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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?

Mauro ALLEGRANZA
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sket
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  • There might not be much difference (on the intended level of interpretation), since there are construals of, "If something is a bachelor, then that thing is an unmarried man," where there is a sort of "implicit inference" involved, and by logical necessity after a fashion, then. (I more often see things like, "If A is the brother of B, then A and B have the same mother," in this vein, IIRC). OTOH, an explicit logical inference can yet count as analytical, too; but perhaps this all goes to show that the analysis/synthesis distinction is weaker than is useful. – Kristian Berry Jul 05 '23 at 18:35
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    You are going to need to explain what you mean by implicit/explicit because it is not at all clear from your example. – David Gudeman Jul 05 '23 at 20:03
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    See e.g. [Willard Van Orman Quine: The Analytic/Synthetic Distinction](https://iep.utm.edu/quine-an/) as well as [The Analytic/Synthetic Distinction](https://plato.stanford.edu/entries/analytic-synthetic/). – Mauro ALLEGRANZA Jul 06 '23 at 13:33
  • See also the post [Understanding the difference between analytic/synthetic vs necessary/contingent](https://philosophy.stackexchange.com/questions/86455/understanding-the-difference-between-analytic-synthetic-vs-necessary-contingent) as well as [Is the synthetic/analytic distinction about metaphysics?](https://philosophy.stackexchange.com/questions/86857/is-the-synthetic-analytic-distinction-about-metaphysics) – Mauro ALLEGRANZA Jul 06 '23 at 13:34
  • The origin is that "analytical" for a statement equates with the predicate is contained into the meaning of the subject. Thus, 'a bachelor is an unmarried man' is analytical because "unmarried" is included into the meaning of "bachelor". But implicit/explicit does not fit with included/excluded. – Mauro ALLEGRANZA Jul 06 '23 at 13:38

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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.

Bumble
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