You're right, but I disagree with your argument that: "the 'laws of logic' are universal axioms that would not change." Axioms are not universal and have been modified or discarded throughout the progression of mathematics [0],[1],[2]. I suppose one could argue that their definition wouldn't change and whether or not one chooses to accept an axiom or not is left to the individual, though.
> You're right, but I disagree with your argument that: "the 'laws of logic' are universal axioms that would not change." Axioms are not universal and have been modified or discarded throughout the progression of mathematics [0],[1],[2]
I love that you point this out here. One of the interesting things is that even still today, as we speak, axioms and their utility are being debated. This stems from the second part of your reply:
> I suppose one could argue...
This is the fundamental reason I do not adhere to axiomatic systems in general. One could always argue any point, and so axioms from the get-go are "self-defeating". Fortunately with ibGib's logic, "self-defeating" is more equivalent to "in some given environment, some statement is not fit enough to survive." So any statement in environment X could conceivably be fit to survive in environment Y.
Both yes and no (and others). That fact that "one could always argue..." exists (as I mention in another comment), gives us the ability to say "no". And we could digress ad nauseam with these kinds meta-statements. It comes down to the economics of your decision whether or not to continue attending any given statement. That said, here is my reasoning for shying away from the given acceptance of Mathematics and axiomatic systems in general (bear in mind I used to be a math dude...800 math SAT, 36 math ACT, 5th place in state math tourney (1st place team), 0 days of homework)
Consider the wikipedia definition of axiom:
> An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Greek axíōma (ἀξίωμα) 'that which is thought worthy or fit' or 'that which commends itself as evident.'
With that in mind, consider this: Once I recognize that I have produced a false statement (made a mistake), then thereafter I have a non-zero probability that any statement I make is also false. This includes any statements that I make that make other statements, i.e. systems. So any axiomatic system, wherein there is at least one statement that is "taken to be true", is built on a foundation of hubris - right from the start.
So I personally have been on a long journey, where presently I am now working on the ibGib library which turns state into Goedelian numbers (content-addressable hashes of merkle trees/forests), essentially black-boxing "things" into a universe-sized fundamentally interconnected nodal network.
I love that you point this out here. One of the interesting things is that even still today, as we speak, axioms and their utility are being debated. This stems from the second part of your reply:
> I suppose one could argue...
This is the fundamental reason I do not adhere to axiomatic systems in general. One could always argue any point, and so axioms from the get-go are "self-defeating". Fortunately with ibGib's logic, "self-defeating" is more equivalent to "in some given environment, some statement is not fit enough to survive." So any statement in environment X could conceivably be fit to survive in environment Y.