A very quick argument against a 'theory of meaning'?

Has Sootica bipolarity?

The second key distinguishing characteristic [or a resolute reading of Wittgenstein] is a rejection of the idea that recognising the nonsensicality of ... any ... proposition requires the application of a theory of meaning - a specification of the conditions under which a sentence makes sense... According to resolute readers, there is no such theory... For to what could such a theory be applied? Suppose we imagine someone claiming that the author of the Tractatus advances bipolarity as a condition for the sense or meaningfulness of a proposition... and so licenses us to dismiss any non-bipolar proposition as nonsense; and now recall the key Tractatus distinction between signs and symbols. The question arises: what is it that lacks bipolarity – a string of signs or a complex of symbols? No mere string of signs could possibly either possess or lack bipolarity; but if we are in a position to treat some given string of signs as symbolizing, then we must have parsed it as symbolizing in a particular way, and hence assigned specific logical roles to its components. If so, then the question of whether or not it possesses bipolarity comes too late; and if not if, that is, we haven’t yet settled on a particular parsing of it – then the question simply doesn’t arise. [Mulhall 2007: 5-6]

I take the point that it makes no sense to ascribe bipolarity to chairs, tables or cats. The question of whether Sootica has bipolarity ‘doesn’t arise’. And thus it seems that every time that the question does arise, it will have to be answered ‘yes’. This suggests some oddness: if S ranges only over (meaningful) sentences then sentence A:

A: S has bipolarity

lacks bipolarity, which may cause problems for a theorist of bipolarity.

But bracketing that aspect of this specific putative condition on what is of meaningful, is Mulhall’s argument in general good? Why could one not self-consciously recognise that an aspect of all propositions, of things that one does take to have meaning, is that they have bipolarity (or whatever other aspect of meaning one fancies). It may be that he is not ruling that out. All depends I think on what he means by:

recognising the nonsensicality of ... any ... proposition requires the application of a theory of meaning

If this is given an epistemological reading, that in order to find out whether something is meaningful then we have first to apply this test, then that seems a nonsense (if not actual nonsense). But surely that is not what a fan of bipolarity – or any other theory of propositional form - would say. They’d give it a constitutive reading: to count as a proposition is to pass the test specified by the theory such that the theory applies to the proposition. Aside from bipolarity’s own odd logic, I’m not sure that there could be an argument as quick as Mulhall’s to reject this idea.

Mulhall, S. (2007) Wittgenstein’s Private Language Oxford: Oxford University Press