Is Logic valid? How might we test it? In very general terms, there are only two possible ways:
1) Logically:
This one would be circular, hence "invalid"
-or-
2) Illogically / alogically:
This one is wrong from the start
So, Logic cannot be proven to be valid.
Therefore: Logic is either:
A) Worthless
(Any idea is as good as any other)
-or-
B) Primordial
(The self-existent source for all proofs)
If it can't be "proven" then it can't be constructed either:
These two are kind of the same thing in this abstract context.
If you can't construct a proof for a concept, then you
can't construct the concept either -- for the same reason:
The necessary parts are missing.
However:
If anything at all exists (and we know that we, ourselves, exist),
Then (even if we ourselves were caused, or constructed from
something else) we still know that there must be something, somewhere, which
is primordial:
One such thing must exist, and, if logic exists, it must be this sort of thing. But, if logic doesn't exist, there is no point in having any kind of "logical" argument or discussion.
So:
If we are to continue (with this argument or discussion),
Then we must conclude that logic:
1) Exists
-and-
2) Is primordial (exists by its own self-state-of-being)
From logic, we can construct all of math:
Informal (short-cut) Proof:
Computers can be constructed completely from logic gates.
(In principle, any computer could be constructed using nothing
but combinations of 2-input NAND gates)
Therefore: Anything a computer does can be done with logic alone.
This includes anything which is mathematical.
Very lengthy formal proof: is provided by Alfred North Whitehead and Bertrand Russell: See Here
In fact, it is frequently claimed (privately, in scientific circles) that the actual "physical particles" themselves don't really need to exist at all; the math alone is all that is really necessary.
Very Informal "Proof: This Wikipedia Article starts with early graphical representations of "reality," but quickly lapses into very abstract mathematics (alone), for which no one has any idea how to construct any kind of "physical" or "graphical" model. Schrödinger's cat and the Bell experiment take it completely past any possible "physical" modeling.
However: This path has led scientists to an ontological morass.
Extremely Informal Proof: You can observe both this thesis and its consequence, for yourself by doing a computer search on: "Quantum mechanics is the basis of physical reality." This search turns up an endless list of very intelligent people who appear to agree that "the source of reality" does not make any kind of sense with which a normal person could possibly agree.
So, what is the "ultimate source of reality?"It's actually reasonably simple: We're all looking at the wrong end of the causality chain.
Let's go back to where we started:
We must conclude that logic:
1) Exists
-and-
2) Is primordial (exists by its own self-ability)
Conclusion: "Logic" (Plato's/Aristotle's "logos") appears to be more than just an abstract synonym for "God" (John 1:1). The two entities appear to share the same roles: All things were "created" by "logic" and "exist" by "logic" (John 1:3, Colossians 1:16,17).
Consequences: Any person who attempts to explain the "logical" workings of the universe is, in reality, attempting to explain the "workings" of the "mind" of God (which is also working in combination with the individual minds of His various creatures -- particularly those who were, "created in His image"). This combination won't necessarily follow any one individual's predictions. And, as we might have expected, the strangest behavior happens whenever an individual's personal choices are directly involved in the experiments.
Corollary: If "God" is both the primordial "Logic" and "the creator," then there can be only one such entity; because if there were two of them, there would also need to be a "context" in which the two could interact, and "that context" would require a third "creator" ... ad infinitum.
Click here for a different argument reaching a similar conclusion