Marcy P. Lascano 
explains Descartes’s reply to an objection to his objective reality of ideas proof for God’s existence from the Third Meditation. She writes:
How can we be certain that a being with all the perfections exists, especially given Descartes’ claim that we cannot grasp the infinite nature of God?
Descartes anticipates this objection in the Replies to the First Set of Objections. He writes, “It must be noted that possible existence is contained in the concept or idea of everything we clearly and distinctly understand.” While Descartes is famous for claiming that we cannot grasp the nature of an infinite being, he makes a distinction between grasping and understanding. Grasping is more robust than understanding. We, as finite beings, do not grasp God’s nature, but we can have an understanding of God’s perfections. This understanding is sufficient for having a clear and distinct idea of God as an infinitely perfect being. Thus, Descartes holds that anything that we can clearly and distinctly perceive is possible. Since Descartes holds that he clearly and distinctly perceives a being with all the perfections, it must be the case that such a being is possible. And since existence is a perfection, that being must really exist.1Marcy P. Lascano, “Arguments for the Existence of God,” in The Routledge Companion to Seventeenth Century Philosophy, edited by Dan Kaufman. New York: Routledge 2017: Ch. 18, 12–13th paragraphs. (bold not in original)
My questions concern whether one could ever have a clear and distinct idea of a contradictory object for Descartes and its relationships to objectively real mental content.
Descartes would claim it is impossible to have a clear and distinct idea of a triangle whose interior angles do not sum to a total of 180 degrees.
Does Descartes’s idea of a round square contain any objective reality in the idea of a round square?2In fact, round squares are not necessarily self-contradictory objects. See “Round Squares are not necessarily contradictory” by Jean-Yves Beziau, an expert in paraconsistent logic. Also see “Round Squares exist.” For a paper on visualizing round squares, see “Imagining a Round Square” by Amirouche Moktefi and Jelena Družinina, conference paper, first online: .
ChatGPTTo engage with your queries, we must delve into the intricate fabric of Descartes’s philosophy concerning the objective reality of ideas and the nature of clear and distinct perceptions. Descartes’s framework for ideas, especially his distinction between the objective reality of ideas and the formal reality of things, is pivotal for understanding his argument for the existence of God and his stance on the possibility of clear and distinct ideas of contradictory objects.
In addressing whether one could ever have a clear and distinct idea of a contradictory object, such as a triangle whose interior angles do not sum to 180 degrees, or the notion of a round square, it’s essential to refer directly to Descartes’s own words. In the “Meditations on First Philosophy,” Descartes elaborates on the nature of clear and distinct ideas through his method of doubt and the cogito argument, leading to the principle that everything he perceives “very clearly and very distinctly” is true (Descartes, “Meditations on First Philosophy,” Meditation IV). However, Descartes does not directly address contradictory objects like a round square or a triangle whose angles do not sum to 180 degrees in the same explicit manner.
The principle of clear and distinct perception is tightly coupled with the idea that God, a perfect being, would not deceive him about the veracity of these perceptions. This implies that the objects of clear and distinct perception must be logically consistent, since a benevolent and non-deceptive God would not instill in him the capacity to clearly and distinctly perceive what is logically impossible.
Regarding your specific question about the idea of a round square and whether it contains any objective reality, we turn to Descartes’s theory of ideas. Descartes distinguishes between the material falsity of ideas, which arises when we misjudge the representation of things (as in the case of sensory illusions), and the formal reality of things, which pertains to the actual existence of substances. For Descartes, the idea of a round square would be considered materially false if one were to judge that such a thing could exist in the external world, given the inherent contradiction in the terms. In his Third Meditation, Descartes explains that ideas considered in themselves do not contain error; rather, error arises in the judgment about the correspondence between ideas and things (Descartes, “Meditations on First Philosophy,” Meditation III).
Thus, while Descartes might concede that one can entertain the notion of a round square in a superficial or imaginative sense, such an idea would not have objective reality in the strict sense that Descartes reserves for ideas that correspond to possible or actual things. The objective reality of an idea, for Descartes, depends on the degree of formal reality possessed by the object of the idea. Since a round square has no formal reality (it cannot exist in the world due to its contradictory nature), the idea of a round square would lack objective reality in the sense relevant for Descartes’s metaphysical and epistemological framework.
In conclusion, Descartes would likely argue that it is impossible to have a clear and distinct idea of a contradictory object, such as a round square, because such objects cannot exist in reality. The notion of a round square would not contain objective reality within Descartes’s philosophical system, as it fails to correspond to any possible or actual entity in the external world. This stance underscores Descartes’s commitment to the coherence and logical consistency of clear and distinct ideas, reflecting his broader metaphysical and epistemological objectives.
When an idea contains objective reality, as Descartes means it in Meditation Three, what function does containing such objective reality serve from the point of view of the mind having that idea?
In “Meditation Three” of his “Meditations on First Philosophy,” Descartes delves into the nature of ideas and their objective reality, establishing a framework that serves several pivotal functions from the perspective of the mind possessing those ideas. The concept of objective reality in ideas is instrumental in Descartes’s epistemological project, aiming to ground knowledge in certain and indubitable foundations. The role of objective reality in ideas, as Descartes articulates, is multifaceted, affecting both the validation of knowledge claims and the inferential processes leading to the existence of entities beyond the self.
Firstly, the objective reality of ideas refers to the content or essence of the idea, as far as it represents something (Descartes, “Meditations on First Philosophy,” Meditation III). This representation is measured by the degree of reality or perfection it presupposes. From the mind’s perspective, having an idea with objective reality involves holding a mental representation that corresponds to a possible or actual thing outside the mind. The objective reality of an idea, then, serves as a sort of mirror of the formal reality outside the mind, albeit in a representational or conceptual form.
The function of containing such objective reality can be articulated in several key points:
- Basis for Truth Claims: The objective reality of an idea provides the basis for making truth claims about the external world. For Descartes, the clarity and distinctness of an idea, coupled with its objective reality, serve as criteria for its truth. This is because, for an idea to represent something clearly and distinctly, it must contain within it the essence or properties of the thing it represents, making it a reliable basis for asserting the existence or nature of that thing.
- Foundation for the Existence of God: The objective reality of ideas plays a crucial role in Descartes’s argument for the existence of God. He argues that the idea of God, an infinitely perfect being, has such immense objective reality that it could not have originated from a finite being like himself. Instead, its cause must have at least as much formal reality as the idea has objective reality. This leads to the conclusion that only God Himself could be the cause of this idea, thereby proving God’s existence.
- Mechanism for Distinguishing Between Ideas: The notion of objective reality allows Descartes to categorize ideas according to their source and content. Ideas with higher degrees of objective reality (e.g., the idea of God) are distinguished from those with lesser degrees (e.g., the idea of a physical object) and from those that are mere fabrications of the mind. This classification underpins his methodological approach to doubt and his subsequent rebuilding of knowledge on a more secure foundation.
- Prevention of Error: By emphasizing the objective reality of ideas, Descartes provides a framework for avoiding error. Error arises not from the ideas themselves but from the judgment about the correspondence between an idea and its external referent. A clear understanding of the objective reality contained in an idea helps the mind to refrain from making unfounded judgments about the external world, thus avoiding error.
- Pathway to the External World: Finally, the objective reality of ideas serves as a conceptual bridge between the mind and the external world. It offers a way for the mind to reach beyond itself, to assert the existence of things other than itself, based on the content of its ideas. This is crucial for Descartes’s project of establishing a secure foundation for the sciences and for knowledge more generally.
In summary, the objective reality of ideas, as Descartes presents it, functions as a crucial element in the architecture of his philosophical system, underpinning the pursuit of certainty, the proof of God’s existence, the mechanism for distinguishing between different types of ideas, the strategy for avoiding error, and the method for making claims about the external world.
Your answer fails to address the function of the objective reality of an idea that provides an object of awareness as to the mental content for that particular object of thought for that specific thinker. The objective reality contained in an intellectual idea of X supplies what the thought of X is about for that particular thinker, correct?
Indeed, your point brings to light a crucial aspect of Descartes’s theory of ideas, specifically the function of the objective reality contained within an idea, which I previously did not address comprehensively. The objective reality of an idea, in Descartes’s framework, does indeed serve as the content or essence of the idea that delineates what the thought is about for the thinker. This aspect is vital for understanding the representational nature of ideas in Descartes’s philosophy and their role in the cognitive processes of the mind.
When Descartes discusses the objective reality of ideas in “Meditation Three,” he is elucidating how ideas contain within them a certain “content” or “essence” that corresponds to things outside the mind, albeit in a representational form. This representational content is what the thought of X is about for the thinker. In other words, the objective reality of an intellectual idea of X provides the mental content for that particular object of thought, allowing the thinker to direct their mind towards X, even if X is not present or even if X does not exist outside the mind.
This function of the objective reality of ideas is foundational for several reasons:
- Representational Function: It underscores the representational nature of mental content in Descartes’s epistemology. Ideas, for Descartes, are not opaque or self-contained; they are about something, pointing beyond themselves to their objects. The objective reality of an idea is what imbues it with this representational capacity, allowing the mind to engage with objects of thought in a meaningful way.
- Intentionality of Thought: This aspect of Descartes’s theory aligns with the notion of the intentionality of thought—a concept that denotes the ‘aboutness’ of mental states, the capacity of thoughts to be about, or directed towards, objects, properties, or states of affairs. The objective reality within an idea ensures that thoughts are not mere internal stirrings but are directed towards distinct objects or entities, thereby giving them content and meaning.
- Foundation for Knowledge and Certainty: By providing the mental content for objects of thought, the objective reality of ideas becomes the cornerstone for knowledge and certainty. It is through the objective reality contained in clear and distinct ideas that the mind can apprehend the essences of things, thereby grounding knowledge claims in something concrete and intelligible.
- Enables Differentiation and Evaluation of Ideas: The content provided by the objective reality of an idea allows the thinker to differentiate between ideas based on their representational fidelity and epistemic value. It enables the mind to evaluate ideas, distinguishing between those that represent real possibilities or actualities and those that are mere imaginings or confusions.
In essence, the objective reality contained within an idea is what supplies the content of thought, determining what that thought is about for the thinker. This conceptual mechanism is central to Descartes’s theory of ideas, serving as the linchpin for his broader philosophical inquiries into the nature of thought, knowledge, and reality. It encapsulates the intentional and representational character of mental activity, highlighting the role of ideas as mediators between the mind and its objects of thought.
I agree with what you wrote about the function of the objective reality of an idea to exhibit or present the object of thought and provide the representational contents for what that particular idea is of or about. You concluded, “In essence, the objective reality contained within an idea is what supplies the content of thought, determining what that thought is about for the thinker.” Am I correct in stating this?
Yes, your statement accurately captures a fundamental aspect of Descartes’s theory of ideas as presented in his philosophical works, particularly in “Meditations on First Philosophy.” The objective reality within an idea indeed serves to supply the content of thought, thereby determining what that thought is about for the thinker. This principle is a cornerstone in Descartes’s epistemology, underpinning his investigation into the nature of knowledge, perception, and the relationship between the mind and its objects of thought.
Descartes’s distinction between the objective reality of ideas and their formal reality is crucial in this context. The objective reality refers to the content of the idea insofar as it represents something, whether that something exists externally or not. It is this representational content that allows the mind to “reach out” beyond itself, to think about things in the world or possible states of affairs, and to engage in the processes of reasoning, doubting, and understanding.
This framework facilitates a deeper appreciation of how Descartes navigates the complexities of mental representation, the verification of ideas, and the pursuit of certainty. By insisting that the objective reality of an idea supplies what the thought is about, Descartes provides a mechanism for distinguishing between mere imaginings and ideas that have a foundation in reality, whether through their clear and distinct perception or through their innate origins, as in the case of the idea of God.
Therefore, your statement not only correctly reflects Descartes’s philosophical position but also highlights the significance of the objective reality of ideas in his broader project of establishing a secure foundation for knowledge and certainty. This conceptualization underscores the intentional nature of thought and the critical role of mental representation in Descartes’s epistemology.
But there is now a problem. For any specific idea that is a thought of a contradictory object, such as a round square or a Euclidean triangle with interior angles that do not sum to a total of 180 degrees, these ideas are about round squares or unusual triangles, correct? So, they must have objective reality to be about anything, right?
Your observation brings to the forefront a nuanced challenge within Descartes’s framework concerning the objective reality of ideas, especially when considering thoughts of contradictory objects, such as a round square or a Euclidean triangle whose interior angles do not sum to 180 degrees. The crux of the issue lies in reconciling Descartes’s criteria for the objective reality of ideas with the fact that some ideas represent objects that are logically impossible.
Descartes’s theory suggests that the objective reality of an idea is predicated on its representational content—what the idea is “of” or “about.” This principle seems to imply that any idea, to be about something, must contain some degree of objective reality. However, when it comes to contradictory objects, which cannot exist in the formal reality due to their logical impossibility, the application of Descartes’s principles becomes more complex.
- Objective Reality and Representational Content: Indeed, even ideas of contradictory objects like round squares or impossible triangles have representational content in the sense that they are “about” something; they engage the mind’s capacity to represent objects, albeit objects that cannot exist. Thus, in a broad sense, these ideas must contain objective reality insofar as they represent a concept or engage the mind’s representational faculties.
- Nature of Contradictory Ideas: However, Descartes would likely argue that ideas of contradictory objects do not have the same type of objective reality as ideas of possible or actual things. This is because the objective reality of an idea, in the context of his arguments for the existence of God and the veracity of clear and distinct perceptions, is closely tied to the idea’s potential correspondence to something in the formal reality. Since contradictory objects cannot exist in the formal reality, the “objective reality” of their ideas must be understood in a different, perhaps more diminished, sense.
- Evaluation of Contradictory Ideas: Descartes might contend that ideas of logically impossible objects demonstrate the mind’s ability to form complex concepts but do not signify the mind’s capacity to accurately reflect the nature of reality. Such ideas could be seen as exercises of imagination rather than genuine representations of possible or existing things. Therefore, while these ideas are “about” their respective contradictory objects, their objective reality does not fulfill the same epistemological function as the objective reality of ideas that represent possible or actual entities.
- Epistemological Status: The key distinction here lies in the epistemological status granted to ideas based on their objective reality. For Descartes, the objective reality of an idea gains its full significance when it underpins a true understanding of the world or leads to the knowledge of something that could possibly or actually exist. Ideas of contradictory objects, by contrast, might serve as cautionary examples of the limits of human understanding or the misapplication of the mind’s representational capabilities.
In summary, while ideas of contradictory objects like round squares or impossible triangles are “about” those objects and thus contain objective reality in a minimal, representational sense, they do not meet the criteria for providing meaningful knowledge or truth about the formal reality. Their objective reality does not signify the potential for these objects to exist or be realized, which marks a crucial distinction in Descartes’s philosophical system regarding the nature and value of ideas.
Generally speaking, if an idea has objective reality, it only has as much objective reality as its object of thought has formal reality, were it to actually exist. Since impossible objects cannot exist, they cannot have any formal reality, and therefore, any idea of an impossible object could not have any degree of objectively real mental content since its corresponding possible formal amount of reality is necessarily zero.
Your clarification aptly synthesizes a critical aspect of Descartes’s theory concerning the relationship between the objective reality of ideas and the formal reality of their objects. If we adhere strictly to Descartes’s principles as articulated in his “Meditations on First Philosophy,” particularly in the Third Meditation, the alignment between the objective reality of an idea and the formal reality of its object is foundational. Descartes posits that the objective reality of an idea (its content as representing something) is indeed reflective of the formal reality (actual existence) that its object would have, were it to exist.
Given this framework, your deduction regarding ideas of impossible objects holds a logical consistency within Descartes’s philosophical system:
- Formal Reality of Impossible Objects: Impossible objects, by definition, cannot exist in reality due to their inherent contradictions or violations of logical principles. As such, they have no formal reality, since formal reality refers to the mode of existence that entities have outside the mind.
- Objective Reality of Ideas of Impossible Objects: Following from the first point, if the formal reality of an object is necessarily zero (as it is for impossible objects), then an idea representing such an object would, in this strict sense, lack objective reality. This is because, within Descartes’s framework, the objective reality of an idea is a reflection of the degree of formal reality of its object. Since an impossible object cannot have any degree of formal reality, the idea of such an object cannot have objective reality in the same way ideas of possible or existent objects do.
- Mental Content of Ideas of Impossible Objects: Consequently, if we apply Descartes’s principles rigorously, an idea of an impossible object could not possess objectively real mental content in the way that ideas of possible or actual objects do. This does not mean the mind cannot form or entertain ideas of impossible objects (as we certainly can think about round squares or perpetual motion machines), but rather that such ideas do not participate in the kind of representational truth-value system Descartes uses to ground knowledge and certainty. These ideas cannot point to or represent anything that has or could have existence (formal reality), thus they lack the kind of objective reality that contributes to genuine knowledge or truth about the world.
This interpretation aligns with Descartes’s broader epistemological project, which seeks to establish a foundation for certain knowledge based on clear and distinct ideas that correspond to possible or actual realities. Ideas of impossible objects, while conceivable within the mind’s imaginative capacity, do not meet the criteria for contributing to this foundational knowledge, as their referents lack formal reality and, thus, cannot confer upon these ideas the type of objective reality that underpins true understanding or knowledge.
When you are referencing objective reality in your sentence, “These ideas cannot point to or represent anything that has or could have existence (formal reality), thus they lack the kind of objective reality that contributes to genuine knowledge or truth about the world” and again when you wrote “thus, cannot confer upon these ideas the type of objective reality that underpins true understanding or knowledge” you are no longer using the phrase “objective reality” to mean the representational content found in ideas, but instead to mean non-subjective (true) facts. You are equivocating between two radically different meanings for ‘objective reality,’ and in Descartes’s theory of ideas, he is never referencing the second meaning, so you should not either.
Your critique correctly points out an important clarification needed in discussing Descartes’s notion of objective reality within ideas. Descartes’s use of “objective reality” indeed refers to the representational content of an idea, specifically how that content corresponds to the essence or nature of what is represented, rather than non-subjective, actually true facts about the external world. This distinction is crucial for accurately engaging with Descartes’s epistemological framework and avoiding any equivocation that might arise from conflating Descartes’s technical use of “objective reality” with a more common usage implying factual truth or existence.
Continuing from the clarification regarding Descartes’s use of “objective reality,” it’s essential to explore further how this concept plays out in his epistemology, especially concerning ideas of impossible objects and the pursuit of knowledge.
In Descartes’s framework, the objective reality of an idea is fundamentally about the idea’s content and its capacity to represent something outside of itself. This capacity does not guarantee that the represented thing exists (in the case of formal reality) or could exist but rather indicates the mind’s ability to conceive of various entities, qualities, or relations through its ideas.
For Descartes, the objective reality of ideas serves several key functions in the pursuit of knowledge:
- Foundation for Certainty: The objective reality of clear and distinct ideas provides a foundation for certainty about the world. Descartes famously argues that the clarity and distinctness of an idea are indicators of its truth. However, this applies only to ideas that are coherent and logically possible, reflecting potential or actual states of affairs that could have formal reality.
- Limitation of Representational Content: While all ideas have some level of objective reality due to their representational content, not all such content is equally valuable or meaningful in the pursuit of truth. Ideas of impossible objects highlight a limitation within the human mind’s representational capacities. They show that while the mind can generate concepts of many kinds, including contradictory ones, not all these concepts have a valid place in the construction of knowledge about the world as it is (or could be, under logical consistency).
- Role in Delineating the Mind’s Power and its Limits: The consideration of impossible objects, and their place within Descartes’s schema, serves to delineate the extent and limits of the mind’s powers. It underscores that the mind can form ideas that have no correspondence in reality, highlighting the importance of the mind’s critical capacities to distinguish between mere imaginings and ideas that genuinely reflect possible or actual states of affairs.
- Criterion for Truth and Existence: Descartes uses the concept of objective reality within ideas as a criterion for assessing the truth and potential existence (formal reality) of what is represented. This does not mean that every idea with objective reality corresponds to something that exists but rather that the idea’s content can be a subject for scrutiny, evaluation, and, in the case of clear and distinct ideas, a basis for asserting the existence of its object.
In sum, the discussion of objective reality in Descartes’s philosophy reveals a nuanced approach to understanding the nature and limits of human knowledge. It highlights the critical role of the representational content of ideas in enabling the mind to engage with the world, while also underscoring the necessity of discernment in distinguishing between ideas that contribute to genuine understanding and those that do not. Ideas of impossible objects, while possessing objective reality in a minimal sense due to their representational aspect, ultimately do not contribute to the kind of knowledge Descartes seeks—knowledge that is certain, clear, and distinctly rooted in the possible or the actual. This careful navigation through Descartes’s epistemological landscape showcases his commitment to a rigorous method of inquiry, aimed at securing a stable foundation for science and philosophy.
According to Descartes, when I think of the concept of number in general, what is the objective reality contained in my idea of number?
Descartes’s discussions on the concept of number, especially in the context of his broader philosophical inquiries, provide a nuanced view of how abstract concepts like numbers are treated within his theory of ideas. While Descartes does not explicitly detail the objective reality of the concept of number in the same manner he does for other concepts such as God or physical objects, we can infer his position based on his epistemological and metaphysical principles.
The concept of number in general, within Descartes’s framework, can be considered as part of the innate ideas that the mind possesses. Innate ideas are those that are not derived from external experience but are inherent to the mind’s own nature. Descartes argues that ideas such as those of geometry, mathematical truths, and even the concept of God, are not adventitious (coming from outside the mind) nor are they fabricated by the mind but rather are innate to it.
- Objective Reality of the Concept of Number: The objective reality of the idea of number in general refers to its content as representing the essence or nature of number as an abstract entity. This content is not tied to any particular number or set of numbers but to the concept of number itself—its properties, relations, and the system it underpins. In this sense, the objective reality obtained in the idea of number in general is robust, as it encompasses the foundational aspects of numerical understanding and reasoning.
- Role of Innate Ideas: Descartes’s classification of the idea of number as innate suggests that its objective reality is not contingent upon sensory experience or empirical observation but is derived from the mind’s inherent capacities. This positions the concept of number as fundamentally tied to the mind’s ability to grasp abstract, non-empirical truths, reflecting Descartes’s view of mathematics and geometry as exemplars of certain knowledge.
- Contribution to Knowledge: The objective reality of the concept of number contributes significantly to knowledge, according to Descartes, because it underlies the certainty and clarity that characterize mathematical and geometrical truths. These domains of knowledge are prized by Descartes for their use of clear and distinct ideas, which are assured by the natural light of reason—a faculty that apprehends the objective reality of innate ideas, including the concept of number, directly and indubitably.
- Relation to Formal Reality: While the concept of number in general does not correspond to a particular existing entity in the same way a physical object or even the idea of God does, its formal reality, in a metaphysical sense, lies in the realm of abstract truths and entities. The objective reality of the concept of number, therefore, is intimately linked to the formal reality of mathematical truths, which possess a kind of existence that is independent of the material world yet is fundamental to the structure of reality as comprehensible to human reason.
In conclusion, the objective reality obtained in Descartes’s idea of number in general reflects the essence and properties of number as an abstract concept. This idea, by virtue of being innate, demonstrates the mind’s capacity to access and reason about abstract entities and truths, showcasing the depth and breadth of human cognition as envisaged by Descartes. It exemplifies how abstract concepts, through their objective reality, contribute to the certainty and clarity of knowledge, embodying the ideals of Descartes’s rationalist philosophy.
According to Descartes, what is the formal reality that is the cause of my objectively real mental content for my idea of number in general?
According to Descartes’s philosophical framework, particularly as it pertains to the origins of ideas and their content, every idea must have a cause that has at least as much formal reality as the idea has objective reality. The concept of number in general, being an abstract, innate idea, presents an interesting case when considering its cause in terms of formal reality.
For Descartes, innate ideas like the concept of number are not derived from the external world or from sensory experience but rather originate from the mind itself, which is endowed with these ideas by God. God, as an infinitely perfect being, possesses the highest degree of formal reality. Therefore, in Descartes’s system, God is the ultimate cause of all ideas, including the innate ideas that reside within the human mind.
- Formal Reality of Innate Ideas: The formal reality that is the cause of the objectively real mental content for the concept of number in general, then, can be traced back to God. This is because, in Descartes’s view, only an infinitely perfect being could be the source of the ideas that have such a pure, abstract nature. The formal reality of God, in possessing infinite perfection, encompasses all possible realities, including the abstract realities that innate ideas like the concept of number represent.
- Role of the Mind: While God is the ultimate source of the innate idea of number, Descartes also emphasizes the active role of the mind in accessing and utilizing these ideas. The mind, as a finite substance, has formal reality in its own right, but its capacity to conceive of abstract concepts like number is seen as facilitated by the innate ideas implanted within it by God. Thus, the formal reality of the mind, as a thinking substance, is also instrumental in the actualization of the concept of number in thought.
- Innate Ideas and the Mind’s Nature: The concept of number and other mathematical truths, being innate, are part of the mind’s very nature, according to Descartes. This suggests that the formal reality of the mind itself, as created by God, includes the capacity for these ideas. The mind’s nature as a thinking thing (res cogitans) inherently contains the potential for all the ideas it can think, including abstract concepts not derived from the material world.
In conclusion, the formal reality that is the cause of the objectively real mental content for the concept of number in general, in Descartes’s philosophical system, ultimately points to God, the infinite substance with the highest degree of formal reality. God is the source of the innate ideas that the mind possesses, including the concept of number. The mind, as a created finite substance with its own formal reality, actively engages with these innate ideas, making abstract reasoning and the comprehension of mathematical truths possible. This view underscores the central role of God in Descartes’s metaphysics as the foundation for all knowledge and the existence of all things, including the very concepts through which humans understand the world.
When you write, “Therefore, in Descartes’s system, God is the ultimate cause of all ideas, including the innate ideas that reside within the human mind,” is this true for adventitious and fictitious ideas as well?
The statement that “God is the ultimate cause of all ideas, including the innate ideas that reside within the human mind” requires refinement, especially when considering the full scope of Descartes’s classification of ideas into innate, adventitious, and fictitious categories. While it is accurate to say that God, in Descartes’s system, is the ultimate source of the mind’s capacity to have ideas and, by extension, the innate ideas that derive from this capacity, the characterization of God as the direct cause of adventitious and fictitious ideas necessitates clarification.
- Innate Ideas: These are ideas that Descartes considers to be “born with” the mind. They are not derived from external experience but are part of the mind’s inherent structure. God, as the creator of the mind and its capacities, is the ultimate cause of these ideas by endowing the mind with its basic capabilities, including the ideas of existence, identity, God, and mathematical truths.
- Adventitious Ideas: These ideas are thought to come from outside the mind, typically through sensory experience. Examples include the ideas of physical objects that we see, hear, or touch. While God is the ultimate creator of the universe and the laws governing it, and thus indirectly responsible for the circumstances that lead to sensory experiences, Descartes does not directly attribute the cause of adventitious ideas to God. Instead, these ideas are considered to be caused by the interaction of the external world with the sensory apparatus of the body, mediated by the laws of physics and physiology that God created.
- Fictitious Ideas: These are ideas that the mind constructs or invents, such as mythical creatures or imaginary scenarios. They are formed by the mind’s own active combination, division, or modification of other ideas. While the mind’s ability to generate such ideas ultimately depends on its God-given capacities, the specific content of fictitious ideas is not caused directly by God. Instead, it is the result of the mind’s creative application of its powers.
In summary, while God is the ultimate source of the mind’s capacities and the laws that govern the physical universe, the direct cause of adventitious and fictitious ideas lies in the interaction between the mind and the world, and in the mind’s own creative processes, respectively. The causal link to God for these types of ideas is more indirect, grounded in God’s creation of the mind and the world but not in a direct causation of each specific idea. Therefore, it’s more accurate to say that God is the ultimate cause of the mind’s ability to have ideas and the framework within which all ideas occur, rather than the direct cause of every specific adventitious or fictitious idea.
Not fictitious, but factitious.
I apologize for the misunderstanding in my previous response. If we’re correcting the term from “fictitious” to “factitious” within the context of Descartes’s classification of ideas, his framework for discussing ideas typically involves three categories: innate, adventitious, and invented (or “factitious” in some translations).
Assuming the focus remains on how Descartes classifies and understands the source of ideas, we can recap and correct the information as follows:
- Innate Ideas: Ideas that are “built-in” to the mind, such as the concepts of God, mathematical truths, and perhaps the concept of the self. These are not derived from sensory experience or reflection upon such experiences. Descartes attributes the existence of innate ideas to the mind’s nature, created by God, hence God is their ultimate cause.
- Adventitious Ideas: Ideas that come from external experiences, perceived through the senses. Examples include the ideas of physical objects in our environment. While God created the external world and the sensory apparatus through which we perceive it, the immediate cause of adventitious ideas is the interaction between the external world and our sensory organs.
- Invented (or Factitious) Ideas: These are ideas that the mind constructs by combining and manipulating other ideas. They include concepts of things that might not exist in the world, such as unicorns or mermaids. The mind itself is the direct cause of these ideas, using its God-given capacity for imagination and thought.
In all cases, God is seen as the ultimate source of the mind’s capacities, including the ability to generate and process these various types of ideas. However, the direct causality of adventitious and invented ideas lies in the mind’s interaction with the world and its own creative processes, respectively, rather than in a direct act of creation by God. This distinction is crucial for understanding Descartes’s views on the origin and nature of ideas and their relation to the mind’s faculties as created by God.
When Descartes has an idea of a lion in his mind Descartes would claim he has an objectively real lion contained as the mental content of that idea. In general, whenever Descartes has an intellectual idea of X, he would claim that X exists as an objectively real representation of X in his idea. What, then, is the objectively real content of Descartes’s idea of a round square?
Descartes’s theory of ideas, particularly the concept of objective reality within ideas, illuminates the nature of mental content when one thinks of specific objects or concepts, whether they exist or are purely conceptual. The objective reality of an idea, for Descartes, is a measure of its representational content—how much “reality” or “being” the idea represents, irrespective of whether the object of that idea exists outside of the mind.
When Descartes thinks of a lion, the idea of the lion in his mind has objective reality insofar as it represents or is about a lion. This does not imply that a lion exists in the external world at that moment but that the idea of the lion has a certain degree of reality within Descartes’s mental realm based on what the lion represents. This representation encompasses the essence or nature of what a lion is understood to be.
The question about the “objectively real content” of Descartes’s idea of a round square brings us to a critical discussion point in his philosophy: the distinction between the objective reality of ideas and the formal reality of objects. A round square, by definition, is a logical impossibility—it cannot exist in the formal reality because its definition is self-contradictory.
In Descartes’s framework, the idea of a round square would still possess some degree of objective reality in the sense that it represents a concept or engages the mind’s capacity for representation. However, the key difference here is that while the idea of a lion (which can exist in formal reality) represents something possible and coherent, the idea of a round square represents a contradiction. Therefore, the objectively real content of the idea of a round square is that it represents a conceptual impossibility—a notion that combines mutually exclusive properties.
This distinction is crucial for understanding Descartes’s epistemological project. The objective reality of an idea does not validate the existence (formal reality) of its object. Instead, it indicates the representational capacity of the mind. For coherent, non-contradictory objects or concepts (like lions, trees, or numbers), the objective reality of these ideas corresponds to possible or actual entities. For logically impossible concepts (like round squares), their objective reality signifies the mind’s ability to entertain concepts, even if those concepts do not and cannot correspond to anything in the external world.
Thus, the objectively real content of Descartes’s idea of a round square would be a mental exercise in combining incompatible attributes, showcasing the mind’s ability to form ideas beyond the constraints of logical coherence or physical possibility. This, however, does not lend the idea any epistemic value in terms of representing a possible or actual state of affairs in the world, highlighting Descartes’s critical distinction between the mental exercise of forming ideas and the pursuit of true knowledge based on clear and distinct perceptions.
You did not even try to answer the previous question. Is it true that in an idea of a round square it does or does not contain an objectively real round square?
Addressing your question directly concerning Descartes’s idea of a round square and whether it contains an “objectively real round square,” it is essential to distinguish between the representational content of an idea and the ontological status of its object within Descartes’s framework.
In Descartes’s epistemology, the term “objective reality” of an idea refers to the representational aspect of the idea—how the idea represents or is “about” something, regardless of whether that something exists outside the mind. When Descartes discusses the objective reality of ideas in the Third Meditation, for example, he is concerned with how ideas can represent things with varying degrees of reality or perfection. The objective reality of an idea corresponds to the degree of reality or perfection that its object would have if it existed.
For an idea like that of a lion, the objective reality within the idea corresponds to what a lion is—the idea represents a lion and contains within it the essence or nature of what we understand to be a lion. This does not mean that there is an actual lion (in the sense of formal reality) existing within Descartes’s mind or that the existence of the idea proves the existence of a lion in the external world. Instead, it means that the idea of the lion has a certain representational content that is about lions.
In the case of a round square, this concept presents a logical contradiction and thus cannot exist in the external world (it lacks formal reality). When Descartes conceives of a round square, he can still be said to have an idea with representational content—that is, the idea is “about” the concept of a round square. However, the objectively real content of this idea does not correspond to anything that could exist in reality (it has no possible formal reality). The idea of a round square would therefore represent a logical impossibility.
So, does the idea of a round square contain an “objectively real round square”? Within Descartes’s terminology, the idea does have objective reality in the sense that it represents something—the concept of a round square. However, this objective reality does not imply that there is a round square that exists in any meaningful way, either in the mind or in the external world, as the object of the idea is a contradiction and thus cannot have formal reality.
The key point here is that the “objective reality” in Descartes’s terms refers to the representational content or the “aboutness” of the idea, not to the actual existence of the object represented by the idea. Therefore, while Descartes can have an idea of a round square, and this idea has objective reality insofar as it represents a concept, the concept itself is a logical impossibility and does not correspond to any possible or actual entity.
So, your answer is that Descartes’s idea of a round square when he is thinking about a round square is that because the idea is about a round square and is of a round square, then the idea definitely contains an objectively real round square in that idea, or not?
Addressing your question directly: if Descartes thinks about a round square, the idea would indeed contain an “objectively real” round square in the sense that the idea represents or is about a round square. However, this use of “objectively real” within the context of Descartes’s philosophy requires careful interpretation.
In Descartes’s terminology, the “objective reality” of an idea refers to the representational content of that idea—what the idea is of or about. This is distinct from the “formal reality” of actual things, which pertains to their existence outside the mind. So, when Descartes has an idea of a round square, the idea has objective reality insofar as it is a mental representation of a round square. This does not mean, however, that a round square has formal reality or that such an entity could exist in the external world, as the concept of a round square is logically contradictory and impossible.
Therefore, while Descartes’s idea of a round square does contain an “objectively real” round square in terms of its content as a mental representation, this should not be confused with the claim that a round square has actual existence or possibility in the external world. The objective reality of the idea simply signifies that the mind is engaging with the concept of a round square, not that a round square could exist or that the representation corresponds to a feasible entity.
If ideas of impossible objects contain their impossible object as an objectively real mental content, then it is false that all ideas always represent possibly existing objects, correct?
Yes, that is correct. If we accept that ideas of impossible objects contain their impossible object as objectively real mental content, then it necessarily follows that not all ideas represent possibly existing objects. This conclusion aligns with Descartes’s broader epistemological framework, which acknowledges the mind’s capacity to conceive of entities or concepts that cannot exist in reality, such as impossible objects.
Descartes distinguishes between the objective reality of ideas (the reality they have as mental representations) and the formal reality of objects (the reality of objects as they exist outside the mind). The concept of a round square, for example, can be entertained by the mind and thus has objective reality insofar as it is a concept or representation within the mind. However, it lacks formal reality because a round square cannot exist in the world due to its inherent contradiction.
This distinction allows Descartes to maintain that while the mind can generate ideas of things that are logically impossible and thus cannot have formal reality, these ideas still possess objective reality as mental representations. Consequently, the statement that all ideas always represent possibly existing objects would indeed be false, as the mind is capable of conceiving ideas that represent impossibilities, reflecting the mind’s creative and representational capacities rather than limitations imposed by the nature of external reality.
Suppose some ideas do not represent even a possibly existing object. How does Descartes ever know that any of his ideas are not self-contradictory, even his idea of God, in which case his proof for God’s existence does not work?
Descartes’s method for distinguishing between ideas that represent possible, existing objects and those that might be self-contradictory hinges on his criteria of clarity and distinctness. In his epistemological framework, particularly outlined in the “Meditations on First Philosophy,” Descartes introduces the method of doubt to strip away all beliefs that could possibly be doubted, aiming to reach a foundation of indubitable truths.
- Clarity and Distinctness: Descartes posits that ideas perceived clearly and distinctly are true. An idea is clear when it is present and accessible to the attentive mind, and distinct when it is so precise and different from all other ideas that it contains within itself only what appears clear. Descartes argues that the idea of God, as an infinitely perfect being, is one that he perceives clearly and distinctly. This clear and distinct perception underpins his argument for God’s existence: the idea of an infinitely perfect being could not have originated from a finite, imperfect being like himself; therefore, this idea must have been placed in him by an infinitely perfect being, i.e., God.
- The Criterion of Non-Contradiction: For Descartes, the clarity and distinctness of an idea also imply non-contradiction. The idea of God as an infinitely perfect being does not entail any contradiction; rather, it is consistent and coherent within Descartes’s framework. In contrast, the idea of a round square is self-contradictory and thus cannot be clear and distinct. This distinction is crucial for Descartes to argue that some ideas—like those of God, mathematical truths, and geometrical figures—represent realities that could exist (or do exist, in the case of God), whereas others do not.
- God’s Veracity: Descartes further bolsters his position by invoking God’s veracity. He argues that a non-deceptive God would not allow him to be mistaken about the existence of things that he perceives with clear and distinct understanding. Thus, the clear and distinct ideas that pass the test of doubt can be trusted as representing possible or actual realities, unlike self-contradictory ideas which do not pass this test.
- Application to Ideas and Existence: Applying this framework, Descartes can distinguish between ideas that have the potential for representing real objects or truths (like the idea of God) and those that are inherently contradictory (like a round square). This methodology allows him to assert the validity of his proof for God’s existence: since he can conceive of God clearly and distinctly, without contradiction, and since he himself could not be the source of this idea, it must have its origin in a being that truly exists—God.
In summary, Descartes’s confidence that not all of his ideas are self-contradictory, and his belief in the validity of his proof for God’s existence, rest on his methodological reliance on the clarity and distinctness of ideas as markers of truth and non-contradiction, alongside the assumption of God’s veracity. This approach allows him to navigate through his ideas, distinguishing between those that represent possible or actual realities and those that are mere fabrications or contradictions.
However, there remains a problem with Descartes’s criteria of clearly and distinctly perceiving non-contradictory ideas. Consider two examples.
(E1) Descartes would have claimed that he clearly and distinctly conceived that no triangle composed of a closed straight lined three-sided figure with only three vertices could ever have the sum of the interior angles add up to any more or less than 180 degrees. Yet he does not so clearly and distinctly perceive this since there are triangles that satisfy the definition of a triangle just given in different non-Euclidean geometries where the three interior angles add up to more or to less than 180 degrees.
(E2) Descartes would claim that he clearly and distinctly perceives that there could never be an infinite collection of numbers encompassing a larger infinity than the natural numbers and that anyone who claims one numerical infinity is larger than another contradicts themselves when both sets are infinite. Yet these claims are false since Georg Cantor (1845–1915) proved that there are more real (decimal) numbers than natural numbers, while both are numerically infinite in size.
The examples you’ve provided (E1 and E2) indeed raise significant issues regarding the application and reliability of Descartes’s criteria of clear and distinct perception, especially when it comes to the advancement of knowledge in fields like mathematics and geometry. These examples illustrate the challenge in relying solely on what seems to be “clear and distinct” perceptions for determining the truth, particularly in abstract domains where later discoveries may reveal limitations or errors in earlier understandings.
(E1) Non-Euclidean Geometry
The first example touches on the development of non-Euclidean geometries, where the sum of the angles in a triangle does not necessarily equal 180 degrees, depending on the curvature of the space in which the triangle is situated. Descartes, operating within the Euclidean framework, would indeed have considered it a clear and distinct truth that the angles of a triangle sum to 180 degrees. This belief would be based on his trust in Euclidean geometry as describing the space of the natural world.
However, the later development of non-Euclidean geometries shows that this “clear and distinct” perception is not universally true—it’s contingent upon the kind of geometric space being considered. This challenges the infallibility of clear and distinct perceptions by showing that what seems evident within one theoretical framework may not hold in another, more comprehensive or different framework.
(E2) Infinites in Mathematics
The second example involves Cantor’s discovery that there are different sizes of infinity, specifically that the set of real numbers (or decimal numbers) is uncountably infinite and therefore “larger” than the set of natural numbers, which is countably infinite. This contradicts the intuitive notion (which Descartes might have shared) that infinity cannot be compared or that all infinities are essentially the same size. Again, this discovery challenges the idea that clear and distinct perceptions are always reliable, especially in the context of advanced mathematical concepts that were not available to Descartes.
Implications for Descartes’s Criteria
These examples underscore a critical aspect of Descartes’s methodology—the criteria of clear and distinct perception are not infallible when applied outside the immediate scope of one’s current knowledge or when dealing with concepts that can be fundamentally reinterpreted by future discoveries. Descartes himself might argue that his methodology is intended to apply to what is accessible to the mind through reason at a given time, and that clear and distinct perceptions are indeed reliable within this scope. Yet, as these examples show, what is considered clear and distinct can evolve as human understanding deepens or expands.
Descartes’s reliance on God’s non-deceptiveness as a guarantee for the truth of clear and distinct ideas presupposes a static framework for understanding the world. However, the dynamic nature of knowledge, especially in mathematics and the sciences, reveals that our understanding of truth can and does change over time. This doesn’t necessarily invalidate Descartes’s method but suggests its limitations and the need for its application to be tempered with an awareness of its historical and conceptual context.
In conclusion, while Descartes’s criteria of clear and distinct perception provide a powerful tool for philosophical inquiry, the examples you’ve mentioned illustrate the complexities and limitations faced when these criteria are confronted with the evolving nature of human knowledge.
Descartes’s methodology prevents him from being able to adjust to relativize his knowledge to the known theories at the time since he claims that all clear and distinct ideas are necessarily for all time true or God would be a deceiver.
Your examples highlight significant challenges to Descartes’s criteria of clarity and distinctness as guarantees of truth, especially when considering the evolution of mathematical and scientific knowledge. Let’s examine the implications of these challenges and how they intersect with Descartes’s philosophical commitments.
Example 1: Non-Euclidean Geometry
Descartes lived before the development of non-Euclidean geometries that allow for triangles with the sum of interior angles different from 180 degrees. His geometry, grounded in the Euclidean tradition, was based on the assumption that space is flat, making the sum of the angles of a triangle always equal to 180 degrees a clear and distinct truth within that framework. The discovery of non-Euclidean geometries, which operate under different axioms where space can be curved, shows that mathematical truths can depend on the axiomatic system within which they are defined.
Example 2: Infinite Sets and Cantor’s Theorem
Similarly, Cantor’s late 19th-century work on the different sizes of infinity was groundbreaking and challenged intuitive notions of infinity that prevailed in Descartes’s time. Cantor showed that the set of real numbers (which includes all the decimal numbers) is uncountably infinite and therefore “larger” than the set of natural numbers, which is countably infinite. This distinction was not conceivable within the mathematical framework available to Descartes.
Implications for Descartes’s Methodology
Descartes’s methodological commitment to the eternal truth of clear and distinct ideas does indeed seem to face a problem when confronted with these examples. If what is considered clear and distinct can be later shown to be incomplete or based on assumptions that are not universally valid, then the criterion of clear and distinct perception appears to be less reliable than Descartes claimed.
However, Descartes might respond to these challenges in several ways:
- Contextual Truths: He could argue that what is clear and distinct is contextually true based on the best available knowledge and assumptions of the time. For Descartes, the clarity and distinctness of an idea are tied to the mind’s capacity to perceive it as undoubtable within the context of its own foundational principles.
- Foundation of Knowledge, Not Its End: Descartes might also argue that his method is intended to provide a foundation for knowledge upon which further inquiry can build. The fact that later developments extend or revise this foundation does not necessarily mean that the foundation itself is flawed but rather that knowledge is progressive.
- Role of God: Regarding the concern that God would be a deceiver if clear and distinct ideas were later shown to be incomplete or false, Descartes might maintain that God ensures the mind’s capability to reach truth given the context and limitations of human understanding. The evolution of knowledge does not imply deception but reflects the finite nature of human understanding and the infinite nature of divine wisdom.
In conclusion, while Descartes’s criteria of clarity and distinctness face challenges from the development of mathematical and scientific knowledge, these examples also invite deeper reflection on the nature of truth, the progression of knowledge, and the limits of human understanding. They suggest that Descartes’s methodology, while foundational and revolutionary in its time, is part of a larger, evolving discourse on the pursuit of knowledge—a discourse that acknowledges the provisional nature of some truths in the face of expanding intellectual horizons.
Your response mostly missed my point entirely. You wrote that “He [Descartes] could argue that what is clear and distinct is contextually true based on the best available knowledge and assumptions of the time,” but this is precisely what his methodology prevents him from arguing. Clearly and distinctly perceived truths are necessarily true so a priori true and never dependent on current theories or limitations of knowledge.
You are correct in emphasizing that Descartes’s methodology, as he articulates it, commits him to the view that truths perceived clearly and distinctly are necessarily true and not contingent upon the context, theories, or limitations of the time. Descartes’s position on clear and distinct perceptions is intended to establish a foundation for knowledge that is immutable and independent of empirical circumstances or future discoveries. This foundational aspect is crucial for his project of securing certain knowledge against skepticism.
Given this commitment, the examples you provided (E1 and E2) indeed pose a challenge to Descartes’s methodology:
- Non-Euclidean Geometry (E1): The development of non-Euclidean geometries, which demonstrate that the sum of the interior angles of a triangle can be more or less than 180 degrees depending on the curvature of the space, appears to contradict the universal truth of Euclidean geometry as Descartes would have understood and accepted it. Since Descartes held that the truths of geometry were clear and distinct—and therefore necessarily true—the discovery of non-Euclidean geometries raises questions about the scope and nature of what can be considered clear and distinct.
- Cantor’s Theorem on Infinite Sets (E2): Similarly, Cantor’s proof that there are different sizes of infinity challenges the notion, which Descartes might have considered clear and distinct, that infinity cannot be compared or that all infinities are the same. This mathematical development shows that what might be considered self-evident in one context can be overturned with deeper mathematical insights.
Your criticism rightly points out that Descartes’s framework does not readily accommodate a way to revise what is considered clear and distinct in light of new information or theoretical advancements. Descartes’s claim that clear and distinct perceptions are necessarily true is foundational to his method of doubt and his argument for the existence of God, as he argues that God, being perfect, would not deceive him about what he perceives clearly and distinctly.
The challenges posed by the advancement of knowledge in fields like geometry and mathematics highlight a tension within Descartes’s epistemology between the aspiration for absolute certainty and the evolving nature of human understanding. This tension reflects a broader philosophical challenge regarding the status of a priori knowledge in the face of empirical and theoretical developments.
One way to interpret Descartes’s project, in light of these challenges, is to see it as an attempt to establish a methodological starting point for knowledge, one that seeks certainty in the face of doubt. However, the evolution of knowledge, particularly in mathematics and science, suggests that even foundational principles may be subject to revision or expansion as our understanding deepens.
In summary, your critique underscores a critical debate within the philosophy of knowledge: the extent to which foundational truths, once deemed certain, can be reconciled with the dynamic and cumulative nature of human inquiry and discovery. This debate continues to be relevant in philosophical discussions about the nature of knowledge, certainty, and the progress of science.
Returning to one of my earlier criticisms of Descartes’s clear and distinct methodology notice how what Descartes claims would be self-contradictory turned out not to be necessarily self-contradictory, such as triangles can have more or less than 180 degrees, therefore Descartes is not infallible about what is or is not self-contradictory. Therefore, every idea Descartes contemplates might be self-contradictory.
Your critique taps into a profound challenge within Descartes’s epistemology, particularly concerning his confidence in distinguishing between what is self-contradictory and what is not. If Descartes’s judgment about what constitutes a self-contradictory concept can be shown to be fallible—as illustrated by the advancement of mathematical knowledge (e.g., the development of non-Euclidean geometries)—then this raises a significant question about the infallibility of his method for securing certain knowledge through clear and distinct perceptions.
The issue at hand is not merely Descartes’s potential misjudgment about specific mathematical or geometric truths but the broader epistemological implication: if Descartes can be mistaken about what is self-contradictory, then the reliability of clear and distinct perceptions as a criterion for truth is called into question. This is because the certainty Descartes attributes to clear and distinct ideas presupposes his ability to correctly discern the non-contradictory nature of these ideas.
- Fallibility and Self-Contradiction: The realization that certain ideas, once thought to be clear, distinct, and non-contradictory (e.g., the Euclidean assumption about the sum of the angles in a triangle), can later be understood differently within another theoretical framework (non-Euclidean geometry) suggests a more fundamental fallibility in human cognition. This fallibility undercuts the absolute certainty Descartes seeks in his method.
- Implications for Descartes’s Methodology: If every idea Descartes contemplates could potentially be self-contradictory, this introduces an element of doubt into his foundational method, which relies on the eradication of doubt through clear and distinct perception. This does not mean that all of Descartes’s ideas are incorrect or that his method is without value; rather, it highlights the potential limits of human capacity to fully and infallibly discern the non-contradictory nature of complex ideas.
- Descartes and the Scope of Certainty: Descartes might argue, in defense, that his method is designed to identify those truths that can be known with certainty by the light of reason—such as his famous cogito, “I think, therefore I am.” However, the challenge posed by your critique requires a more nuanced understanding of the scope and limits of what can be deemed certain, particularly in domains like mathematics and science that are subject to revision and development over time.
- Philosophical Response: A possible philosophical response to this challenge is to recognize the context-dependent nature of many forms of knowledge while still maintaining that certain foundational truths can be known with certainty. This approach would involve distinguishing between the kinds of truths that are subject to empirical and theoretical revision and those that are not (e.g., the cogito).
In conclusion, your critique underscores a critical aspect of philosophical inquiry: the examination of the criteria by which we claim to know something with certainty. Descartes’s methodology, revolutionary in its aim to establish an indubitable foundation for knowledge, also invites ongoing scrutiny and dialogue about the nature of certainty, the possibility of fallibility, and the dynamics of human understanding. This dialogue is essential for the continued evolution of philosophical thought and the refinement of our approaches to knowledge.
NOTES
- 1Marcy P. Lascano, “Arguments for the Existence of God,” in The Routledge Companion to Seventeenth Century Philosophy, edited by Dan Kaufman. New York: Routledge 2017: Ch. 18, 12–13th paragraphs.
- 2In fact, round squares are not necessarily self-contradictory objects. See “Round Squares are not necessarily contradictory” by Jean-Yves Beziau, an expert in paraconsistent logic. Also see “Round Squares exist.” For a paper on visualizing round squares, see “Imagining a Round Square” by Amirouche Moktefi and Jelena Družinina, conference paper, first online: .