Nomological Statements and Admissible Operations

Nomological Statements and Admissible Operations

Nomological Statements and Admissible Operations

Nomological Statements and Admissible Operations

Excerpt

The problem of a 'reasonable' implication has frequently occupied logicians. Whereas in conversational language this kind of propositional operation is regarded as having a clear and well- defined meaning, logicians have been compelled to define as implication a term of much wider meaning; and it appears extremely difficult to go back from this implication in a wider sense to the narrower and very specific meaning assumed for implication in a non-formalized language. We face here a discrepancy between usage and rules: whereas in actual usage everyone is quite able to say whether an implication is reasonable, he would be at a lose to give rules which distinguish reasonable implications from unreasonable ones. The term 'reasonable', therefore, is a challenge to the logician for finding rules delineating a usage that follows unconscious rules.

The problem of uncovering such rules appears even more difficult when it is realized that 'reasonable' implications of conversational language are not restricted to implications expressing a logical entailment , but include what may be called a physical entailment . For the first kind, we may use as an illustration the implication, 'if all men are mortal and Socrates is a man, then Socrates is mortal'. The second kind may be illustrated by the implication, 'if a metal is heated, it expands'. Since the latter kind of implication expresses what is called a law of nature, whereas the former may be said to express a law of logic, I have proposed to include both kinds under the name of nomological implications.

It is easily seen that the problem under consideration is not specific for implication, but concerns all propositional operations alike. The 'or', for instance, can have an 'unreasonable' as well as a 'reasonable' meaning. To say, 'snow is white or sugar is sour', appears as unreasonable as saying 'if snow is not white, sugar is . . .

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