DEDUCTION AND NOVELTY 1 Danny Frederick* Slightly expanded version of a paper that was published in The Reasoner, 5/4: 56-57 (2011) The interesting interview with Alan Musgrave (The Reasoner, 5.1) contained much that is worthy of discussion. Here I want to comment only on Musgrave’s claim that “the conclusion of a valid deductive argument is contained in its premises and says nothing new” (p.2). The claim has been a commonplace in discussions of deduction for centuries. An alternative way of making the claim is to say that every deductively valid argument is a petitio principii. This is a formulation which Musgrave himself echoes when he says: “Non-circular valid deductive arguments for P simply beg the question in a less obvious way [than do blatantly circular ones]” (p.2). However, notwithstanding its general acceptance, this hoary claim about deductive validity is false. Ironically, it was Musgrave’s teacher, Karl Popper, who refuted it. The hoary claim about deductive validity is associated with an equally hoary theory of deductive reasoning, which is found more or less explicitly in both empiricist and rationalist philosophers of the modern period and which is still popular today. The hoary theory says that a deductive reasoner arrives at a conclusion of an argument by analysing the content of its premises. This content is supposed to be accessible to the reasoner, at least upon reflection; indeed, it is often supposed to be made up of ideas in his mind, or concepts grasped by him, so that the ideas or concepts contained in the conclusion are extracted from those that make up the * Webpage: http://independent.academia.edu/DannyFrederick, Email: dannyfrederick77@gmail.com DEDUCTION AND NOVELTY 2 premises. This hoary theory of deductive reasoning may seem to entail the hoary claim about deductive validity: for if the reasoner arrives at a valid conclusion by unfurling the content of a set of premises, it may seem that, in a valid argument, the conclusion must already be discoverable in the premises and thus say nothing new. But we will see that this apparent entailment does not hold. Popper refuted the hoary claim about deductive validity in the following way (Unended Quest, Glasgow, Fontana, 1976, pp. 25-28). Let ‘N’ stand for Newton’s theory of gravitation and let ‘E’ stand for Einstein’s theory of gravitation. Since N is incompatible with E, the following argument is deductively valid: N Therefore, not-E. But the conclusion of this argument would certainly have said something new in Newton’s time. Newton could not foresee Einstein’s theory; and none of his contemporaries could have arrived at a statement of the negation of Einstein’s theory simply by unfurling the implicitly known content of Newton’s theory. Watkins offers a recipe for constructing somewhat similar examples. “Take some powerful new scientific theory which has recently led to a striking new prediction. Formulate all the premises used in the derivation of this prediction. Among these there will almost certainly be a truism known long before the new theory was invented. Call this a, call the theory together with all the other premises b, and call the prediction c. Then an impressive implication of the truism a is: if b then c” (Hobbes’s System of Ideas, second edition, London, Hutchinson, 1973, p.9). But if we go back to a time before the powerful new scientific theory had been invented, DEDUCTION AND NOVELTY 3 anyone announcing the deductively valid conclusion, if b then c, from the premise, a, would certainly have been saying something new. Popper distinguishes between the objective content of a theory and the part of that content that is available to a particular reasoner in a particular situation. The objective content includes each of those propositions that would be a deductively valid conclusion from the theory as premise. A great deal of this content will be inaccessible to someone who has learned the theory: it can become available to him only piecemeal as new theories are discovered. For example, the negation of E is part of the objective content of N, even though it is not part of the content of N that was accessible to anyone before Einstein came up with E. Thus, Newton did not, and could not, know the complete objective content of his own theory. Popper says, ironically, “we never know what we are talking about” (op. cit., p. 27). This is a kind of incompleteness: at every time there are some deductively valid consequences of a theory that cannot be formulated, and thus cannot be formally derived from the theory, by reasoners at that time. We could call this ‘Popper-incompleteness’ (to coin a term). Given this distinction between the objective content of a theory and the part of that content available to a particular thinker in a particular situation, we could consistently retain the hoary theory of deductive reasoning while rejecting the hoary claim about deductive validity. For we could maintain that: (i) any deductively valid conclusion from a set of premises to which we can reason deductively must be contained in that part of the content of the premises that is already available to us; DEDUCTION AND NOVELTY (ii) 4 there are many important deductively valid conclusions from those premises to which we are currently (and, in some cases, perhaps forever) unable to reason deductively and which would therefore tell us something new even though they are part of the objective content of the premises. On this view, every piece of deductively valid reasoning, but not every deductively valid argument, would merely unfurl things that we already know, explicitly or implicitly. However, the falsity of the hoary claim about deductive validity casts doubt on the hoary theory of deductive reasoning. Indeed, I think that the hoary theory of deductive reasoning can also be shown to be false, and for Popperian reasons, though I cannot explain that here.