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But what is second-order rules of discourse? — Lionino

The examples I gave were:

Even in English when we say, "If you make that claim you will be contradicting yourself," we are shifting between two different registers: first-order claims and second-order rules of discourse (i.e. Thou shalt not contradict thyself). — Leontiskos

Note, though, that, "You are contradicting yourself," or, "This is a contradiction," is a different genus, and deviates from first-order discourse, moving into the meta-language. — Leontiskos

So an example of a second-order rule of discourse is, "Thou shalt not contradict thyself."

To which the dialetheist may simply say "so much for Aristotle". — Banno

I would suggest actually reading Metaphysics IV.

It's been a while. If there were something in it that addressed the issue, I'm sure you would be able to tell me about it.

I am thinking of what SEP calls, "Aristotle’s Challenge to the Opponent to Signify Some One Thing."

More:

The Aristotelian can counter that without those qualifications the dialetheist has not said anything meaningful at all. — SEP | 11. Dialetheism, Paraconsistency, and Aristotle

"If X, then Y" is incorrect.
"If X, Y" or "X, therefore Y", not both. — Lionino

"If you go, then I will go" is not okay grammatically. — Lionino

"If X then Y" is incorrect because you think "If you go, then I will go" is not grammatical?

Why would an ordinary sentence form be incorrect? Every time someone says "If ___ then ___" they are incorrect?

And "If you go, then I will go" is missing a period. But otherwise it seems fine to me.

"If X, Y" or "X, therefore Y", not both. — Lionino

I don't know what you mean to say there.

I don't think there are laws of logic that cannot be broken — Lionino

What do you mean by not being able to "break"?
— TonesInDeepFreeze

There being cases in which a law does not apply. — Lionino

What do you mean by "apply"?

And do you mean there are cases in which no law applies? Or do you mean that, for any law, there are cases in which that law does not apply?

What are some laws and cases you have in mind?

there are laws of thought that can't be broken (for obvious reasons). — Lionino

What are some of those laws of thought that can't be broken but are not laws of logic? How do you state the difference between laws of logic and laws of thought? What are the obvious reasons they can't be broken?

Some laws of logic may express those laws of thought. But that is just a semantic contention. — Lionino

What "semantic contention"?

There being cases in which a law does not apply. — Lionino

The most problematic foundational law in logic (Boole's "laws of thought") is in my opinion the law of the excluded middle (LEM), which implicitly assumes that the question at hand is decidable.The indiscriminate use of this law is intuitionistically objectionable:

https://en.m.wikipedia.org/wiki/Constructivism_(philosophy_of_mathematics)

Much constructive mathematics uses intuitionistic logic, which is essentially classical logic without the law of the excluded middle. This law states that, for any proposition, either that proposition is true or its negation is. This is not to say that the law of the excluded middle is denied entirely; special cases of the law will be provable. It is just that the general law is not assumed as an axiom.

The law of identity may also be problematic because of the existence of indiscernible numbers. However, this problem is not frequently mentioned in the literature.

The only foundational law that seems to withstand foundational scrutiny by constructive mathematics, is the law of non-contradiction:

The law of non-contradiction (which states that contradictory statements cannot both be true at the same time) is still valid.

The law is not considered unassailable, though:

https://en.m.wikipedia.org/wiki/Law_of_noncontradiction

The law of non-contradiction is alleged to be neither verifiable nor falsifiable, on the ground that any proof or disproof must use the law itself prior to reaching the conclusion. In other words, in order to verify or falsify the laws of logic one must resort to logic as a weapon, an act that is argued to be self-defeating.

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sentences of the kind "If --, then --" are not grammatically correct. — Lionino

They are grammatically correct in English. Why would you claim otherwise?

Every time someone says "If ___ then ___" they are incorrect?
— TonesInDeepFreeze

Yes, just like when someone says "I am literally dying right now" but they are alive and well. — Lionino

"If ____, then ___" is ordinary grammatical English.

"I am dying now" said when not dying is ordinary grammatical English, but is a false sentence.

"The laws of physics don't apply here", the meaning is clear. You yourself use the word without any apparent confusion:

for any law, there are cases in which that law does not apply
— TonesInDeepFreeze — Lionino

(1) I know the ordinary general sense of 'apply'. But this is a particular subject, and I'm wondering whether you have an explication of your use or whether 'apply' should just be taken as undefined by you. (2) I was asking you about your use of 'apply'; I didn't assert my own use of it. I didn't assert what you quoted of me; it was part of a question to you.

And the question still stands:

And do you mean there are cases in which no law applies? Or do you mean that, for any law, there are cases in which that law does not apply? — TonesInDeepFreeze

But you do say:

for any law, there are cases in which that law does not apply
— TonesInDeepFreeze

This, but one can make up scenarios and/or systems where that law does not apply. That was one of the answers at least to the liar paradox: making a completely different system. — Lionino

What law and system are you referring to?

What are some of those laws of thought that can't be broken but are not laws of logic?
— TonesInDeepFreeze

I don't think there any, as soon as we can express our thoughts in language we can also express the rules our thoughts follow in language (this language being logic sometimes). — Lionino

You said that there are laws of thought that can't be broken. And you said laws of logic can be broken. What are some laws of thought that can't be broken but are not laws of logic?

What are the obvious reasons they can't be broken?
— TonesInDeepFreeze

For example, I can't conceive of anything as being other than it is, because as soon as I conceive it, it is what it is, and not something else. I cannot imagine something as being otherwise. — Lionino

You can't conceive it. But that doesn't entail that others cannot conceive it. Also, conceiving that a contradiction holds does not entail that the contradiction holds.

Yes, the periods are "missing". — Lionino

If we put a period at the end of "If ___ then ___" , then it is a punctuated English sentence. Just as with that sentence itself.

the law of the excluded middle (LEM), which implicitly assumes that the question at hand is decidable. — Tarskian

In context of modern logic, 'decidable' means either (1) the sentence or its negation is a theorem, or (2) There is an algorithm to decide whether the sentence is a member of a given set, such as the set of sentences that are valid, or the set of sentences that are true in a given model.

LEM is not that. LEM syntactically is the theorem: P v ~P, and LEM semantically is the theorem that for a given model M, either P is true in M or P is false in M (so, either P is true in M or ~P is true in M)

The law of identity may also be problematic because of the existence of indiscernible numbers. — Tarskian

The law of identity, the indiscernibility of identicals, and the identity of indiscernibles are different. What specific problem with the law of identity are you referring to?

The only foundational law that seems to withstand foundational scrutiny by constructive mathematics, is the law of non-contradiction: — Tarskian

You think that the only law that constructivism allows is non-contradiction? You've gone through all other laws and found that they are not constructivisitically acceptable?

Some laws of logic may express those laws of thought. But that is just a semantic contention.
— Lionino

What "semantic contention"? — TonesInDeepFreeze

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If — then — is only used in math/logic because it is clearer to look at than If —, —. — Lionino

It's not used only in logic and mathematics. In everyday discourse, people write "If ___, then" commonly. The source you cited mentioned mentions "If ___, ___" only but I would not take that to preclude also "If ___, then". Are there grammarians who explicitly disallow it? Are there not grammarians who do allow it? Perhaps there are grammarians explicitly disallow "If ___, then ___", but that would be pedantic, especially in this context, in face of the fact that "If ___, then ___" is not only used in everyday discourse, but in all kinds of writing. Moreover, since it is taken as grammatical in logic and mathematics, then that's good enough here, since logic is the subject. I don't know what point you are making about logic when you rule out "If ___, then ___".

That is why I said "I am literally dying now" instead of "I am dying now". It is an incorrect usage of the word 'literally' if you are not really dying, therefore grammatically incorrect. — Lionino

As far as I can tell, it is grammatical. 'literally' is an adjective to the noun 'dying'. But the sentence is false. "I am hopelessly dying", "I am unhappily dying", "I am literally dying". Grammatical as far as I know.

their usage of the word is often just grammatically incorrect. — Lionino

What rule of grammar is violated. I wouldn't take using a word with an incorrect meaning is not a violation of grammar. If someone thought 'choleric' means 'melancholic', then "Jack is choleric" is still grammatical even though Jack is not choleric.

not lying or confused about their health — Lionino

Yes, they are not lying or confused about their health. They simply mispoke while still grammatical.

"I am literally dying now" may be true or it may be false. But in either case, it is grammatical.

Dialetheism and the denial of LNC — Lionino

I would need to re-read that article, but, as I recall, dialetheism is a philosophy not a system. Though, as you mention, there are paraconsistent systems. Yes, that is an example. But, for any for any law of thought there may be a system that denies the law, so any law of thought could be denied.

If your point is that one is free to choose any system one wants to use, then, of course, one could not dispute that. But also one is free to choose whatever ways of thinking one wants to choose.

The laws of thought are facts of the matter. Whatever they are, without them human rationality is not possible — otherwise they wouldn't be laws. — Lionino

That something is necessary for rationality (under a given definition of 'rationality') doesn't entail that people may not break "laws of thought".

Can you conceive something as other than what it is? — Lionino

Whether or not I can conceive it doesn't entail that others cannot. It is not precluded that, for example, people in mystic states do experience suspension of non-contradiction. And it does not dialetheism permit conceiving such things?

You said, "Some laws of logic may express those laws of thought. But that is just a semantic contention."

Now:

Leontiskos said laws of logic can't be broken. I said that it is the laws of thought that can't be broken instead. Despite the disagreement in choice of words, I still understand the content of his post. — Lionino

I guess 'that' referred to the difference in the way you two stated the idea. Okay.

/

I asked, "Do you mean there are cases in which no law applies? Or do you mean that, for any law, there are cases in which that law does not apply?"

I surmise you mean the latter.

.

For example, I can't conceive of anything as being other than it is, because as soon as I conceive it, it is what it is, and not something else. I cannot imagine something as being otherwise. This reminds of the law of identity, and it just might be. — Lionino

This is very close to the way that Aristotle defends the PNC in Metaphysics IV. Much of this is just a question of what we mean by 'logic'.

n context of modern logic, 'decidable' means either (1) the sentence or its negation is a theorem, or (2) There is an algorithm to decide whether the sentence is a member of a given set, such as the set of sentences that are valid, or the set of sentences that are true in a given model.

LEM is not that. LEM syntactically is the theorem: P v ~P, and LEM semantically is the theorem that for a given model M, either P is true in M or P is false in M (so, either P is true in M or ~P is true in M) — TonesInDeepFreeze

"the sentence or its negation is a theorem" ignores the existence of true but unprovable sentences. So, it should rather be "the sentence or its negation is true". They don't need to be provable theorems.

I do not see the difference between "the sentence or its negation is true" and "P v ~P".

The law of identity, the indiscernibility of identicals, and the identity of indiscernibles are different. What specific problem with the law of identity are you referring to? — TonesInDeepFreeze

I was referring to the identity of indiscernibles: ∀x ∀y [ ∀F ( F x ↔ F y ) → x = y ]
For any x and y, if x and y have all the same properties, then x is identical to y.

You think that the only law that constructivism allows is non-contradiction? You've gone through all other laws and found that they are not constructivisitically acceptable? — TonesInDeepFreeze

I was referring to Boole's laws of thought:

- the law of identity (ID)
- the law of contradiction (or non-contradiction; NC)
- the law of excluded middle (EM)

https://en.wikipedia.org/wiki/Law_of_thought

The title of George Boole's 1854 treatise on logic, An Investigation on the Laws of Thought, indicates an alternate path. The laws are now incorporated into an algebraic representation of his "laws of the mind", honed over the years into modern Boolean algebra.

Boole did not "invent" these foundational laws but he did systematize them somewhat.

"the sentence or its negation is a theorem" ignores the existence of true but unprovable sentences. So, it should rather be "the sentence or its negation is true". They don't need to be provable theorems. — Tarskian

I'm just telling you what the definition is. It doesn't matter what you think "should" be or what "needs" to be.

I do not see the difference between "the sentence or its negation is true" and "P v ~P". — Tarskian

The definition of 'decidable' is not "the sentence or its negation is true".

I was referring to the identity of indiscernibles — Tarskian

And that is not the law of identity. And it doesn't bear on the law of identity the way you claimed it does.

You think that the only law that constructivism allows is non-contradiction? You've gone through all other laws and found that they are not constructivisitically acceptable?
— TonesInDeepFreeze

I was referring to Boole's laws of thought:

- the law of identity (ID)
- the law of contradiction (or non-contradiction; NC)
- the law of excluded middle (EM) — Tarskian

And constructivism uses the law of identity, so it is not the case that the only one of those three laws allowed by constructivism is non-contradiction.

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And constructivism uses the law of identity, so it is not the case that the only one of those three laws allowed by constructivism is non-contradiction.
1h — TonesInDeepFreeze

That is not what I said. Straw man.

The only foundational law that seems to withstand foundational scrutiny by constructive mathematics, is the law of non-contradiction: — Tarskian

The law of identity is allowed by constructivism. It "withstands foundational scrutiny" by constructivism. No strawman.

Using a word to mean something other than what it does is exactly a violation of grammar. — Lionino

"What it does" meaning its syntactical role, yes.

"What it means", no.

If I think 'red' means 'loud' and I say "The trombone is red", then still "The trombone is red" is grammatical even though it is false and false due to the speaker's mistake in the meaning of the word 'red'.

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And constructivism uses the law of identity, so it is not the case that the only one of those three laws allowed by constructivism is non-contradiction.
1h — TonesInDeepFreeze

I didn't write '1h'.