Term for an argument that is only valid because of another view that the person you're arguing against holds, that you disagree with

Couldn't think of a better title.

But this is is the gist: an argument that is only valid because of another view that the person you're arguing against holds, that you disagree with.

You said cats are no. I say dogs are no. But don’t even try and tell me cats are yes because you already said cats are no.

This question is not really about the validity of arguments, but their soundness (the truth or plausibility of the premises is irrelevant to the validity of an argument, which depends solely on the logical relationship between the premises and the conclusion).

So the question is what to call a valid argument that takes as one or more of its premises something that is believed by the person that the argument is addressed to, but not by the person putting forward the argument. In such a case, the former person is committed to regarding the argument as sound, even though the latter regards it as unsound.

One term that is occasionally used for such arguments is legitimate ad hominem. The term ad hominem, by itself, is a well-established name for the fallacy of using something logically irrelevant about a person in an attempt to refute that person's views. Here, the argument is not ad hominem in that sense (because a person's existing beliefs are relevant to what else the person is rationally committed to believing), but it is ad hominem in the literal sense ('to the specific person'), which makes legitimate ad hominem an apt term for it.

If the overall purpose of the argumentation is to criticise some aspect of the views of one's interlocutor, the argumentation can be referred to as immanent criticism. What makes it immanent is that its starting point is within the interlocutor's own viewpoint, that the criticism does not depend on the assumptions that are outside that viewpoint.

Both of the above terms can be used not only when the person who puts forward the argument disagrees with its premises, but also when that person merely suspends judgment as to whether the premises are true.

Finally, if the purpose of the argument is to show that the beliefs of one's interlocutor lead to the conclusion that is obviously false, in the hope that this will lead the interlocutor to reconsider the argument's premises, the argument is a reductio ad absurdum.