I am writing a paper on cognition, and to simplify my discussion I need an adjective or descriptor for particular category of argument as follows: I am arguing for the necessity of a construct with a set of particular properties, but I do not produce an example or identity of that construct. 'Hypothetical' is wrong, as I am claiming necessity of existence. 'Existence proof' might work, except I am trying to distinguish it from using exemplars or testable properties (that are also existence proofs, I guess). Is there a descriptor that is helpful for this purpose? Or does my question have some flaw?
The specific domain (in case it helps) is theory of computation; although there are 'proofs' of the sort described in this domain, I cannot find any discussion of the nature of such a proof as distinct from (say) proof by exemplar; I am also going to ask some mathematicians, but it doesn't seem to be a semantic problem in math or symbolic logic.. in math you simply pick a symbol and imbue it with properties (There exists an x such that x has the following properties..).
Any help/ideas appreciated.