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Key Concepts:

• Certainty as the criteria of truth
• Methodical doubt vs. Hyperbolical doubt
• Cogito, ergo sum (I think, therefore I am)
• Res cogitans (thinking thing)
• Cartesian dualism (mind-body separation)
• Innate, adventitious, and factitious ideas
• Ontological argument for God's existence
• Res extensa (extended substance)
• Cartesian mechanicism

1. Descartes' Search for Certainty and the Influence of Mathematics:

• René Descartes, considered the father of modern philosophy, was driven by a "ceaseless search for certainty."
• His "criteria of truth" was "certainty, subjective conviction." Anything with even minimal doubt should be rejected.
• He was influenced by the "splendour of the new scientific method" and the "strictness of mathematics," which provided "exact, precise and doubtless results."
• He was "very much disappointed with philosophers" due to their constant disagreement and lack of progress.

2. Descartes' Method of Doubt:

• Descartes proposed that philosophy should adopt a method as rigorous as mathematics.
• "Only doubting everything, at least once a lifetime," can one reach truth.
• Doubt is a "method, a path to certainty" to establish "doubtless bases of philosophy's building."

3. The Four Rules of Descartes' Method:

• Rule of Certainty: "Never accept nothing as true unless I am completely convinced of it." Avoid "judgment rashness" until certainty is achieved. The criteria of truth is "clarity and distinction."
• Rule of Analysis: "One should divide problems in as many parts as possible and necessary." Break down complex problems into simple, clear, and distinct ideas.
• Rule of Synthesis: "Once I've arrived to the most simple, I need to conduct my thought with order and keep ascending until I reach that which is complex." Translate the certainty of simple ideas to complex ones through "careful logic and rational steps."
• Rule of Enumeration: "Repeting and reviewing all steps that have been done until I am completely sure that I've left nothing out."

4. First Meditation: The Scope of Doubt:

• Descartes aims to doubt all "ancient opinions" ("vetus opinio") and start from zero to find an undoubted truth.
• He doubts "sensitive knowledge" because senses have deceived him in the past (e.g., a straight stick appearing bent in water, mistaking Joana for Peter).
• He questions the ability to distinguish between dreaming and being awake.
• He introduces the concept of an "evil genius" who might deceive him about mathematical truths (e.g., making him believe 2 + 2 = 4 when it's actually 5).
• This leads to "hyperbolical doubt," an extreme form of doubt.

5. Second Meditation: The Cogito and the Nature of the Self:

• Descartes discovers an "un-doub-ta-ble" truth: "Cogito, ergo sum" (I think, therefore I am).
• Even an evil genius cannot deceive him about his own doubt.
• He exists as a "thinking thing," a "res cogitans."
• This establishes a "radical distinction between soul, or 'I', and body," forming the basis of "cartesian dualism."
• The "intermittence of the cogito" is a problem: the cogito only exists when it thinks.

6. Third Meditation: Arguments for God's Existence:

• Descartes identifies three types of ideas: "Innate ideas," "adventitious ideas," and "factitious ideas."
• First Argument: He finds the idea of a "perfect and infinite God" within himself, which cannot originate from his finite self. God must have placed this idea in him.
• Second Argument: He could not exist without God, as he is an imperfect and finite substance. God is the cause of his existence.
• The God he discovers is "perfect" and "totally good" and "cannot be a deceiver."

7. Fourth Meditation: The Problem of Error:

• Descartes explains that error arises from the imbalance between "intelligence" (finite) and "will" (infinite).
• Error occurs when "my will wants to run faster than my intelligence" and rushes to judgment.
• This is not God's fault but the fault of our will not following the limits of our intelligence.
• God has provided a method (the four rules) to avoid error.

8. Fifth Meditation: The Ontological Argument:

• Descartes presents the "ontological argument" for God's existence.
• The idea of God necessarily implies his existence, just as the idea of a mountain implies a valley.
• A God that didn't exist would be imperfect, lacking the perfection of existence.
• The "hypothesis of the evil genius" is refuted, and mathematical truths are rescued. God guarantees the validity of knowledge.

9. Sixth Meditation: Recovering the Sensible World:

• Descartes recovers the sensible world by trusting his senses, as God is not a deceiver.
• It would be contrary to divine goodness if the ideas perceived from the outside world did not correspond to reality.
• He can trust what "nature teaches me" because "nature, considered in general, is nothing else but God."
• Error is not common, and the method helps avoid mistakes.

10. Three Substances and Cartesian Mechanicism:

• The meditations lead to the identification of three substances: "res cogitans" (finite thinking substance), "res infinita" (infinite substance/God), and "res extensa" (material or extramental reality).
• Exterior reality is reduced to "extension," leading to "cartesian mechanicism," where reality is understood in a mechanical manner.
• This creates difficulties in explaining the relationship between soul and body, as they are understood as completely different substances.
• Animals are reduced to "lifeless machines."

11. Conclusion:

Descartes' philosophy, driven by the pursuit of certainty, uses methodical doubt to establish fundamental truths. The "cogito" establishes the existence of the self as a thinking being, and arguments for God's existence serve to guarantee the validity of knowledge and the reality of the external world. However, the resulting dualism and mechanicism raise further questions about the relationship between mind and body and the nature of reality.