A Test for Ambiguity... Tewtally Pwned

I’m reading Zwicky and Sadock’s (1973) paper on “Ambiguity Tests and How to Fail Them” for a paper on the ontology of senses (of linguistic expressions) that I’m working on.* They discuss different types of arguments for or against a sentence (or a crucial expression in the sentence) being ambiguous. One type, called “inconstancy under substitution” caught my eye. Fully spelled out, I think inconstancy under substitution arguments work something like this:

1. F is synonymous with G / F is a hypernym of G / G is a hypernym of F.
2. “… F …” has distinct understandings p and q.
3. “… G …” has p, but not q / “… G …” has an understanding that is acceptable if p, but no understanding that is acceptable if q / “… G …” has an understanding that is acceptable only if p, but none that is acceptable only if q.
4. Therefore, “… F …” is ambiguous between p and q.

Some comments: as it stands, the conclusion doesn’t logically follow from the premises. It’s hard to say what the implicit premise is that makes the conclusion seem warranted. At any rate, I don’t want to question the validity of this line of argument here. The big problem is antecedently establishing the first premise. Intuitively, the fact that substitution of G for F does not transform the possible understandings in the appropriate way** is evidence for the semantic relation not obtaining between F and G. To take one of the relations, it seems that we come to call F and G synonyms because of their intersubstitutability across diverse sentential and conversational contexts. Granted, of course, that intersubstitutability can fail in certain sorts of contexts without telling against the synonymy of the two terms; the argument from inconstancy of substitution (which does not involve reference to conversational contexts) works precisely when the sentential context is of such a sort. But we need to be able to identify those contexts prior to making the judgment that F and G are synonymous. But this entails that we can already recognize that, in the context quoted in the argument, F is ambiguous between the reading with which G is synonymous and some more idiomatic reading. So it seems that in order for us to establish the soundness of the premises of an argument from inconstancy of substitution, we must already be in a position to know that the conclusion is true.
____________________

* - The first paper I’ve started to work on since graduating from Bard. Kind of exciting.
** - The appropriate way when F and G are synonymous would be that “… F …” can be understood precisely in all the ways that “… G …” can. The appropriate way when F is a hypernym of G would be that there is a certain one-to-one correspondence between the understandings of “… F …” and the understandings of “… G …”, such that an understanding of the latter is acceptable only when the corresponding understanding of the former is acceptable, or something like that.