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Is 'appeal' the correct word in:

Method A solves Problem B without appeal to the C-principle.

This sentence tries to say that there is an obvious solution to Problem B that can be found using a very general principle C, but method A is actually a more specialized method tailored to Problem B that is found without using the general solution principle C.

I feel like I am confusing 'appeal' with the similar sounding correct word, since I do know of usages of 'appeal to' that are different from the one I intend (e.g. 'it had no appeal to him').

I couldn't find my intended usage in dictionary entries for 'appeal'

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It is correct but I would prefer "without appealing to the C-principle".

See for example a stack exchange answer

Of course, there are certain specific instances where one can do this without appealing to the Axiom of Choice:

  • if you only have to make finitely many choices; or
  • if these choices can be made in a uniform manner
  • I happen to also need this for a math manuscript. I guess that's where I picked up the phrase in the first place – Bananach Jul 15 '18 at 19:16
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You say you might be confusing appeal with a similar-sounding word. I'm guessing that word is apply:

Method A solves Problem B without applying the C-principle.

Here, apply would mean:

apply (verb) To put to use; to use or employ for a particular purpose

Macmillan defines it as:

apply (verb) to use a particular method, process, law, etc.

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