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The statement 'a bachelor is an unmarried man' is an implicit and analytic statement.

What is the difference between implicit/explicity and analytic/synthetic? Is there even a difference?

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The short version is that thinking of analyticity in terms of what is contained or implicit is too narrow.

There are at least four different accounts of analyticity. The term was coined by Kant, and he understood an analytic statement to be one where the predicate is contained in the subject. This seems to be what you are describing by saying that your sentence is implicit. I take it that you are saying that 'unmarried man' is implicit or contained within 'bachelor'.

The problem with this reliance on the concept of containment is that it is too narrow: it only covers cases of sentences that are in subject-predicate form. Frege proposed instead that a proposition is analytic if it can be derived from a logical truth by substitution of definitions. This is much better, though it depends on the use of some logic to make the concept of logical truth precise. Frege held that arithmetic is analytic, so 2+2=4 is an analytic statement, though it is not a case of what is contained or implicit. Likewise, for Frege, "if John is unmarried then John is unmarried or tall" is analytic though we wouldn't say that 'unmarried or tall' is contained in 'unmarried'.

The logical positivists were fond of talking about analyticity and preferred to think of it in terms of meanings, or linguistic conventions. On this view, a proposition is analytic if it is true only in virtue of its meaning, or only in virtue of the linguistic conventions that govern its use. These accounts are even broader, though less precise, than Frege's.

Bear in mind that plenty of logicians do not accept the analytic/synthetic distinction at all, or at least not the traditional accounts of it.

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