The Great Conversation: Induction
By Gabriel Blanchard
Induction, or reasoning from particulars, can be a powerful and deceitful endeavor.
Induction is one of the two chief branches of logic, the other being deduction. Deductive logic (sometimes simply called “logic” without qualification) reasons by eliminating the intrinsically impossible, such that, if the premises of a deduction are true and its form is valid, the conclusion must necessarily be true. Induction, by contrast, amasses individual facts and summarizes them, or generalizes from them, in order to get a rule—with the appropriate level of confidence in the rule being proportional to the number and quality of the particulars it is based on, and thus never absolute.
Induction is sometimes treated as the red-headed stepchild by those who prefer their logic deductive, but this is an injustice to induction. Aristotle, in both his theory of knowledge and his approach to argument, treats induction rather than deduction as primary, because it is only by induction—that is, observing particulars and generalizing from them—that we can obtain grist for the deductive mill at all. He thus positions himself in the more or less empiricist tradition of knowledge, as distinct from the Platonist idea of inner illumination or recollection on the one hand, and the severities of total skepticism on the other. Sympathizers with both Platonism and skepticism often eagerly point out that induction does not give absolute certainty; the empirically minded tend to retort, not without reason, that we have nothing in the end to work with but the observable facts.
Yet induction is to be distinguished from what Aristotle calls intuition, the things that we “just see” have to be true no matter what, like the law of non-contradiction. Nor can such intuitions be regarded as deductions; they are the principles by which deduction operates. Intuitions on that order are like sense data: capable of being misinterpreted or misapplied, but not simply wrong.
One of the most respected and fruitful systems of induction, of course, is the scientific method. Exact formulations vary, but the core idea—inventing hypotheses to explain observed facts, and then testing those hypotheses by repeated experiment—is constant. It is this accent on experiment that distinguishes the scientific method of the Enlightenment and the Modern era from the science of earlier periods, which did engage with observed facts but was far less curious about precisely repeatable results. The devout pedantry of men like Robert Boyle, Sir Isaac Newton, Antoine Lavoisier, and Edward Jenner allowed for the discovery of the laws of motion, the tabulation of the elements, and the invention of vaccines; ultimately, both the Industrial and the Technological Revolutions were rendered possible only by the results of the scientific method.
Another major concern of induction is the mathematical field of statistics. Statistics, like probability, involve us in a number of counterintuitive and even paradoxical problems, only some of which involve skewed data. The most famous statistical “false flag” is of course that correlation does not always imply causation. A more challenging problem is Simpson’s Paradox, which shows that a statistical trend that appears in multiple subsets of data can disappear, or even reverse, when the subsets are combined; this typically reveals that there is some other factor at work that the researcher has not yet taken into account, prompting deeper and more exacting investigation.