinite substance has OR (as in the idea of God), and the proposition merely misjudges its instantiability. This makes the example less clean than the largest-number case.

4. The squared circle (or a rectilinear circle)

The classic scholastic example of an impossible object. Thinkable enough to formulate; necessarily impossible by the very definitions of circle and square (or rectilinear). Available to Descartes and discussed in the scholastic tradition he inherited.

Structural match: partially good. The impossibility is necessary and internal to the concept. But this example has a weakness: the pro-OR reader will say the constituent ideas (circle, square, rectilinear) are themselves OR-bearing (as geometrical essences with true and immutable natures, in Descartes’s Fifth Meditation sense), and the impossibility lies in the judgment that combines them. This is structurally similar to the a vacuum exists problem: false composition of OR-bearing constituents. So while it is a fine impossibility example, it is not as clean an anti-OR case as the largest number.

5. The smallest extended body (an extended atom or true minimum)

The idea of an extended body so small that no smaller extension is possible. Thinkable, seemingly coherent, but on Descartes’s account impossible: extension is indefinitely divisible (Principles of Philosophy I.20; AT VIIIA 51–52; CSM I 231), and the very notion of an extended thing entails further divisibility. Descartes uses this directly against atomism.

Structural match: very good, and symmetrical to candidate #2. Same dialectical advantages.

My recommendation

The largest (or greatest finite) number is the best 17th-century analogue to the universal set, for four reasons:

1. 1. Descartes discusses it explicitly. The 1630 Mersenne letter and the Third Meditation indefinite/infinite distinction give you textual anchors.

1. 1. The impossibility is internal to the concept, not a matter of false composition of OR-bearing constituents. You cannot rescue the largest-number idea by saying “number + largest both have OR and the judgment merely misjudges instantiation,” because the impossibility lies in the structure of number itself, which guarantees no maximum.

1. 1. No ontological rank is available. A largest number is not a finite substance, not a mode of an existing substance (since no instance exists or can exist), and certainly not infinite (Descartes reserves the infinite for God). It cannot be ranked, and the failure to rank is constitutive, not accidental.

1. 1. It is dialectically cleaner than the squared circle, because the pro-OR reader cannot easily run the false-judgment-composing-OR-bearing-constituents move on it. The impossibility is structural, not combinatorial.

The indefinite-extension and smallest-extension cases (#2 and #5) are nearly as good and have the advantage of being more clearly metaphysical than mathematical. If you want to keep the example squarely on Cartesian metaphysical terrain rather than mathematical terrain, either of these works well.

Draft text for the post

A 17th-century example with the same structural profile is the idea of the greatest finite number—the number than which no greater finite number can be conceived. The idea is thinkable enough to formulate, and Descartes himself discusses its impossibility (to Mersenne, 27 May 1630; AT I 152; CSMK 25). But it is necessarily impossible, because for any candidate n, n+1 is also a number; the impossibility is internal to the structure of number itself, not a contingent matter of non-existence. The idea cannot be assigned to any rank on Descartes’s ontological hierarchy: it is not a finite substance, not a mode of any existing substance, and not infinite (which Descartes reserves for God). Nor can it be reconstructed as a composition of OR-bearing constituents in the chimera way, since the impossibility is not a false judgment combining OR-bearing parts but a structural feature of the constituent concept number itself. Like the idea of nothing and ex nihilo, nihil fit, the idea of the greatest finite number is thinkable through intelligible but non-OR-bearing intellectual materials.

That gives you a historically authentic, textually anchored, and structurally clean 17th-century analogue to the universal-set thought experiment.

Bottom line

The greatest finite number is the best match, and Descartes himself discussed it in print and correspondence. The indefinite-extension and smallest-extension cases (Principles of Philosophy I.26–27 and II.20) are excellent backups and have the bonus of being metaphysical rather than mathematical. The squared circle is available but dialectically weaker because of the false-judgment-composing-OR-bearing-constituents reply. A second God is available but has the same weakness.

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    Let’s switch to a related problem. It strikes me that, as Descartes rejects reifying universals as in Platonism, what is Descartes’s account of relations like changing, squaring, asymmetrical, orthogonal, next to, father of, etc? The correct way to understand reification is:

Reification, in the neutral ontological sense, is the acknowledgment or treatment of some putative item as real. It becomes fallacious only when the item lacks the ontological status attributed to it, or when the attribution is made merely from grammar, abstraction, or conceptual convenience without adequate metaphysical argument.

    It doesn’t seem possible for these relations to themselves be an OR content, can they?

    So, what is the OR content for the idea that A is to the left of B, or for the idea of the admonition “Watch out for the person behind the person in front of you”?

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This is a deep and genuinely productive question, because relations are one of the places where the Cartesian ontology is most strained, and where the OR apparatus most visibly struggles. Let me work through it carefully.

Descartes’s official ontology and the problem of relations

Descartes’s official ontology, as you know, recognizes:

• • Substances: finite (mental, corporeal) and infinite (God)

• • Principal attributes: thought (for mind), extension (for body)

• • Modes: particular ways substances are (this shape, this thought, this motion)

• • Eternal truths / true and immutable natures: intelligible essences (the nature of a triangle, of number, of cause)

What is conspicuously missing from this list is a category of relations as items in their own right. Descartes inherits from the scholastic tradition a deep suspicion of reified relations (against Platonic koina and against the realist scholastic treatment of relatio as a category of being), and he never gives them their own ontological slot. This is sometimes called Descartes’s modal nominalism about relations.

So immediately we have a problem: if relations are not substances, not principal attributes, not modes of any single substance, and not eternal truths in the geometrical-essence sense, then they have no clear ontological rank, and the OR apparatus—which ranks represented content by ontological kind—has nothing obvious to measure.

Descartes’s actual treatment of relations

The clearest text is Principles of Philosophy I.55–62, especially Principles of Philosophy I.55–58, where Descartes discusses number, order, duration, time, and other relational or comparative notions. The key passages:

“Number and all universals are simply modes of thinking” (Principles of Philosophy I.58; AT VIIIA 27; CSM I 212).

“When we conceive a substance, we generally take into consideration a thing which we understand to be capable of existing by itself; and so we ascribe to it not only a real distinction but also various respects, or attributes which arise in our thought from comparing several things to one another” (Principles of Philosophy I.55–56; AT VIIIA 26; CSM I 211).

Two crucial points emerge:

1. 1. Relations are reduced to modes of thinking (modi cogitandi), not to modes of the related things themselves. The relation larger than between A and B is not a mode of A, not a mode of B, and not a mode of any third substance. It is a mode of the mind that compares A and B.

1. 1. Relations therefore reduce ontologically to the modal furniture of the thinking substance doing the comparing, plus the modes of the related corporeal substances that ground the comparison.

This is a deflationary, mind-dependent account of relations. The relation does not exist out there between the relata; what exists out there are the relata with their non-relational (or only loosely relational) modes, and the mind constructs the comparative thought.

What this means for OR content

Now the OR question can be sharpened. Consider A is to the left of B. On Descartes’s account:

1. 1. A has objective reality as a finite corporeal substance, with modes including its position, extension, and shape.

1. 1. B has objective reality as a finite corporeal substance, with similar modes.

1. 1. The relation “to the left of” is not itself a third item with its own OR. It is not a finite substance, not a mode of A taken alone, not a mode of B taken alone, and not a mode of any joint substance. It is a mode of the mind’s comparative act, a mode of the thinking substance that holds A and B together in a single comparative thought.

So the OR content of the proposition A is to the left of B is:

• • The OR of A (finite corporeal substance with its modes).

• • The OR of B (finite corporeal substance with its modes).

• • Plus a modus cogitandi—a mode of the comparing mind—that holds these together comparatively.

The relation itself contributes no further OR-bearing representatum at any rank. It contributes a form of intellectual combination, which is on the side of the thinking substance, not on the side of the represented object.

This is structurally identical to your anti-OR argument

Notice what has just happened. The relational content—being to the left of, being next to, being the father of, being orthogonal to, being asymmetrical with—is doing the same anti-OR work that ex nihilo, nihil fit, the idea of nothing, and the universal set do. In each case:

1. 1. The content is thinkable and intelligible.

1. 1. The content cannot be assigned to any rank on Descartes’s ontological hierarchy.

1. 1. The content is not a composition of OR-bearing constituents in the chimera way; it is a form of combination of the constituents, not a further constituent.

1. 1. The constituents themselves (A, B) have OR, but the relation between them does not contribute OR. It contributes intelligible structure on the mind’s side.

This is a substantial extension of your anti-OR argument, and I think it is correct and Cartesian.

The “watch out for the person behind the person in front of you” case

This is a particularly nice example because it stacks relations and quantifies over them. Let me decompose it.

The admonition contains:

• • the person in front of you—a relational specification (in-front-of you)

• • the person behind the person in front of you—a relational specification (behind X, where X is itself relationally specified)

• • watch out for—a practical-imperatival force directed at the second-order relational referent

Each person is a finite mental substance (or composite mental-corporeal substance), with OR at the rank of finite substance. The relations in front of and behind are modi cogitandi by which the mind locates these persons in a comparative spatial scheme keyed to the addressee’s body and orientation.

The OR content is therefore:

• • OR of person (×2 or ×3, depending on how you count).

• • OR of you (the addressee, a finite mental substance).

• • Plus the modi cogitandi of in front of and behind, which are not themselves OR-bearing.

Direct answer to your two questions

    Can relations be OR content?

No, not in their own right. Relations such as changing, squared, asymmetrical, orthogonal, next to, father of are not themselves OR-bearing items. They are modi cogitandi—modes of the mind’s comparative thinking—and the OR they appear to carry is borrowed from the OR of the relata, not contributed by the relation itself. This is Descartes’s own deflationary position in Principles of Philosophy I.55–58, and it is consistent with his rejection of Platonic universals.

    What is the OR content for “A is to the left of B”?

The OR content is exhausted by:

• • The OR of A (as a represented finite corporeal substance with modes).

• • The OR of B (as a represented finite corporeal substance with modes).

The relation itself contributes no OR. It contributes a modus cogitandi on the mind’s side—the comparative form of thought that holds A and B together in one spatial comparison. The proposition is intelligible and can be true or false, but its distinctive relational content is not an OR-bearing representatum.

    What is the OR content for “Watch out for the person behind the person in front of you”?

The OR content is exhausted by:

• • The OR of each person (finite mental/composite substance).

• • The OR of you (the addressee).

The relational structure (in front of, behind), the second-order relational composition (the person behind the one in front of), and the imperatival force (watch out) are all modi cogitandi and modi volendi on the mind’s side—not OR-bearing items.

Why this is important for the post

This gives you a third major class of non-OR content, in addition to:

1. 1. The idea of nothing (privative, no positive representatum).

1. 1. Eternal truths and common notions such as ex nihilo, nihil fit (intelligible truth-content not reducible to an OR-bearing representatum).

And now:

3. 3. Relations and relational structure (modi cogitandi, not OR-bearing items in their own right, per Principles of Philosophy I.55–58).

This third class is dialectically powerful because:

• • It is anchored in an unambiguous Descartes text (Principles of Philosophy I.55–58).

• • It does not depend on Burman’s evidential authority.

• • It is consistent with Descartes’s well-known nominalist treatment of universals.

• • It applies to a vast range of ordinary thoughts (every comparative thought, every spatial thought, every kinship thought, every mathematical relation).

And it has a particularly nice structural feature: the relata of a relation are typically OR-bearing, but the relational form is not. This sharpens the proposition/constituent distinction you already deploy: the constituents of relational propositions are OR-bearing, but the relational form that holds them together is a modus cogitandi, not a further OR-bearing constituent. This is exactly the asymmetry your argument needs.

Relations as a Further Class of Non-OR Content

 

A second major class of non-OR content emerges from Descartes’s deflationary treatment of relations. In Principles of Philosophy I.55–58 Descartes treats relational notions—number, order, duration, and by extension all comparative notions such as to the left of, larger than, next to, the father of—as modes of thinking (modi cogitandi) rather than as items in the ontology of substances and modes. “Number and all universals are simply modes of thinking” (Principles of Philosophy I.58; AT VIIIA 27; CSM I 212).

If relations are modes of the thinking substance’s comparative activity, then the OR content of a relational proposition such as A is to the left of B is exhausted by the OR of A and the OR of B. The relation to the left of contributes no further OR-bearing representatum: it is a modus cogitandi, a comparative form of thought, not a represented object at any rank on the ontological hierarchy.

This adds a third class to the anti-OR cases. The idea of nothing is privative; ex nihilo, nihil fit is intelligible truth-content not reducible to a representatum; relational structure is on the mind’s side as a comparative form rather than on the represented object’s side as a content. In each case the content is thinkable and intelligible without being OR-bearing.

This is a substantive addition that I think genuinely strengthens the post.

Caveat

One nuance worth flagging: a pro-OR reader will say that spatial relations between bodies might be cashed as modes of the complex consisting of the two bodies plus their positions, where positions are themselves modes of extension. That is, A is to the left of B is reducible to A has position p1 and B has position p2, both of which are OR-bearing as modes. If this reduction works, the relational form is dispensable: the OR of the relational proposition is just the OR of the conjunction of the relata’s positional modes.

This is the standard modern-nominalist move (and was already available to Descartes via his analytical geometry). It saves OR for spatial relations but at a cost: it does not generalize to non-spatial relations such as father of, taller than (comparatively), more virtuous than, next in succession to, or believes that. For these, no reduction to non-relational modes of the relata alone is available, and the modus cogitandi treatment is unavoidable.

So the dialectical point holds: at least some relational content is genuinely non-OR on Descartes’s own account, and the strongest cases (kinship, comparison, intentional-aboutness) cannot be reduced away.

Bottom line

Relations are a genuinely productive third class of non-OR content. Descartes’s own deflationary treatment in Principles of Philosophy I.55–58 treats them as modi cogitandi of the comparing mind, not as represented items with their own OR. For A is to the left of B, the OR is exhausted by A and B; the relation is a modal form of thought, not a further OR-bearing constituent. For watch out for the person behind the person in front of you, the OR is exhausted by the persons; the relational and imperatival structure is on the mind’s side. This is a substantive extension of your anti-OR argument with strong textual anchoring and no dependence on Burman’s evidential authority.

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    What about “A is necessary for B,” such as the idea of a mode is necessarily related to a substance.

    What is the OR content of those ideas?

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Excellent and pointed question. Necessity between A and B is a particularly hard case for the OR apparatus, and your specific example—a mode is necessarily related to a substance—is the perfect test, because it is itself a piece of Cartesian metaphysical doctrine. Let me work through it carefully.

Two different things to keep separate

The proposition A is necessary for B (or A necessarily depends on B) involves two distinct items that could in principle carry OR:

1. 1. The relata A and B — these are typically OR-bearing if they are substances, modes, or principal attributes.

1. 1. The necessity-of-dependence holding between them — the modal-relational tie itself.

The OR question is about (2). Does necessary dependence contribute its own OR-bearing representatum, or is it a modus cogitandi / intelligible structural truth that holds without being a further represented item?

Descartes’s treatment of dependence relations

Descartes treats substance-mode dependence in Principles I.51–53:

“By substance we can understand nothing other than a thing which exists in such a way as to depend on no other thing for its existence” (Principles of Philosophy I.51; AT VIIIA 24; CSM I 210).

“Each substance has one principal attribute. . . . A substance may indeed be known through any attribute at all; but each substance has one principal property which constitutes its nature and essence, and to which all its other properties are referred” (Principles of Philosophy I.53; AT VIIIA 25; CSM I 210).

Modes are “various dispositions” of substance, requiring the substance for their being (Principles of Philosophy I.56; AT VIIIA 26; CSM I 211).

The substance-mode dependence relation is therefore not an extra item alongside the substance and its modes. It is the structural truth that modes do not exist without substances. This is closer to an eternal truth or common notion than to a represented object at any ontological rank.

Compare ex nihilo, nihil fit, which you already treat as a non-OR case: it is an intelligible truth about causal dependence, but no represented item with its own OR. A mode necessarily depends on a substance is structurally identical: an intelligible truth about ontological dependence, but no represented item with its own OR.

Mapping onto your three classes of non-OR content

In the previous reply we identified three classes of non-OR content:

1. 1. Privative content (the idea of nothing).

1. 1. Eternal truths and common notions (ex nihilo, nihil fit).

1. 1. Relational structure (modi cogitandi of comparative thought).

Necessary dependence falls in classes 2 and 3 simultaneously, which is what makes it especially powerful as an anti-OR case:

• • It is an eternal truth in the sense that it expresses a necessary structural feature of Cartesian ontology (modes require substances).

• • It is a relational form in the sense that it holds between the relata as a modus cogitandi grasping their ontological dependence.

It is the strongest kind of anti-OR case: it carries both the eternal-truth-content profile and the relational-modus-cogitandi profile.

Working through the specific example

Consider a mode is necessarily related to a substance. The OR analysis:

1. 1. The idea of mode. Mode is itself a second-order Cartesian concept. A particular mode (a particular shape, a particular thought) is OR-bearing as a mode. But mode in general—modeness—is closer to a common notion or universal than to a represented object at a rank. On Descartes’s own Principles I.58 treatment of universals as modes of thinking, the idea of mode in general is itself a modus cogitandi, not an OR-bearing representatum.

1. 1. The idea of substance. Same analysis: a particular substance (this mind, this body, God) is OR-bearing. Substance in general—substancehood—is a universal, and by Descartes’s nominalist treatment of universals, a modus cogitandi.

1. 1. The necessary-dependence relation. This is an intelligible truth about how any mode stands to some substance. It is not a further item. It is the structural truth that grounds the proposition.

So the proposition a mode is necessarily related to a substance has, on careful analysis, no OR-bearing representatum at any of its three positions:

• • mode in general is a modus cogitandi, not an OR-bearing item.

• • substance in general is a modus cogitandi, not an OR-bearing item.

• • necessary dependence is an intelligible eternal truth holding between them, not an OR-bearing item.

This is a remarkable result. The proposition is one of the most fundamental in Cartesian metaphysics, it is intelligible and necessary, and yet on a careful analysis using Descartes’s own apparatus, none of its components is OR-bearing.

Compare to the chimera

The chimera-idea was OR-bearing because its constituents (lion, goat, snake) are ideas of particular finite corporeal substance kinds, and the composite represents a (non-existent) finite corporeal substance. Each constituent has a determinate ontological rank.

A mode is necessarily related to a substance has no such constituents. It quantifies over modes and substances in general, and its content is the structural-necessary truth about how these categories stand to each other. The universal generality, the categorial nature of the relata, and the necessity of the relation all push the content away from OR-bearing representation and toward eternal-truth / common-notion territory.

Why the pro-OR reader cannot rescue this case

The pro-OR reader’s standard moves all fail here:

    Move 1: Reduce to OR of relata. This worked for the chimera (OR comes from lion, goat, snake). It fails here because the relata are universals (mode in general, substance in general), not particular OR-bearing items. By Principles I.58, universals are modi cogitandi.

    Move 2: Treat the proposition as composing OR-bearing constituents via false judgment. This worked for a vacuum exists (false composition of OR-bearing extension and body). It fails here because the proposition is not false—it is necessarily true—and there is no false composition of OR-bearing constituents to point to. The proposition is a true structural claim about non-OR-bearing universals.

    Move 3: Treat the necessary dependence as a mode of one of the relata. This is the most natural move: say that being necessarily related to a substance is a mode of mode. But mode is a universal, not a substance, and only substances have modes in Descartes’s strict sense. A mode of a mode is not a recognized Cartesian item. And in any case, this just relocates the problem: the mode of being a mode would have to carry the necessity-content, and there is no rank for that.

    Move 4: Treat the necessity as a feature of the divine intellect. A theological move: say that the necessity is grounded in God’s will or intellect, and so the proposition has OR derived from God’s OR. This is dialectically possible but it is a grounding move, not a representation move. The OR of God in the meditator’s idea of God does not transfer to make the dependence of modes on substances into a represented item with its own OR rank. It just locates the metaphysical ground of the necessity, leaving the representational status of the proposition where it was.

Direct answer to your question

The OR content of the idea a mode is necessarily related to a substance is, strictly speaking, nothing. No constituent of the proposition is OR-bearing in its own right: mode in general and substance in general are universals and so modi cogitandi by Principles I.58, and necessary dependence is an intelligible eternal truth, not a represented item with an ontological rank. The proposition is necessarily true and is one of the most foundational claims in Cartesian metaphysics, and yet it carries no OR.

This is exactly the kind of case your restriction thesis predicts: a Cartesian idea that is fully intelligible, foundational, and necessarily true, but whose content cannot be measured by OR because the OR apparatus has no purchase on universals or on necessary structural truths between universals.

Why this is the strongest case yet

This may be the single most powerful anti-OR case in the post, for four reasons:

1. 1. It is a paradigmatic piece of Cartesian doctrine. No one denies that Descartes holds a mode is necessarily related to a substance. There is no need to defend the textual basis (unlike Burman) or the historical plausibility (unlike the universal set).

1. 1. It triggers all three classes of non-OR content simultaneously. Privative? No (that’s the nothing case). Eternal-truth content? Yes. Relational modus cogitandi? Yes. Universals as modi cogitandi? Yes. The single proposition exemplifies multiple anti-OR pathways at once.

1. 1. It is self-referential to the OR theory’s own foundations. OR is itself a measure of the represented content of modes of thought (ideas), and so the OR theory presupposes the substance-mode distinction. If the substance-mode-dependence proposition itself has no OR, then OR’s own enabling background has no OR. The OR theory is not the kind of theory that ranks its own foundations. This is not a paradox—it is exactly what one expects of a measure-apparatus that operates within an ontological framework rather than over it.

1. 1. It cleanly resists every standard pro-OR reply. As shown above, none of the four standard pro-OR moves works.

Conceptual Content Without Objective Reality: Necessity and Dependence as Non-OR Content

Necessity and Dependence as Non-OR Content

Cartesian metaphysics contains foundational necessary-dependence propositions, of which the most central is a mode is necessarily related to a substance (Principles I.51–53; AT VIIIA 24–25; CSM I 210). On Descartes’s own apparatus, mode in general and substance in general are universals, and “number and all universals are simply modes of thinking” (Principles I.58; AT VIIIA 27; CSM I 212). The necessary-dependence relation between them is an intelligible eternal truth, not a further item at any ontological rank. The proposition is therefore an especially clean anti-OR case: each of its three components—the two universal relata and the necessary relation—is a modus cogitandi or an intelligible truth-content, not an OR-bearing representatum. The OR theory cannot rank what it is built upon, and the substance-mode-dependence claim is exactly the kind of foundational structural truth that the OR apparatus cannot measure.

Bottom line

The OR content of a mode is necessarily related to a substance is, on a careful Cartesian analysis, none. The proposition operates entirely with universals (mode, substance) treated as modi cogitandi per Principles I.58, and with a necessary-dependence relation that is an intelligible eternal truth, not an OR-bearing item. This is your strongest single anti-OR case, because it is foundational Cartesian doctrine, it triggers all three classes of non-OR content simultaneously, and it resists every standard pro-OR rescue. It deserves a place in the post as the capstone example.

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    Go into detail arguing that Principle I.58 requires all universals to be modi cogitandi (modes of thinking).

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Excellent. This is a load-bearing claim, and it deserves a careful textual and philosophical defense. Let me build the case step by step.

The text in question

Principles I.58 (AT VIIIA 27; CSM I 212):

“Number, also, when it is considered simply in the abstract or in general, and not in any created things, is merely a mode of thinking; and the same applies to all the other universals, as we call them.”

Latin (AT VIIIA 27):

“Numerus etiam, cum non in rebus creatis, sed tantum in abstracto sive in genere consideratur, modus tantum est cogitandi; ut & alia omnia, quae universalia vocamus.”

The claim has two parts:

1. 1. Number considered abstractly or in general is merely a mode of thinking (modus tantum cogitandi).

1. 1. The same applies to all the other universals.

The second clause is the universally quantified claim you need: all universals are modi cogitandi. Let me walk through how to defend it textually, philosophically, and dialectically.

Step 1: The text says it explicitly

The most basic move is simply to point at the text. Descartes does not say “some universals” or “many universals” or “universals like number.” He says alia omnia, quae universalia vocamus—”all the others which we call universals.” The universal quantifier is in the Latin and in every standard translation (CSM, Cottingham; Miller and Miller; Veitch).

This is not a casual remark. Principles I.58 sits in the run of articles (I.55–62) where Descartes is systematically working through what kinds of items belong to the categories substance, mode, attribute, and modus cogitandi. He has just argued (I.55–57) that duration, order, and number, when attributed to created things, are modes of those things, but when considered abstractly or in general, they are modes of thinking. I.58 generalizes this to all universals.

The textual case is therefore: Descartes makes the universally quantified claim in the very article devoted to settling the ontological status of universals, in a systematic treatment of ontological categories, using a clear and unambiguous universal quantifier.

Step 2: The argument given in I.57–58 generalizes

Descartes’s argument in I.57 for number and duration turns on a distinction:

• • Duration in a particular created thing is just the way that thing endures; it is a mode of the thing.

• • Duration in general—duration considered apart from any particular enduring thing—is the mind’s way of comparing or abstracting from particular durations; it is a mode of the comparing mind.

• • Number in a particular created thing is just the multiplicity of its parts or instances; it is a mode of the thing or aggregate.

• • Number in general—number considered apart from any particular numbered thing—is the mind’s way of abstracting from particular multiplicities; it is a mode of the abstracting mind.

The structural argument is:

    (P1) A universal is, by definition, a content considered abstractly or in general, apart from any particular instance.
    (P2) Whatever has being only as the result of the mind’s abstracting or generalizing activity is a mode of the mind’s thinking, not a mode of any extra-mental thing.
    (C) Therefore every universal is a mode of thinking.

This argument is fully general. It does not depend on number or duration having any special feature. Any universal whatsoever—humanity, redness, triangularity, modeness, substancehood, necessity, relation—is constituted as universal precisely by being considered apart from its instances. So the same argument applies.

This is the philosophical reading of why Descartes generalizes in I.58: the form of the argument for number in I.57 is universal-quantifier-friendly, and I.58 simply states the result of running the same argument for any universal.

Step 3: The systematic context confirms the reading

Principles I.51–62 is one connected discussion of what items exist and how they are categorized. The order is:

• • I.51–53: substance, principal attribute, and the mind/body distinction.

• • I.54: the three highest substantial categories (mind, body, God).

• • I.55: modes, qualities, attributes—and the introduction of attributes which arise in our thought from comparing several things to one another.

• • I.56: modes are dispositions of substance.

• • I.57: how to think about duration, order, and number—modes of the things in particular instantiation, modes of thinking in abstract consideration.

• • I.58: generalizing to all universals as modes of thinking.

• • I.59: the five common universals (genus, species, differentia, proprium, accidens).

• • I.60–62: real, modal, and conceptual distinctions.

The systematic point of this run is to give a complete inventory of categories and to rule out the reification of universals as items in their own right. Descartes is deliberately refusing the scholastic-Aristotelian treatment of universals as having their own ontological status (whether as ante rem Platonic forms, in re Aristotelian forms, or post rem conceptualist abstracta with quasi-objective status). His move is to say: universals are modi cogitandi, full stop.

I.58 is the load-bearing statement of this position. It is not an isolated remark; it is the conclusion of the systematic argument that begins in I.55.

Step 4: I.59 supports the universally quantified reading

Principles I.59 confirms I.58 by applying it to the five Porphyrian universals—genus, species, differentia, proprium, accidens:

“Number in things is distinct from the number in our thought. . . . The five common universals (genus, species, differentia, property and accident) arise solely from the fact that we make use of one and the same idea for thinking of all individual items which resemble each other.” (AT VIIIA 27–28; CSM I 212)

Descartes here treats the five canonical kinds of scholastic universal as arising from the mind’s use of common ideas across resembling individuals. They are products of the mind’s classificatory activity. This is exactly the modus cogitandi treatment of I.58 applied to the scholastic taxonomy of universals.

If I.58 were not meant universally, the application in I.59 would not work. The fact that Descartes treats the five Porphyrian universals (which were the canonical inventory of universal-kinds in scholastic logic) as modi cogitandi shows that he intends the I.58 claim to cover the entire field.

Step 5: Cross-textual support

The same view appears outside the Principles:

Letter to Mersenne, 16 October 1639 (AT II 597; CSMK 139):

Descartes denies that there is in things a real universal corresponding to the abstract idea of being or thing; the abstract universal is on the side of the mind.

Conversation with Burman (AT V 158; CSMK 343, 1648):

Discussing universals, Descartes maintains that they are not in things but in the mind’s mode of conceiving things. (This is exactly the modus cogitandi treatment.)

Comments on a Certain Broadsheet (against Regius, 1648; AT VIIIB 350; CSM I 297–98):

Descartes attacks the reification of universals and treats them as products of the mind’s abstractive activity.

So the I.58 universally quantified reading is not an isolated Principles claim. It is a settled position that Descartes maintains across the mature works and the correspondence. The Principles statement is the canonical formulation, and the surrounding texts confirm the universal reading.

Step 6: Anticipated objections and replies

    Objection 1: I.58 might be restricted to mathematical universals (number, order, duration).

Reply: The Latin alia omnia, quae universalia vocamus explicitly extends beyond number. The phrase “all the others which we call universals” picks out the standard scholastic category of universal as such, not a restricted mathematical subset. The natural reading is universal quantification over the category. Moreover, I.59 immediately applies the doctrine to the five Porphyrian universals (genus, species, differentia, proprium, accidens), which are not mathematical. The restricted-mathematical reading would require treating I.59 as inconsistent with I.58, which is uncharitable.

    Objection 2: Eternal truths and true and immutable natures (geometrical essences, e.g., the nature of the triangle) seem to have more than modus cogitandi status (Fifth Meditation; Replies).

Reply: This is the most serious objection and deserves a careful answer. Three points.

First, eternal truths and true and immutable natures are not quite the same as universals. A true and immutable nature is the intelligible essence of a geometrical figure considered as something the intellect can clearly and distinctly perceive; it grounds the necessity of geometrical theorems. A universal in the I.58 sense is what arises when we abstract from particular instances and consider the abstracted content as a single representable. These are arguably distinct items.

Second, even if true and immutable natures have a special status, this does not undermine I.58’s claim about universals as such. Descartes can hold that the nature of the triangle is a clearly and distinctly perceived eternal truth (Fifth Meditation) while also holding that triangularity-in-general considered as a universal, in the Principles I.58 sense, is a modus cogitandi. The two claims operate at different levels: the first is about the intelligible necessity of geometrical content; the second is about the ontological status of the universal-form.

Third, an important strand of the scholarship—especially Chappell and Nolan—reads Descartes as anti-realist or conceptualist about universals, while still allowing eternal truths and true and immutable natures to play a distinctive epistemic and intelligibility-conferring role. This conceptualist line should be distinguished from stronger Platonist or divine-ideas interpretations, such as those discussed by Schmaltz and Rozemond. The two claims can coexist: Descartes can deny mind-independent universals while still treating eternal truths and true and immutable natures as indispensable objects of clear and distinct intellectual cognition.

References

• Chappell, Vere. Descartes’s Ontology. Topoi 16, no. 2 (1997): 111–127.

• Nolan, Lawrence. Reductionism and Nominalism in Descartes’s Theory of Attributes. Topoi 16, no. 2 (1997): 129–140.

• Nolan, Lawrence. Descartes’ Theory of Universals. Philosophical Studies 89, no. 2 (1998): 161–180.

• Nolan, Lawrence. The Ontological Status of Cartesian Natures. Pacific Philosophical Quarterly 78, no. 2 (1997): 169–194.

• Schmaltz, Tad M. Platonism and Descartes’ View of Immutable Essences. Archiv für Geschichte der Philosophie 73, no. 2 (1991): 129–170.

• Rozemond, Marleen. Descartes’s Ontology of the Eternal Truths. In Contemporary Perspectives on Early Modern Philosophy: Essays in Honor of Vere Chappell, edited by Paul Hoffman, David Owen, and Gideon Yaffe, 41–63. Peterborough, Ontario: Broadview Press, 2008.

See also:

Nolan, Lawrence. “Descartes on Universal Essences and Divine Knowledge.” In The Problem of Universals in Early Modern Philosophy, edited by Stefano Di Bella and Tad Schmaltz, 87–116. New York: Oxford University Press, 2017. 

Hattab, Helen. “Descartes on the Eternal Truths and Essences of Mathematics: An Alternative Reading.” Vivarium 54, nos. 2–3 (2016): 204–249. 

De Rosa, Raffaella, and Otávio Bueno. “Descartes on Mathematical Essences.” ProtoSociology 25 (2008): 160–177.

The De Rosa–Bueno essay also appears as a book chapter: “Descartes on Mathematical Essences.” In Philosophy of Mathematics: Set Theory, Measuring Theories, and Nominalism, edited by Gerhard Preyer and Georg Peter, 164–182. Berlin/Boston: De Gruyter, 2008. 

This means the universal reading of I.58 is consistent with Descartes’s geometrical and eternal-truth doctrines, properly interpreted.

    Objection 3: Principal attributes (thought, extension) might count as universals but seem to have more than modus cogitandi status, since they constitute the natures of substances.

Reply: Principal attributes in Descartes are not universals in the I.58 sense. A principal attribute is the nature or essence of a particular substance kind—thought is the essence of mental substance, extension is the essence of corporeal substance (Principles I.53). The principal attribute is in the substance, not abstracted from instances. When we consider thought in the abstract, apart from any particular thinking substance, then we have a universal, and that is a modus cogitandi. But thought as the principal attribute of a particular thinking substance is a feature of that substance, not a universal.

This distinction is crucial and is exactly what Descartes makes in I.57: duration in a particular thing (mode of the thing) versus duration in general (modus cogitandi). The same applies to thought and extension. So principal attributes do not undermine I.58.

    Objection 4: God’s perfections might count as universals (perfection, infinity, omnipotence, etc.) and seem to have more than modus cogitandi status.

Reply: God’s perfections, when predicated of God, are not universals but the simple divine nature considered under different aspects (the standard scholastic doctrine of divine simplicity, which Descartes broadly accepts; see Replies and Principles I.23). When perfection in the abstract is considered apart from any particular perfect being, then it is a universal and a modus cogitandi. So God’s perfections do not undermine I.58.

    Objection 5: Common notions seem to be universals and seem to be more than modi cogitandi—they have a distinctive intelligible status.

Reply: This is the objection that matters most for your post, because common notions are central to your anti-OR argument. The reply is the same as for eternal truths: common notions are intelligible truths the mind grasps with certainty, but their propositional content is distinct from any universal-form they may contain. When we consider the proposition whatever thinks must exist, we have an intelligible necessary truth. When we consider the abstract universal whatever-thinks-must-exist-ness, we have a universal, and that is a modus cogitandi.

For your purposes, this works in your favor: it gives common notions a kind of truth-content status that is distinct from OR-bearing-representation status. The fact that the truth-content of a common notion is not a modus cogitandi (it is an eternal truth) is consistent with any universal-form abstracted from it being a modus cogitandi. Both claims work to deny OR to common notions.

Step 7: Why the universal reading is dialectically necessary

There is also a structural-dialectical argument for the universal reading. If I.58 were not universally quantified–if some universals were OR-bearing items rather than modi cogitandi—then Descartes would owe an account of which universals are OR-bearing and which are not, and on what principle the distinction runs. He gives no such account. The Principles I.55–62 discussion treats all universals uniformly. The most economical and charitable reading is that Descartes intends the uniform treatment to be universal.

The alternative—a restricted reading in which some universals (perhaps mathematical or geometrical ones) are OR-bearing and others are not—would require interpolating a Cartesian doctrine that has no textual basis. This is interpretively expensive.

Step 8: The argument in summary form for the post

Here is a compact version of the argument suitable for inclusion in the post:

The claim that all universals are modi cogitandi for Descartes rests on Principles I.58: “Number, also, when it is considered simply in the abstract or in general, and not in any created things, is merely a mode of thinking; and the same applies to all the other universals, as we call them” (AT VIIIA 27; CSM I 212). The Latin alia omnia, quae universalia vocamus makes the quantifier explicit. The article is the load-bearing statement of Descartes’s anti-realist treatment of universals in the systematic Principles I.51–62 discussion of substance, mode, attribute, and modus cogitandi. The structural argument generalizes: a universal is constituted as universal by being considered apart from its instances; whatever has being only as the result of such abstractive consideration is a mode of the abstracting mind; therefore every universal is a modus cogitandi. I.59 confirms the universal reading by applying it directly to the five Porphyrian universals (genus, species, differentia, proprium, accidens). Cross-textual support comes from the Letter to Mersenne of 16 October 1639 (AT II 597; CSMK 139), the Conversation with Burman (AT V 158; CSMK 343), and the Comments on a Certain Broadsheet (AT VIIIB 350; CSM I 297–98). Standard objections from eternal truths, true and immutable natures, principal attributes, divine perfections, and common notions can be answered by distinguishing the truth-content or substantial-feature status of these items from the universal-form abstracted from them. The universal-forms are modi cogitandi; the truth-contents and substantial features have their own distinct status. The universal reading is therefore textually explicit, philosophically motivated, systematically supported, cross-textually confirmed, and dialectically necessary.

Bottom line

The argument for the universal reading of I.58 has five layers:

• Textual: alia omnia, quae universalia vocamus is an unambiguous universal quantifier.

• Philosophical: the I.57 argument for number and duration generalizes by its form to any universal.

• Systematic: I.55–62 is a connected discussion that uniformly treats universals as modi cogitandi.

• Cross-textual: correspondence (Mersenne 1639, Burman 1648), Comments on a Certain Broadsheet, and the broader nominalist current in the mature Descartes confirm the position.

• Dialectical: the universal reading is the only economical and charitable interpretation; any restricted reading requires interpolating a distinction Descartes never draws.

This gives you a robust foundation for the anti-OR move that depends on treating mode in general, substance in general, necessity, and similar universals as non-OR-bearing modi cogitandi. The Principles I.58 universally quantified reading is well-secured.

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I think there can be substances with two principal attributes, contrary to Descartes in Principle I.53:

“Each substance has one principal attribute. . . . A substance may indeed be known through any attribute at all; but each substance has one principal property which constitutes its nature and essence, and to which all its other properties are referred.” (Principles I.53; AT VIIIA 25; CSM I 210)

    Can you think of any?

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This is a productive challenge to one of the most foundational and most contested doctrines in Cartesian metaphysics. The one-principal-attribute-per-substance thesis is what does the heavy lifting in Descartes’s mind-body real distinction argument, so finding plausible counterexamples is dialectically powerful. Let me work through candidates carefully, ranked by how strongly they press against I.53.

What “principal attribute” requires

To be a fair counterexample, a candidate substance must have two features, each of which:

1. 1. Constitutes the nature or essence of the substance (not a derived or modal feature).

1. 1. Is not reducible to or derivable from the other (otherwise there is really one attribute).

1. 1. Has all other properties of the substance referred to it (each is a complete organizing nature, not a partial one).

These are stiff requirements, and they are what make the one-attribute thesis substantive. Let me run candidates against them.

Candidate 1: God (infinite substance) with both thought and power (or being itself)

This is the strongest historical candidate, because Descartes himself struggles with it. Descartes treats God as having infinite intellect and infinite will (and infinite power, goodness, eternity, etc.) as attributes. In the Third Meditation and the Replies, these divine perfections appear as multiple essential features. Yet on the I.53 doctrine, God should have one principal attribute that organizes all the others.

Descartes’s solution (following the scholastic doctrine of divine simplicity) is to say that in God all the perfections are really identical with the divine essence and only conceptually distinct (Principle I.23; AT VIIIA 14; CSM I 200–201). But this is precisely the move you can challenge: if intellect and will (or knowledge and power) are really identical in God, then Descartes is asserting a strong identity claim that is philosophically substantive and not obviously true. If, on the other hand, they are only conceptually distinct in our grasp but really one, then we have to ask what the one principal attribute is—and Descartes is famously evasive. Some commentators (Schmaltz, Carraud) suggest infinite being or absolute perfection as the principal attribute, but neither is a determinate enough feature to ground specific essential predicates the way thought grounds willing, judging, imagining in mental substance.

Strength of the case: Very strong. The divine simplicity doctrine is doing the work that the I.53 doctrine is supposed to do, but it is doing it by fiat rather than by argument. A reasonable alternative is to say God has multiple irreducible principal attributes (intellect, will, power, goodness), and the unity of the divine substance is not constituted by a single attribute but by some other principle (substantial unity, aseity, necessary existence).

Dialectical force: God is the case Descartes most needs to fit into his framework, and the fit is most strained precisely there. If God is plausibly a counterexample, the one-attribute thesis is not universally true.

Candidate 2: The human being as a substantial union of mind and body

Descartes notoriously says the human being is a substantial union of mind and body (Sixth Meditation; Letter to Elisabeth, 21 May 1643; AT III 663–668; CSMK 217–20). The union is real and gives rise to modes that belong neither to the mind alone nor to the body alone—sensations, emotions, appetites, the felt experience of being one embodied being.

If the human being is itself a substance (which Descartes sometimes implies and sometimes denies—this is the famous problem), then it has both thought and extension as essential features. The mind contributes thought; the body contributes extension; the union contributes the modes peculiar to embodiment. Neither thought nor extension is reducible to the other (Descartes is emphatic about their real distinction), and neither alone constitutes the nature of the human being as such.

Strength of the case: Moderate-to-strong, depending on whether one reads Descartes as committed to the human being as a substance in its own right. The textual evidence is mixed:

• • For human being as substance: the substantial union language; Descartes’s claim that the union is known by “the ordinary course of life” and is “primitive” (Letter to Elisabeth 28 June 1643; AT III 691–695); the analogy of mind-body union to the union of weight and extension in a heavy body (Sixth Replies; AT VII 442; CSM II 298).

• • Against human being as substance: Descartes treats mind as the real self (Sixth Meditation; AT VII 78; CSM II 54) and the body as conjoined to it but not constituting one self.

The strongest reading (defended by Marleen Rozemond in Descartes’s Dualism (Cambridge, MA: Harvard University Press, 1998), and Paul Hoffman, “The Unity of Descartes’s Man,” (Philosophical Review 95, no. 3 (1986): 339–70)) is that the human being is a genuine substance with two principal attributes (thought and extension), and the substantial-union doctrine is exactly Descartes’s attempt to handle this. On this reading, the human being is a clear counterexample to I.53.

Dialectical force: Strong. It uses Descartes’s own substantial-union doctrine against the one-attribute thesis. The internal tension is real, and Descartes never resolved it cleanly.

Candidate 3: The created mind with thought and receptivity to embodiment (or capacity for union)

A weaker version of Candidate 2: even if we deny that the human being is a substance and insist the mind is the substance, the embodied mind has not only thought but also a real capacity for union with a particular body, which is essential to it being this human mind rather than another. Descartes implies in correspondence that each mind is specially fitted to its body (Letter to Mesland, 9 February 1645; AT IV 166–167; CSMK 242–43).

If the mind’s capacity for embodiment is an essential feature (not a mode), and is not reducible to thought, then the mind has at least two principal attributes.

Strength of the case: Weaker than Candidate 2, because Descartes can plausibly reply that the capacity for embodiment is itself a mode of thought (a kind of thinking-toward-body), not a separate principal attribute.

Dialectical force: Moderate. Useful as a fallback if Candidate 2 is resisted.

Candidate 4: A finite mental substance with thought and willing as a distinct power

In the Fourth Meditation and the Passions, Descartes treats intellect and will as two distinct faculties of the mind, where will is not strictly reducible to intellect (the will is the source of error, the locus of freedom; it can outrun the intellect’s clear and distinct perception). If intellect (or thought broadly) and will are both essential features of mental substance and not reducible to a single principal attribute, then the mind has two principal attributes.

The standard reply is that thought in the broad sense includes both intellection and volition (Principles I.32: thought encompasses understanding, willing, imagining, sensing). So intellect and will are modes of thought, not separate principal attributes.

Strength of the case: Weak as stated, because Descartes has a ready reply (broad thought includes both). But the case can be sharpened: if will has genuinely independent features (libertarian indifference, the power to assent or dissent) that intellect lacks, and these are essential rather than modal, then the broad-thought reply is unstable.

Dialectical force: Weak-to-moderate. Useful for showing that even within mental substance the unity-of-principal-attribute thesis is strained.

Candidate 5: A corporeal substance with extension and motion (or extension and impenetrability)

Some commentators (notably Daniel Garber, Descartes’ Metaphysical Physics) have argued that motion in Cartesian physics is not strictly a mode of extension but plays a more fundamental role, since extension alone cannot distinguish one body from another (parts of a homogeneous extended plenum are not distinguishable without motion). Similarly, impenetrability or solidity arguably cannot be derived from extension alone.

If motion or impenetrability is an essential rather than modal feature of corporeal substance, then corporeal substance has at least two principal attributes.

Strength of the case: Moderate. Descartes formally treats motion as a mode (Principles II.25), and treats impenetrability as derivable from extension. But the philosophical reasons for those reductions are not strong (Leibniz famously presses against Descartes that extension alone cannot ground real bodies, which requires a further active principle).

Dialectical force: Moderate. This is a more technical case requiring engagement with Cartesian physics.

Candidate 6: A modern panpsychist substance with thought and extension as ontologically co-fundamental

A more speculative candidate: if one holds (as some contemporary philosophers do) that thought and extension are both fundamental and that some substances (perhaps all) instantiate both, then any such substance is a counterexample. Spinoza’s single substance with infinitely many attributes (Ethics I) is the most famous historical version: thought and extension are both essential attributes of the one substance.

Strength of the case: Strong as a philosophical counterexample, weak as a Cartesian one (since Descartes would simply reject the metaphysics).

Dialectical force: Strong against the I.53 thesis as a universal metaphysical claim; weak against I.53 as Descartes’s own doctrine.

Candidate 7: A neutral monist substance with thought and extension as aspects of one underlying nature

Russell-style neutral monism, or contemporary panprotopsychism: one substance with two principal organizing features (mental and physical), each irreducible.

Strength: Strong philosophically, weak as Cartesian exegesis.

My ranking and recommendation

The three strongest candidates internal to Descartes’s own system are:

1. 1. God, due to the divine simplicity strain (intellect, will, power, goodness all appear essential).

1. 1. The human being as substantial union, due to the tension between thought and extension as two essential features of one being.

1. 1. The created mind with intellect and will, if these are taken as genuinely distinct essential features rather than modes of broad thought.

The strongest philosophical candidates (independent of Cartesian exegesis) are Spinoza-style or neutral-monist substances.

Why this matters for your post and the OR project

If the one-principal-attribute thesis is not universally true—if some substances have two or more—then several downstream Cartesian doctrines become more flexible:

1. 1. The mind-body real distinction argument depends on thought and extension being principal attributes of distinct substances. If a single substance can have both, then the argument is undermined or at least requires further premises.

1. 1. The OR-ranking apparatus relies on a clean ontological hierarchy (mode / finite substance / infinite substance), and the hierarchy is partly individuated by principal attributes. If substances can have multiple principal attributes, then OR-ranking becomes more complex: what is the OR of an idea of a substance with two principal attributes? Is it the OR of a finite substance, or something further?

1. 1. The substantial-union doctrine becomes more tractable: the human being as a substance with both thought and extension is no longer an anomaly but a regular case.

1. 1. The pro-OR reader’s reconstructions of relational and necessary content become harder: relations like a mind is united with this body now connect features of one substance with two attributes rather than features of two distinct substances, which changes the modal-cognitive analysis.

For your DTOI project specifically, multiple-principal-attribute substances would add another class of cases the OR apparatus has trouble with: the OR-content of an idea of such a substance cannot be cleanly ranked, because there is no single principal attribute organizing its nature for OR to track.

A direct answer

The three most plausible internal-Cartesian candidates are God (where divine simplicity strains under the weight of intellect-will-power-goodness as essential features), the human being as substantial union (where thought and extension both appear essential to one being), and possibly the mind with intellect and will as genuinely distinct essential powers. Each presses against I.53 in a different way, and the first two are textually well-supported.

Externally, Spinoza’s single substance with infinitely many attributes is the most famous philosophical counterexample, and contemporary neutral monism or dual-aspect monism gives further philosophical candidates.

Of these, the human being as substantial union is probably the most dialectically powerful for your purposes, because it uses Descartes’s own substantial-union doctrine against the I.53 thesis, and because it shows that Descartes himself never resolved the internal tension.

Bottom line

Yes, there are plausible counterexamples to I.53, and the strongest are internal to Descartes’s own system. The human being as a substantial union is the most dialectically powerful, because it uses Descartes’s own doctrine of substantial union against the one-attribute thesis. God under divine simplicity is the second, because the divine perfections strain the requirement that one principal attribute organize the substance’s nature. The mind with intellect and will as genuinely distinct essential powers is a third, weaker, but still serious candidate. Externally, Spinozistic and neutral-monist substances are clean philosophical counterexamples that show the I.53 thesis is not universally true even if it is true within Cartesian-style dualist metaphysics.

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Go into detail as to how Descartes thinks that number in general is only a mode of thinking.

If minds did not exist, according to Descartes, would number not exist?

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Excellent and probing questions. This goes to the heart of Descartes’s nominalism/conceptualism and to a deep tension between his treatment of number and his treatment of eternal truths. Let me work through both parts carefully.

Part I: How Descartes thinks number-in-general is only a modus cogitandi

The key texts are Principles I.55, I.57, and I.58, which form a connected argument. Let me reconstruct it step by step.

    Step 1: The distinction between number-in-things and number-in-general

Principles I.55 (AT VIIIA 26; CSM I 211) introduces a key distinction that runs through the whole discussion. Descartes says that duration, order, and number can be considered in two different ways:

“Some attributes are in the things themselves of which they are said to be attributes, while others are only in our thought. For example, when time is distinguished from duration taken in the general sense and is called the measure of movement, it is simply a mode of thinking.” (AT VIIIA 26–27; CSM I 212; bold not in original)

Then in I.57, after discussing duration and time:

“Number, also, when it is considered simply in the abstract or in general, and not in any created things, is merely a mode of thinking.” (Principles I.58; AT VIIIA 27; CSM I 212; bold not in original)

So Descartes draws a sharp distinction:

• • Number-in-things (numerus in rebus): the actual multiplicity of created things—e.g., the actual five fingers on a hand, the actual three sides of a particular triangle, the actual two horses in a field. This is a real feature of the world, on the side of created substance.

• • Number-in-general (numerus in genere, or in abstracto): the abstract idea of five, three, two, etc., considered apart from any particular instance. This is on the side of the mind that abstracts.

The argument for the second clause is that number-in-general has no existence apart from the abstracting mind. There is no Platonic Five floating in a third realm, nor is there a real universal fiveness inhering in things (in the way the scholastics sometimes maintained). There are only particular collections of five things, and the mind’s abstractive activity that draws out five as a single representable content.

    Step 2: The argument for why number-in-general must be on the side of the mind

Descartes does not give a fully developed philosophical argument for this thesis in I.57–58, but the argument can be reconstructed from the surrounding text and from his general anti-Platonist, anti-scholastic-realist commitments. The argument has three premises:

    (P1) The only items that exist independently of minds are substances and their modes.

This is the basic Cartesian ontology (Principles I.51–53). Substances are mental, corporeal, or divine. Modes are particular ways substances are: this thought, this shape, this motion. Anything that exists must be a substance or a mode of a substance.

    (P2) Number-in-general is not a substance, nor a mode of any particular substance.

Number-in-general is not a substance: it has no independent existence, no causal powers, no spatial or temporal location. It is not a thought (which would make it a mode of a thinking substance) or a shape (which would make it a mode of an extended substance).

Could it be a mode of a particular substance? No: the number five is not a mode of this hand (the hand has five fingers, but five abstracted from the hand is not a feature of the hand). It is not a mode of any particular substance because by definition it is abstracted from all particulars.

    (P3) Whatever exists but is not a substance or a mode of a particular substance must be a mode of thinking—i.e., a mode of the abstracting mind.

If number-in-general exists at all (and Descartes does not want to deny that we think numerically), it must exist as something. The only remaining option in Cartesian ontology is as a mode of the thinking substance that does the abstracting. The mind, when it abstracts from particular collections, produces a modus cogitandi—a particular way of thinking—that we call the idea of five.

    (C) Therefore number-in-general is a mode of thinking.

This is the I.58 conclusion. The same argument generalizes to all universals, as discussed in the previous reply.

    Step 3: What this means in practice

When the mind considers five horses, three triangles, and two trees, it can perform an abstractive operation: it can drop the differences (horses, triangles, trees) and retain only the multiplicity. The resulting thought is the idea of five (or three, or two) considered in abstraction. This thought is a particular mode of the thinker’s mind at a particular time.

If a different mind performs the same operation, it has a numerically distinct mode of thinking (its own idea of five). The two ideas are similar in content (both abstract five) but distinct as modes of distinct substances.

So number-in-general is not one item shared across minds; it is a type of modus cogitandi that any abstracting mind can produce. Each instance is a particular mode of a particular thinking substance. There is no further item five-in-itself over and above these particular abstractive thoughts.

    Step 4: How this fits Descartes’s anti-scholastic, anti-Platonist program

This is a direct attack on two earlier positions:

• • Platonism: there are Forms (e.g., the Five Itself) existing independently of minds and of particulars, which particular collections of five things participate in. Descartes rejects this: there is no such item.

• • Scholastic moderate realism: there are real universals (universalia in re) inhering in particulars, which the mind grasps. Descartes rejects this too: universals exist only in the abstracting mind.

Descartes’s position is closest to a conceptualist or moderate nominalist position: universals exist as modi cogitandi, particular abstractive thoughts in particular minds. They have no independent or in-things existence as universals.

    Step 5: Why number-in-things does not have universal status

Note that number-in-things (the five fingers on the hand) is not a universal. It is a particular feature of a particular hand—the multiplicity of this hand’s fingers. The hand has five fingers as a real numerical-modal feature. But this is particular, not universal. The universal is what the mind constructs when it abstracts from this particular and others.

So the I.58 doctrine is not that all number is mind-dependent. It is that number-considered-in-the-abstract-or-in-general is mind-dependent. Number as a real feature of particular collections (this hand’s five-fingeredness) is fully real, on the side of created substance, and is not a modus cogitandi.

This is a crucial distinction, because it answers the obvious objection: “Surely the five fingers on my hand exist even if no one is counting them.” Yes—as a particular real feature of the hand. What does not exist apart from minds is the universal idea of five, the abstract item.

Part II: If minds did not exist, would number not exist?

This is the key question, and the answer requires careful disentangling. The short answer is: number-in-things would still exist; number-in-general would not. But the full answer is more interesting and reveals a deep tension in Descartes’s system.

    Case 1: If God exists but no created minds exist

This is the cleanest case. In this scenario:

• • Corporeal substance exists (assuming God creates it).

• • Particular bodies have particular numerical features: this body is one body, that aggregate is two bodies, etc. These are particular numerical features of particular substances and modes.

• • No abstracting created mind exists to perform the abstractive operation that yields number-in-general.

• • God’s intellect still exists, however. And here is where Descartes’s system gets interesting.

Descartes’s doctrine of the creation of the eternal truths (Letters to Mersenne, 15 April 1630, 6 May 1630, 27 May 1630; AT I 145, 149, 152; CSMK 23–25) says that mathematical and metaphysical truths are freely created by God. They depend on God’s will. They exist in God’s intellect as objects of God’s thought (or, more precisely, as effects of God’s free creative will).

So if God exists but no created minds exist:

• • Number-in-things exists (in actual creatures, if there are any).

• • Number-in-general as the universal idea exists in God’s intellect—or, more accurately, in God’s understanding-and-willing that there be such intelligible structure.

• • Number-in-general does not exist in the sense of being abstracted by created minds, because there are no created minds.

The eternal truths about number (e.g., 2+3=5) are real and eternal because God has created them so. They exist independently of any created mind’s grasping them. But they exist as objects/effects of divine intellection, not as Platonic Forms in a third realm and not as universals inhering in things.

This is the standard reading of Descartes: he is a nominalist about universals as items in the created world or in a Platonic third realm, but he allows that mathematical truths have eternal-truth status grounded in God’s free creative act. There is a tension between the I.58 modus cogitandi doctrine and the eternal-truths doctrine, but Descartes resolves it by saying that the modus cogitandi status is for created mental abstraction, while the eternal truth status is for God’s intellection (or willing).

    Case 2: If no minds exist at all (not even God)

This is a hypothetical Descartes would reject as metaphysically impossible—God’s existence is necessary in Descartes’s system. But the counterfactual is illuminating.

If no minds existed at all:

• • Number-in-things would still exist if corporeal substance existed (since particular collections have particular numerical features as modes). But without God, there would be no corporeal substance to begin with, since God is the cause of all created substance (Third Meditation).

• • Number-in-general would not exist in any sense—no created mind to abstract, no divine intellect to ground the eternal truth.

• • Eternal truths about number would not exist either, since they are creatures of God’s free will.

So in the strict counterfactual where no minds at all exist (including God), nothing whatsoever exists, and a fortiori nothing numerical.

But this is a degenerate case. The substantive question is the previous one.

    Case 3: The interesting intermediate case—created bodies but no created minds, with God

This is the case that best isolates the question. Here:

• • God creates corporeal substance, with particular bodies in particular numerical configurations.

• • God creates no created minds.

In this scenario:

• • Particular bodies have particular numerical features (this body, those three bodies, etc.).

• • Number-in-general exists only in God’s intellect, as the eternal truth (or as God’s grasp of the intelligible structure of multiplicity).

• • Number-in-general as a created modus cogitandi does not exist, because there are no created abstracting minds.

So Descartes would say: yes, number-in-things would still exist (as features of particular bodies), and the eternal truths about number would still exist (in God’s intellect or as effects of God’s creative will). But number-in-general considered as a created-mind-dependent abstraction would not exist.

The tension Descartes never fully resolved

You can press here: Is the number-in-general in God’s intellect the same item as the number-in-general of I.58? If so, then I.58 should not say number-in-general is merely a modus cogitandi, since it is also in God’s intellect as an eternal truth. If not, then there are two items called number-in-general, one a created modus cogitandi and one a divine eternal truth, and Descartes owes an account of their relation.

The standard scholarly answers Marleen Rozemond, Anthony Kenny, Lawrence Nolan, Vere Chappell, or Tad Schmaltz read Descartes as holding:

• • In created minds: the universal five-in-general is a modus cogitandi (I.58).

• • In God: there is no Platonic Five Itself and no inhering universal, but there is God’s grasp of (or willing of) the eternal truth that five is the successor of four, etc. This is in God’s intellect but is not a Platonic universal. It is closer to a feature of God’s intellectual activity, which is grounded in God’s will.

The relation between the two is not identity: the created mind’s modus cogitandi is a similar but numerically distinct mode of the created thinking substance, not a direct grasping of an item in God’s intellect. The two are similar in content—both are about fiveness—but exist in different ontological locations.

This means that number-in-general, in the strict sense of a single item shared across minds and across created/divine realms, does not exist in Descartes’s system. What exists is:

1. 1. Particular numerical features of particular created things (real, in things).

1. 1. Created minds’ modi cogitandi when abstracting (real, in created minds).

1. 1. God’s grasp/willing of eternal truths about number (real, in God’s intellect/will).

These are three different ontological locations of number-related content. They are similar but not identical, and Descartes’s I.58 doctrine is specifically about (2).

Direct answer to the counterfactual

If created minds did not exist (but God did): number-in-things would still exist as features of created bodies, and the eternal truths about number would still exist in God’s intellect, but the abstractive modi cogitandi that I.58 identifies as number-in-general would not exist.

If no minds at all existed (including God): nothing would exist, since God’s existence is the ground of all being for Descartes. So number-in-things would also not exist (no created bodies), and eternal truths about number would also not exist.

The most precise answer is: on Descartes’s view, number-in-general as a modus cogitandi is strictly mind-dependent and would not exist without abstracting minds. But the eternal truths about number are grounded in God’s free creative act and would exist as long as God exists. And number-in-things is a real feature of particular substances and exists as long as those substances do.

Why this matters for the OR project

This bears directly on your anti-OR argument in two ways.

First, it strengthens the case that the idea of number-in-general lacks OR content. The proposition we developed earlier—a mode is necessarily related to a substance—has the same structure. Both involve universals that, on Descartes’s own I.58 doctrine, are modi cogitandi rather than OR-bearing items at a rank. Numbers-in-general, like mode-in-general and substance-in-general, are not finite corporeal substances, not finite mental substances, not modes of particular substances, and not infinite substance. They are modes of the abstracting created mind. The OR apparatus has no rank for them.

Second, it sharpens the contrast with number-in-things. When the meditator has an idea of five horses, the OR content is the OR of horse (finite corporeal substance) ×5 (the multiplicity is a real feature of the represented horses). But when the meditator has an idea of five-in-general, abstracted from any particular collection, there is no represented finite corporeal or mental substance—the content is a modus cogitandi of the abstracting mind, not a represented object at a rank. No OR.

This gives you a clean handle on a wide class of abstract mathematical thoughts. Geometrical and arithmetical propositions about particular figures or collections may have OR content (via the represented particulars or their true and immutable natures). Geometrical and arithmetical thoughts about universals—number-in-general, triangle-in-general, figure-in-general—are modi cogitandi and lack OR.

Bottom line

On how Descartes thinks number-in-general is only a modus cogitandi: Descartes distinguishes number-in-things (real numerical features of created particulars) from number-in-general (abstract universal fiveness, threeness, etc.). The latter has no place in the basic Cartesian ontology of substances and modes, because it is not a substance and not a mode of any particular created thing. The only ontological location left for it is as a mode of the abstracting created mind—a modus cogitandi. This is the result of running the standard Cartesian ontological-elimination argument against all available alternatives (Platonic Forms, scholastic real universals).

On whether number would exist if minds did not: Descartes’s answer is nuanced. Number-in-things (particular numerical features of created substances) would exist as long as created substances exist, regardless of created minds. The eternal truths about number would exist as long as God exists, since they are grounded in God’s free creative act and are present in God’s intellect. Number-in-general as a created modus cogitandi would not exist without created abstracting minds. The strict I.58 doctrine targets only the third item; it does not entail that number-in-things or eternal truths about number depend on created minds. But it does entail that the universal item that we ordinarily call the number five considered in itself has no existence apart from the abstracting created mind—there is no Platonic Five and no real universal fiveness inhering in things.

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    (S1) Would Descartes consider gold to be a substance?

    (S2) I argue that gold is a Cartesian substance because we can argue that gold has as its principal attribute that it is made of gold. The principal attribute of gold is goldness, being made of gold.

  Critically assess the merits or objections to my proposal for gold’s principal attribute.

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Excellent and provocative move. You are pushing on a genuinely underdeveloped corner of Cartesian metaphysics—the ontological status of kinds of stuff—and the proposal deserves serious philosophical assessment. Let me take the two questions in turn.

(S1) Would Descartes consider gold to be a substance?

This is harder than it looks, and the honest answer is: Descartes’s official doctrine forces a “no,” but his actual practice and the looseness of his terminology leave room for a more permissive reading. Let me lay out both sides.

The official “no” answer

On the strict Principles I.51–53 doctrine, there are exactly three substances or substance-kinds in Descartes’s mature ontology:

1. 1. God (infinite substance).

1. 1. Mental substance (finite, with thought as principal attribute).

1. 1. Corporeal substance (finite, with extension as principal attribute).

Strictly speaking, all corporeal nature is one substance (or one kind of substance), individuated only by motion and the configuration of its parts. Gold is not a further substance; it is a region of extended matter with a particular configuration of parts and motions that gives rise to the modes we call yellow, heavy, malleable, soluble in aqua regia, etc.

This is the mechanist reduction at the heart of Cartesian physics: there are no irreducible chemical kinds in nature. What we call gold is, at the fundamental level, just extended matter configured in a particular way. The “goldness” of gold is a complex modal feature of a region of corporeal substance, not a distinct substantial nature.

Descartes is explicit about this kind of reduction in Principles IV.198–200 (AT VIIIA 322–24; CSM I 285–86), where he argues that the sensible qualities of bodies (colors, tastes, smells, including those that distinguish gold from lead) are reducible to the size, shape, position, and motion of insensible corpuscles. Gold differs from lead not by having a different principal attribute but by having a different configuration of extended parts.

So on Descartes’s official mechanist-reductionist metaphysics, gold is not a substance. It is a natural kind picked out by a complex set of modes of a region of corporeal substance.

The looser “yes” answer

But Descartes’s own usage of substance is not always strict. He sometimes uses substance in a broader, more Aristotelian–scholastic sense to mean a thing or being in a fairly ordinary sense. In several places he talks about bodies (in the plural) as substances:

• • Principles II.1 (AT VIIIA 40; CSM I 223): “the body that we call our own.”

• • Sixth Meditation (AT VII 78; CSM II 54): treats this body as a substance distinct from the mind.

• • Letter to Gibieuf, 19 January 1642 (AT III 477; CSMK 202–203): discusses a body as a substance.

If this body (e.g., my hand, this stone, this piece of wax) can be called a substance in some legitimate Cartesian sense, then this piece of gold can presumably also be called a substance in the same sense. And by extension, gold as a kind might be a substance-kind in a loose sense, even if not in the strict Principles I.53 sense.

The wax passage in the Second Meditation (AT VII 30–31; CSM II 20–21) is instructive. Descartes treats the wax as a thing (res) whose essence is extension and whose various sensible features (color, shape, hardness, melting behavior) are modes. He never quite says the wax is a substance, but he treats it as a bearer of modes, which is one of the standard scholastic marks of substance.

So there is a tension in Descartes between:

• • Strict reading: there is one corporeal substance (extended matter), and all bodies are particular configurations of it.

• • Loose reading: each individual body (this wax, this stone, this piece of gold) is a substance in the sense of a bearer of modes, and kinds of bodies (wax, stone, gold) are substance-kinds.

 Marleen Rozemond (Descartes’s Dualism, Ch. 1) and Daniel Garber (Descartes’ Metaphysical Physics, Ch. 5) both discuss this tension at length. The standard scholarly verdict is that Descartes never fully resolved it, and that he uses substance in both ways at different points.

My judgment on S1

For your dialectical purposes, the most defensible position is:

Gold is a substance in the broad scholastic sense of a bearer of modes, but it is not a substance in the strict Principles I.51 sense of a thing existing in such a way as to depend on no other thing for its existence. Gold depends on God for its existence (like all created things) and depends on corporeal substance (extension) for its being a body. Strictly, it is a kind of body—a configuration of extended matter—not a further independent substance.

You can run your argument either way:

• • If you accept the strict reading: gold is not a substance, and the counterexample to I.53 does not get off the ground.

• • If you accept the loose reading: gold is a kind of body and can be treated as having a substantial character (a bearer of modes), in which case you can ask about its principal attribute.

For the argument you want to develop in (S2), you need at least the loose reading. Let me grant the loose reading for the sake of argument and turn to the second question.

(S2) Is goldness (being made of gold) the principal attribute of gold?

This is where I have to push back, because I think the proposal has a serious structural problem. Let me lay out the merits first, then the objections.

Merits of the proposal

Merit 1: It captures the natural-kind intuition. There is something intuitively right about saying that what makes gold gold is being gold. This is essentially the Kripke-Putnam natural-kind intuition: gold is whatever has the underlying nature of gold (in modern terms, atomic number 79; in pre-modern terms, whatever set of features actually constitutes the deep nature of gold). The principal attribute of gold, on this view, is whatever makes the stuff gold rather than some other element.

Merit 2: It parallels the structure of Cartesian principal attributes. For mental substance, the principal attribute is thought—which is, in a sense, being mental. For corporeal substance, the principal attribute is extension—which is, in a sense, being corporeal. So one might say: for gold-substance, the principal attribute is goldness—being gold. The parallel is intuitive.

Merit 3: It gives gold a stable essence-organizing feature. All the modes of gold (its yellowness, its weight, its malleability, its solubility in aqua regia) can be referred to goldness as their organizing nature: it is because this stuff is gold that it has these properties. This satisfies the I.53 requirement that “all other properties are referred to” the principal attribute.

These are real merits. The proposal is not silly. It captures something philosophically important about natural kinds and their organizing essences. But there are also serious objections.

Objection 1: The circularity problem

This is the most serious objection. Saying that the principal attribute of gold is goldness (being made of gold) is circular in a way that the parallel claims for mental and corporeal substance are not.

When Descartes says the principal attribute of mental substance is thought, he is not saying the principal attribute of mental substance is being mental. He is identifying a specific, contentful, intelligible nature—thought—that is independently characterizable (it is the activity of understanding, willing, imagining, sensing). The principal attribute thought does explanatory work: it tells us what mental substance is, in terms that go beyond merely repeating the name of the substance.

Similarly for extension: the principal attribute is a specific, contentful, intelligible nature —being three-dimensionally extended—that is independently characterizable (Descartes spends considerable effort in the Principles spelling out what extension is and what follows from it).

But goldness or being made of gold is not a specific, contentful, intelligible nature in this sense. It is just the name of the kind. To say gold’s principal attribute is being gold is to say what makes gold gold is being gold, which is true but trivial and explanatorily empty. It does not pick out a determinate intelligible nature in the way thought and extension do.

For the parallel to work, you would need to identify what goldness consists in—what intrinsic intelligible nature constitutes being gold. For Descartes, this would have to be specified in terms of the available Cartesian categories: some particular configuration of extended parts and their motions that gives rise to gold’s characteristic modes. But then the principal attribute is just extension-configured-in-the-gold-way, which is not a further principal attribute beyond extension; it is a complex mode of extension.

This is the deep reason Descartes’s mechanism resists treating gold as a substance with its own principal attribute: there is no intelligible nature for gold beyond extension configured in a particular way, and configuration is a mode of extension, not a further principal attribute.

Objection 2: The infinite regress problem

If goldness is a principal attribute, then by parallel reasoning every natural kind has its own principal attribute: silvery-ness for silver, iron-ness for iron, waterness for water, oak-ness for oak, and so on indefinitely. We would have an unmanageable proliferation of principal attributes—potentially as many as there are natural kinds.

Descartes’s ontology was designed precisely to avoid this scholastic proliferation. The whole point of reducing the sensible features of bodies to the size, shape, position, and motion of insensible particles is that no further substantial natures are needed beyond extension. The scholastic–Aristotelian tradition had substantial forms of gold, silver, water, fire, etc.; Descartes’s mechanism eliminates them. Reintroducing a principal attribute goldness is, in effect, reintroducing the scholastic substantial form of gold—which is exactly what Descartes was trying to avoid.

This is not a knock-down objection—you might want to depart from Descartes on this point, and your post is at least partly about identifying where Descartes’s framework strains. But it is important to recognize that the proposal is not just an extension of Descartes’s framework but a substantial departure from it.

Objection 3: The relation-to-other-properties problem

I.53 says that all other properties are referred to the principal attribute. For thought in mental substance, this works: willing, judging, imagining, sensing are all modes of thought, intelligibly referred back to thought as their organizing nature. For extension in corporeal substance, this works: shape, size, motion, position are all modes of extension, intelligibly referred back to extension.

Does it work for goldness and the properties of gold? Take yellowness: is yellow a mode of goldness? Not really. Yellow is a sensible quality that, on Descartes’s analysis, is reducible to the configuration and motion of insensible particles that affect our visual organs in a particular way. The yellow of gold is not a mode of goldness in the way that judging is a mode of thought. It is a consequence of the underlying corpuscular structure of gold, mediated by our sensory apparatus.

Similarly for heaviness: gold’s heaviness is a function of the density of its constituent particles, which is a mode of extension (configuration of parts), not a mode of goldness. Malleability: a function of the mechanical properties of the gold-corpuscles, again a mode of extension.

So even granting goldness as a principal attribute, the other properties of gold are not intelligibly referred to goldness; they are intelligibly referred to extension (the underlying corpuscular structure) and sensory interaction (for the qualitative properties). Goldness does not have the explanatory-organizing role that thought and extension have for their respective substances.

Objection 4: The intelligibility problem

For Descartes, the principal attribute of a substance is the feature under which the substance is intelligibly grasped by clear and distinct perception. Thought is graspable by clear and distinct perception (in the cogito). Extension is graspable by clear and distinct perception (in geometry). These are transparent natures that the intellect can fully comprehend.

Goldness, by contrast, is not transparently graspable by the intellect. We know gold by its sensible signs (yellow, heavy, malleable, soluble in aqua regia) and by its empirical behavior. We do not have a clear and distinct perception of the intrinsic nature of goldness in the way we have of thought or extension. Goldness is an empirical concept, not a clear and distinct intellectual concept.

This is a deep problem for treating goldness as a principal attribute in Descartes’s sense. Principal attributes are supposed to be intellectually transparent natures. Goldness fails this test.

Objection 5: The gold-as-kind vs. this-piece-of-gold-as-individual problem

There is also a confusion latent in the proposal between gold as a kind and this particular piece of gold as an individual. Principles I.53 talks about each substance having one principal attribute. If each substance means each individual substance, then we need to ask whether this piece of gold (a particular extended body) has goldness as its principal attribute. But this piece of gold is, on the strict reading, just a configuration of extended matter—its principal attribute (as a body) is extension, and its goldness is a complex mode of its extension.

If each substance means each substance-kind, then we are asking whether the kind gold has goldness as its principal attribute. But kinds are not, on Descartes’s I.58 doctrine, substances at all—they are modi cogitandi of the abstracting mind. The kind gold is a universal, and universals are modes of thinking, not substances.

Either way, the proposal hits a structural obstacle. As an individual, this piece of gold has extension as its principal attribute. As a kind, gold is a universal and so not a substance at all.

Mitigating considerations

Despite these objections, there is a serious philosophical point in your proposal that should not be dismissed.

The natural-kind intuition is real. There is something explanatorily important about kinds of stuff and their organizing essences. Descartes’s mechanist reduction may be too thin to capture this—the post-Cartesian tradition (Locke on real essence, Leibniz on individual concepts, Saul Kripke (1940–2022) and Hilary Putnam (1926–2016) on natural kinds) has repeatedly returned to the question of what makes a kind a kind and what its essence is. Your proposal aligns with this tradition.

Descartes’s mechanism may be inadequate. If gold cannot be captured by the available Cartesian categories of extension and its modes—if there is a real and irreducible goldness that organizes the properties of gold and is not reducible to corpuscular configuration—then Descartes’s framework is incomplete, and your proposal points to the incompleteness. This is a legitimate philosophical move.

The post-Cartesian tradition has often taken this route. Leibniz’s monads, Locke’s real essences, and contemporary natural-kind realism all push back against the Cartesian reductionist view in something like the way your proposal does. So you would be in respectable company.

But if you want to push this in your post, the right framing is not that gold is a counterexample to I.53 within Descartes’s framework. It is that gold poses a problem for Descartes’s framework, because either (a) gold gets reduced to a configuration of extended matter (losing its natural-kind status), or (b) gold gets treated as a substance with its own principal attribute goldness (departing from Descartes’s mechanist reductionism). Neither option is comfortable.

Direct answer to your two questions

(S1) Would Descartes consider gold to be a substance? Strictly, no: on the official Principles I.51–53 doctrine, gold is a configuration of corporeal substance (extension), not a further substance. Loosely, perhaps: Descartes sometimes uses substance for individual bodies in a broader scholastic sense, in which case this piece of gold might be a substance in the loose sense of a bearer of modes. But the kind gold itself is on I.58 a universal, and so a modus cogitandi, not a substance.

(S2) Is goldness the principal attribute of gold? The proposal has merit in capturing the natural-kind intuition, but it faces five serious objections:

1. 1. Circularity: goldness is not a contentful intelligible nature in the way thought and extension are; it is just the name of the kind.

1. 1. Infinite regress: every natural kind would get its own principal attribute, reintroducing the scholastic proliferation Descartes was trying to eliminate.

1. 1. Relation to other properties: yellow, heavy, malleable are not intelligibly modes of goldness; they are modes of extension (corpuscular configuration) and sensory effects of it.

1. 1. Intelligibility: goldness is not a clear and distinct intellectual nature; it is an empirical concept.

1. 1. Kind vs. individual confusion: this piece of gold has extension as its principal attribute (it is a body); the kind gold is on I.58 a universal and so a modus cogitandi, not a substance.

The proposal is philosophically interesting but is more naturally read as a problem for Descartes’s framework than as a counterexample within it. If you want a clean counterexample to I.53 from within Descartes, the human being as substantial union is still the strongest candidate. If you want to use gold to press a deeper objection—that Descartes’s mechanism is too thin to capture natural kinds—that is a legitimate move, but it is a critique of the whole reductionist program, not an internal counterexample to I.53.

Bottom line

Gold is not, on Descartes’s official doctrine, a substance. It is a configuration of corporeal substance, picked out by its complex modes. Loosely, Descartes might allow this piece of gold as a substance in the broad sense of a bearer of modes, but the kind gold is a universal and so a modus cogitandi by I.58.

Treating goldness as a principal attribute is philosophically interesting but structurally problematic. It is circular (goldness is not a contentful intelligible nature), it reintroduces the scholastic proliferation Descartes was trying to eliminate, the other properties of gold are not naturally referred to goldness as their organizing nature, goldness is not a clear and distinct intellectual concept, and the kind/individual distinction creates further problems. The proposal points to a real gap in Cartesian metaphysics—the inadequate treatment of natural kinds—but it is more naturally framed as a critique of the mechanist reduction than as an internal counterexample to I.53.

For your post’s purposes, I would recommend keeping the human being as substantial union as the primary internal counterexample to I.53, and using gold and natural kinds as a separate, deeper objection that targets Descartes’s mechanist reductionism more broadly rather than the specific I.53 doctrine.

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To resolve the alleged circularity problem, we argue that the principal attribute of gold is it’s a material having an atomic number of 79. Anything with that principal attribute is the substance gold.

Critique it.

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Excellent revision. This is a substantial improvement over the goldness formulation because it identifies a determinate, contentful, intelligibly specifiable nature rather than a circular self-reference. Atomic number 79 is exactly the kind of feature that, in modern philosophy of natural kinds (Kripke, Putnam), plays the role of the “real essence” of gold. Let me assess the merits and the remaining objections carefully.

Merits of the revised proposal

    Merit 1: It dissolves the circularity objection. Atomic number 79 is not a redescription of goldness; it is an independently specifiable physical feature. Just as thought is contentful (understanding, willing, imagining, sensing) and extension is contentful (three-dimensional spatial magnitude), having atomic number 79 is contentful (having 79 protons in the nucleus of each atom). The proposal now picks out a determinate intelligible nature rather than circling back to the name of the kind.

    Merit 2: It captures the modern natural-kind intuition rigorously. Kripke’s Naming and Necessity and Putnam’s “The Meaning of ‘Meaning'” argue that natural kinds have real essences that are discoverable by science and that fix the kind across all possible worlds. Gold is necessarily the element with atomic number 79; anything with atomic number 79 is gold; nothing without atomic number 79 is gold. Your proposal aligns precisely with this Kripke-Putnam view.

    Merit 3: It satisfies the all-other-properties-referred-to requirement non-trivially. The other properties of gold—its yellow color, its density, its malleability, its resistance to corrosion, its solubility in aqua regia—are causally explained by the atomic structure with 79 protons. The electronic configuration that follows from 79 protons explains gold’s optical properties (its yellow color is a consequence of relativistic effects on its outer electrons), its chemical inertness, and its physical properties. So all other properties of gold are in a deep sense referred to atomic number 79 as their explanatory ground. This is structurally analogous to the way modes of thought (willing, judging, imagining) are referred to thought as their organizing principal attribute.

    Merit 4: It gives a substance-individuating criterion. “Anything with atomic number 79 is gold” provides a clean identity condition for gold-substance: gold is the kind whose members are all and only the atoms with 79 protons. This parallels the way thought individuates mental substance (whatever thinks is a mind) and extension individuates corporeal substance (whatever is extended is a body).

These are real and significant improvements over the original formulation. But several deeper objections remain, and they are now more interesting because they probe genuine tensions between Descartes’s framework and the Kripke-Putnam natural-kind framework you are implicitly invoking.

Objection 1: The anachronism problem

Descartes did not have, and could not have had, the concept of atomic number. Atomic number as a concept emerges from the work of Henry Moseley in 1913, building on Rutherford’s nuclear model of the atom (1911), itself built on Dalton’s atomic theory (1808), which was itself a development beyond Cartesian corpuscular mechanism. The concept of the nucleus of an atom with a determinate number of protons presupposes nineteenth- and twentieth-century chemistry and physics.

This is not by itself a knock-down objection—you can offer the proposal as what Descartes should have said or what the Cartesian framework would say if updated with modern chemistry. But it raises a question: is the proposal interpreting Descartes or revising him? If interpreting, the anachronism is fatal. If revising, the proposal becomes a neo-Cartesian claim, and we have to ask whether the revision preserves the structural features of Descartes’s framework that made principal attributes do their work.

The most honest framing is: the proposal is a neo-Cartesian revision that uses modern chemistry to specify what Descartes himself could only gesture at as “the corpuscular configuration of gold.” Descartes’s own answer would have been something like “a particular configuration of extended particles of such-and-such size, shape, and motion that produces the sensible qualities of gold.” Your proposal substitutes the modern, precise specification (atomic number 79) for the Cartesian-era vague gesture.

This is a legitimate move, but it should be flagged.

Objection 2: The reduction-to-extension problem

This is the most serious remaining objection within the Cartesian framework. Atomic number 79 is, on any plausible analysis, a mode of extension—specifically, a structural feature of the corpuscular configuration of a region of corporeal substance.

To have atomic number 79 is to have 79 protons in the nucleus of each atom. Protons are extended particles. The arrangement of 79 of them in a nucleus is a spatial configuration. The atom as a whole is an extended object with a particular structure. So atomic number 79 is, ontologically, a mode of extension—a determinate way that extended matter is configured.

If this is right, then the proposal does not identify a new principal attribute beyond extension. It identifies a determinate mode of extension that distinguishes gold from other elements. But modes are not principal attributes; they are the ways principal attributes are particularized.

The parallel is instructive. In mental substance, thought is the principal attribute. Judging that 2+2=4 is a particular mode of thought. Judging that 2+2=4 is not a further principal attribute alongside thought; it is a determinate way thought is occurring. Similarly, atomic number 79 is not a further principal attribute alongside extension; it is a determinate way extension is configured.

So on the strict Cartesian reading: atomic number 79 is a mode of corporeal substance, not a principal attribute of a distinct substance. Gold remains a kind of body (a configuration of extended matter), not a substance with its own principal attribute.

This is a powerful objection, and it does not have an easy answer within Cartesian metaphysics. The natural reply is to depart from the strict Cartesian framework: to say that some configurations of extended matter rise to the level of distinct substances with their own principal attributes. But this is a substantive metaphysical claim that requires independent defense. It is not Descartes’s view.

Objection 3: The intelligibility problem (modified)

In the original goldness proposal, I objected that goldness is not a clear and distinct intellectual nature. The atomic-number-79 revision largely answers this objection. Having 79 protons in the nucleus of each atom is, in principle, a clear and distinct content—it can be grasped intellectually as a determinate structural specification.

However, a residual version of the objection remains. For Descartes, the principal attributes thought and extension are clear and distinct a priori by the natural light. Thought is grasped by the cogito; extension is grasped by geometrical reflection. Neither requires empirical investigation. They are the two intelligible natures that the meditator’s intellect grasps with certainty.

Atomic number 79, by contrast, is empirically discoverable. The meditator does not know by the natural light that gold has atomic number 79. This is a posteriori knowledge, obtained through chemistry and physics. So atomic number 79, even if intelligible, is not the kind of intelligible nature that Descartes had in mind as a principal attribute.

This is not a fatal objection, but it points to a structural difference between Descartes’s principal attributes and the natural-kind essences of modern philosophy of chemistry. Descartes’s principal attributes are a priori intelligible; natural-kind essences are a posteriori discoverable. Treating atomic number 79 as a principal attribute conflates two different kinds of intelligibility.

A neo-Cartesian could respond: the distinction between a priori and a posteriori intelligibility is not essential to the principal-attribute concept; what matters is that the feature be intelligibly specifiable as an organizing nature of the substance. This is a defensible move but again represents a revision of Descartes rather than an interpretation of him.

Objection 4: The proliferation problem (returns)

The original proposal faced an infinite regress problem: every natural kind would get its own principal attribute. The atomic-number revision does not solve this problem; it sharpens it.

If atomic number 79 is the principal attribute of gold, then atomic number 47 is the principal attribute of silver, atomic number 26 is the principal attribute of iron, atomic number 1 of hydrogen, atomic number 8 of oxygen, and so on through all 118 known elements. Each element becomes a distinct substance with its own principal attribute.

And it goes further. Compounds (water, salt, glucose) presumably also have their own principal attributes (their molecular structures). So molecular structure H₂O would be the principal attribute of water, and so on for every chemical compound. The number of substance-kinds would explode into the millions.

This proliferation is exactly what Descartes’s mechanist reductionism was designed to prevent. Scholastic–Aristotelian metaphysics had substantial forms for each natural kind (gold, silver, water, fire, oak, lion, man), and the Cartesian revolution consisted in collapsing all of these into the single principal attribute extension, with the various kinds emerging as modes of extended matter. Reinstating distinct principal attributes for each chemical element (and each compound, and each biological species) is essentially a return to scholastic substantial forms, only with modern chemistry filling in the details.

This is not necessarily a fatal objection—you might think that modern chemistry has vindicated a richer ontology than Descartes allowed. But it should be recognized that the proposal is deeply at odds with the spirit of Cartesian mechanism, not just at odds with the letter of I.53.

Objection 5: The substance-versus-kind problem (returns)

The earlier discussion noted that I.53 talks about each substance having one principal attribute, and that we need to distinguish gold as a kind from this particular piece of gold as an individual.

On the atomic-number revision:

• • This particular piece of gold is an individual extended body whose principal attribute (as a body) is extension. Its having atomic number 79 throughout is a complex mode of its extension (its corpuscular structure).

• • Gold as a kind is a universal, and by I.58 universals are modi cogitandi, not substances. So the kind gold is not a substance and cannot have a principal attribute.

The atomic-number revision does not resolve this. It just relocates the problem. If you say the principal attribute of gold is atomic number 79, you have to specify whether you mean the principal attribute of this piece of gold (which is extension; atomic number 79 is a mode of that extension) or the principal attribute of the kind gold (which is a universal and so a modus cogitandi, not a substance).

Neither location supports the proposal cleanly. The strict Cartesian framework does not have a place for kinds-as-substances-with-their-own-principal-attributes.

Objection 6: The principal-attribute-versus-essence problem

This is a more subtle objection. Even granting everything else, we should ask whether atomic number 79 plays the role of a principal attribute (in Descartes’s specific I.53 sense) or merely the role of a real essence (in Kripke-Putnam’s sense). These are not the same.

A principal attribute in Descartes’s sense:

• • Constitutes the nature and essence of the substance.

• • Is the feature under which the substance is intelligibly grasped (clear and distinct perception).

• • All other properties are referred to it as their organizing principle.

• • Is the complete organizing nature—a substance has exactly one.

A real essence in Kripke-Putnam’s sense:

• • Fixes the identity of the natural kind across possible worlds.

• • Is discovered by science.

• • Explains the observable properties of the kind via causal mechanisms.

• • Picks out the micro-structure underlying the macro-properties.

These are related but distinct concepts. Atomic number 79 clearly plays the Kripke-Putnam role for gold. But does it play the Cartesian principal-attribute role? Only on a revised Cartesian framework that accepts (i) kinds as substances, (ii) a posteriori intelligibility for principal attributes, and (iii) proliferation of principal attributes across natural kinds. Each of these is a substantial departure from Descartes.

So the revised proposal works if you accept the substitution of Kripke-Putnam real essence for Cartesian principal attribute. But the substitution is itself a revision, not an interpretation, and it changes the character of the framework significantly.

Mitigating considerations: what the proposal does well

Despite these objections, the proposal has genuine philosophical force, and a charitable assessment should acknowledge what it accomplishes.

It identifies the right kind of feature. If anything is going to play the principal-attribute role for gold, it should be something like atomic number 79. The proposal correctly identifies the modern scientific answer to the question “what makes gold gold?”

It illustrates a real gap in Cartesian metaphysics. Descartes’s mechanism is too coarse-grained to capture the difference between gold and silver, or between water and ethanol, as anything more than complex modes of extension. Modern chemistry shows that there are real, deep, structural differences between elements and compounds that are not adequately captured by configuration of extended particles alone. The proposal points to this inadequacy.

It provides a clean platform for arguing that I.53 is incomplete. If natural kinds have real essences that organize their properties in the way that atomic number 79 organizes gold’s properties, and if such essences are not reducible to modes of extension, then I.53’s two-principal-attributes (thought, extension) inventory is incomplete. The world has more substance-organizing features than Descartes recognized.

It connects Descartes to live debates in contemporary metaphysics. Kripke-Putnam natural-kind essentialism, scientific essentialism (Brian Ellis, Alexander Bird), and dispositional essentialism are all contemporary frameworks that take natural-kind essences seriously. The proposal puts Descartes in dialogue with these frameworks.

Direct assessment

Strengths of the revised proposal:

1. 1. Dissolves the circularity objection. Atomic number 79 is a determinate, intelligibly specifiable nature, not a redescription of goldness.

1. 1. Aligns with modern Kripke-Putnam natural-kind essentialism, which is a respectable contemporary metaphysical framework.

1. 1. Causally and explanatorily grounds the other properties of gold (color, density, malleability, chemical behavior).

1. 1. Provides a clean identity condition: anything with atomic number 79 is gold.

Remaining weaknesses:

1. 1. Anachronism: Descartes lacked the concept of atomic number. The proposal is neo-Cartesian revision rather than Cartesian interpretation.

1. 1. Reduction to extension: atomic number 79 is, on any plausible analysis, a mode of extension (a structural-spatial feature of the corpuscular configuration). It is not a new principal attribute alongside extension.

1. 1. A priori vs. a posteriori intelligibility: Descartes’s principal attributes are graspable by the natural light; atomic number 79 is empirically discoverable. The two kinds of intelligibility are different.

1. 1. Proliferation: the proposal commits to a distinct principal attribute for every element (and presumably every compound), reintroducing the scholastic proliferation of substantial natures that Descartes was trying to eliminate.

1. 1. Substance vs. kind: the kind gold is, on I.58, a universal and so a modus cogitandi, not a substance. This piece of gold is an extended body whose principal attribute is extension. Neither location supports a distinct gold-substance with its own principal attribute.

1. 1. Principal attribute vs. real essence: atomic number 79 plays the Kripke-Putnam real-essence role but not, strictly, the Cartesian principal-attribute role. The substitution is a substantive revision.

Bottom line

The atomic-number revision is a significant improvement over goldness, because it identifies a determinate, contentful, intelligibly specifiable nature. It dissolves the circularity problem and aligns the proposal with modern natural-kind essentialism. As a neo-Cartesian claim about what should play the principal-attribute role for natural kinds, it is defensible and philosophically interesting.

However, as an internal counterexample to I.53 within Descartes’s own framework, it still faces serious objections. Atomic number 79 is most naturally analyzed as a mode of extension (a structural-spatial feature of corpuscular configuration), not as a new principal attribute. The kind gold is, on I.58, a universal and so a modus cogitandi, not a substance. This piece of gold is a body whose principal attribute (as a body) is extension. And the proposal commits to a proliferation of principal attributes across all chemical kinds, which is structurally at odds with Cartesian mechanist reductionism.

The strongest framing for the post is: Gold and natural kinds pose a problem for Descartes’s mechanist framework. If natural-kind essences (such as atomic number 79 for gold) are real and not reducible to modes of extension, then Descartes’s I.53 inventory of principal attributes (thought, extension) is incomplete. Modern chemistry suggests that such real essences exist. This is not an internal counterexample to I.53 but an external pressure on the Cartesian framework, calling for revision in the direction of contemporary natural-kind essentialism.

For your DTOI project, this remains a deeper objection that targets the mechanist reductionism rather than the specific I.53 doctrine. As before, the human being as substantial union remains the cleanest internal counterexample, while gold points to a more sweeping inadequacy in Cartesian metaphysics.

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According to Descartes (Principles I.57; AT VIIIA 27; CSM I 212), it seems “time is the measure of movement.” John Cottingham translation below:

Doesn’t it follow that if nothing moves, then time does not pass? Is that correct?

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Excellent question. This presses on a real tension in Descartes’s treatment of time and duration, and the answer requires distinguishing several Cartesian concepts that often get conflated. Let me work through it carefully.

The key texts

Principles of Philosophy I.57 (AT VIIIA 27; CSM I 212):

“Some attributes or modes are in the things themselves of which they are said to be attributes or modes, while others are only in our thought. For example, when time is distinguished from duration taken in the general sense and is called the measure of movement, it is simply a mode of thinking. For the duration which we understand to be involved in movement is certainly no different from the duration involved in things which do not move.” (bold and bold italic not in original)

This is the load-bearing passage. Descartes draws a sharp distinction between two items that are often confused:

1. 1. Duration (duratio): a real attribute or mode of things that exist or endure.

1. 1. Time (tempus): the measure of movement, a modus cogitandi.

The distinction is essential to answering your question correctly.

Duration vs. time: the Cartesian distinction

Duration is, for Descartes, a real attribute of every existing thing. Anything that exists endures—exists over some stretch—and its enduring is its duration. This is true of God (whose duration is eternity), of mental substances (whose duration is the continued existence of their thinking), and of corporeal substances (whose duration is their continued existence as extended bodies). Duration is in things, as a real mode or attribute of their existence.

Critically, Descartes says: “the duration which we understand to be involved in movement is certainly no different from the duration involved in things which do not move.” This is the decisive line for your question. A thing that does not move still has duration—it still endures, it still exists over time. Duration does not require motion.

Time, by contrast, is the measure of movement. It is what we get when the mind compares the duration of one thing (e.g., a swinging pendulum, the rotation of the heavens, the ticking of a clock) with the duration of other things, in order to measure or quantify them against a standard. Time in this sense is a modus cogitandi—a way the mind organizes and measures duration by reference to motion.

So Descartes has two distinct items:

• • Duration: real, in things, a feature of their continued existence.

• • Time: the mind’s measure of duration via motion, a modus cogitandi.

Direct answer to your question

Your reasoning was: if time is the measure of movement, then if nothing is moving, time is not passing.

On Descartes’s view, this is partially correct, but it requires a crucial qualification. Let me lay out what follows and what does not.

What does follow:

If nothing whatsoever moves in the entire universe, then time as the measure of movement does not occur, because there is nothing to measure and no standard motion to measure by. Time in this strict I.57 sense requires motion, by definition: it is the measure of movement. No movement, no measure, no time-in-this-sense.

What does not follow:

It does not follow that duration ceases. Things that exist still endure, still exist over stretches of their being, even if they do not move. Duration is in things, and a non-moving thing still has duration as long as it exists. The continued existence of a non-moving stone, a non-moving mind contemplating an eternal truth, or a non-moving angel is still a real enduring. The thing is still temporally extended in the sense of having a real duration; it just is not being measured against a moving standard.

So the precise Cartesian answer is:

• • Time-as-measure-of-movement would not occur if nothing moved. You are right about that.

• • Duration would still occur, because duration is real-in-things and does not require motion.

• • Time-passing-changing-occurring is ambiguous between these two senses. In the strict I.57 sense (time = measure of movement), no. In the looser sense (time = duration of things), yes—things would still endure.

The deeper question: can things endure without changing?

Your question raises a further philosophical issue: can a thing endure without changing in any respect? If duration is real-in-things and does not require motion, then yes—a thing can endure (have real duration) without moving. But can it endure without any change at all?

Descartes’s answer here is nuanced. He distinguishes:

    (a) Local motion (motion in the spatial sense, change of place): this is a mode of corporeal substance, and is precisely the kind of movement that I.57 is talking about. A non-moving body has no local motion but still has duration.

    (b) Other kinds of change: alteration of qualities, change of thought in a mind, change of state more generally. A mind that is contemplating an eternal truth is not locally moving, but it is in some sense active—its thought is occurring. The mind has duration, and the mind’s acts of thinking are themselves temporally structured.

    (c) Continued existence as such: even something perfectly unchanging—say, an unmoving angel contemplating a single eternal truth—has duration as long as it exists. Its duration is just its continued being.

So Descartes can say: even in a universe where no local motion occurs, minds that are thinking and bodies that exist (without moving) still have duration. Duration is more fundamental than time-as-measure-of-movement.

This is why Descartes carefully distinguishes the two. Duration in the general sense is a real attribute. Time in the strict sense is the mind’s measure of duration via motion. The latter is what depends on motion; the former does not.

A complication: Descartes’s continuous-creation doctrine

There is a wrinkle here worth flagging. Descartes holds that God continuously creates the world at each moment (Third Meditation; AT VII 49; CSM II 33; Principles I.21; AT VIIIA 13; CSM I 200). On this view, the duration of any created thing is the continued act of divine creation that sustains it in being moment by moment.

This means even duration is, in a sense, dependent on something occurring—namely, God’s continuous creative act. If God’s act is dynamic (as Descartes suggests), then duration involves a kind of metaphysical “occurring” at the divine level, even if no creature moves.

But this does not undermine the I.57 distinction. The point of I.57 is that duration is on the side of things (real, in things), whereas time-as-measure-of-movement is on the side of the mind (a modus cogitandi). Continuous creation explains the metaphysical ground of duration but does not make duration into a measure-of-movement.

What you can say in the post

If you wanted to incorporate this into your project, a precise formulation would be:

Descartes distinguishes duration, which is a real attribute of every existing thing (Principles I.57; AT VIIIA 27; CSM I 212), from time, which is the mind’s measure of duration via motion and is therefore modus cogitandi. The proposition time is the measure of movement concerns the latter, not the former. If nothing moved, then time in the measure-of-movement sense would not occur, because there would be no movement to measure and no standard motion to measure by. But duration would still occur—things that exist still endure, whether or not they move. Descartes is explicit: “the duration which we understand to be involved in movement is certainly no different from the duration involved in things which do not move.” So the strict reading of time is the measure of movement yields an interesting result: time in the measure-of-movement sense is mind-dependent and motion-dependent, while duration as a real feature of existing things is mind-independent and motion-independent.

Why this matters for the OR project

The duration/time distinction maps onto your OR analysis in a clean way:

• • Duration is a real-in-things attribute, akin to number-in-things. The duration of a particular existing thing has OR content insofar as it is a real feature of that thing (and the thing has OR as a finite or infinite substance).

• • Time as measure of movement is a modus cogitandi, akin to number-in-general. As a modus cogitandi, it has no OR-bearing representatum at any rank.

This gives you another clean case of the real-feature vs. modus-cogitandi split that runs through the I.55–58 discussion. Just as number-in-things has OR and number-in-general does not, duration-in-things has OR (via the durating thing) and time-as-measure-of-movement does not. The OR apparatus can rank the real durations of substances but cannot rank the mind’s measuring activity.

Bottom line

Your reasoning is correct in the strict I.57 sense but requires the duration/time distinction to be stated precisely. If time is the measure of movement and nothing moves, then time in this sense does not occur—there is no measurement and no measured motion. But duration, which is not the measure of movement but a real attribute of existing things, would still occur. Things that exist still endure, whether or not they move. Descartes says explicitly that the duration of moving and non-moving things is the same kind of duration.

So the precise answer is: if nothing moves, time-as-measure-of-movement does not occur, but duration still does. Time in the strict I.57 sense requires motion. Duration in the I.57 sense does not. The conflation of these two is one of the most common interpretive mistakes about Cartesian time, and your question helpfully isolates exactly where the precision is needed.

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Suppose nothing in the universe moves for two seconds, then duration has occurred for two seconds of the existing universe, while no time measurement was possible, so no time changes took place.

  Is that a coherent Cartesian interpretation?

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Yes, that is a coherent Cartesian interpretation, and it is in fact close to the most natural reading of Principles I.57. But the precise formulation requires one important refinement, because the way you describe the scenario contains a subtle internal tension that needs to be resolved. Let me work through it.

The scenario as stated

You propose: nothing in the universe moves for two seconds. During that interval, duration occurs (the universe exists and endures for two seconds), but no time measurement is possible (because time is the measure of movement, and there is no movement to measure), so no time changes take place.

The basic structure of this is correct and Cartesian. Let me confirm what works and then flag the refinement needed.

What works in the interpretation

Duration occurs without motion. This is exactly Descartes’s view in I.57. “The duration which we understand to be involved in movement is certainly no different from the duration involved in things which do not move.” A motionless universe still endures, because duration is a real attribute of every existing thing, independent of motion. If the universe exists for two seconds without anything moving, the universe has two seconds of duration. The duration is real, in things, and motion-independent.

Time as measure of movement does not occur. Also correct. If time is the measure of movement and nothing moves, then there is no movement to measure and no standard motion to measure by. Time in the I.57 measure-of-movement sense does not occur in such a scenario. The mind cannot construct time as measure without motion as its object.

The duration is mind-independent; the absence of time-measurement is mind-relative. This captures the core I.57 distinction. Duration is in things; time is in the mind, as a modus cogitandi. The universe’s two seconds of duration are real features of the universe’s continued existence. The absence of time-measurement is an absence at the level of the mind’s measuring activity.

So far the interpretation is solid.

The refinement needed: the description of the interval

Here is the subtle tension. You describe the scenario as “nothing in the universe moves for two seconds.” But the phrase “for two seconds” already invokes a time-measurement. Two seconds is a specific quantity of measured time, defined in terms of a standard motion (originally the rotation of the Earth, now the oscillations of a cesium atom). To say the universe is motionless for two seconds is to apply a time-measurement to an interval in which, by hypothesis, no time-measurement is possible.

This is not a fatal problem, but it requires careful handling. Let me lay out three ways to resolve it.

Resolution 1: External standpoint. We can describe the interval from outside the motionless universe, using our own time-measurement as observers in a moving frame. From the standpoint of an observer in a frame where motion continues (or from a hypothetical “God’s-eye” standpoint that can measure duration directly), the motionless interval lasts two seconds. The two-second specification is our measurement, made from outside the motionless scenario; it does not occur within the motionless scenario itself.

This resolution preserves the scenario but locates the time-measurement at the level of the describer, not at the level of the described.

Resolution 2: Duration without time-measurement, described qualitatively. Drop the “for two seconds” specification and describe the scenario qualitatively: the universe exists motionless for some duration. The duration is real (the universe endures), but no specific time-measurement applies, because no motion is occurring. The duration is then unmeasured but still real.

This resolution is cleaner conceptually but less vivid. It preserves the I.57 distinction in pure form: real duration, no measurement.

Resolution 3: God’s measurement. Descartes’s continuous-creation doctrine (Third Meditation; AT VII 49; CSM II 33) holds that God sustains the world in being at each moment. God’s creative act is itself the metaphysical ground of duration, and God presumably “knows” how long the motionless interval lasts in some non-measurement-dependent way. So the interval might have a determinate length to God even if no creature can measure it. The two-second specification could be understood as the duration God knows the interval to have.

This resolution invokes Descartes’s theology and is the most metaphysically robust, but it goes beyond what I.57 explicitly says.

The cleanest formulation for your purposes is probably Resolution 2 (qualitative description) combined with Resolution 1 (external observer standpoint) where vivid specification is wanted.

The reformulated scenario

Here is the scenario reformulated to remove the internal tension:

Suppose nothing in the universe moves for some interval. During that interval, duration occurs—the universe exists and endures throughout the interval—but no time-measurement is possible, because time is the measure of movement and there is no movement to measure. Described from outside the scenario by an observer whose own frame contains motion, the interval lasts (say) two seconds; but described from within the scenario, the interval is real duration without measured time. The duration is mind-independent and real-in-things; the absence of time-measurement is a feature of the mind’s measuring activity, which has no object in the motionless interval.

This reformulation preserves your insight, removes the internal tension, and aligns precisely with the I.57 framework.

Whether “no time changes take place” is correct

Your phrase “no time changes took place” needs unpacking, because “time changes” is ambiguous.

    Reading A: No measured time elapsed (in the strict I.57 sense). Correct. Time as the measure of movement did not occur, so no time-changes in this sense took place. There was no ticking of clocks, no rotation of standards, no measurable temporal flow.

    Reading B: No change occurred at all. This is by hypothesis (nothing moves), but it is a separate claim from the time-measurement claim. The absence of motion is the condition of the scenario; the absence of time-measurement is the consequence. The two should be kept distinct.

    Reading C: Duration did not change. Tricky. Duration accumulates—the universe has more duration at the end of the interval than at the beginning. So in some sense duration progresses even without motion. But the progression of duration is not a change in any thing; it is just the continued existence of things over time. Descartes does not treat duration’s progression as a change in his technical sense. Change (mutatio) for Descartes typically requires alteration of mode (local motion, alteration of quality, change of thought), and a motionless universe undergoes no such alteration. So in the technical sense, no change occurred during the interval, even though duration accumulated.

So the precise statement is: during the motionless interval, duration accumulates without change. The accumulation of duration is not itself a change; it is the continued existence of things.

A subtle complication: do minds count?

Your scenario specifies “nothing in the universe moves.” But minds (finite mental substances) presumably continue to exist during the interval, and minds think. Is thinking a kind of motion or change?

Descartes is clear that thought is not local motion (it is not motion in space). But thought is active in some sense—judging, willing, imagining, sensing are all activities, and they unfold over time. A mind that is thinking is doing something, and what it does is temporally structured.

So if minds continue to think during the motionless interval, there is a kind of mental change (succession of thoughts, alteration of mental states) that is not local motion but is still temporally structured. The mind’s own thinking could provide a non-motion-based “internal time” measurement.

To make the scenario pure, you would need to stipulate that no minds are thinking during the interval—or perhaps that only God thinks, and God’s thought is eternal and not temporally successive (as Descartes’s Augustinian theological commitments suggest).

A truly motionless and mindless universe—pure existing bodies with no local motion and no thinking minds—would be the cleanest case. In such a universe, only duration occurs; no motion, no thought, no change, no measurement. Just the continued existence of bodies sustained moment by moment by divine creation.

This is the cleanest Cartesian scenario for your purposes.

Bottom line

Yes, your interpretation is coherent and substantially correct. A motionless universe still endures (duration is real-in-things), but time-as-measure-of-movement does not occur (no motion to measure). This is precisely the I.57 distinction.

The one refinement needed is to handle the “for two seconds” specification carefully. The phrase invokes a time-measurement that, by the scenario’s own terms, cannot occur within the scenario. The cleanest fix is either (a) to attribute the two-second measurement to an external observer outside the motionless scenario, or (b) to describe the interval qualitatively as “some duration” without specifying a measured quantity.

A further refinement would stipulate that no minds are thinking during the interval, so that no internal temporal succession of thoughts provides an alternative measurement. A purely motionless and mindless universe is the cleanest case.

The precise Cartesian formulation: In a motionless and mindless interval, duration accumulates as the real continued existence of bodies, but no time-measurement occurs because time-as-measure-of-movement requires motion that is, by hypothesis, absent. Duration is mind-independent and real-in-things; time-measurement is a modus cogitandi that has no object in such an interval, and therefore does not occur. No change of any kind takes place—neither local motion nor mental succession—but the universe still endures.

This is a coherent and philosophically rich extension of I.57, and it cleanly illustrates the duration/time distinction at the heart of Cartesian temporal metaphysics.

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Create a table covering the points we made above regarding Descartes on relations, nececessity, substance, principal attributes, etc. and how they relate to ideas of those items with regard to having objectively real representational content (OR).

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Here is a consolidated table covering the points developed across our recent exchanges. I have organized it by item, with columns tracking the ontological status, the Cartesian framework treatment, and the OR-bearing status of the corresponding idea.

Idea of	Ontological Status (in re)	Cartesian Framework Treatment	Idea’s OR-Bearing Status	Rationale
God	Infinite substance	Principal attribute: infinite perfection; sole truly independent substance (I.51)	OR at infinite-substance rank	God is the supreme OR-bearing representatum; idea of God has maximal OR
Mental substance (finite)	Finite substance	Principal attribute: thought (I.53); modes include willing, judging, imagining, sensing	OR at finite-substance rank	Real substance with intelligible nature; idea of mind has finite-substance OR
Corporeal substance (finite)	Finite substance	Principal attribute: extension (I.53); modes include shape, size, motion, position	OR at finite-substance rank	Real substance with intelligible nature; idea of body has finite-substance OR
Modes of thought (willing, judging, imagining, sensing)	Real modes of mental substance	Referred to thought as organizing principal attribute (I.53, I.56)	OR at mode rank	Real-in-things; idea of a mode has mode-level OR
Modes of extension (shape, size, motion, position)	Real modes of corporeal substance	Referred to extension as organizing principal attribute (I.53, I.56)	OR at mode rank	Real-in-things; idea of a mode has mode-level OR
Gold (kind)	Universal; modus cogitandi (I.58)	Not a substance; kind is a way the mind abstracts from particulars	No OR (modus cogitandi has no OR-bearing representatum)	Universals are mind-dependent; no real-in-things representatum to rank
This piece of gold (individual)	Configuration of corporeal substance	Body whose principal attribute (as body) is extension; goldness is complex mode of its extension	OR at finite-substance rank (as a body), with mode-level OR for its configuration	The individual body has OR as a body; its goldness-features are mode-level OR of extension
Goldness / atomic number 79	Mode of extension (corpuscular configuration)	Not a further principal attribute; structural-spatial mode of extended matter	OR at mode rank (as mode of extension)	Treating it as a distinct principal attribute would require neo-Cartesian revision
Duration	Real attribute of every existing thing (I.57)	In things; motion-independent; same kind of duration in moving and non-moving things	OR-bearing (tied to OR rank of the durating thing)	Real-in-things; inherits OR rank from the substance whose duration it is
Time (measure of movement)	Modus cogitandi (I.57)	Mind’s measure of duration via motion; not in things	No OR (modus cogitandi has no OR-bearing representatum)	Parallels number-in-general: mind-dependent measuring activity, no representatum to rank
Number-in-things	Real feature of things numbered	A real attribute of the plurality of things (I.55, I.58)	OR-bearing (tied to OR rank of the numbered things)	Inherits OR rank from the items it numbers
Number-in-general (the abstract universal)	Modus cogitandi (I.58)	Universal; abstracted by the mind from numbered things	No OR	Universal abstraction; no real-in-things representatum to rank
Order, place, duration-in-general	Modus cogitandi (I.55–58)	Mind’s general modes for organizing thought about things	No OR	Mind-dependent organizing modes; no representatum to rank
Relations (resemblance, comparison, identity, difference)	Modus cogitandi in most cases	Mind’s act of comparing or relating two or more things (I.55–58 family)	No OR for the relation itself; OR for the relata as substances/modes	Relation is mind-supplied; only the relata bear OR
Common notions / eternal truths (“ex nihilo nihil fit”; “nothing has no properties”)	Not things or modes; propositional truths	Innate principles known by natural light; not items in re	No OR (not strict ideas of things/modes per restriction thesis)	Common notions are non-OR-bearing; they govern thought but lack a representatum to rank
Idea of nothing	No representatum	Nothing has no properties, so no content to specify	No OR	Decisive non-OR case; no representatum at any rank
Necessity (modal status: “must be,” “cannot be otherwise”)	Modus cogitandi in most uses; sometimes a feature of essences	Mind’s grasp of what cannot be otherwise; tied to clear and distinct perception	No OR for necessity itself; OR for the substance/mode whose essence is necessarily as it is	Necessity is modal-relational, not a representatum; the essence it qualifies bears OR
Principal attribute (as an item of thought)	Real-in-things (the nature it picks out is real)	The intelligible nature under which a substance is clearly and distinctly grasped (I.5)	OR-bearing (tied to OR rank of the substance it constitutes)	The principal attribute is the substance’s nature; ideas of it inherit the substance’s OR rank
Substantial union (mind–body)	Disputed; possibly a third substance-kind (To Elizabeth, 21 May 1643; AT III 665; CSMK 218)	Tension with I.53’s two-principal-attributes inventory; sensations and emotions belong to the union	Disputed OR status; if a finite substance-kind, OR at finite-substance rank	Internal pressure on I.53; the union may require its own principal attribute

Notes on the table’s organizing logic

The OR/modus cogitandi divide is the central axis. Items that are real-in-things (substances, modes, principal attributes, duration, number-in-things) bear OR at a determinate rank. Items that are modi cogitandi (universals, time-as-measure, number-in-general, order, relations, common notions) lack OR because they lack a real-in-things representatum to rank.

Rank inheritance. Modes inherit their OR rank from the substance they modify. Principal attributes inherit their OR rank from the substance they constitute. Duration inherits its OR rank from the durating thing. Number-in-things inherits its OR rank from the things numbered. This pattern reflects the I.53–58 structure of attributes and modes referred to substances.

Universals and abstractions consistently fall outside OR. Kinds (gold, silver), abstract universals (number-in-general, time-in-general, duration-in-general, order), and modi cogitandi generally have no OR-bearing representatum, because the items they apply to are not real things or modes but mind-dependent abstractions.

Relations and necessity sit on the modus cogitandi side, with OR carried by their relata. The relation itself is mind-supplied; the items related bear OR. Necessity is modal-relational; the essence it qualifies bears OR.

Internal pressures on the framework. The substantial union, gold-as-kind-with-its-own-principal-attribute, and the duration-without-time scenario each press on different aspects of the Cartesian framework. The table records the standard Cartesian verdict and flags the disputed cases.

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Conclusion: Overview of the Philosophical Significance

The cumulative results of this post point to a single, structurally precise conclusion: Descartes’s apparatus of objective reality is a restricted—not a universal—theory of representational content. It succeeds, and succeeds powerfully, wherever the represented item can be ranked on the mode / finite-substance / infinite-substance hierarchy, including in the difficult cases of non-existent composites (chimeras), false judgments about OR-bearing constituents (a vacuum exists), and geometrical essences with true and immutable natures. But it falls constitutively silent across four interlocking classes of perfectly intelligible Cartesian content: privative ideas (the idea of nothing), eternal-truth content (ex nihilo, nihil fit), relational structure and universals (Principles I.55–58), and modal-necessity content (a mode is necessarily related to a substance). The significance of this result lies less in the negative claim—that OR has limits—than in where the limits fall and what their location reveals about the architecture of Descartes’s metaphysics as a whole.

First, the limits are not anomalies but predictable structural features. Every decisive anti-OR case shares the same diagnostic: it cannot be reconstructed as a composition of OR-bearing constituents at any ontological rank, even in principle. This is what distinguishes nothing and ex nihilo, nihil fit from the chimera and the vacuum, and what makes the universal set, the greatest finite number, and the smallest extended body cleaner anti-OR cases than the squared circle. The pattern is not a set of awkward exceptions for OR theory to absorb. It is the signature of a different ontological category—modi cogitandi and intelligible truth-content—that operates alongside ranked representata rather than within their hierarchy. Recognizing this changes the dialectical situation: pro-OR interpreters who reconstruct difficult cases as composites of OR-bearing parts are doing real work, but their move presupposes constituents available only in the cases where OR was always going to succeed. The genuinely anti-OR cases are precisely the ones where no such constituents exist.

Second, the capstone case—”a mode is necessarily related to a substance”—has self-referential force that no pro-OR rescue can absorb. The proposition is not peripheral. It articulates the very dependence relation that makes the Cartesian hierarchy a hierarchy at all. Yet by Principles I.58, mode-in-general and substance-in-general are universals and hence modi cogitandi; and necessary dependence is an eternal truth, not a representatum. The framework’s own load-bearing background is therefore not itself OR-bearing. This is not a contradiction in Descartes; it is the expected behavior of a measure-apparatus operating within an ontology rather than over it. But it does mean that any reading of OR as a universal theory of thinkable content over-extends the doctrine into territory Descartes’s own systematic texts (I.55–62) explicitly assign elsewhere.

Third, the result clarifies what OR actually is. OR is best understood as a ranking-and-measurement apparatus for represented items that have a determinate ontological kind. It is not a theory of intelligibility as such, nor a theory of every thinkable content, nor a theory of the relational and modal scaffolding by which the intellect compares, abstracts, and necessitates. Misreading OR as universal forces commentators into one of two unsatisfying positions: either inflating modi cogitandi into quasi-substances (which Descartes refuses at I.58), or deflating non-OR content into “not really ideas at all” (which sits poorly with Burman’s reluctant concession that even nothing is, in some sense, an idea). The restriction thesis offers a third path: OR is what it claims to be—a doctrine of represented ontological rank—and the non-OR classes are real, intelligible, and structurally distinct.

Fourth, the collateral pressures on I.53 (the human substantial union, divine simplicity, duration vs. time, natural kinds) show that the strain is not confined to OR. The same systematic features that make OR a restricted apparatus—the sharp separation of real-in-things items from modi cogitandi, the deflationary treatment of relations, the createdness of eternal truths—generate pressure throughout Cartesian metaphysics wherever the framework is asked to do more than rank substances and their modes. This suggests that the restriction thesis (see the definition at the top of this post) is not an isolated finding about one doctrine but a diagnostic instrument for reading Descartes’s mature metaphysics generally.

Finally, the philosophical payoff for contemporary philosophy of mind and representation. Modern theories of mental content frequently inherit, often without acknowledgment, the assumption that all intelligible content must be analyzable as the representation of some object, structure, or property. The restriction thesis suggests that this inheritance is too strong even for Descartes himself, and that a more honest descendant of Cartesian representationalism would distinguish representational content (ranked items) from structural content (relations, universals, modes of comparing), truth-content (eternal truths and common notions), and privative content (the negative limits of being). Each of these is intelligible. None reduces to the others. And the apparatus that measures one is not obliged to measure all.

The conclusion of this post, then, is not that Descartes’s theory of objective reality fails. It is that the theory succeeds exactly where it was designed to succeed—in measuring ranked representational content—and that recognizing the boundary of that success is itself a contribution to understanding what Descartes’s theory of ideas really is. OR is silent on its own foundational background not because the doctrine is defective, but because measurement-within-a-framework cannot, in principle, take the framework itself as its object. The silence is structural, expected, and instructive.