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The Problem of Induction

Gig Φ Philosophy: Published April, 2026

Introduction to Induction

Inductive reasoning is a method of logic that attempts to make a conclusion more likely or probable based on evidence, though its conclusions are not logically guaranteed. In scientific practice, induction is used to move from singular statements (which document past, factual observations) to universal statements (that make general predictions about all future occurrences). The core philosophical dilemma arises from asking how a series of past occurrences can justify the assumption that the same pattern will continue in the future.

Don't give me that "constant conjunction doesn't imply causal connection" hokum it's yours! HUME CARTOON Pregnant woman yelling at man.

David Hume &
the Classic Problem

READ Hume's "The Problem of Induction" HERE

The foundational problem of induction was posed by the Scottish empiricist David Hume. Hume noted that scientific knowledge regarding the real world (which he called "Matters of Fact") relies entirely on cause and effect. However, Hume argued that what we perceive as "causality" is actually just a habit developed from seeing two events constantly conjoined in the past.

To assume true cause and effect, we rely on two underlying assumptions:

The future will equal the past.
The Principle of Uniformity, which assumes that the laws of nature responsible for past connections will continue to hold true without suddenly changing.

Hume demonstrated that the Principle of the Uniformity of Nature cannot be rationally justified. It cannot be justified via deductive arguments because we can easily imagine the opposite happening (e.g., it is possible that the sun will not rise tomorrow). Furthermore, it cannot be justified via inductive arguments (appealing to past experience) because using induction to prove the validity of induction relies on circular reasoning, or begging the question. Therefore, Hume concluded that inductive reasoning in science fundamentally lacks rational justification.

Proposed Solutions & Further Complications

Following Hume, several major philosophers attempted to solve, bypass, or reframe the problem, leading to new developments in the philosophy of science:

Probability
(Russell & A.F. Chalmers)

READ Chalmer's "Deriving theories from the facts: induction" HERE

One potential solution is to apply a probabilistic reformulation, weakening scientific claims so they only assert that a theory is probably true in light of the evidence. However, this fails to overcome the problem. Since general laws attempt to cover an infinite number of possible observations, deriving them from a finite number of past observations will logically yield a probability of zero. Additionally, A.F. Chalmers notes that statistical models carry their own ambiguities, such as Simpson's Paradox, where statistical overlap can yield contradictory recommendations.

Falsification
(Karl Popper)

READ Popper's "Induction, Prediction, and Evidence" HERE

Karl Popper accepted Hume's problem and completely rejected probability, arguing it only leads to an infinite regress of justification. Instead, Popper claimed that science is not inductive, but purely deductive. Popper argued that science does not arrive at definitive truths but rather deduces expected observations from theories and rigorously tests them. Theories are either falsified by negative results or "corroborated" by withstanding severe testing, completely removing the need for induction.

Rational Prediction
(Wesley Salmon)

READ Salmon's "Rational Prediction" HERE

Wesley Salmon criticized Popper's reliance on corroboration, arguing that corroborated theories hold no predictive power and cannot explain why scientific claims are more reliable than blind guesswork. However, Salmon conceded that we still cannot formally justify inductive reasoning. If we assume an inductive rule without begging the question, we end up logically validating contradictory "counter-inductive rules" right alongside it.

The New Riddle of Induction
(Nelson Goodman)

READ Goodman's "New Riddle of Induction" HERE

Nelson Goodman expanded the dilemma by proving that the formal structure of inductive reasoning leads to contradictory conclusions. Goodman created a new property called "Grue" [defined as an object being first observed before a specific date (like January 1st, 2020) and green, OR not observed before that date and blue]. Because all emeralds observed in the past have been green, that exact same evidence can be used to inductively conclude both that "all emeralds are green" and "all emeralds are grue". This paradox demonstrated that induction struggles to distinguish between true law-like statements and accidental ones, meaning that formally, "anything confirms anything".