Asemics :=: Degree of Assent: Locke, Hume, Bayes: Induction and Probability - AI / EZE, 2026

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Locke, Hume, and Bayes fundamentally shaped the understanding of knowledge, probability, and induction. John Locke grounded knowledge in sensory experience, while David Hume famously challenged the rational basis of induction, arguing our expectation of the future is based on habit, not logic. Thomas Bayes provided a mathematical framework (Bayesianism) that uses probabilistic reasoning to update beliefs based on evidence, offering a potential—though debated—response to Hume’s skepticism by quantifying how experience justifies induction. [1, 2, 3, 4, 5]

David Hume: The Problem of Induction

Hume argues in his Treatise of Human Nature and Enquiry that induction—the process of drawing general conclusions from specific observations (e.g., "the sun will rise because it always has")—is not grounded in reason or logic. [1, 2]

• 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]

John Locke: Empirical Foundations

Locke's empiricism laid the groundwork for Hume's work. [1]

• 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]

Bayes and the Probabilistic Response

Bayesianism uses probability to quantify the degree of belief in a hypothesis (posterior probability) based on prior knowledge (prior probability) and new evidence. [1, 2, 3, 4]

• 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]

Summary Table

Philosopher [1, 2, 3, 4, 5]	Key Concept	Perspective on Induction
Locke	Empiricism (Tabula Rasa)	Knowledge is derived from experience.
Hume	Problem of Induction	Inductive inferences are from habit, not reason.
Bayes	Probabilistic Inference	Induction is updating beliefs using conditional probability.

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