{"id":47196,"date":"2026-07-07T06:08:17","date_gmt":"2026-07-07T06:08:17","guid":{"rendered":"https:\/\/drdavidcring.net\/descartes-ideas\/?p=47196"},"modified":"2026-08-06T18:21:56","modified_gmt":"2026-08-06T18:21:56","slug":"do-cartesian-universals-have-objective-reality-genus-species-and-the-modes-of-thinking-without-representata","status":"publish","type":"post","link":"https:\/\/drdavidcring.net\/descartes-ideas\/objective-reality\/do-cartesian-universals-have-objective-reality-genus-species-and-the-modes-of-thinking-without-representata\/","title":{"rendered":"Do Cartesian Universals Have Objective Reality? Genus, Species, and Modes of Thinking without Representata"},"content":{"rendered":"\n
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[NOTE:<\/span><\/strong> Words below in magenta<\/a> or blue underlined<\/u><\/span><\/a> are clickable hyperlinks. For many of the hyperlinked glossary items you may need to scroll down to see that entry after clicking on it. Hit the back button in your browser afterwards to return to this post.]<\/p>\n\n\n\n

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Medium Abstract<\/mark><\/h3>\n\n\n\n
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This post examines whether the five Porphyrian predicables<\/a>\u2014genus<\/a><\/em>, species<\/a><\/em>, differentia<\/a><\/em>, proprium<\/a><\/em> (typically translated as \u201cproperty<\/a>\u201d), and accident<\/a><\/em>\u2014possess objective reality representational content<\/a> (OR<\/a><\/strong>) in Descartes\u2019s theory of ideas when they are considered as second-order classificatory roles<\/strong> (concepts applied to other concepts to indicate their place within a logical classification\u2014for example, whether a concept functions as a genus, species, differentia, proprium, or accident).1<\/a><\/sup>The expressions first-order<\/strong> and second-order<\/strong> distinguish two different levels at which the intellect can think. First-order ideas<\/strong> are ideas of things or of their principal attributes, true and immutable natures, and modes. Thus the ideas of animal<\/em>, human<\/em>, triangle<\/em>, extension<\/em>, and motion<\/em> are first-order ideas because they represent what things are or the natures, principal attributes, or modes they possess.

Second-order ideas<\/strong>, by contrast, are ideas about<\/em> first-order ideas. They do not introduce additional represented natures alongside animal<\/em> or triangle<\/em>; instead, they classify the logical role that first-order ideas play within a taxonomic scheme. Thus, when the intellect judges that animal<\/em> is a genus<\/strong> relative to human<\/em>, or that human<\/em> is a species<\/strong> relative to animal<\/em>, the represented nature animal<\/em> remains exactly the same. What changes is not the represented nature but the way the intellect classifies that first-order idea. Likewise, rational<\/em> functions as a differentia<\/strong>, risible<\/em> as a proprium<\/strong>, and white<\/em> as an accident<\/strong> relative to the species human<\/em>.

The distinction is therefore one of level<\/strong>, not of represented object. First-order ideas<\/strong> represent substances, principal attributes, true and immutable natures, or modes. Second-order ideas<\/strong> represent ways of classifying<\/em> those first-order ideas. The latter do not thereby introduce additional first-order natures or modes alongside the ideas they classify.

This distinction is fundamental to the argument of this post. My Restriction Thesis<\/u><\/span><\/a> does not deny that first-order universal ideas, such as the idea of animal<\/em>, may contain objective reality. The question is whether the second-order classificatory ideas of genus<\/strong>, species<\/strong>, differentia<\/strong>, proprium<\/strong>, and accident<\/strong> contribute any additional OR-bearing representatum<\/em> beyond the first-order ideas to which they are applied. The argument defended here is that they do not. They classify first-order ideas without thereby introducing a new substance, principal attribute, true and immutable nature, or mode as an additional representatum<\/em>.<\/span>
<\/span> Objective reality<\/a> is the ontologically rankable internal representational content contained in a Cartesian strict idea<\/a>: the representational presence within the idea of a representatum<\/em> considered as a substance<\/a>, principal attribute<\/a>, true and immutable nature<\/a>, or mode<\/a>. Its degree corresponds to the ontological standing of the representatum<\/em> (item represented). Ideas of finite substances and their principal attributes possess finite substantial objective reality, whereas ideas of possible modes and the true and immutable natures of possible modes possess modal objective reality. Conceptual determinacy, however, does not by itself establish the presence of any such representatum<\/em>.<\/p>\n\n\n\n

See my posts in support: <\/p>\n\n\n

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\"An\u201cThe Core DTOI Argument: Sensations Without Cartesian Objective Reality<\/a><\/p>\n

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\"An\u201cCondensation: Why Objective Reality Cannot Be Descartes\u2019s Theory Of Thought: Burman, Common Notions, And The Failure Of The Strict Idea Model<\/a>\u201d<\/p>\n

\"AnSee the complete uncondensed version \u201cWhy Objective Reality Cannot Be Descartes\u2019s Universal Theory Of Thought: Burman, Common Notions, And The Failure Of The Strict-Idea Model<\/a>\u201d<\/p>\n

\"Anand its companion piece \u201cWhy Objective Reality Cannot Be Universal In Descartes\u2019s Theory Of Ideas: Nothing, Eternal Truths, Sensations, And Fear With Claude Opus 4.6<\/a>.\u201d<\/p>\n

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The argument therefore distinguishes first-order universal ideas from second-order predicables. A first-order universal idea, such as the idea of triangularity, extension, or animal<\/em>, may possess OR<\/a> through the nature, principal attribute, or mode it represents. By contrast, when the intellect classifies animal<\/em> as a genus<\/a><\/em> relative to human<\/em> or horse<\/em>, that second-order classificatory status does not obviously introduce a further represented nature or mode beyond the first-order nature animal<\/em>. In Principles<\/a><\/em> I.58\u201359, Descartes explains number and universals as modes of thinking arising through intellectual comparison, abstraction, and general naming. Yet identifying those formally real intellectual operations as the origin or ground of classification is not equivalent to showing that the classificatory role itself is internally represented as an OR<\/a>-bearing modification of thinking substance.<\/p>\n

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Preliminary test cases establish the governing distinction between conceptual determinacy and objective reality. The round square<\/a> shows that a formally real and intelligible act of thought may employ independently OR-bearing component ideas without containing a coherent unified representatum<\/em>.<\/p>\n

Unlike \u2018round square, the impossibility of a largest natural number does not arise from an internally contradictory combination of its constituent concepts, but from the mathematical structure of the natural numbers: for every natural number, there is a greater one. Comparative notions such as largest<\/em> and smallest<\/em> may possess determinate application conditions and track objectively grounded relations without representing additional intrinsic modes of the objects compared. Cartesian common notions<\/a> may be necessary, self-evident, and inferentially indispensable without every constituent notion contributing objective reality, while distinctions of reason<\/a> may differentiate inseparable aspects of an OR<\/a>-bearing nature without adding a further modal representatum<\/em>. These cases jointly establish that intelligibility, necessity, inferential structure, and conceptual determinacy do not entail objective reality.<\/p>\n

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Three positions are then evaluated through the test case GSD<\/strong>: \u201cthe predicable role of genus<\/em> is distinct from the predicable role of species<\/em>.\u201d Position 1<\/mark><\/strong> denies that GSD<\/b> contains any additional OR<\/a>-bearing representatum<\/em> corresponding to those predicable roles. Position 2<\/mark><\/strong> assigns them modal objective reality<\/a> because universals are modifications of thinking substance. Position 3<\/mark><\/strong> assigns them weakened or derivative objective reality as idealized classificatory forms abstracted from actual intellectual operations. The second and third positions should not be understood as attributions to Descartes or as reconstructions of any single commentator. They are philosophical reconstructions introduced to test whether second-order predicables can be brought within the objective-reality framework by the strongest available lines of argument.<\/p>\n

The objections to Positions 2<\/span><\/strong> and 3<\/strong><\/span> are structurally parallel. Position 2<\/strong><\/span> confuses the formal reality<\/a> of the intellectual operations grounding classification with the represented content of the classificatory thought. Position 3<\/strong><\/span> confuses determinate conceptual structure with objective reality<\/a>. Neither formally real intellectual grounding nor conceptual determinacy establishes that the predicable roles are internally represented as substances, principal attributes, true and immutable natures, or modes.<\/p>\n

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The post concludes that Position 1<\/mark><\/strong> provides the best Cartesian account. Second-order predicable roles are conceptually determinate and indispensable to logical and taxonomic cognition, but they do not themselves contribute distinct OR<\/a>-bearing representata<\/em>. Thoughts employing them may contain objective reality through the first-order ideas being classified, and a further strict idea representing a particular classificatory act may possess modal objective reality because that act is an actual mode of thinking substance. Neither exercising nor thematizing the predicable role, however, converts the role itself into a represented substance, principal attribute, true and immutable nature, or mode.2<\/a><\/sup>By exercising<\/strong> a predicable role (using a first-order concept in its classificatory role as genus, species, differentia, proprium, or accident) I mean employing it in an act of classification without making the role itself the object of reflection. Thus, when one judges that animal is a genus relative to human and horse, the intellect uses the predicable role of genus as a classificatory instrument for organizing first-order concepts. The thought is principally about the nature animal and its taxonomic relation to human and horse, not about genus itself. By thematizing<\/strong> a predicable role I mean making that role itself the explicit topic of intellectual inquiry\u2014for example, by asking, \u201cWhat is a genus?\u201d or \u201cHow does genus differ from species?\u201d In this second case, the intellect\u2019s attention shifts from using the classificatory role to examining it.<\/span>

\nWhat changes, however, is only the direction and purpose of intellectual attention. What does not change is the predicable role itself: its logical function, its ontological status, and, on the interpretation defended here, its status as lacking any distinct OR<\/u><\/span><\/a>-bearing representatum all remain exactly the same. Reflection therefore changes the mind\u2019s cognitive relation to genus without changing the ontological status of genus. The philosophical significance of this distinction is that reflection is epistemically reflexive but not ontologically creative. Merely making a predicable role the subject of investigation cannot transform it into a substance, principal attribute, true and immutable nature, or mode, nor thereby endow it with objective reality. Otherwise, every logical connective, comparative notion, rule of inference, or classificatory device would acquire objective reality simply because philosophers chose to reflect upon it.<\/span>

\nMy Restriction Thesis<\/u><\/span><\/a> developed at Descartes\u2019s Theory of Ideas<\/u><\/span><\/a> (DTOI<\/u><\/span><\/a><\/strong>) rejects that consequence because objective reality is not generated merely by directing intellectual attention toward something. A thought acquires objective reality<\/u><\/span><\/a> only if it contains an ontologically rankable representatum<\/em> objectively present within a strict Cartesian idea<\/u><\/span><\/a>. Reflection may alter the focus of attention, but it cannot by itself supply a new substance, principal attribute, true and immutable nature, or mode for the idea to represent. Redirecting attention toward a logical or classificatory role cannot by itself create the ontologically rankable representatum<\/em> required for objective reality. Reflection changes the intellect\u2019s mode of attention without changing the ontological kind of the object under consideration. Accordingly, neither exercising nor thematizing a predicable role converts it into an OR<\/u><\/span><\/a>-bearing representatum<\/i>; whatever objective reality<\/u><\/span><\/a> is present belongs instead to any first-order ideas employed or to a distinct strict idea whose representatum<\/em> is the particular act of reflection itself.<\/span>
<\/span> The result supports my Restriction Thesis<\/a> developed at Descartes\u2019s Theory of Ideas<\/a> (DTOI<\/a><\/strong>): objective reality<\/a> is not a universal feature of every Cartesian thought or every intellectually determinate content, but begins only where a strict Cartesian idea contains the representational presence of an ontologically rankable representatum<\/em>. The post concludes with a comprehensive table summarizing the ontological standing, Cartesian and DTOI<\/a> treatment, and objective-reality status of the principal representational items examined. The table contrasts first-order universal ideas with the five Porphyrian predicables<\/a>, GSD<\/strong>, exercised and thematized classificatory roles, particular reflective acts, comparative notions, a conditional ordering principle analogous to a common notion, impossible unified objects, their independently intelligible component ideas, and necessarily inseparable geometrical determinations distinguished by reason. It thereby provides a systematic synopsis of which contents possess objective reality, which possess it only through constituent strict ideas<\/a>, and which contribute no additional OR<\/a>-bearing representatum<\/em>.<\/p>\n

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Introduction<\/h3>\n

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Descartes introduces objective reality<\/a> in the Third Meditation<\/em> to distinguish ideas according to what they internally represent. Considered merely as formally real modes of thought, ideas possess the same ontological standing: each is a modification of a finite thinking substance. Considered according to their representational content, however, they differ because they present items of different ontological ranks. Descartes writes:<\/p>\n

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\u201cIn so far as the ideas are considered<\/em> simply as modes of thought, there is no recognizable inequality among them: they all appear to come from within me in the same fashion. But in so far as different ideas are considered as images which represent different things<\/em>, it is clear that they differ widely.\u201d (AT VII 40<\/a>; CSM II 27\u201328<\/a>; italics not in original)<\/p>\n

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He immediately adds:<\/p>\n

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\u201cUndoubtedly, the ideas which represent substances to me amount to something more and, so to speak, contain within themselves more objective reality than the ideas which merely represent modes or accidents.\u201d (AT VII 40<\/a>; CSM II 27\u201328<\/a>)<\/p>\n

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Two features of this doctrine govern the argument developed below.<\/p>\n

First<\/strong>, objective reality<\/a> (OR<\/a><\/strong>) is the ontologically rankable internal representational content contained in a strict Cartesian idea<\/a>: the representational presence within the idea of a representatum<\/i> considered as a substance, principal attribute, true and immutable nature, or mode. Its degree corresponds to the ontological standing of the representatum<\/em>. Thus ideas representing God possess infinite objective reality<\/a>; ideas representing finite substances possess finite substantial objective reality; ideas representing the principal attributes of finite substances likewise possess finite substantial objective reality, since they represent the essential natures of those substances; and ideas representing possible modes or the true and immutable natures of possible modes possess modal objective reality. It is this ontological standing of the representatum<\/em>, rather than the mere determinacy of conceptual content, that determines the amount of formal or eminent reality<\/a> required of the idea\u2019s adequate cause.3<\/a><\/sup>Descartes nowhere explicitly introduces a fourth ontological rank corresponding simply to true and immutable natures<\/em>. Rather, the degree of objective reality is best understood as determined by the ontological status of the representatum<\/em>. Consequently, true and immutable natures need not all possess the same degree of objective reality. The idea of extension<\/em> represents the principal attribute and therefore the essence of corporeal substance, while the idea of thought<\/em> represents the principal attribute of thinking substance. The interpretation defended here, considers ideas of these principal attributes to possess finite substantial objective reality<\/em>, since they represent the essential natures of finite substances rather than possible modes. By contrast, the idea of triangularity<\/em> represents the true and immutable nature of a possible mode of extension and therefore possesses modal objective reality<\/em>. Thus the degree of objective reality depends not upon an item\u2019s being a true and immutable nature as such, but upon the ontological category of the representatum<\/em> whose nature the idea represents.<\/span>
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Second<\/strong>, objective reality<\/a> is not identical<\/em><\/strong> with conceptual content generally. A conscious thought may be determinate, intelligible, inferentially articulated, and even necessarily true without containing an internal representatum<\/em> of the kind required for objective reality<\/a>. Objective reality<\/a> belongs to strict Cartesian ideas<\/a> and to broader thoughts only insofar as those thoughts contain strict ideas as constituents.4<\/a><\/sup>See my posts \u201cStrict And Broad Ideas In DTOI<\/u><\/span><\/a>\u201d and \u201cCondensation: Why Objective Reality Cannot Be Descartes\u2019s Theory Of Thought: Burman, Common Notions, And The Failure Of The Strict Idea Model<\/u><\/span><\/a>,\u201d among many others.<\/span>
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The word \u201caccidents\u201d in the second Third Meditation<\/em> passage must be distinguished from the Porphyrian predicable<\/a> accident<\/em> discussed later. Descartes there uses \u201caccidents\u201d as an ontological designation for dependent items ranked below substances. A Porphyrian accident<\/a>, by contrast, is one of five logical predicables and classifies the way a feature may belong to a kind without belonging necessarily or exclusively to it. The first is an ontological category; the second is a classificatory role. Conflating them would import Descartes\u2019s hierarchy of substances and modes into a logical taxonomy to which it does not directly apply.<\/p>\n

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Before asking whether universals possess objective reality<\/a>, it is equally necessary to distinguish two very different kinds of universality. In one sense, a universal idea is a first-order general idea of a substance, principal attribute, true and immutable nature, or mode. The idea of triangle in general represents triangularity as a true and immutable geometrical nature capable of instantiation in possible triangular modes of extended substance. The idea of extension represents the principal attribute of corporeal substance. The idea of animal<\/em> may represent a general nature applicable to individual living things. Such ideas do not represent particular triangles, particular bodies, or particular animals, but they may nevertheless contain determinate objective reality because their representata<\/em> are genuine substances, principal attributes, true and immutable natures, or possible modes within Cartesian ontology.<\/p>\n

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Generality of application is therefore not sufficient to place an idea outside the objective-reality framework. An idea may apply to indefinitely many individuals while still internally representing a true and immutable nature or an ontologically rankable general nature. Descartes\u2019s Fifth Meditation<\/em> reasoning depends upon precisely this possibility: the idea of triangle in general represents triangularity as a determinate nature whose properties are discovered rather than invented. The representational content is general, but it is not merely classificatory. First-order universals in this sense correspond to what the Routledge Encyclopedia of Philosophy<\/em> entry on universals<\/a> treats as properties, relations, and features that particular individuals may instantiate.<\/p>\n

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The target of the present argument is different. It concerns the five Porphyrian predicables<\/a>\u2014genus<\/a><\/em>, species<\/a><\/em>, differentia<\/a><\/em>, proprium<\/a><\/em>, and accident<\/a><\/em>\u2014considered as second-order classificatory roles. These predicables do not name additional first-order natures alongside animal, human, rational, risible, or pale. They classify the logical relations in which first-order concepts and natures stand within a scheme of division. Animal<\/em>, for example, may be considered as a genus<\/a> relative to human and horse and as a species<\/a> relative to living thing. The represented nature animal does not change when its classificatory position changes. What changes is the way the intellect situates that first-order concept within a taxonomic structure.<\/p>\n

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The traditional distinction between first and second intentions<\/a> captures the contrast. First intentions concern things and their real features: animal, human being, extension, triangularity, motion, and other substances, principal attributes, true and immutable natures, or modes. Second intentions concern the intellect\u2019s treatment of first-order concepts: their status as genus<\/em>, species<\/em>, differentia<\/em>, proprium<\/em>, or accident<\/em>. A second intention is therefore a concept of a concept or, more exactly, a concept of the logical role played by a first-order concept. Calling these predicables \u201csecond-order universals\u201d does not commit the argument to treating them as additional higher-order entities instantiated by first-order universals. The designation marks their classificatory order, not their ontological independence.<\/p>\n

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The terminology of proprium<\/a><\/em> and accident<\/a><\/em> requires special care. \u201cProperty\u201d in contemporary metaphysics is a broad term<\/strong> for an attribute, feature, or relation that may be instantiated by individuals. A proprium<\/em> is much narrower<\/em>: it is a feature belonging necessarily and exclusively to a species<\/a> without stating its essence or entering its definition. Risibility<\/a> is traditionally treated as a proprium<\/em> of human beings. The Porphyrian accident<\/em>, by contrast, is a feature that may belong to members of a kind without belonging necessarily or exclusively to them. Both are predicable roles describing how features relate to kinds; neither should be confused with Descartes\u2019s ontological use of \u201caccident\u201d for a dependent modification of a substance.<\/p>\n

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The principal question can now be stated precisely. When the intellect thinks that animal<\/em> is a genus<\/a>, the idea of animal may contain objective reality<\/a> through the general nature represented. But does the classificatory notion genus<\/em> contribute an additional OR<\/a>-bearing representatum<\/em>? When the intellect reflects upon genus as such, does thematization transform that classificatory role into an internally represented mode of thinking substance? More generally, does the conceptual determinacy of a second-order predicable suffice to establish objective reality<\/a>?<\/p>\n

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The post defends a negative answer<\/strong>. Its governing Restriction Thesis<\/a> holds that objective reality<\/a> is the ontologically rankable representational content contained in a strict Cartesian idea<\/a>. It therefore belongs only where a thought is itself a strict Cartesian idea containing the representational presence of an actual or possible substance, principal attribute, true and immutable nature, or mode, or where a broader thought contains such a strict idea as a constituent. This restriction does not imply that every conscious state lacking objective reality<\/a> is contentless. Sensations may possess phenomenal content; common notions<\/a> may possess inferential and axiomatic structure; comparative notions may have determinate application conditions; and second-order predicables may perform indispensable classificatory functions. The claim is only that these forms of content do not automatically constitute objective reality.<\/p>\n

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A contemporary comparison helps isolate the point. The logical connective and<\/em> has a determinate inferential role: from P<\/em> and Q<\/em>, one may infer P \u2227 Q<\/em>; from P \u2227 Q<\/em>, one may infer either conjunct. Mastery of those rules can constitute possession of the concept without requiring and<\/em> to represent an object, substance, property, or mode. Whatever one ultimately thinks about inferentialism as a general theory of concepts, the example demonstrates the intelligibility of conceptually determinate content that is not item-representational. The Cartesian question is correspondingly not whether genus<\/em> and species<\/em> are meaningful, usable, or conceptually distinct, but whether they internally represent ontologically rankable representata<\/em>.5<\/a><\/sup>Whether concepts are always representations is disputed in contemporary philosophy of mind. Representationalist theories treat concepts as mental representations, while dispositionalist, inferentialist, enactivist, Fregean, and Wittgensteinian approaches deny that representation is fundamental to every kind of conceptual content. The relevance here is limited: conceptual determinacy alone does not establish that a concept has an OR-eligible representatum<\/em> in Descartes\u2019s technical sense.<\/span>

\nFor representationalism<\/strong>, see Jerry A. Fodor, The Language of Thought<\/em> (Cambridge, MA: Harvard University Press, 1975) and Concepts: Where Cognitive Science Went Wrong<\/em> (Oxford: Clarendon Press, 1998).
For dispositionalism<\/strong>, see Gilbert Ryle, The Concept of Mind<\/em> (London: Hutchinson, 1949).
For conceptual-role and inferentialist accounts<\/strong>, see Robert B. Brandom, Making It Explicit: Reasoning, Representing, and Discursive Commitment<\/em> (Cambridge, MA: Harvard University Press, 1994); Brandom, Articulating Reasons: An Introduction to Inferentialism<\/em> (Cambridge, MA: Harvard University Press, 2000); and Wilfrid Sellars, \u201cEmpiricism and the Philosophy of Mind,\u201d in Minnesota Studies in the Philosophy of Science<\/em>, vol. 1, ed. Herbert Feigl and Michael Scriven (Minneapolis: University of Minnesota Press, 1956), 253\u2013329.
For enactivist accounts<\/strong>, see Daniel D. Hutto and Erik Myin, Radicalizing Enactivism: Basic Minds without Content<\/em> (Cambridge, MA: MIT Press, 2013) and Evolving Enactivism: Basic Minds Meet Content<\/em> (Cambridge, MA: MIT Press, 2017).
For proof-theoretic inferentialism concerning logical connectives<\/strong>, see Gerhard Gentzen, \u201cUntersuchungen \u00fcber das logische Schlie\u00dfen,\u201d Mathematische Zeitschrift<\/em> 39 (1935): 176\u2013210, 405\u201331, translated as \u201cInvestigations into Logical Deduction,\u201d in The Collected Papers of Gerhard Gentzen<\/em>, ed. M. E. Szabo (Amsterdam: North-Holland, 1969), 68\u2013131; and Dag Prawitz, Natural Deduction: A Proof-Theoretical Study<\/em> (Stockholm: Almqvist and Wiksell, 1965).<\/span>
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The argument proceeds through a series of increasingly difficult cases. Impossible combinations such as a round square establish that the formal reality and intelligibility of a mental act do not guarantee a coherent unified representatum<\/em>. The largest natural number shows that an intelligible description may be necessarily unsatisfied without being internally contradictory in the same way. Comparative notions such as largest<\/em> and smallest<\/em> then demonstrate that determinate application conditions and objectively grounded relational statuses need not introduce additional intrinsic modes or OR-bearing representata<\/em>. Cartesian common notions<\/a> show that necessity and self-evidence do not confer objective reality upon every constituent notion. Distinctions of reason<\/a> further reveal that intellectual differentiation can operate upon OR-bearing ideas without adding further represented entities or modes.<\/p>\n

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These cases prepare the central analysis of second-order universals. Descartes\u2019s characterization of universals as modes of thinking may be interpreted in at least three ways. According to Position 1<\/mark><\/strong>, thoughts employing genus<\/a><\/em> and species<\/a><\/em> contain no additional OR-bearing representatum<\/em> corresponding to those predicable roles. According to Position 2<\/mark><\/strong>, reflective thought represents them as genuine modifications of thinking substance and therefore gives them modal objective reality. According to Position 3<\/strong><\/span>, they possess a weakened or derivative objective reality as idealized classificatory forms abstracted from actual intellectual operations.<\/p>\n

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The objections to Positions 2<\/mark><\/strong> and 3<\/strong><\/mark> are structurally parallel. Position 2<\/mark><\/strong> confuses the formal reality<\/a> of the intellectual operations grounding classification with the represented content of the thought employing the classification. Position 3<\/mark><\/strong> confuses conceptual determinacy with objective reality<\/a>. Neither the fact that classification is performed through formally real mental acts nor the fact that classificatory roles possess determinate logical structure establishes that those roles are internally represented as substances, principal attributes, true and immutable natures, or modes.<\/p>\n

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The thesis defended is not that second-order predicables are unreal, meaningless, arbitrary, or cognitively dispensable. It is that their function is classificatory rather than item-representational. Thoughts employing them may contain objective reality<\/a> through the first-order ideas classified, and a further idea representing a particular act of classification may possess modal objective reality because that act is a genuine mode of mind. But the predicable roles themselves contribute no additional OR<\/a>-bearing representata<\/em>, whether they are exercised in classification or thematized in reflective thought. Conceptual determinacy and objective reality<\/a> remain distinct.<\/p>\n

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One qualification is therefore needed at the outset. The claim that second-order universals such as genus<\/a><\/em> and species<\/a><\/em> contribute no additional objective reality<\/a> applies both when they are exercised within classificatory acts and when they are thematized as objects of reflective thought. When exercised, whatever objective reality<\/a> is present belongs to the first-order ideas being classified. A thought that classifies animal<\/em> as a genus may contain objective reality through the idea of animal, while the predicable role genus<\/em> contributes none of its own. When thematized, the classificatory role becomes an object of intellectual scrutiny, but reflection alone does not transform it into a represented substance, mode, principal attribute, or true and immutable nature. Thematization changes the mode of consideration without supplying a new OR<\/a>-bearing representatum<\/em>.<\/p>\n

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In this respect, second-order predicables resemble common notions<\/a> in falling partly or wholly outside the objective-reality framework, although the reasons differ. Common notions are principles of intelligible order; second-order predicables concern the intellect\u2019s classificatory ordering of first-order ideas. A common notion may be clearly and distinctly entertained without every constituent notion contributing objective reality, just as a second-order classificatory status may be fully determinate without internally representing an ontologically rankable item.<\/p>\n

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The question I address is whether second-order universals<\/a> such as genus<\/a><\/em>, species<\/a><\/em>, and their kindred predicables<\/a> fall within the objective-reality economy<\/a> so defined. Throughout, \u201cuniversals\u201d in the target sense must be sharply distinguished from first-order universals<\/a> representing genuine substances, principal attributes, true and immutable natures, or possible modes. The argument concludes that second-order predicable roles do not contribute distinct OR<\/a>-bearing representata<\/em>, whether exercised or thematized. Their conceptual determinacy, classificatory indispensability, and grounding in formally real intellectual acts do not establish objective reality.<\/p>\n

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Impossible Objects and the Absence of a Unified OR-Bearing Representatum<\/em><\/h3>\n

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Consider first the idea of a round square<\/a>. Applying Descartes\u2019s account of objective reality<\/a>, this idea does not contain an objectively real round square.<\/p>\n

Objective reality is the ontologically rankable internal representational content contained in a strict Cartesian idea: the representational presence within the idea of a representatum<\/em> considered as a possible substance, principal attribute, true and immutable nature, or mode. A round square cannot supply such objectively real representational content because roundness and squareness are internally incompatible geometrical determinations: they cannot be combined into one coherent unified nature or representatum<\/em>.6<\/a><\/sup>Staffan Angere<\/u><\/span><\/a> finds round squares to be perfectly acceptable in some contexts, as argued in his \u201c<\/span>The Square Circle<\/u><\/span><\/a>.\u201d<\/span>
<\/span> What one has is a genuine act of thinking involving the verbal formula \u201cround square\u201d and the component ideas of roundness and squareness, but not an idea whose representatum<\/em> is a coherent round square. The impossibility therefore lies in the internally contradictory combination of the represented geometrical determinations, not in the actual mental act. Roundness and squareness may each be genuinely represented, but their conjunction does not constitute a possible object or a true and immutable nature.<\/p>\n

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A somewhat different analysis applies to \u201cthe largest natural number.\u201d Unlike \u201cround square,\u201d this description is not internally contradictory merely in virtue of combining the meanings of its component terms. It is intelligible what it would be for a natural number to be larger than every other natural number. Nevertheless, the description is necessarily unsatisfied: for every natural number n<\/em>, n<\/em> + 1 is also a natural number and is greater than n<\/em>. There can therefore be no natural number satisfying the description. The phrase \u201cthe largest natural number\u201d is an intelligible verbal formula employing numerical and comparative notions, but it does not yield an idea whose unified representatum<\/em> is a possible largest natural number. The round square and the largest natural number thus fail in different ways. The former combines internally incompatible determinations; the latter imposes intelligible conditions that no possible natural number can satisfy. In neither case is there a possible unified representatum<\/em> corresponding to the complete expression.<\/p>\n

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These cases do not, however, empty the underlying ideas of OR<\/a> entirely. The idea of roundness and the idea of squareness, taken separately, each have a genuine geometrical representatum<\/em> and carry OR<\/a> at the modal level. Similarly, the thought of a largest natural number employs intelligible numerical and relational notions, but the OR-status of those component notions must be assessed independently. The present argument establishes only that no OR<\/a> corresponds to a unified largest-natural-number representatum<\/em>; it neither establishes nor requires that every conceptual component of the description possesses OR. Impossible thoughts or descriptions may therefore be intelligible at the level of their component notions and may employ component ideas that independently possess OR while nevertheless lacking any OR corresponding to the alleged unified object.<\/p>\n

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The examples accordingly illustrate two distinguishable ways in which a determinate thought may fail to contain an OR-bearing unified representatum<\/em>: internal contradiction among its component determinations and necessary non-satisfaction of an otherwise intelligible description. They establish only a negative principle, but it is crucial for what follows: a thought\u2019s intelligibility, compositional structure, or conceptual determinacy does not by itself show that it contains an OR-bearing representatum<\/em>.<\/p>\n

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Comparative Notions: Largest<\/em>, Smallest<\/em>, and Comparative Structure Without Additional OR<\/h3>\n

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Consider the ideas of largest<\/em> and smallest<\/em>. These comparative ideas possess conceptually determinate application conditions. The idea of largest<\/em> applies to a member of an ordered domain when every member of that domain is less than or equal to it under the relevant ordering, while the idea of smallest<\/em> applies to a member when it is less than or equal to every member of that domain. Their conceptual determinacy, however, does not by itself establish that the comparative statuses of being largest and being smallest constitute distinct OR<\/a>-bearing representata<\/em> within those ideas, over and above any objects, quantities, or determinate magnitudes being compared.<\/p>\n

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