the process that occurred to logicians was an appeal to the ‘self-evident’ truth of ‘intuitions’; but this has been shown to be argumentatively worthless.  From this difficulty the pragmatist alone escapes, by assuming his premisses provisionally and arguing forwards, in order to test them by their consequences.  If the deduced conclusion can be verified in fact, the premisses grow more assured.  Thus every real inference is an experiment, and ‘proof’ is an affair of continuous trial and verification—­not an infinite falling back upon an elusive ‘certainty,’ but an infinite reaching forwards towards a fuller consummation.

(f) So long as the logician regards his premisses not as hypotheses to be tested, but as established truths, he must condemn the Syllogism as a formal fallacy.  It is inevitably a petitio principii.  If the argument ‘All men are mortal; Smith is a man, therefore Smith is mortal,’ means that we know, before drawing our inference, that literally all men are mortal, we must already have discovered that Smith is mortal; if we did not know beforehand that Smith is mortal, we were not justified in stating that all men are mortal.  Nor is it an escape to interpret ’All men are mortal’ to mean that immortals are excluded from ‘man’ by definition.  For then the question is merely begged in the minor premiss.  That ‘Smith is a man’ cannot be asserted without assuming that he is mortal.  If, lastly, ‘All men are mortal’ be taken to state a law of nature conjoining inseparably mortality and humanity, the logician either already knows that Smith is rightly classed under the species ‘man,’ and so subject to its mortality, or else he assumes this.  But how does he know Smith is not like Elijah or Tithonus, a peculiar case, to which for some reason the law does not apply?  Will he declare it to be ‘intuitively certain’ that whatever is called, or looks like, a case of a ‘law’ ipso facto becomes one?

The logician’s analysis of reasoning, then, breaks down.  In whichever way he interprets the Syllogism it is revealed as either a superfluity or a fallacy:  it is never a ‘formally valid inference’ that can compel assent.  But common sense is undismayed by the pragmatist’s discovery that if the Syllogism is to have any sense its premisses must be taken as disputable; for, unlike Formal Logic, it has perceived that men do not reason about what they think they know for certain, but about matters in dispute.

4.  It is not necessary to dwell at length on the futility of the formal notion of Induction.  Formal Induction presupposes that enough particular instances have been collected to establish a general rule; but in actual practice inductions always repose, not on indiscriminate observation, but on a selection of relevant instances, and never claim to be based upon an exhaustive knowledge of particulars.  Hence in form the most satisfactory induction is always incomplete, and differs in no wise from a bad one.  ‘All bodies fall to the ground’ is an induction which has worked.  ‘All swans are white’ broke down when black swans were discovered in Australia.  The validity of an induction, then, is not a question of form.