The claim of any undeterminability in existence necessitates that the stability of the claims truth cannot be determined. Thus the purpose for asserting the claim as true is self refuting.
Firstly, I’m willing to argue the point.
Secondly, to address (hopefully) whatever ambiguity remains of this statement, I’ll explain further.
Let’s say you have a logical formulation that concludes undecidability. Undecidability, is a method of expressiong indeterminability within the ‘sphere’ of thought. Although, granted, it could leave open that there is still an operative causality - just that it’s not accessable to thought.
But, this interpretation, I believe is false, for it is still declaring an indeterminancy in existence - as thought itself exists.
The key here, is that by declaring an undecidability within thought, one is declaring an undeterminability within existence. This is contingent upon the acceptance that the perception of thought, and the perception of a conclusion of undeterminancy in this perception of thought both exist.
So, in this instance one is claiming either that existence itself is undeterminable or that something is undeterminable within existence (a perception of a perception of thought would be what exists in this instance, that is used to “observe” the belief of an undeterminancy conclusion – so as to humor the solipsists).
The problem, and the refutation, emerges when one realizes that they have consigned themselves, or rather, assented to the existence of undeterminancy as necessary, even if it is only necessary as a conclusion that follows from some abstract premises that themselves may not even be true or valid.
Again, the important part, is that it has been accepted in some way, that undeterminancy exists.
The problem, is that if there is actually an aspect of existence (or rather existence itself) that is undetermined, then there is a logical backhole that necessarily exists from which the stability of the statements’ truth value cannot be determined. The very act of asserting the truth value of the statements’ undeterminiability is false.
The conclusion is that statements cannot have undeterminancy as a conclusion without refuting the act of making the claim on the part of the person who concludes such an answer.