Formal semantics purports to be something like 'the study of structured meaning in human linguistic communication', I suppose.
However, "all grammars leak". Our "meanings" are actually more idiosyncratic, more irregular, and (somehow) less ambiguous than formal semantics lets on, which is to say that the formalisms of semantics only loosely constrain communicative reality.
But to say that entails (

) that it
does constrain reality in some manner. This fact seems to manifest in a very strange way:
Semantics, like mathematics, is not an 'evolved discovery' of some independent external
thing or "law" but the outcome of rough cognitive patterns noticing rough cognitive patterns. This limits what we can say about the existence of formal semantics to the concrete; it really exists only in the brains that know of it, in other words. The aforementioned rough patterns are progressively refined and given further layers of abstraction - by these same brains.
What I'm getting at is, formal semantics is inward-looking, and this impinges on productive,
communicative semantics. The one continuously modulates the other, and moreover this happens
automatically.
Putting together all of the above, we come to the realization that formal semantics is ultimately the study of the effect of formal semantics on formal semantics. Semantics is actually meta-semantics, and so on.
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