Draw three black balls from an urn of twenty, and guess what?
Pull four balls from an urn holding twenty, see three black and one white, and you might guess fifteen black in total. That is one of seventeen possible answers. Inductive reasoning lives in that gap: it moves from what we have seen to what we have not, and its conclusions are only ever probable.
Deduction guarantees its conclusion if the premises hold. Induction cannot. It covers several families of argument, including generalisation from a sample, prediction of the next case, statistical syllogism, analogy and causal inference. Each earns a different degree of trust. Oddly, the procedure mathematicians call induction is actually deductive and delivers certainty.
Generalisations are only as good as their samples. A large random poll finding 66 per cent support for a measure can be trusted within a stated margin of error. A book club where six of ten members share a politics says almost nothing about everyone else, because the group is small and hand-picked. Leaping from a Little League team's six wins in ten games to a season forecast is weaker still, since nothing about the sample is random and future conditions cannot be calculated. Such inferences quietly assume that nature behaves uniformly, a principle that cannot itself be proved from data; arguments that lean on it are sometimes called Humean, after the philosopher who first scrutinised them.
A statistical syllogism runs the other way, from group to individual. If 90 per cent of a school's graduates go on to university, a given graduate probably will too, and the probability is exact even though the outcome is not. Analogy reasons that things alike in some respects are likely alike in others. John Stuart Mill argued in his System of Logic that every relevant resemblance adds some weight. The danger is cherry-picking: two stones may share origin and texture yet differ in exactly the property that matters, and a coincidence such as both appearing in early Spanish explorers' records adds nothing.
Causal inference moves from correlation toward cause, but extra factors must be confirmed before the precise link is known. Two broad routes build generalisations. Enumerative induction piles up supporting instances, growing stronger with each one, while eliminative induction works by ruling alternatives out. Techniques like Bayesian updating and maximum likelihood estimation can put numbers on how likely each explanation is.
Source: Inductive reasoning
