Information, Deduction, and the A Priori

Abstract

1. A scandal of deduction. C. D. Broad has called the unsolved problems concerning induction a scandal of philosophy.' It seems to me that in addition to this scandal of induction there is an equally disquieting scandal of deduction. Its urgency can be brought home to each of us by any clever freshman who asks, upon being told that deductive reasoning is tautological or analytical and that logical truths have no empirical content and cannot be used to make factual assertions: In what other sense, then, does deductive reasoning give us new information? Isn't it perfectly obvious that there is some such sense, for what point would there otherwise be to logic and mathematics?2 This question is apt to cause acute embarrassment, for no such sense has ever been defined in the literature. The only honest answer to our imaginary freshman's question is given by those few unregenerate logical positivists who are bold enough to deny the existence of any objective (nonpsychological) sense in which deductive inference yields new information.3 This is a straightforward answer, although its consequences (which are not always explicitly mentioned) are somewhat implausible. If no objective, non-psychological increase of information takes place in deduction, all that is involved is merely psychological conditioning, some sort of intellectual psycho-analysis, calculated to bring us to see better and without inhibitions what objectively speaking is already before our eyes.4 Now most philosophers have not taken to the idea that philosophical activity is a species of brainwashing. They are scarcely any more favourably disposed towards the much more far-fetched idea that all the multifarious activities of a contemporary logician or mathematician that hinge on deductive inference are as many therapeutic exercises calculated to ease the psychological blocks and mental cramps that initially prevented us