Induction – Definitions
Induction as a method of reasonning by which a general law or principle is inferred from observed particular instances. The word “induction” is derived from the latin translation of Aristotle “epagoge”, which seems in turn to have been taken from earlier Greek writers on military tactics.
The term is employed to cover all arguments in which the truth of the premises, while not entailing the truth of the conclusion, nevertheless purports to constitute good reason for accepting it. The expression “ampliative argument” suggested by C.S. Peirce, is also used. There is no generally accepted subclassification of inductive or ampliative arguments, tough induction is often thought to be the fundamental form : from A1 is 0, A2 is 0, A3 is 0, and so on, this proceeds to the conclusion that all A s are 0, probably.
With the growth of natural science philosophers became increasingly aware that a deductive argument can only bring out what is already implicit in its premises, and hence onclined to insist that all new knowledge must come from some form of induction. It was in this understanding that Francis Bacon was the prophet of inductive science, who rang a bell to call the wits together”.
Hume and the problem of induction
What is now called the problem of induction was set by David Hume, who himself did not actually use the word in this context. Hume represented the nerve of all argument from experience as an attempted syllogism, the problem being to show how we can be entitled to move from a first premise that all observed so-and-sos have been such and such to the conclusion that all so-and-sos without restriction have been, are, and will be such and such.
A second premise that would complete a valid syllogism is that all so-and-sos have been if fact observed. But this suggestion is disqualified, since where it applies we have an analysis of not an argument from experience. THe only alternative second premise condsidered by Hume would make reference to the uniformity of nature. This he ruled out on the grounds that it could only be known to be true by a question-begging appeal to arguments of the very kind here in question.
The moral that Hume drew is that argument from experience must be without rational foundation. He seems nevertheless to have felt few scruples over the apparent inconsistency of going on to insist, first, that such argument is grounded in the deepest instincts of nature, and, second, that the rational man everywhere proportions his belief to the evidence.