Law of excluded middle

[brimstoneSalad]

In the "reality"? Yeah, we do this all the time. The classical logic is just another tool to talk precisely (as much as possible at least...) about things around us, so one shouldn't get too attached to it, especially when it ceases to be that useful.

Don't you think its more useful to have one broad system that can explain all things rather than two disconnected ones that can only explain things in their domain (e.g. quantum physics and relativity)?

It's more accurate, better all around in terms of understanding, but sometimes it's more computationally intense so simplified systems (which are wrong but give results that work for crude purposes) can be better in practice.

Kind of how you can usually use a flat-head screwdriver to unscrew a cross-head screw. If it basically works for your purposes that's what matters in practical applications.

But in terms of philosophy, it's still wrong: we want real accuracy, any deviation from the truth is a failure.
That's why none of these special paraconsistent etc. "logics" (which are built to deal easily with things like crude models of mental contradictions) are valid for our purposes. They don't represent an accurate reality, just a useful system to deal with crude models.

@brimstoneSalad, why do you stop at classical logic if you can go broader?

I suppose you would if you could. But if you go "broader" into something like dialetheism the system breaks down; you can't go broader by allowing contradictions, the whole thing collapses.

[Cirion Spellbinder]

Kind of how you can usually use a flat-head screwdriver to unscrew a cross-head screw. If it basically works for your purposes that's what matters in practical applications.

That's a way better example than I could think of. My first thought was Taylor polynomials.

I suppose you would if you could. But if you go "broader" into something like dialetheism the system breaks down; you can't go broader by allowing contradictions, the whole thing collapses.

Do all broaders systems tend towards dialetheism? And in any case, isn't that more of a practical concern? If humans and human language are "too dumb" to make sense of dialetheism, could it not still be a more precise language for reality given a "more intelligent" speaker if it is broader?

[brimstoneSalad]

Do all broaders systems tend towards dialetheism?

Well, classical logic has very few core rules; you'd have to change one or more to try to make something broader.

Like removing the law of non-contradiction (which is what dialetheism claims to do). It's completely absurd, though, and provides no means to distinguish between truth and falsehood. It fails on every level.

And in any case, isn't that more of a practical concern? If humans and human language are "too dumb" to make sense of dialetheism, could it not still be a more precise language for reality given a "more intelligent" speaker if it is broader?

No.

[Cirion Spellbinder]

Well, classical logic has very few core rules; you'd have to change one or more to try to make something broader.

But that does not mean I could not do it.

And in any case, isn't that more of a practical concern? If humans and human language are "too dumb" to make sense of dialetheism, could it not still be a more precise language for reality given a "more intelligent" speaker if it is broader?

No.

I know its an outlandish and presumptuous question, so sorry, but why?

[brimstoneSalad]

But that does not mean I could not do it.

Doesn't mean you can either. It's very very unlikely that you would be able to; very intelligent people have been trying for thousands of years.

You can surely remove a leg from a four legged chair and reconfigure things, but can you remove a leg from a three legged chair and still get something that can stand on its own?
Or going a bit deeper into physics, we could talk about Earnshaw's theorem.

There are certain minimum requirements for stability.

I know its an outlandish and presumptuous question, so sorry, but why?

The rules necessary to make it work have never been proposed. There's not even something on the table there.
Dialetheism as it is, is not a system, it's a "what if we removed this" with no contending with the actual consequences of doing that.

[Cirion Spellbinder]

You can surely remove a leg from a four legged chair and reconfigure things, but can you remove a leg from a three legged chair and still get something that can stand on its own?
Or going a bit deeper into physics, we could talk about Earnshaw's theorem.

Why would adding truth values be analogous to removing a leg?

[brimstoneSalad]

You can surely remove a leg from a four legged chair and reconfigure things, but can you remove a leg from a three legged chair and still get something that can stand on its own?
Or going a bit deeper into physics, we could talk about Earnshaw's theorem.

Why would adding truth values be analogous to removing a leg?

Adding contradiction as a valid state of truth destabilizes logic.

[Cirion Spellbinder]

Adding contradiction as a valid state of truth destabilizes logic.

Wouldn't it be better to say that it makes it useless for describing the real world? I would hesitate to call anything that is consistent unstable.

[brimstoneSalad]

Adding contradiction as a valid state of truth destabilizes logic.

Wouldn't it be better to say that it makes it useless for describing the real world? I would hesitate to call anything that is consistent unstable.

It isn't consistent, since it violates non-contradiction. Everything is true and everything is false. If you want to call that consistent by another definition (of sameness) sure, but it also has no reliable output. That makes it essentially a non-system. It can not differentiate truth from falsity, validity from invalidity.

[mkm]

Is that a problem?

It's not classical anymore. It becomes a problem if one wants to formulate everything in classical logic and keep the correspondence with the reality.

Don't you think its more useful to have one broad system that can explain all things rather than two disconnected ones that can only explain things in their domain (e.g. quantum physics and relativity)?

Sure, but the reality trumps our wants every time. I would rather have two disconnected which are useful in their domains, rather than one, which is only partially ok.

Why is it a problem? And if it is, what is wrong with Aristotle's solution? Also I'm going to harass @brimstoneSalad because I know he is also familiar with physics and may have an interesting solution.

Aristotle's solution is basically intruducing modal logic. Nonclassical.

I suspect that you can't prove that either. I'm inclined to favor the proposition that you can, as I can't see any sense in living a life without being able to deduce things. That seems like absolute insanity and how could I even reach such a conclusion without deduction?

Any attempt of proof would be circular at best, so it doesn't really make sense. Anyway, you misunderstood me. I don't say we should abandon logic (any) altogether. I say we should be aware that there is no one and only "true" formal system in which we should formulate our thoughts.