AI
- Uniformity Principle (UP): Inductive leaps assume nature follows a uniform course, where the future resembles the past.
- The Dilemma:
- Demonstrative Reasoning: Proving the UP is impossible because its opposite is not a contradiction (i.e., we can imagine the future being different).
- Probable/Moral Reasoning: Using past experience to prove the future will resemble the past is circular reasoning, as it assumes the very principle it tries to prove.
- Skeptical Solution: Hume concludes that induction is not irrational, but rather a "natural instinct" or custom/habit. [1, 2, 3, 4, 5]
- Knowledge from Experience: Locke argued against innate ideas, proposing the mind is a tabula rasa (blank slate) filled by experience.
- Degrees of Assent: While Locke did not fully tackle induction, he did distinguish between certain knowledge and probability, noting that much of human life is guided by "opinion" and "probability" based on observation. [1, 2, 3, 4, 5]
- Updating Beliefs: The Bayesian framework updates the probability of a hypothesis (\(H\)) based on new data (\(E\)), using Bayes's Theorem: \(P(H|E) = \frac{P(E|H)P(H)}{P(E)}\).
- Addressing Hume: Some philosophers argue that while induction cannot be proved a priori (as Hume insisted), Bayesian conditioning acts as a logical "consistency constraint" that allows us to build reasonable predictions.
- Empirical Limits: The Bayesian solution relies on an initial "prior" (a prior belief), which is empirical rather than rational, meaning it may not provide the purely logical solution Hume said was impossible. [1, 2, 3, 4, 5]
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