How can an Epistemological Nihilist argue against something that logic presupposes?

Proven without requiring logic appears to be a contradiction.

How is proven defined?

I interpret it to exist in the formal spectrum.

As for epistemological nihilism, it apears to be in fact open to the concept of epistemology.

How is the concept eliminated?

Apparently, what you mean by "proven" is the provision of a formal or LOGICAL proof. That is not what I seek when I pursue a feeling of certainty; what I mean by subjective certitude is an empirical indication*. I pursue sensory evidence rather than a conceptual formula. For all I know E=MC2 is fraudulent. I DO have "faith" in it (and I need that faith because of my math-theory naivete).
*Since my approach is INformal, I am not bothered by the hypothetical possibility that my "evidence" is illusory.

Very well, I do agree, though acknowledge that I am assuming only logical necessity, in all my philosophical arguements.

Also, sensory information is interpreted, the inferences required are of a logical basis.

For example, our inferences would not be of a 0=2 universe, this is illogical.

There is a general consensus that define this as induction, I deny this being 'logical'.

For clarification, my 'logic' is deduction, the premise is certain, and is not subjected to empirical circularity.

As for E=MC2, that is a physical/scientific law and acknowledges physical quantity, not an axiom or theorem, such as an 'axiom of equality'.

Yes, sensory information must be interpreted, but is that interpretation dependent solely on formal logic, or can a "reasonable" basis rest also on aesthetic, intuitive and emotional values?
BTW, on what grounds is a deductive premise itself logically certain? Does it not beg the question to base that certitude on logic? How is logical circularity (tautology) any better than "empirical circularity"?

To deny logic has some logical root.

...and how can you do that without referring to logic itself? Its a contradiction in terms to stand for relativism with so much certainty when logic at large is to be faulted...

A framework for a belief to "not believe", or whatever, might even have the option to express itself in a system that is not explosive like classical logic. Paraconsistent logic can at least suspend conclusions about some inconsistencies or treat them as informative, rather than as a target to either be solved or rejected via seeking an initial assumption to be incorrect. Maarten McKubre-Jordens offered a bare bones ditty pertaining to the salvaging of an otherwise good scheme marred by a mole on its face:

"The thought is this: suppose I have a pretty good theory that makes sense of a lot of the things I see around me, and suppose that somewhere in the theory a contradiction is hiding. Paraconsistent logicians hold that this does not (necessarily) make the theory incoherent, it just means one has to be very careful in the deductions one makes to avoid falling from contradiction into incoherence. For the most part, it makes no difference to us if the liar sentence really is both true and false, and the paraconsistent perspective reflects that. By removing RAA [reductio ad absurdum] (or altering it), and making a few other tweaks to classical logic, we can create a logic and mathematical system where contradictions are both possible and sensible." --This is not a carrot: Paraconsistent mathematics

Hmmm, paraconsistent logic. Interesting--sounds consistent with the reality described by zen and Taoism.

Your arguement appears to be metalogical, perhaps.

Aesthetic, intuitive (from experience) and emotional values are variants, furthermore the spectrum opens to further empirical suggestion, such as neurology of other organisms that deviate from humans, yet empirical facts do appear to be consistent in this case.

Deduction may be interpreted 'circular' (iff), however this 'circular' is of different cognitive properties to that of 'circular reasoning/induction', being 'necessarily true'.

If (if and only if) all swans are white =/= all (empirical suggestion) the swans are white

What is 'necessarily true'?
Axiomatic derrivations of proof, theorems can be derrived to the axioms, such as Peano's Axiom of natural numbers.

This entailment is a deductive consequence, be it syntatical or semantical, my biased cognitive faculties suggest this to be 'necessarily true', it is consistent formation rules.

Are you familiar with Godel?

View his incompleteness theorems, this may clarify.

Are you familiar with quantum mechanics?

It has been suggested that wave-particle dualism deconstructs axioms of equality, this self refuting logic.

As an example, wave is wave and -wave (particle), particle is particle and -particle (wave), consistently.

If quantum interpretations are inconsistent with cosmological interpretations, are these suggestions of uncertainty (in principle) 'necessarily true'?

There is no basis for a human to interpret this, this basis suggests virtual particles that exist and do not exist, can a human actualise non existence?

It does not appear to exist.

I have no technical knowledge of QM. Maybe they hold that the cosmos is a probabilistic reality and it consists of wavicles.
Maybe "virtual particles" are consistent with zen ontology: the world is empty (sunya) but that emptiness always takes form. Indeed, the Heart Sutra emphasizes that form is emptiness and emptiness is form.
I never tire of saying it.

All I'm saying is those who take that leap to denounce logic may be confronted by reasons why one would do so. I don't necessarily denounce logic and agree that logic is self referential. Thus to deny it can be seen as a paradoxical move.