Logic and Conversation

Logic and Conversation - 2 Logic and Conversation It is a...

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2 Logic and Conversation It is a commonplace of philosophical logic that there are, or appear to be, divergences in meaning between, on the one hand, at least some of what I shall call the formal devices--, 1\, V, :J, ('t/x), (3x), (LX) (when these are given a standard two-valued interpretation)-and , on the other, are taken to be their analogues or counterparts in natural language-such expressions as not, and, or, if, all, some (or at Least one), the. Some logicians may at some time have wanted to claim there are in fact no such divergences; but such claims, if made at all, have been somewhat rashly made, and those suspected of making them have been subjected to some pretty rough handling. Those who concede such divergences exist adhere, in the main, to one or the other of two rival groups, which I shall call the formal- ist and the informalist groups. An outline of a not uncharacteristic formalist position may be given as follows: Insofar as logicians are concerned with the formulation of very general patterns of valid inference, the formal devices possess a decisive advantage over their natural counterparts. For it will be possible to construct in terms of the formal devices a system of very general formulas, a considerable number of which can be regarded as, are closely related to, pat - terns of inferences the expression of which involves some or all of the devices: Such a system may consist of a certain set of simple formulas must be acceptable if the devices have the meaning that has been assigned to them, and an indefinite number of further formulas, many of which are less obviously acceptable each of which can be shown to be acceptable if the members of the original set are accept- able. We have, thus, a way handling dubiously acceptable patterns of inference, and if, as is sometimes possible, we can apply a decision
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Logic and Conversation 23 procedure, we have an even better way. Furthermore, from a philo- sophical point of view, the possession by the natural counterparts of those elements in their meaning, which they do not share with the corresponding formal devices, is to be regarded as an imperfection of natural languages; the elements in question are undesirable excres- cences. For the presence of these elements has the result both that the concepts within which they appear cannot be precisely or clearly de- fined, and that at least some statements involving them cannotvin some circumstances, be assigned a definite truth value; and the indef- initeness of these concepts not only is objectionable in itself but also leaves open the way to metaphysics-we cannot be certain none of these natural language expressions is metaphysically "loaded." For these reasons, the expressions, as used in natural speech, cannot be regarded as finally acceptable, and may turn out to be, finally, not fully intelligible. The proper course is to conceive and begin to con- struct an ideal language, incorporating the formal devices, the sen- tences of which will be clear, determinate in truth value, and certifia-
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Logic and Conversation - 2 Logic and Conversation It is a...

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