On Logical Validity and Informal Appropriateness

Abstract

The following note on valid logical implications, which, though formally correct, are yet in certain contexts pragmatically or otherwise inappropriate, is mainly intended to indicate the nature of conflicts between logical validity and informal inappropriateness and to consider various methods for the solution of such conflicts. In undertaking this task, the note also provides a reply to a cluster of objections raised by Professor Jonathan Harrison against my use of one of these methods and, it may well be, against the method itself.' Let us imagine a doctor and a lawyer both of whom always reason correctly in accordance with a system of logic which on the one hand is rich enough for their deductive needs and which on the other hand allows for the deduction of tautological conclusions. Thus, if the doctor tells us that his medical knowledge together with the description of our symptoms logically implies that we have influenza or do not have influenza, he is stating a logical implication with a tautologous conclusion which-at least by itself-does not give us any information about our state of health. Similarly, if the lawyer tells us that the legal code of a certain country together with the description of our situation logically implies that we are obliged to pay income tax or not to pay income tax, he states a logical implication with a vacuous conclusion which-at least by itself-does not give us any information about our legal obligations. Towards such logical implications the following positions, among others, may be-and have in fact been-taken up: (i) They are trivial, but unobjectionable, since the question of their triviality or degree of triviality has nothing to do with logical validity. This is the position of many mathematicians. (ii) The logical implications are odd, must be avoided and should be avoided by means of an 'informal logic' which somehow connects the oddity of statements with their falsehood or invalidity. This is the position of some ordinary-language philosophers. (iii) The logical implications are logically defective and their occurrence should be avoided by replacing-whenever possible-the system of formal logic in which they occur by another in which they cannot occur. This is