Yakk wrote:Yes, A=C was invented. It didn't exist before humanity thought it up.
The concept of equality was invented. The abstractions that take the world and produce number (and other abstractions) is a human (or other intelligence, possibly sub-human animal) invention. Without that abstraction, A=C has no meaning.
This is gibberish. Just because there isn't an example of somethig in nature doesn't mean the concept is meaningless, and if the concept of equality has meaning then the laws that go with it hold.
Besides which, if we invented
"A=C", then logically we could change
Yes, we can. Odds are the abstraction defined by that would be less useful.
We can change engines and languages and toasters. Improve them. We could make A>C, say. Of course, by substitution that would mean that C>A, but we could invent it so that that's OK. Or invent it so that substitution doesn't work.
That doesn't mean toasters and engines would change. How we talk about them would. Language would change.
I make no guarantee that an arbitrary change in our habits and systems of abstraction and formalization would produce useful
Just like, if you invent a toaster, you could change it. You could remove the plug! ... and leave the rest the same. This new invention would be a pretty damn useless invention, but it doesn't mean that toasters where discovered.
And indeed, we could construct a form of metalogic where all these things are true, as long is it was internally consistent (or held that internal consistency was for girls). But whenever we test it in real life, A does keep coming out as C, doesn't it?
Yes, if we use the same habits and patterns of abstraction, and the same definitions for terms, a different system of formal logic can end up giving nonsense results.
On the other hand, you can create formal logic systems in which you can reason from contradition (ie, A and ~A does not imply false), or in which proof by contradiction isn't valid (Ie, ~~A does not imply A). Both of these varients can talk about the real world in a sensible way.
So from a philosophical point of view, sure, yeah, your point sort of stands. But from an experimental point of view, I think we've amassed enough evidence by now to dispense with all this sillyness and just accept the laws of reason.
I happen to personally find ~~A->A to be a particularly poor law of reason. Once you accept it, you end up with non-demonstrateable existence proofs: logic that prooves "X must exist", yet provides no reason to think that X can be actually found in reality
when you create a physical analogue of the problem.
So no, the laws of reason are not holy and inviolate.
The abstraction of "number" or "counting" happens to be an insanely useful one
. It is the one that underlies "A=B, B=C => A=C".
For example, the Zeroth Law Of Thermodynamics states, essentially, that if T1=T2 and T2=T3 then T1=T3. This is a rule so fundamental it precedes even the First Law of Thermodynamics. And it states that if A=B and B=C then A=C.
So it seems to me that the universe has some ideas about logic without people having to "invent" them.
Yes, Thermodynamics rests on our ability to generate abstractions about the universe.
Did you know that the laws of Thermodynamics are statistical laws? They are laws of large numbers. When you build them from more basic principles, you end up with "X is far more likely by a large extent in reasonably large systems" instead of "X always happens".
This isn't a level of detail that is all that useful, when using thermodynamics on "human" and above scales, simply because X is so insanely more likely to happen it isn't funny.
This doesn't mean that the law of thermodynamics is a bad law: rather, it is a set of laws that apply to an abstraction of the world.
That beautiful ability to abstract, then to manipulate those abstractions, is what provides mankind with it's ability to break down and understand chunks of the universe.