Truth, Reference and Realism

What is Logic?

iAN rumfitt What is logic? 1 notions of consequence What is logic? Textbooks typically introduce the subject as the science of consequence. Thus in an early section of his estimable primer—a section entitled “What logic is about”—we find Benson mates explaining that logic investigates the relation of consequence that holds between the premises and the conclusion of a sound argument. an argument is said to be sound (correct, valid) if its conclusion follows from or is a consequence of its premises; otherwise it is unsound.1 (mates 1965, 2) in a similar spirit, e.J. lemmon begins Beginning Logic by writing that Only §5 of this essay overlaps substantially with my lecture in Budapest, the rest of which now strikes me as much ado about little. But the nature of logic is a topic of perennial interest, so i hope that the present piece will contribute something to the proceedings of an unusually pleasant and stimulating conference. The essay draws on material presented to seminars in Oxford and london, and on the first of my nelson lectures, given at the university of michigan at ann arbor in september 2004. i am grateful to Jonathan Barnes, dorothy edgington, crispin Wright, and the editors of this volume for their comments on a draft. 1 some logicians call an argument “valid” when its conclusion follows from its premises, and reserve the term ‘sound’ for valid arguments whose premises are true. i shall not follow them. The term ‘valid’ is tied in many people’s minds to the idea that there is a canonical, “logical” standard for validity; and this idea is one i wish to challenge. i4 Truth.indb 125 2011.08.15. 8:57 126 Truth, reference and realism logic’s main concern is with the soundness and unsoundness of arguments … Typically, an argument consists of certain statements or propositions, called its premises, from which a certain other statement or proposition, called its conclusion, is claimed to follow. We mark, in english, the claim that the conclusion follows from the premises by using such words as ‘so’ and ‘therefore’ between premises and conclusion … logicians are concerned with whether a conclusion does or does not follow from the given premises. if it does, then the argument in question is said to be sound; otherwise unsound. (lemmon 1965, 1) Both of these passages suggest that we have some pre-theoretical grasp of the relationship of one thing’s following from some others. The laws of logic are then taken to say, in general terms, which things stand in this relationship. Thus a logical law which classical logicians accept, but which intuitionist logicians do not accept without restriction, says that a proposition follows from the negation of its negation. many other passages could be cited which express this view of logic’s business. There is, to be sure, one important matter over which adherents of the view differ: the nature of the relata of the consequence relation. lemmon writes of one statement’s following from some others; by a statement he means something which is stated, or which could be stated , by the utterance of a declarative sentence on a given occasion of use (1965, 6). This way of speaking is undeniably natural: it comes easily to say “The statement that every set can be well ordered follows from the statement that there is a choice function on every set.” There are, though, problems with this account of the relata of consequence, at least if it is deployed early in an investigation into the nature of logic. if consequence is a relation among objects, then its relata must be subject to the discipline of the identity relation, for such subjection is the mark of objects. There are reasons to doubt, though, if our ordinary standards for assessing whether two utterances “say the same thing” can really sustain judgments of strict identity between what lemmon calls statements.2 a theorist may of course try to supplement those ordinary standards with additional criteria that can sustain such judgments , and i have no argument to show that this attempt must fail. 2 i set out these reasons in my essay “Objects of Thought” (rumfitt forthcoming). i4 Truth.indb 126 2011.08.15. 8:57 127 What Is Logic? it seems certain, however, that any attempt of this kind will invoke a number of logical laws, and so is best delayed (if possible) until after...