Einstein famously said, “The definition of insanity is doing the same thing over and over again and expecting different results.” I believe one of the reasons this quote is so famous is because it hits upon a fundamental truth – past experience is a good predictor of future experience. Put more formally, inductive reasoning is conditionally valid. The condition being that any conclusion drawn from inductive reasoning can be thrown out if enough conclusive counter examples are found.
How does this work in everyday life? It’s fundamental to our everyday functioning. When we get hungry, we eat because past experience has shown that eating satiates hunger. We expect our future behavior of eating to have the same outcome as our previous experiences of eating. When we drive, we press the gas pedal to accelerate. Why do we not hit the brake pedal to accelerate? Because past experience has proved to us that braking decelerates the car. Inductive reasoning is so fundamental to our experience that Einstein uses the rejection of it, “doing the same thing over and over again and expecting different results,” as the very definition of insanity.
What I find interesting is that this axiom of experience is rationally unfounded. The Scottish philosopher David Hume pointed this out in An Enquiry concerning Human Understanding. Thus the fact that we all accept induction as valid makes it an article of faith (defined as belief without rational justification). I believe that induction qualifies as an axiom (often called a postulate as well) – a simple claim accepted without proof on the basis of being self-evidently true.
Axioms function as starting points upon which other statements can be logically derived. For instance, in geometry, one of Euclid’s axioms is that a straight line segment can be drawn connecting any two distinct points. This is not proved via geometry but instead used with other axioms to derive all of geometry. Similarly, induction serves as a starting point for or experience of reality. It cannot be proven by experiencing reality, but can be used to understand our experience of reality.
Thus I call inductive reasoning the fundamental axiom of experience. This has some interesting implications which I hope to explore in future posts. What do you think?