In modern times, we take for granted the importance of evidence. In the sciences and humanities, but also throughout our normal everyday interactions, we use evidence to support or refute our conclusions. We take this basic concept for granted now. But just a few hundred years ago, the need for evidence-based conclusions was not yet so obvious.
Induction is defined as the derivation of general ideas from specific cases and data. We use evidence to make inductive arguments all the time. Every branch of science is built on it. Scientific theories all use inductive reasoning to bear out evidence gathered from experiments. And inductive reasoning would not exist if the definition of probability had not undergone a fundamental shift.
A great example of this comes from the same historical era as Pascal and Fermat. When Galileo began experimenting on the nature of gravity, he did so by rolling a ball down an inclined plane. He did this hundreds of times, and with several different angles and distances. Galileo gathered all of this data in order to support the idea that objects approach Earth at a constant rate. He was not certain of this conclusion. He only arrived at this conclusion after the evidence yielded what was most probable.
Two Kinds of Evidence
The evidence used to prove a scientific theory’s validity has a direct link to probability. Data of this kind is easily measured, but always finite and thus fallible. Evidence of this kind leads to an induction, in that some kind of scientific conclusion stems directly from analyzing data. The hard sciences benefited greatly from this embrace of imprecision.
Quantifiable data is useful to science, even if scientific theories are not infallible. Gut-level, epistemic evidence is trickier, though. This second kind of evidence was still unquantifiable in the 17th Century. The seminal work on logic, The Port-Royal Logic, perhaps states this conundrum best:
Some truths cannot be easily measured. Law comprises these very notions of induction and evidence-based degrees of belief. Probability’s new definition was expansive and occasionally contradictory. Pascal, Fermat, Galileo, and the Port-Royal Logic all helped to further define this muddy concept. We still have quite a ways to go, however. Our history continues next week.