We can have explicit rules of, say, chess or football; however, we cannot have explicit rules for using language – at least not generally.
Restricting ourselves to the two most prominent reducienda of the meaning of an expression, namely the use of the expression and the mental entity ('cognitive content') 'behind' the expression, the following main possibilities seem to emerge as to what a diagram associated with a sentence, or, more generally, with an expression, can amount to: (i) a description of the meaning of the expression (ii) a description of the way the expression is used 6 (iii) a description of a mental entity associated with the expression (iv) a translation of the sentence into another language The first alternative seems to offer the most promising route: what could be a more direct realisation of the task of semantics than displaying expressions alongside with their meanings?8 However, this proposal is rather tricky; for what could count as a description of meaning, which, as we have concluded in the preceding section, is best seen not as a 'real' object, but rather as a value?
If the rules which we consider are the rules of syntax (i.e. if they provide for the criterial reconstruction of well-formedness), then the resulting categories are known as syntactic categories (they express the expressions' behaviour from the viewpoint of constituting well-formed expressions and statements); if they are the rules of semantics (i.e. if they amount to truth, assertibility, or use in general), then the categories are meanings (they express the expressions' behaviour from the viewpoint of truth, or, more generally, from the viewpoint of their employability within language games).
And what can be said about numbers, can, more generally, be said about meanings: the meaning of an expression is not one or another definite thing conforming to our usage of the expressions within language; at most it may be said to be what all such things have in common.
And expressions are synonymous only if they contribute in the same way to truth, i.e. only if they are intersubstitutive salva veritate (or, more generally, if they are intersubstitutive with respect to the usability of language statements in various language games).
We still lack a proper characterization of this second class of analytic statements, and therewith of analyticity generally, inasmuch as we have had in the above description to lean on a notion of 'synonymy' which is no less in need of clarification than analyticity itself.
In effect such a language enjoys the benefits also of descriptions and class names and indeed singular terms generally, these being contextually definable in known ways.
Such a language can be adequate to classical mathematics and indeed to scientific discourse generally, except in so far as the latter involves debatable devices such as modal adverbs and contrary-to-fact conditionals.
Such a language can be adequate to classical mathematics and indeed to scientific discourse generally, except in so far as the latter involves debatable devices such as contrary-to-fact conditionals or modal adverbs like 'necessarily'.
The notion of analyticity about which we are worrying is a purported relation between statements and languages: a statement S is said to be analytic for a language L, and the problem is to make sense of this relation generally, for example, for variable 'S' and 'L.'