Law of excluded middle

[carnap]

What does it mean to disprove something in many valued logic then? I have only ever heard it with respect to proving a contradiction.

In most cases you could just prove the negation of the statement and so long as the logic is consistent then you know you cannot prove the original statement. If the logic is complete you could show that the statement is false semantically and then you'd know via completeness that its not provable. It just depends on the details of the logic.

What about modal logic in addition to classical logic instead?

Instead of what? Modal logic is an extension to classical logic. Though you can define a modal constructive logic as well.

Do you think it is provable and if so, why, and do you think genetic modification can change that?

I'm not sure what you're asking here. Is what provable?

[Cirion Spellbinder]

Instead of what? Modal logic is an extension to classical logic. Though you can define a modal constructive logic as well.

Classical logic on its own.

I'm not sure what you're asking here. Is what provable?

Is it provable that there is a limit to human reason and the logic it can employ?

[carnap]

If it is said that humans have moral value because of "reason™", and "reason™" is defined as an arbitrary standard of specifically human thought process, all you're really doing is begging the question.

There is nothing arbitrary about defining reasoning in relation to the way humans solve abstract problems. But I imagine many people that believe the moral premise you're citing would have a more platonic view of "reason" but I don't think that would be essential.

You need emotion to motivate reasoning (as it's needed to motivate any behavior), but reason as a tool works without emotion influencing its process.

As a tool where? A platonic form? If we are talking about how humans think, that is, how the brain works....then there is no way to detach emotion from our thinking. There is no way to turn-off the emotional centers of the brain while you think in some rational ideal.

Also emotion is critical for decision making not just motivation.

So?
You can use reason without perfect information. Statistics is based on that; we can understand the probability of X observation being by chance, we can also reason based on induction without other information as long as we understand its limits.

Statistics and probability are mathematical theories and both don't deal with imperfect information as a whole. To even think about probabilities you need to first define a sample space, a probability distribution, etc. In contrast when thinking about the real world in real time we deal with concepts that are themselves very fuzzy and poorly conceived and reason from them.

Formal tools like probability theory, logic, etc are great but they don't represent how we actually reason and ultimately make decisions. Now you can uphold some formal theory, for example a natural deduction calculus for classical logic, as what reasoning should be.....what we should be trying to do. But the selection would be arbitrary unless you can explain why the chosen system has some sort of metaphysical significance over the others.

They have some meaning in English. Nitpicking this isn't useful unless you're going to say something substantive to contradict my explanations.

The meaning of the terms in natural language are irrelevant, we are talking about mathematics and the notion needs to be rigorously defined mathematically.

[carnap]

Classical logic on its own.

Still not sure what you're asking on this.

Is it provable that there is a limit to human reason and the logic it can employ?

I think this question is rather loaded. When we talk about limits to "human reasoning" we could mean a variety of things. Firstly since humans can follow syntactical rules they can implement any logically system so in that sense there is no limit. But there is a limitation to what we can hope to reason about, for example, first-order classical logic is undecidable which means that there is no finite procedure that can tell you whether some statement is provable or not. But even if the logic is decidable that doesn't mean we can efficiently reason with it. For example I could write an algorithm that can find proofs in propositional logic dramatically faster than you can, not only that, you'll likely never figure out some of the proofs that the algorithm can readily find.

But its not just about reasoning, its about what we can conceive. For example, while we can model 4 dimensional spaces mathematically we cannot conceive of them and that is very likely to limit discovery.

[mkm]

@brimstoneSalad

Your question/statement lacks the necessary precision.

X must be: spin up in one universe (we'll call it the "up" universe) and spin down in another universe (we'll call it the "down" universe).

If you can be more precise, E.g. What's the truth value of "upon the measurement IN THE UP UNIVERSE the electron's spin along the certain angle will be X"?
That's easy to answer. It's tautological, even.

So, going back to the "tomorrow will be a sea battle", would you consider the "in some possible universes yes, and in some no" the answer in classical logic? I don't, maybe we have different notions of the classical logic.
Anyway, I think you just dodged my question. It doesn't lack precision, you just can't answer it in the classical logic and you reformulate the problem in something that looks like semantics of possible worlds, i.e. modal logic. It just proves my point. All in all, upon measurement you will have some realization, you can't just say what it will be before.

@Cirion Spellbinder

Is the problem with the law of excluded middle evaluable in a tripartite system?

What does it mean? It doesn't hold in three-value logic, and holds in classical.

Can you prove things in arithmetic from things not relying on or being arithmetic?

What that would even mean? Proving things in the arithmetic without the arithmetic? You may work in extensions of the arithemtic and there prove things about arithmetic.

Ah, okay. I see the problem now. Is modal logic more than two valued?

Why don't you just check Wiki what is it about?

I don't think this means that logic cannot describe these things afterwards, given that induction works.

Yeah, but induction is sketchy. You may assume it, but still.

It is my understanding that circular arguments go somewhat like A→B, B→C, C→A to substantiate A, whereas I am proposing to substantiate An because [...]An-3→An-2→An-1→An.

I don't how it would work. Everytime someone is asking you "why?" you just expand your language in a way to justify the thing. If your chain of languages doesn't stabilize you gonna have unjustified things anyway, since formulas are finite.

A better rule is no arbitrary rules but this one are permitted. If we want any coherence, we need to permit the least amount of assumptions which we only value because we believe these assumptions will permit the most order. That is of course an arbitrary interest by an arbitrary organism with many other arbitrary characteristics, but concessions must be made for the first premises.

Tha's economic approach, reasonable, but doesn't follow from logic. Therefore arbitrary

And if nothing is wrong with arbitrariness, I'm sure you'd be willing to arbitrarily concede to use classical logic?

Nothing wrong in the sense that you won't get away without it. It doesn't mean that I will accept any assumption you want. For myself I'm the one to pick and choose

[brimstoneSalad]

If it is said that humans have moral value because of "reason™", and "reason™" is defined as an arbitrary standard of specifically human thought process, all you're really doing is begging the question.

There is nothing arbitrary about defining reasoning in relation to the way humans solve abstract problems.

What do you think "solve" means?

If you just think it means that the person is subjectively satisfied with the answer and is no longer compelled to think about it then that wouldn't be relevant to objective morality/moral realism.

But I imagine many people that believe the moral premise you're citing would have a more platonic view of "reason"

Yes.

but I don't think that would be essential.

As I explained above, it is quite essential.

If you regard "the Bible tells us everything we need to know" as a solution to all existential and moral problems, does that make it a valid solution?
It hinges on your notion of what a solution is. If it's something objective, then this notion you've presented of emotionally loaded human reason is very much arbitrary.

As a tool where? A platonic form?

You can call it that if you want. Much like mathematical notions, like pi.

Notions of platonic ideals for things like "dogs" are incoherent, but that doesn't mean there isn't any concept with an ideal.

If we are talking about how humans think, that is, how the brain works....then there is no way to detach emotion from our thinking. There is no way to turn-off the emotional centers of the brain while you think in some rational ideal.

Of course there is: convert it to symbols and do it on paper instead to get it away from those emotional biases that corrupt your reasoning.

Also emotion is critical for decision making not just motivation.

I have no idea how you have come to the conclusion that those are different things.

Are decisions unmotivated?
We weigh decisions based on our motivations.

Reason is used to know what's what, not necessarily to compel action on its own. Questions of binding force of morality are interesting, but not necessary to answer. A student of mathematics doesn't need to be compelled to always answer "4" to the question of "what is 2+2?" in order for 4 to remain the correct answer.

In contrast when thinking about the real world in real time we deal with concepts that are themselves very fuzzy and poorly conceived and reason from them.

That's fine if you're doing that provisionally for survival in situations your intuitive induction adapted you to; making lucky guesses is important. The problem is assuming this messy process is equivalent to actual truth or Reason with a capital R.

Now you can uphold some formal theory, for example a natural deduction calculus for classical logic, as what reasoning should be.....what we should be trying to do.

Which is what I said.

But the selection would be arbitrary unless you can explain why the chosen system has some sort of metaphysical significance over the others.

And I did.

But even if you don't, starting with the premise of classical logic isn't a hard sell. It's also a forum rule, because we don't want to have to endlessly justify the validity of logic in every thread. So, if nothing else: it's because that's what we do here.

The meaning of the terms in natural language are irrelevant, we are talking about mathematics and the notion needs to be rigorously defined mathematically.

I think I gave a pretty rigorous definition. If validity = 1 and invalidity = 0, then the OR operator in computer logic gates is a pretty self explanatory way of bridging multiple systems.
If you're confused about what I said, I'll try to clarify but you'll have to explain what you didn't understand in a way that isn't suffering from the same problems of the ambiguity you accuse me of.

[brimstoneSalad]

So, going back to the "tomorrow will be a sea battle", would you consider the "in some possible universes yes, and in some no" the answer in classical logic? I don't, maybe we have different notions of the classical logic.

"Tomorrow will be a sea battle" is simply false as a SET of claims because it's loaded with incorrect metaphysical claims about determinism. It has nothing to do with the "sea battle" part and it doesn't mean that tomorrow will not be a sea battle.

The claim "Tomorrow will be a sea battle" is also the claim that there is a single universe in which future claims are absolute (loaded into "tomorrow will be"), which is the part that is false, so "tomorrow will not be a sea battle" is no more true.

It's a SET of statements.

Like this: Santa wears pants. This is a set of implicit statements: {Santa exists. He wears Pants. and more...}
Saying that is false in a logical sense as a SET which contains at least ONE false claim is not a claim of negation for any arbitrary one of the premises while leaving the others in-tact. "Santa wears pants" being false should not imply that Santa exists but doesn't wear pants, it could also mean that Santa does not exist but does wear pants (in the stories), or that he does neither of those things.

The bottom line is lack of precision: you need to break down your claims into EVERYTHING they're suggesting, then those claims can be evaluated one by one. If you evaluate them as a set you have to say it's false if it contains one false claim, and then due to ambiguity in English that falsehood may be incorrectly attributed to a specific part of the claim.

English semantics are loaded with many implicit premises. If any ONE of those is false, then the set is not true.

Does that answer the question better?

Obviously you can form any number of incoherent statements in English, like "this sentence is a lie"; that doesn't invalidate classical logic, it shows that English is not rigorously consistent or metaphysically accurate.

Anyway, I think you just dodged my question. It doesn't lack precision,

It does lack precision. Hopefully the above answers more clearly. You need to break down the statement and be specific about what you're asking.

you just can't answer it in the classical logic and you reformulate the problem in something that looks like semantics of possible worlds, i.e. modal logic.

No, the question contained implicit metaphysical claims that were false.

It just proves my point. All in all, upon measurement you will have some realization, you can't just say what it will be before.

Now I think you're just begging the question.

[Cirion Spellbinder]

Still not sure what you're asking on this.

Don't worry about, I don't actually know either.

But even if the logic is decidable that doesn't mean we can efficiently reason with it. For example I could write an algorithm that can find proofs in propositional logic dramatically faster than you can, not only that, you'll likely never figure out some of the proofs that the algorithm can readily find.

But you would agree that efficiency of reasoning does not equal ability of reasoning, right? A child who takes a few minutes to understands syllogisms could know them just as well as an adult that can process them quickly.

But its not just about reasoning, its about what we can conceive. For example, while we can model 4 dimensional spaces mathematically we cannot conceive of them and that is very likely to limit discovery.

That's true. Hopefully computers can solve that for us.

[Cirion Spellbinder]

Yeah, but induction is sketchy. You may assume it, but still.

I'm willing to make practical concessions to be able to reason about the real world. Induction is sketchy, but we don't have a full picture yet.

I don't how it would work. Everytime someone is asking you "why?" you just expand your language in a way to justify the thing. If your chain of languages doesn't stabilize you gonna have unjustified things anyway, since formulas are finite.

What does it mean that formulas must be finite?

Tha's economic approach, reasonable, but doesn't follow from logic. Therefore arbitrary

I've already acknowledged that the first premises are arbitrary, but it is rational to minimize arbitrariness if I want to be able to have meaningful views and maximize coherence.

Nothing wrong in the sense that you won't get away without it. It doesn't mean that I will accept any assumption you want. For myself I'm the one to pick and choose

Do you agree that introducing more arbitrary things detracts from order? Given that you can see the flaws of induction, I'd have to image you'd prefer an ordered world. If you act rationally with this interest, you will attempt to minimize the amount of assumptions you need to make to the greatest extent to which you are still able to describe reality. If you don't care about being able to understand as efficiently as you can, then sure, make arbitrary assumptions which will not help you in any way, but you can't say that you want to have meaningful opinions on anything (unless we have supposed it as a premise ).

[Cirion Spellbinder]

The rest of what I've said to you I can research on my own, like you've pointed it out, since you hate me so

Yeah, but induction is sketchy. You may assume it, but still.

I'm willing to make practical concessions to be able to reason about the real world. Induction is sketchy, but we don't have a full picture yet.

I don't how it would work. Everytime someone is asking you "why?" you just expand your language in a way to justify the thing. If your chain of languages doesn't stabilize you gonna have unjustified things anyway, since formulas are finite.

What does it mean that formulas must be finite?

Tha's economic approach, reasonable, but doesn't follow from logic. Therefore arbitrary

I've already acknowledged that the first premises are arbitrary, but it is rational to minimize arbitrariness if I want to be able to have meaningful views and maximize coherence.

Nothing wrong in the sense that you won't get away without it. It doesn't mean that I will accept any assumption you want. For myself I'm the one to pick and choose

Do you agree that introducing more arbitrary things detracts from order? Given that you can see the flaws of induction, I'd have to image you'd prefer an ordered world. If you act rationally with this interest, you will attempt to minimize the amount of assumptions you need to make to the greatest extent to which you are still able to describe reality. If you don't care about being able to understand as efficiently as you can, then sure, make arbitrary assumptions which will not help you in any way, but you can't say that you want to have meaningful opinions on anything (unless we have supposed it as a premise ).