But, if I recall correctly, you said that in general laws of logic can be broken, as you even gave an example of breaking the law of noncontradiction.
— TonesInDeepFreeze

Yes — Lionino

Which brings me back to my point that is sustained:

But if any law of logic may be also a law of thought, then there are laws of thought that may be broken too.
— TonesInDeepFreeze

Instead, if a law of logic can somehow holistically and correctly express a law of thought, that law of logic cannot be broken. If it can, it is not longer a law of thought, as by the definition I gave above.
— Lionino

But, if I recall correctly, you said that in general laws of logic can be broken, as you even gave an example of breaking the law of noncontradiction. Moreover, if there is a single law of logic that can be broken, and that law of logic corresponds with a law of thought, then there is a law of thought that can be broken. Moreover, even that point is not required, since we know that people do break laws of thought. Though, of course, if a certain law of thought is required for rationality then it can't be broken without incurring irrationality. — TonesInDeepFreeze

You would say the first one is grammatically wrong, because 'criteria' is plural. Here is the problem: there are actually some people in the world whose first name is Criteria. — Lionino

I can't believe you stooped to such a sophomoric argument. Obviously, we consider a context in which we at least agree as to the kind of word. Your argument is horrible desperation.

And still it doesn't answer that the "The cat is black" is seen to be grammatical even if the author of the sentence is anonymous, and even if we don't know whether the author is a human being or understands anything about language, as the expression could have been randomly generated and only by luck came out grammatical.

For about the dozenth time:

If you show me "The cat is black" then I will mark it as grammatical, not matter where you got the sentence.

"Rob have a piink horn on his forhead", syntax is fine — Lionino

The syntax is not fine. (1) 'have' should be 'has' (2) 'piink' is not a word (3) 'forhead' is not a word'.

Syntax checks. Are these words? Are the words in an allowed order based on their kind? Are the words in correct case, inflection, etc.

Semantics checks: What are the meanings of the words? What are meanings of the clauses? What is the meaning of the sentence?

Same with formal logic. Syntax cheks: Are these symbols of the language? Do the sequences of symgols form formulas? Are the sequences of formulas allowed as proofs according to the rules?

Semantics with formal logic: To what do the symbols refer? What are the truth values of the sentences based on the meanings of the symbols and subformulas?

"The cat is black" and ask, "is that grammatical?" You don't track down the speaker and find out whether he knows the definitions of 'cat' and 'black'.
— TonesInDeepFreeze

Of course. It doesn't mean however that it was grammatically correct. We assume it is because we assume the speakers know how to use words. — Lionino

No, we don't need to make any such assumption. You're just stipulating that out of thin air.
We might know nothing about who or what wrote an expression.

If I display a sentence on a piece of paper and leave it on the sidewalk, and you pick it up and read it, "The cat is black", then you recognize that as grammatical, no matter whether written by Shakespeare or a random word generating machine or an insane person who thinks 'cat' means 'screwdriver' and 'black' means 'wet'.

Suppose you have a job correcting school assignments, and you are never in the classroom, never met the kids, you just correct the papers. Then you don't know the vocabularies of the kids. You don't know which ones know the correct definitions of the words used. But you can still correct and grade the grammar. If you see, "The car engine is noisome", then you mark the sentence as grammatical, even though you don't know whether the kid knows that 'noisome' means 'noxious' and not 'noisy'.

Really, that is so plain that if you still refuse to understand it, then indeed you defy rationality.

Stick to logic; you [Lionino] seem to know that well — tim wood

He doesn't.

My post there is from 3 hours ago. I was not reiterating anything. — Lionino

You're reiterating your claim as you made it at the start of this round.

So, I'll reiterate:

"Jack is happy" is grammatical even when the speaker misused the word 'happy' while thinking it meant 'doleful'.

We don't have to ask the speaker what he meant to check whether he knows the correct meanings of the words. We just have to look at the sentence to see that it obeys the formation rules for the language.

And, in logic, which I hope was the original context, the usual distinction is between syntax and semantics, and with 'grammar' sometimes mentioned rather than 'syntax'.

Now we're full circle more than three times at least.

You can just click on the arrow to see what post the person is referring to instead of guessing. — Lionino

I'm not talking about guessing what post was quoted. I'm talking about the fact that it is ridiculous to expect a reader to factor in the peculiarities of the formatting of quotes to know whether the emphasis was original or added.

A reader shouldn't have to click back to find out where the bolding came from. It is the responsibility of the quoter - not the reader and not the quotee - to indicate that the emphases were added.

Merriam [emphases added]:

grammar

: the study of the classes of words, their inflections (see inflection sense 2), and their functions and relations in the sentence

: a study of what is to be preferred and what avoided in inflection (see inflection sense 2) and syntax (see syntax sense 1)

: the characteristic system of inflections (see inflection sense 2) and syntax of a language

: a system of rules that defines the grammatical structure of a language

syntax

: the way in which linguistic elements (such as words) are put together to form constituents (such as phrases or clauses)

: the part of grammar dealing with this

/

Nothing there about semantics or meanings. Rather, the structural aspects.

Especially in logic and philosophy of language, usually 'syntax' and 'grammar' are understood together. And semantics is different. Syntax concerns whether an expression is well formed. Semantics concerns the meaning of the expression.

But one of yours [emphases added]:

the whole system and structure of a language or of languages in general, usually taken as consisting of syntax and morphology (including inflections) and sometimes also phonology and semantics. — Lionino

Not that I trust "Google dictionary", but you proffered it. So:

The usual sense of 'grammar' is 'syntax'. But sometimes it includes semantics. So I will award myself the point that usually 'grammar' and 'syntax' are used the same. I will award you the point that sometimes semantics is included. But consider that in logic, usually a sharp distinction is made between syntax and semantics and use of 'grammar' would align with 'syntax' not 'semantics'. The quotes you give do indicate a more extended sense of 'grammar'. I haven't seen that sense in logic or philosophy of language, but if you insist. Meanwhile, you could have easily ascertained that 'syntax' and 'grammar' are commonly used interchangeably but that your context is different.

Oh wait, the Google entry is just the Oxford entry, so as you posted it redundantly, I will too:

The whole system and structure of a language or of languages in general, usually taken as consisting of syntax and morphology (including inflections) and sometimes also phonology and semantics; grammar was one of the seven liberal arts.
— Oxford Reference — Lionino

Whether it was three decades ago or three seconds ago, it is not proper to display someone's quotes with emphases they didn't use unless you indicate that the emphases were added.

When you quote people here, the original italics or bold are lost, so it is of common understanding that, when a quote features those, it is the quoter who has added them for a purpose. — Lionino

What? You don't know how "[emphasis added]" works?

My original did not have bold. You added bold to my quote. When you do that, you should include a note that you added the emphasis. It is not up to the reader nor me to recall the peculiarities of the formatting processes of this site to then reason, "So the bold would have been lost if it were quoted, so if it appears, then it must have been added."

You just need to put in "[emphasis added"].

Everytime you say those well-formed phrases are syntactically correct, I agree. But they are not grammatically correct if the speaker thought/meant something other than what those words actually mean. So I cannot say they are grammatically correct. — Lionino

Now, you're arguing by reiteration of your claim. When it comes full circle like that more than once, rational discussion is diminished.

for any law of thought there may be a system that denies the law, so any law of thought could be denied
— TonesInDeepFreeze

I imagine by 'law of thought' you mean 'law of logic' here? — Lionino

Right, my typo.

By syntactical, I mean grammatical.
— TonesInDeepFreeze — Lionino

When you add emphases (such as bold or italics) to my quotes, you should indicate that the emphases were added.

And it wasn't stated as to what systems may deny, but merely as to what laws may deny.
— TonesInDeepFreeze

Wasn't it? — Lionino

↪Leontiskos I don't think there are laws of logic that cannot be broken, but that there are laws of thought that can't be broken (for obvious reasons). Some laws of logic may express those laws of thought. But that is just a semantic contention. — Lionino

Syntax and grammar are synonymous in some contexts and nearly synonymous in others.

Semantics stands opposed to them.

Look it up.

What is regarded as rational may be different for different people.
— TonesInDeepFreeze

I addressed that before, it is tangential: — Lionino

If people have different concepts of rationality, then they may differ as to what laws of thought they adhere to, thus there are laws of thought that may be broken.

Doesn't matter what the definition is. People may break all kinds of norms of rationality in their thinking.
— TonesInDeepFreeze

Ok, clearly you are operating under a thin definition of rationality, where one even can think irrationality. — Lionino

That is exactly what I am not saying. I am not at all saying that rationality permits irrationality. Rather, I am saying that people may break rationality, thus they may break a given law of thought. I even said that, of course, tautologically, adhering to rationality requires adhering to rationality.

Let's understand instead 'laws of thought' as the necessary conditions/operations for my/human/any rationality. Since they are necessary, they cannot be broken. If a mind does not obey them, that mind is no longer a (my/human) rationality. — Lionino

That's okay. But it is different from saying that the laws of thought cannot be broken. If we consider those laws of thought to be necessary for rationality, then they cannot be broken without incurring irrationality. But they still can be broken.

The way it read was that there are laws of logic that may be broken but not laws of thought.
— TonesInDeepFreeze

Correct.

But if any law of logic may be also a law of thought, then there are laws of thought that may be broken too.
— TonesInDeepFreeze

Instead, if a law of logic can somehow holistically and correctly express a law of thought, that law of logic cannot be broken. If it can, it is not longer a law of thought, as by the definition I gave above. — Lionino

But, if I recall correctly, you said that in general laws of logic can be broken, as you even gave an example of breaking the law of noncontradiction. Moreover, if there is a single law of logic that can be broken, and that law of logic corresponds with a law of thought, then there is a law of thought that can be broken. Moreover, even that point is not required, since we know that people do break laws of thought. Though, of course, if a certain law of thought is required for rationality then it can't be broken without incurring irrationality.

Semantics is part of grammar. — Lionino

It's interesting that you say that. Because it is very wrong.

Semantics concerns the meanings of words. Syntax (grammer) concerns the rules for formation of expressions.

My mistake about 'adjective'; I do know that it is an adverb.

But there's another example:

"'literally' is an adjective" is grammatical, even though false, and even though it is false by dint of the speaker using a word incorrectly.

And I'm merely talking about the fact certain parts of speech are required to be certain positions and in relation with other parts of speech. "Black the is cat beautiful' is not grammatical as the part of speech are not in correct order, but "The black cat is beautiful" is grammatical.

It is not in physics, not in javascript, neither is it in morality, it is in grammar, therefore it is grammatically incorrect. — Lionino

Ah, how conveniently you left out 'semantically'.

It is wrong semantically, as it uses the wrong meanings of the words. It is semantically wrong, but not grammatically wrong.

You keep evading:

"Bob is a splenetic guy" is grammatical even though the speaker misused the word 'splenetic' thinking it means what we mean by 'splendiferous'.

As to teaching English, of course it is needed not only to say that the sentence is false but that it is false because the words don't mean what the speaker thinks they mean. But that still doesn't make "My cat is black" ungrammatical. It is both (1) False and (2) False on account of the wrong words being used. But it is still grammatical.

When we consider whether an utterance is grammatical, we don't first check what the speaker meant by the utterance. We merely look at the words themselves. If I give you this:

"The cat is black" and ask, "is that grammatical?" You don't track down the speaker and find out whether he knows the definitions of 'cat' and 'black'.

When people say — not lying or confused — that their cat is black, but they actually have a dog who is white, and they are thinking of their white dog but saying "My cat is black", they are using the words 'cat' and 'black' wrongly. — Lionino

But not ungrammatically.

"My cat is black" is grammatical even though it is false and the speaker meant that his dog is white.

You keep evading that very simple point.

By syntactical, I mean grammatical.

"Bob has a red French horn" is grammatical, even though it is false and even though Bob is misusing the word 'red' when he means 'loud'.

It was an answer to the relevance of Godel's theorem. Of course, it only applies to systems in which it is provable. — Tarskian

But you start out by mentioning logic in general, thus giving the impression that systems in general are incomplete, thus adding to the general confusion so prevalent on this point.

The system is a theory with a language. — Tarskian

I usually take a (logistic) system to consist of a language, axioms and inference rules. And I take a theory to be a set of sentences closed under provability. A theory may be the set of theorems in a language and derivable from axioms with rules. So, with each system, there is the theory induced by that system.

Thank you.

He said they are mathematical objects, not platonic objects. — Lionino

More exactly, I said they may be regarded as objects, and that we may discuss in what sense they are or are not objects. But the crank runs all over that like a loose lawn mower. The crank lies at will.

I should add that the above does not opine that those things are platonic things. Moreover, there is not a particular sense in which I am saying they are things. Moreover, I'm not opining that saying "things" or "objects" requires anything more than an "operational" sense: we use 'thing' or 'object' in order to talk about mathematics, as those notions are inherent in communication; it would be extraordinarily unwieldy to talk about, say, numbers without speaking, at least, as if they are things of some sort. But, it is not inappropriate to discuss the ways such things as rules are or are not mathematical things of some kind. — TonesInDeepFreeze

I explicitly said that I do not claim platonism. And I explicitly said that I am not advocating any particular sense of the notion of object. And I even said that we may discuss ways in which rules are or are not mathematical things of some kind. And I said that even if we don't commit to mathematics as talking about objects, communication about mathematics would be extraordinarily difficult if we did not at least talk as if we are talking about objects.

I wrote it explicitly. Yet the liar crank flat out lies that I said the opposite. The crank has no shame.

The lying crank wrote, "Tones is arguing that rules are Platonic objects just like numbers are."

That's yet another of the crank's lies about me. The crank needs to stop lying about me.

Thank you for that cite. That's interesting.

Again, you bring up someone else's quote, and it turns out that it contrasts with your post on account of the quote being fairly clear, though it is incorrect:

For a denumerable language, there are the same number of unprovable statements as provable ones, viz. denumerably many.

And he switched from 'statements' to 'facts', thus throwing off the count.

Why would that be an "overbroad mischaracterization"? — Tarskian

Too bad I'm not getting paid for correcting your stuff:

You can perfectly know the construction logic of a system but that does still not allow you to know its complete truth. — Tarskian

Incompleteness doesn't pertain to systems in general. Only to systems of a very certain kind.

"know its complete truth" is vague. What we could say is, "there are true sentences that are not provable". And no person can know individually infinitely many true sentences anyway.

"know the construction logic of". What is a "construction logic"? Maybe you mean the construction of the syntax? Better yet, just to say "the syntax rules".

You write slop. Though, that post is not your worst.

Regarding constructivism, we were talking about the law of identity.

What are some criticisms in mathematics of the identity of indiscernibles? (Of course, it is not first order axiomatizable.)

Here's a proof:

Definition: .999... = lim(k = 1 to inf) SUM(j = 1 to k) 9/(10^j).

Let f(k) = SUM(j = 1 to k) 9/(10^j).

Show that lim(k = 1 to inf) f(k) = 1.

That is, show that, for all e > 0, there exists n such that, for all k > n, |f(k) - 1| < e.

First, by induction on k, we show that, for all k, 1 - f(k) = 1/(10^k).

Base step: If k = 1, then 1 - f(k) = 1/10 = 1(10^k).

Inductive hypothesis: 1 - f(k) = 1/(10^k).

Show that 1 - f(k+1) = 1/(10^(k+1)).

1 - f(k+1) = 1 - (f(k) + 9/(10^(k+1)) = 1 - f(k) - 9/(10^(k+1)).

By the inductive hypothesis, 1 - f(k) - 9/(10^(k+1)) = 1/(10^k) - 9/(10^(k+1)).

Since 1/(10^k) - 9/(10^(k+1)) = 1/(10^(k+1)), we have 1 - f(k+1) = 1/(10^(k+1)).

So by induction, for all k, 1 - f(k) = 1/(10^k).

Let e > 0. Then there exists n such that, 1/(10^n) < e.

For all k > n, 1/(10^k) < 1/(10^n).

So, |1 - f(k)| = 1 - f(k) = 1/(10^k) < 1/(10^n).

It's handwaving. The argument invokes an utterly undefined notion. It's a garbage argument as far as mathematics goes. And it doesn't even have explanatory value, since it merely defers the question of what '...' means to the question of what subtraction on infinite sequences means.

I have no comment about the other poster in this context.

But I am glad that I made my quite relevant point that rules also may be regarded as mathematical objects.

Unlike your post, that quote seems at least fairly clear and doesn't make an overbroad mischaracterization of incompleteness.

One may choose different ways of thinking but every way of thinking that one may choose still has fundamental rules of rationality. — Lionino

What is regarded as rational may be different for different people. And people may choose even to think irrationally by any standard. But, of course, given a particular conception of rationality, some thoughts will not be rational and will violate certain attendant laws of rational thinking.

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

I can't imagine how it does not entail unless you are working under a very thin definition of rationality. — Lionino

Doesn't matter what the definition is. People may break all kinds of norms of rationality in their thinking. But, of course, tautologically, they can't break those norms with out breaking those norms.

And it does not dialetheism permit conceiving such things?
— TonesInDeepFreeze

I personally don't think dialethism is universally applicable or says anything deep about human rationality. It may be helpful as a gimmick to work around self-reference paradox, but that is about it. — Lionino

Whatever one thinks about dialetheism, the point stands that people may conceive dialetheistically. A person may say of himself that he cannot conceive other than by certain rules regarded as irrational not to conceive by. But that doesn't entail that other people can't conceive outside of those rules. Indeed, in such things as art, dreams, ruminations and mystical experiences, people can conceive in all kinds of ways. But, again, if the point is that people can't think irrationally without thinking irrationally, then of course, it would be irrational to deny that point.

I just pointed out that there are issues in assuming two of them. — Tarskian

No, you said that the only law that "withstands scrutiny" for constructivism is non-contradiction. And that is false.

Is grammar not the rules which give us what can be said right or wrong in language? — Lionino

Grammar doesn't dictate what is true or false, only what is well formed.

"I was literally dying" is well formed even if untrue.

"Bob's French horn is red" is well formed even if untrue.

We can give millions of examples in which the speaker misuses a word, but the sentence is still grammatical. Since you are wont to skip that point, here's one more:

The speaker may think 'melancholic' means 'mellow', then say, "The song is melancholic" when the song is not at all melancholic. A false but grammatical utterance.

Are you going to continue to skip that fact?

My reply to Leontiskos, which you asked about, is exactly that, except that it is laws of logic that a system may deny, not laws of thought. — Lionino

The way it read was that there are laws of logic that may be broken but not laws of thought. But if any law of logic may be also a law of thought, then there are laws of thought that may be broken too. And it wasn't stated as to what systems may deny, but merely as to what laws may deny.

Rhetorical question: is it possible to misspeak, which is to say to speak wrongly, without committing a grammar mistake? — Lionino

What does 'speak wrongly' mean? Speak ungrammatically or speak falsely?

Of course it is possible to use the wrong word and still be grammatical. People do it all the time.

One could make up examples all day, or observe them.

'literally' is an adjective. "I was literally dying" is grammatical. It is not made ungrammatical by the fact in the world that the speaker happened to not be dying and not literally dying.

neither am I interested if English "grammarians" — Lionino

Yet you cited one.

I don't know what point you are making about logic when you rule out "If ___, then ___".
— TonesInDeepFreeze

None. I made the comment standalone without tagging anyone and you replied to it.

But it is not that important, I write it wrongly too for the purpose of clarity. — Lionino

I thought you might have intended some point about logic. Good to know that you didn't.

You say it yourself: "syntactical role". — Lionino

No, 'literally' there is not violating the syntactical role of an adjective.

And at this point, you are merely arguing by reiteration of your assertion.

"Bob has a red French horn" is syntactical even though the speaker meant that Bob's French horn is loud.