3.3 The Problem of Induction

What this lecture covers

This lecture gives a detailed treatment of Hume's problem of induction, the topic previewed in the earlier lectures on Hume. Millican works through Hume's key distinction between relations of ideas and matters of fact, rebuilds the billiard-ball argument in more rigorous form, and shows why Hume concludes that we have no rational justification for assuming the future will resemble the past.

By the end you should be able to state Hume's distinction between relations of ideas and matters of fact, reconstruct the argument for why induction cannot be justified without circularity, and describe several classic attempts to answer Hume along with Millican's assessment of why they fail.

Key ideas

• Relations of ideas vs matters of fact: relations of ideas (roughly, analytic propositions like "all bachelors are unmarried") can be known just by examining our ideas; matters of fact (synthetic propositions like "the sun will rise tomorrow") depend on experience, not logic.
• The billiard-ball case: predicting that a struck ball will move is a matter of fact, not something knowable from the mere ideas of billiard balls and motion.
• Adam's predicament: a being with no prior experience, such as Michelangelo's newly created Adam, would have no basis whatsoever for predicting what happens when one ball strikes another.
• The uniformity assumption: any inference to unobserved matters of fact rests on assuming that observed patterns (causal relations learned from experience) will continue to hold, and this assumption cannot itself be proven by logic, sense experience, or further inductive reasoning without circularity.
• Intuitive, demonstrative, sensible and moral evidence: Hume's fourfold classification of evidence, borrowed from earlier philosophers, where "moral" evidence means inductive reasoning from experience, not ethical reasoning.
• Humean skepticism about induction: since the uniformity assumption cannot be rationally grounded, our confidence in causal reasoning rests on animal instinct rather than insight.
• The demarcation problem: if induction has no rational basis, what distinguishes scientific reasoning from superstition such as reading tea leaves or tarot cards?
• Hume's own answer: consistency—since everyone, including the superstitious, unavoidably relies on the assumption that the future resembles the past, the rational course is to accept it and apply it systematically, which is what science does.

Walkthrough

Relations of ideas and matters of fact (1:11)

Millican introduces Hume's foundational distinction from the Enquiry Concerning Human Understanding, section 4. Relations of ideas, such as "all bachelors are unmarried" or "3 times 5 equals half of 30," can be known purely by analyzing the ideas involved—what we now call analytic propositions. Matters of fact, such as whether a released pen will fall, cannot be known this way; their truth depends on experience, making them synthetic propositions.

The billiard-ball argument restated (4:12)

Returning to the billiard-ball example, Millican shows that predicting a struck ball's motion is a matter of fact we cannot know just by perceiving or remembering it, since it concerns the future. Hume argues the only basis for such predictions is causal reasoning, and all causal knowledge comes from experience. The Adam thought experiment illustrates that without any prior experience, no prediction—ball stopping, exploding, or "turning into a frog"—could be favored over any other.

The circularity of justifying induction (7:15)

Millican works through Hume's fourfold division of evidence (intuitive, demonstrative, sensible, moral) drawn partly from Locke, then poses Hume's central question directly: what ground do we have for assuming causal laws that held in the past will hold in the future? He shows it is not self-evident, not provable by logic, not knowable by the senses, and cannot be established by inductive reasoning itself without begging the question—since that is the very form of reasoning under examination.

The uniformity assumption and Humean skepticism (11:19)

The lecture summarizes Hume's argument as showing that all factual inference beyond immediate perception and memory rests on an unprovable assumption of uniformity. Millican notes the wide influence of this conclusion on later philosophy of science, including Popper's attempt to build an account of science that avoids relying on induction altogether, and stresses that Hume's result reduces human reasoning to a difference of degree, not kind, from animal instinct.

The demarcation problem and Hume's answer (15:24)

Millican raises the natural worry that Hume's skepticism seems to license "anything goes," collapsing the distinction between science and superstition. He explains Hume's own response: everyone, without exception, relies on the assumption that the future resembles the past just to function day to day, so the rational move is to accept this assumption consistently and build systematic science on it, which is why science is preferable to superstition even though neither can claim a purely rational foundation.

Attempts to answer Hume (19:27)

In the closing minutes, Millican surveys three families of response to Hume: probabilistic justifications of induction (associated with figures such as Simon Blackburn, John Mackie and Roy Harrod), the analytic justification associated with Peter Strawson (that induction is rational "by definition"), and justification by induction's past success or by pragmatic considerations. He gives his own brief assessment that none of these responses really defeats Hume—arguments from past success are circular, and pragmatic justifications are beside the point, since Hume already agrees we cannot help but rely on induction; the only live question is whether we do so consistently.

Before you watch

• Watch the two earlier lectures introducing Hume, since this lecture assumes familiarity with the billiard-ball thought experiment and Hume's general approach to science.
• It helps to recall Locke's distinction between demonstrative and probable reasoning, which Millican references as background to Hume's fourfold classification of evidence.

Check your understanding

1. What distinguishes a "relation of ideas" from a "matter of fact" in Hume's terminology, and which category does "the sun will rise tomorrow" fall into?
2. Why can't the assumption that the future will resemble the past be justified by appeal to past experience, according to Hume?
3. What is the demarcation problem that Hume's skepticism raises, and how does Hume try to answer it?
4. Why does Millican think a pragmatic justification of induction fails to engage with Hume's actual position?
5. What does Hume mean by "moral evidence," and how does it differ from the everyday sense of "moral"?