NB: please set pedantic mode to full. I'm not asking for general vague feelings, but for justification or rejection of a hypothesis from specific (and preferably quoted) rules.

So, the question is: can contractions be formed freely? If there is no l'ss of cl'rity, and the res'lt'ng st'm'nt is not amb'g's, can they just be created at will?

For context: I was discussing with a friend an obviously incorrect sign outside a shop yesterday that read "Sandwich's." We both agreed that this is not the correct plural form of the noun "sandwich".

I then engaged pedantic mode, and pointed out that it could be correct on the grounds that the plural of sandwich is not sandwichs but sandwiches, and that the apostrophe could be indicating the missing e, therefore sandwich's could be correct on the grounds that it is a contraction of the plural form. There is no ambiguity; the shop clearly sells sandwiches, and there is no indication that they may be selling stuff that may belong to a sandwich (besides, the sign only contained that one word).

Unfortunately my friend rejected this position out of hand, and refused point blank to discuss it any further. This argument was wrong; that was the end of the matter, and there was no point discussing it further (a rather worrying attitude, IMHO, for a school teacher.)

If contractions can be formed freely, then my point is valid and the sign is technically correct. If my point is not valid, then logically there must be rules on the formation of contractions that this word violates, hence my NB above, and I suppose the bottom line is: if "sandwich's" is incorrect, even as a contraction of the plural, why, exactly?
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Comments  (Page 2) 
Anonymous By definition a contaction is contracting multipletwo words into one. The apostrophe is placed where the 'missing' letter(s) would have been.
Untrue. A contraction could just as easily be employed in a single word, mostly in the middle of the word, but sometimes also in the beginning word. For example, ma'am, li'l, and 'cause, for madam, little, and because, respectively.
I disagree. The examples you use, 'cause, ma'am and li'l are not proper contractions, but rather a writer's means to indicate speak that has a local dialect, or the way it is normally pronounced in casual speech. Fro example, want a, as in 'I want a sandwich.' is often pronounced wanna; 'I wanna sandwich.'
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