Verificationism

Verification independent statements cannot be known to be either true or false.

There is no matter of fact as to P or not-P (which is the law of the excluded middle).

Only the law of non-contradiction holds for truth and falsity, not the law of bivalence. Not everything before us can be known to be strictly true or false in terms of propositions, only that something can't be both true and false. Something can have indeterminate meaning to us if it is not a matter of fact, verifiable by experience.

The law of the excluded middle is a tautology without regard to matters of fact. It always holds to be true no matter the truth of the terms. The alternative of not-A to A can mean anything. Both claims A or not-A cannot be both false; this doesn't make them true either.

Tautologies don't refer to anything that actually exists. That A is A (identity) and not-B (non-contradiction) is true, but that A is either A or not A doesn't mean anything in terms of true or false propositions. Much like when someone says they'll either do it or they don't. That doesn't mean anything even though it's not contradictory.

Non-contradiction does not prove that something exists as a matter of fact. Whatever exists as a matter of fact cannot be denied, but as to something which cannot be verified, the only way to prove this something a priori is if its opposite implies a contradiction. If something implies a contradiction, then it is inconceivable. But everything factual can be conceived not to exist. Therefore nothing can be proved to exist as a matter of fact prior to experience.

"… there is an evident absurdity in pretending to demonstrate a matter of fact, or to prove it by arguments a priori. Nothing is demonstrable, unless the contrary is a contradiction. Nothing, that is directly conceivable, implies a contradiction. Whatever we conceive as existent, we can also conceive as non-existent. There is no being, therefore, whose non-existence implies a contradiction. Consequently there is no Being whose contradiction is demonstrable." David Hume, Dialogues Concerning Natural Religion

This makes necessary truths, which are always true, not meaningful to anything outside of the concept. The laws of nature, for example Newton's second law force equals mass times acceleration F=ma, are true according to the phenomena they describe. As exceptions appear, such as the impossibility of accelerating matter faster than the speed of light, the law remains true for what it describes, but more and more isn't able to give us any new knowledge or answer questions. Thus a completely necessary truth is tautologous, insofar as it is devoid of synthetic claims, describing its own terms and not anything else. They hold for any possible combination of facts.

"When someone hides something behind a bush and looks for it again in the same place and finds it there as well, there is not much to praise in such seeking and finding. Yet this is how matters stand regarding seeking and finding "truth" within the realm of reason." Nietzsche, On Truth and Lie

In some cases we may not be able to prove P nor prove not-P. To say that it must be one or the other doesn't tell us anything.

The truths of conjunction and disjunction are not denied. Conjunctive propositions are only true if both terms are true. The truth or falsity of one does not determine the truth or falsity of the other. If A is true then B can be false, making the statement false. Only if A and B are both true is the statement true.

Disjunctive propositions can be false, if both terms are false. If either A is true or B is true, then the proposition is true. A or B is true if we can prove A or B. But we cannot prove A or not A is true because we may not be able to prove A or prove not-A. If it isn't possible to prove a statement, then it isn't true or false.

Being independent of verification does not necessarily make something not true or meaningful. What is verified can be true independent of the act of verification, but can only be known to exist if verified.

This opens us up to mysticism suggested at the end of Wittgenstein's Tractatus, comaparable to Freud's Oceanic Feeling and Schopenhauer's platonic forms
.
6.44 Not how the world is, is the mystical,but that it is.
6.45 The contemplation of the world sub species aeterni is its contemplation as a limited whole.
The feeling of the world as a limited whole is the mystical feeling.