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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.

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Two descriptors that may fit the requirement are non-constructive proof and pure existence proof.

From wikipedia:

In mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object. This is in contrast to a non-constructive proof (also known as an existence proof or pure existence theorem), which proves the existence of a particular kind of object without providing an example. For avoiding confusion with the stronger concept that follows, such a constructive proof is sometimes called an effective proof.

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How about metaproof?

I did a web search for the term, and found the following excerpt in a paper entitled, "'Metaproofs' (and their Cryptographic Applications)"1:

We develop a non-interactive proof-system which we call “Metaproof” (µ-NIZK proof system); it provides a proof of “the existence of a proof to a statement”. This metamathematical notion indeed seems redundant when we deal with proving N P statements, but in the context of zero-knowledge theory and cryptography it has a large variety of applications.

1 https://eprint.iacr.org/2012/495.pdf

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