I believe Aristotle’s logic (with the “Law of Excluded Middle”, which is designed to disallow contradiction) is not above G-d.
Beliefs that are contradictory via Aristotle’s logic may still be compatible. What holds primacy?
Oh logic is still relevant in quantum physics. It just gets more complicated.
But at the root of mathematics itself is a built-in paradox that can’t be resolved by math
The set of all complete sets contains all the sets of the incomplete sets which makes the complete set incomplete while also complete.
This is my poor rendition of Set theory.
Anyway, the fact that theoretical physics is primarily built upon mathematics, and mathematics has a paradox at the root of it, it means mathematics will necessarily be incomplete.
At the same time, it is an excellent tool for mapping reality. Once you overlook the core paradox, logic is employed widely: otherwise the math couldn’t work at all.
Theoretical physics allows them to do temporarily “unlikely” things like borrowing from anti-time. These aren’t reflections of reality though: they’re mathematical ‘tricks’ used to get them over stumbling blocks in hopes to find deeper truths.
But logic is still relevant: it’s just more flexible there.
Axiom + proof gets to an even deeper level of the “problem” with Aristotle style logic.
“a statement or proposition that is regarded as being established, accepted, or self-evidently true”
Proofs are built upon axioms, and the proofs can lead to other axioms.
But what if you want to get deeper than the first axioms?
What if you don’t believe it’s “self-evident”? Then.. the whole system can be made to fall apart.
it works so we use it and it’s a good thing. I just like noticing the “failure points” of systems.
Here is an illustration of why I brought up Set Theory: It’s usually considered the “most inclusive math”. It comes out of logic.
I don’t believe that logic “as we have mapped it” contains all of what’s in our mind though.
There are other systems other than logic. I prefer metaphors/analogies. They’re not as strict as logic and don’t conform well to mathematics but they are very effective.
I have friends who are logicians. For them, at the root of all things is logic. They understand very complicated logics, such as the Vedic logic, many valued logic.
But yes, I agree. There is a higher beyond.. I think it’s marvelous that they have found system that works for them and yet I also feel sad for them because they’re missing that “something more” that seems just out of reach. I use the word “agnostic” to describe myself because “I don’t know”. But that’s not entirely true: I *do* understand in part but I don’t know how to explain, so I have to default to “I don’t know”.
We can explain singularities “in part” – whether by logic or by words or by drawings or even music. There’s ways to express understanding up to a point.
We have have bounded them by a name: singularity.
Yet, by their nature a singularity is truly unique: it is single. One. There is no “other” to compare it to, not completely.
So, logic will fail to describe a singularity.
We can use analogies and metaphors to come “close” to describing a singularity but we’ll always be a little shy of complete comprehension.
You’re welcome. I find the deeper I dig, the more there is. When I “zoom out” to see the ‘big picture” I see the tapestry is even larger than I could imagine and I’m a part of it. In the end, I’m just glad to be here to be a part of it all. Truly amazing to be here at all.