Philosophical Methods: Galileo to Hume

Galileo's Scientific Method

Methodological Principles

• Resolution (Analysis): Sensitive data analysis to discover essential elements.
• Composition (Synthesis): Preparation of a mathematical model linking data with theorems or laws, and deduction of consequences.
• Experimental Resolution: Modern experimentation and production of predicted effects through specific setups, asking precise questions to nature.

René Descartes: Philosophy & Method

Mechanistic Worldview

Interpretation whereby all qualities of the physical world are the result of extension and motion. These should be treated mathematically.

Rules of Method

1. Evidence: Never admit anything as true unless it is so clear and distinct that it cannot be doubted.
2. Analysis: Divide complex ideas into simpler components to solve them more easily.
3. Synthesis: Reorganize all thoughts, starting with the simplest and most easily known, as provided by the analysis.
4. Enumeration: Continually review all steps in research to ensure that each and every one of them is fully justified and nothing is omitted.

Skepticism & Certainty

Doubts include: the data of the senses, the existence of an external world (dream argument), and even mathematical truths (Evil Genius argument). This radical doubt leads to the undeniable truth of "Cogito, ergo sum" (I think, therefore I am).

Types of Ideas

• Adventitious: Ideas coming from external experience.
• Factitious: Ideas formed by combining other ideas (e.g., a chimera).
• Innate: Ideas born with us (e.g., God, perfection, infinity).

Arguments for God's Existence

• Ontological Argument: God, as a perfect being, must exist.
• Argument from Infinity: The idea of an infinite being could only come from an infinite being.
• Causation Argument: Applied to the self, acknowledging one's own imperfection and dependence on a perfect cause.

Metaphysical Concepts

• Substance: That which exists in such a way as to need no other thing in order to exist (e.g., God, mind, matter).
• Attributes: Essential properties of a substance (e.g., thought for mind, extension for matter).
• Modes: Non-essential properties or modifications of attributes.
• "I" (Mind): A thinking substance, whose essence is thought.
• World (Matter): An extended substance, whose essence is extension.

Principles Governing the World

• Principle of Inertia
• Principle of Direction of Motion
• Principles of Collision and Conservation of Momentum

Descartes also sought to rationally justify moral precepts.

Gottfried Leibniz: Truths of Reason & Fact

Distinction Between Truths

Truths of Reason

• Analytical and innate, concerning essences.
• Based on the Principle of Non-Contradiction.
• Their negation implies a contradiction.
• Independent of experience, derived from reason alone.

Truths of Fact

• Not analytical; the subject is not contained in the predicate.
• Derived from empirical knowledge.
• Assume the existence of a subject to which they relate.
• Based on the Principle of Sufficient Reason.
• Their negation does not imply a contradiction.

John Locke: Ideas & Knowledge

Types of Ideas

• Simple Ideas: Passively received by the mind from experience (sensation) and reflection (internal sense). Examples include ideas of substance, modes (qualities), and relations.
• Complex Ideas: Formed by the mind combining simple ideas.

Degrees of Knowledge

• Intuitive Knowledge: The most secure and immediate (e.g., "I exist").
• Demonstrative Knowledge: Requires other ideas to prove (e.g., mathematical proofs).
• Sensitive Knowledge: Acceptance of the existence of particular external objects through sensation.

David Hume: Perceptions & Objects of Reason

Perceptions of the Mind

• Impressions: Vivid and forceful perceptions entering the mind directly (e.g., sensations, emotions).
• Ideas: Faint or attenuated images of impressions, associated in the mind through memory and imagination.

Objects of Human Reason

• Relations of Ideas: Truths discoverable by the mere operation of thought, independent of what is anywhere existent in the universe. These are analytical judgments (e.g., mathematics, logic).
• Matters of Fact: Truths concerning existence, which can be conceived as false without contradiction. Their truth is established through experience and observation.