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Two Ways Hume Argued We Can Arrive at Certain Knowledge

• Relations of Ideas: Propositions true by definition, known through logical analysis, and describe deductive reasoning.
• Matters of Fact: Knowledge from relationships between ideas which describes observation and predictions about the future.

Direct vs. Indirect Passions (Hume)

• Direct Passions: Emotions directly tied to immediate experiences, such as love or hatred.
• Indirect Passions: Emotions stemming from reflection or interpretation of experiences, like pride or humility.

Bertrand Russell on the Value of Philosophy

• Philosophical knowledge provides unity and structure to the sciences, encourages critical thought, and broadens the mind to explore new possibilities.

What Makes an Argument Deductively Valid?

• Deductively Valid Argument: The conclusion logically follows from its premises, so if the premises are true, the conclusion must also be true.
• Soundness: An argument is considered sound if it is both valid and has true premises.

When a Conclusion Relies on the Definition of a Concept

• Deductive Definition/Analytic Argument: The conclusion restates or is a logical outcome of the concept as defined in the premise.

Hume on Cause and Effect

-Cause and effect cannot be directly observed; only events occurring in sequence are seen, leading to an assumption of causality.

• Belief in cause and effect stems from habit, not from reason or direct observation.
• Hume argues that causality is neither real nor true, and cannot be grounded by Relations of Ideas or Matters of Fact.

Leibniz's Conclusion in "The Best of All Possible Worlds

• This world balances the greatest amount of good with the least amount of evil.
• The statement supports the idea of a rational, benevolent creator.

William Paley on a Law of Nature and Efficient Cause

• A law of nature (e.g., gravity) only describes behavior, not the underlying cause.
• An efficient cause should explain both how and why something occurs or exists.

William James on Live vs. Dead Hypotheses

• A hypothesis is "live" or "dead" depending on its personal relevance and possibility to the individual.
• A live hypothesis is one that a person can genuinely consider as a possible truth.

Pascal's Wager and a Live Option for Pascal

• Pascal's Wager was a live option because he had a personal stake in believing in God.
• The wager was meaningful because of his circumstances, unlike someone who rejects theism.

Formal vs. Informal Fallacy

• Formal Fallacy: A defect in the structure or logical form of an argument (e.g., affirming the consequent).
• Informal Fallacy: A defect in the content or reasoning, often due to incorrect assumptions or irrelevant premises (e.g., ad hominem attacks).

Nozick's Fundamental Value Against the Experience Machine

• People value Authenticity and Reality over pleasurable experiences.
• The artificial pleasure in an 'experience machine' would not satisfy most people.

Descartes' Most Significant Conclusion on Certain Knowledge

• Reason, especially through methodical doubt, is the only real source of certain knowledge.
• "Cogito, ergo sum" (I think, therefore I am): The act of thinking proves one's existence.

Why Descartes is Certain of His Own Existence Despite Radical Skepticism

• Even when doubting everything else, Descartes is still aware that he is doubting.
• The ability to think and doubt confirms his existence, making it certain.