§3 The Problem of Induction

Even if we master the Criteria of Adequacy and the T.E.S.T. method, we eventually hit a wall that has troubled philosophers for centuries. This is the Problem of Induction. It is the startling realization that while inductive reasoning (including IBE and generalizations) is the foundation of all science and everyday life, we cannot technically “prove” that it works without using circular logic.

3.1 Hume’s Dilemma

The Scottish philosopher David Hume (1711–1776) provided the most famous articulation of this problem in An Enquiry Concerning Human Understanding. Hume noted that every inductive inference relies on the Principle of the Uniformity of Nature (PUN)—the assumption that the future will resemble the past.

• The Problem: How do we justify the PUN? Hume argued that there are only two types of reasoning:

  1. Deductive (Relations of Ideas): These are true by definition (e.g., $2 + 2 = 4$). We cannot prove the PUN this way because we can easily imagine a world where the laws of physics change tomorrow.

  2. Inductive (Matters of Fact): We could argue that “nature has been uniform in the past, so it will be uniform in the future.”

• The Circularity: Using induction to prove that induction works is Circular Reasoning. It is like trying to prove a witness is trustworthy by asking that same witness if they are a liar.

3.2 Russell’s Expectation of Cause

To illustrate the danger of relying on “habit” rather than “reason,” Bertrand Russell told the story of the Inductive Chicken (often adapted as a Turkey in American contexts).

The chicken noticed that on the first day, the farmer arrived and fed it. On the second day, the same thing happened. Being a good “inductive” thinker, the chicken collected hundreds of data points over a year. It calculated a high probability that the farmer’s arrival meant “food.” However, on the morning of the 365th day—Christmas morning—the farmer arrived and wrung the chicken’s neck.

• The Lesson: A pattern can be perfectly consistent for a long time and still be fundamentally wrong about the future. Inductive “strength” does not equal deductive “certainty.”

3.3 Chalmers’ Probabilistic Reformulation

Modern philosophers of science, such as A.F. Chalmers, have tried to rescue induction by shifting the goalposts from “Certainty” to “Probability.”

• The Defense: We may not know for certain that the sun will rise, but we can say that it is highly probable based on the laws of physics and the mass of evidence.

• The Counter-Critique: Hume’s ghost still haunts this solution. To calculate a “probability” of a future event based on past data, you still have to assume that the laws of probability and physics will remain constant tomorrow. The circularity remains.

3.4 The “Reasonable Person” Response

If we cannot prove induction, does that mean we should stop using it? Hume’s own answer was no. He argued that we are biologically “hard-wired” to use induction. It is a “custom” that is necessary for survival.

The Reasonable Person acknowledges that their knowledge of the world is based on a “leap of faith” in the consistency of nature. This leads to Epistemic Humility: we believe what is best supported by the evidence, while remaining open to the possibility that the “farmer” might arrive with a different plan tomorrow.

§3 Summary Table: The Crisis of Induction