P=P is a Contradiction

What is the basis for reason? And mathematics?

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Skepdick
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Re: P=P is a Contradiction

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Immanuel Can wrote: Mon Oct 05, 2020 3:11 am And algebra is not linguistic. It's mathematical. The "letters" do not form words, phrases, sentences, paragraphs and so forth, as they do in natural languages.
They do form words. And phrases. And sentences.

Clearly you don't speak any formal languages Like Logic/Mathematics.
Averroes
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Re: P=P is a Contradiction

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Immanuel Can wrote: Mon Oct 05, 2020 3:11 am
Averroes wrote: Mon Oct 05, 2020 1:54 am mathematical linguistic
No, it's either a mathematical placeholder OR a linguistic one. It's not both.
I understand your statements and wishes, but that's not how it works out in real life. In reality, mathematical linguistic is a real and now well established field of study and it dates back to the 1950s. I am not making this up! As I already said mathematics is used in every field of study. Linguistics is no exception. This should not come as a surprise to you at this point.
Immanuel Can wrote: Mon Oct 05, 2020 3:11 am Maths is not a "natural language," just as you have already said.
I never said that in our exchange on this thread!
By "maths", I think you mean LSL. Please, you have to be very attentive to what is being said,  otherwise you will keep drowning yourself. What I said were very precise statements about LSL sentence letters having no references unlike words in natural languages. These were very precise statements. LSL is part/branch of maths. The keyword here is the word "part/branch". Mathematics is a vast subject and we have pure mathematics and applied mathematics.
Immanuel Can wrote: Mon Oct 05, 2020 3:11 am And algebra is not linguistic. It's mathematical.
So you are saying that you consider algebra to be part of mathematics. Thank you for replying to my question. As an aside, I think you might benefit to know that algebra is used in mathematical linguistic. Check this course on mathematical linguistic on YT: https://youtu.be/5zNCyLQPY10

Immanuel Can wrote: Mon Oct 05, 2020 3:11 am The "letters" do not form words, phrases, sentences, paragraphs and so forth, as they do in natural languages. In algebra, letters are used only as mathematical placeholders.
Alright, I read what you wrote. May I now please ask you whether you consider the sequence of strings/symbols "¬(P∧¬P)" to be part of natural language or not? If so, please inform me what natural language have "¬(P∧¬P)" as a statement/sentence?
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Re: P=P is a Contradiction

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it seems that we haven't changed a diaper in a while

P P happens several times a day

-Imp
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henry quirk
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Re: P=P is a Contradiction

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Impenitent wrote: Mon Oct 05, 2020 10:22 am it seems that we haven't changed a diaper in a while

P P happens several times a day

-Imp
the pee in the puddle is that pee and no other
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Immanuel Can
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Re: P=P is a Contradiction

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Averroes wrote: Mon Oct 05, 2020 9:21 am
Immanuel Can wrote: Mon Oct 05, 2020 3:11 am
Averroes wrote: Mon Oct 05, 2020 1:54 am mathematical linguistic
No, it's either a mathematical placeholder OR a linguistic one. It's not both.
I understand your statements and wishes, but that's not how it works out in real life.
Actually, it is. Mathematics is a universal code system. It works the same in all languages and cultures. "Natural languages," as you call them, do not. That's one of the big differences between linguistics and mathematics. They are not interchangeable, and to call maths a "language" is to mistake a metaphor for a reality. It's not actually a "language": it's a universal code for quantities.

That's why people who, say, study in other countries often prefer to study mathematical subjects like computers, engineering or physics, and often shy away from linguistic ones like the Humanities. It's because maths is, if not any easier, at least accessible universally, across all languages and cultures; but subject dependent on natural languages are far more difficult and inaccessible cross-culturally. Math does not require things like linguistic competency, cultural awareness, idioms, metaphors, implications, mythologies, vocabularies, morphologies, syntactics, social dynamics, grammar and pronunciations.
Alright, I read what you wrote. May I now please ask you whether you consider the sequence of strings/symbols "¬(P∧¬P)" to be part of natural language or not?

No, it's not strictly part of natural language. No natural language contains it, and person unfamiliar with the linguistic content or the symbology of this logical system is going to understand what it means. And unlike, say, a sentence in English, it lacks the syntactic-grammatical and cultural elements required of English.

Instead, it contains both placeholders for concepts, such as "¬" and mathematical symbols, like brackets, and linguistic placeholders, such as "P." But "P" there is not algebraic. It stands for "proposition." It's linguistic. So symbolic logic is neither purely maths nor purely linguistics: it's an artificial hybrid, designed to try to impose mathematical precision on linguistic contents.

And what practitioners of symbolic logic always discover is that the more precision is imposed, the less real-world connection there is in symbolic logic. As the operations become too formal, they become increasingly removed from the empirical realities and natural vicissitudes they are intended to represent and manage. To a degree, they help impose rigour on linguistic operations; but there is clearly a limit to their applicability. And were it not so, then all philosophy after Quine et al. would surely have become nothing but a matter of symbol systems; for why would one not opt for the maximally-rigorous formulations, if they always also worked better in reality?
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Re: P=P is a Contradiction

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Skepdick wrote: Mon Oct 05, 2020 7:56 am Clearly you don't speak any formal languages Like Logic/Mathematics.
They're not "languages." Not in actuality, though we sometimes speak metaphorically as if they were. Like languages, they can be used to communicate. But that's where the resemblance stops.

They're actually universal code systems. Natural languages are not universal, and depend on many elements that must be internalized intuitively, through recursions of culturally-rich experiences, not through one-to-one correspondence of items, like in maths.

That's why you can't convert Chinese into English merely by using pinyin. They're separate languages. But you can send maths to China, and believe me, the Chinese will understand immediately.
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Re: P=P is a Contradiction

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henry quirk wrote: Mon Oct 05, 2020 2:26 pm the pee in the puddle is that pee and no other
That's the law of identity...in a puddle. :D
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Re: P=P is a Contradiction

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Immanuel Can wrote: Mon Oct 05, 2020 2:51 pm They're not "languages." Not in actuality, though we sometimes speak metaphorically as if they were. Like languages, they can be used to communicate. But that's where the resemblance stops.
Formal languages can be used for every single purpose a natural language can be used for. That's what makes them languages.

Poetry, description, representation, memory/recall...
Immanuel Can wrote: Mon Oct 05, 2020 2:51 pm They're actually universal code systems.
Universal? :lol: :lol: :lol: :lol: :lol: :lol:

Which encoding is the "universal" one?

What's the universal meaning of X?
Immanuel Can wrote: Mon Oct 05, 2020 2:51 pm Natural languages are not universal, and depend on many elements that must be internalized intuitively, through recursions of culturally-rich experiences, not through one-to-one correspondence of items, like in maths.
:lol: :lol: :lol: :lol: :lol: So formal languages are internalized EXACTLY like "natural languages" then...

Recursively-enumerable language.
Immanuel Can wrote: Mon Oct 05, 2020 2:51 pm That's why you can't convert Chinese into English merely by using pinyin.
But you can translate Chinese to English using a formal method, yeah?

https://translate.google.com/
Immanuel Can wrote: Mon Oct 05, 2020 2:51 pm They're separate languages.
But they are languages...
Immanuel Can wrote: Mon Oct 05, 2020 2:51 pm But you can send maths to China, and believe me, the Chinese will understand immediately.
So why are you having trouble understanding maths if it's "universal"?
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Re: P=P is a Contradiction

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Skepdick wrote: Mon Oct 05, 2020 4:06 pm
Immanuel Can wrote: Mon Oct 05, 2020 2:51 pm They're not "languages." Not in actuality, though we sometimes speak metaphorically as if they were. Like languages, they can be used to communicate. But that's where the resemblance stops.
Formal languages can be used for every single purpose a natural language can be used for. That's what makes them languages.

Poetry, description, representation, memory/recall...
Great. Let's see your mathematics poem. I'm sure it will be beautiful.
Immanuel Can wrote: Mon Oct 05, 2020 2:51 pm Natural languages are not universal, and depend on many elements that must be internalized intuitively, through recursions of culturally-rich experiences, not through one-to-one correspondence of items, like in maths.
So formal languages are internalized EXACTLY like "natural languages" then...
Not at all. That's why so many of the international students flock to things like computers, engineering and math, and why many assiduously avoid Humanities, if they can. It's also why so many who would never hesitate at a maths test are terrified of the English language competency exams.

And in Business schools, they've started pre-testing for language competency, because they were getting too many people who were adept in maths, but who were not so competent in the linguistic business of negotiating a culture, holding a discussion, or making a presentation.

If there were no difference between maths competence and language competence, that would be inexplicable.
Immanuel Can wrote: Mon Oct 05, 2020 2:51 pm That's why you can't convert Chinese into English merely by using pinyin.
But you can translate Chinese to English using a formal method, yeah?
"A formal method"? What do you mean by that? Do you mean you imagine you can translate with a one-to-one correspondence, just like maths?

No, you cannot. But you'll need to speak with a Chinese person who has made the crossover to English acculturation to know how true that is.
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Re: P=P is a Contradiction

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Immanuel Can wrote: Mon Oct 05, 2020 2:51 pm
henry quirk wrote: Mon Oct 05, 2020 2:26 pm the pee in the puddle is that pee and no other
That's the law of identity...in a puddle. :D
philosophy for the vulgarian
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Re: P=P is a Contradiction

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Immanuel Can wrote: Mon Oct 05, 2020 4:43 pm Not at all. That's why so many of the international students flock to things like computers, engineering and math, and why many assiduously avoid Humanities, if they can. It's also why so many who would never hesitate at a maths test are terrified of the English language competency exams.
Because they haven't figured out how to unify both fields through linguistics?

Is kinda sad, because learning how to learn is fundamentally an exercise in Metalinguisttic abstraction.

Immanuel Can wrote: Mon Oct 05, 2020 4:43 pm And in Business schools, they've started pre-testing for language competency, because they were getting too many people who were adept in maths, but who were not so competent in the linguistic business of negotiating a culture, holding a discussion, or making a presentation.
You've never seen Mathematicians negotiate, hold discussions or make presentations amongst themselves? What planet are you from?
Immanuel Can wrote: Mon Oct 05, 2020 4:43 pm If there were no difference between maths competence and language competence, that would be inexplicable.
You've never seen Chinese speakers unable to negotiate culture, hold a discussion or make a presentation to English speakers?

Almost as if there's a cultural barrier or something. Whether the barrier is English <-> Chinese, or English<-> Mathematics is kinda moot...

Immanuel Can wrote: Mon Oct 05, 2020 4:43 pm "A formal method"? What do you mean by that? Do you mean you imagine you can translate with a one-to-one correspondence, just like maths?
Maths is not one-to-one. Who lied to you?
Immanuel Can wrote: Mon Oct 05, 2020 4:43 pm No, you cannot. But you'll need to speak with a Chinese person who has made the crossover to English acculturation to know how true that is.
Oh, like you need to speak to a Mathematician who also speaks English?

As it happens English is not my 1st language. It's precisely because I speak a bunch of languages is why I can assert that Mathematics is a language.
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Re: P=P is a Contradiction

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Immanuel Can wrote: Mon Oct 05, 2020 2:46 pm Actually, it is. Mathematics is a universal code system. It works the same in all languages and cultures. "Natural languages," as you call them, do not. That's one of the big differences between linguistics and mathematics. They are not interchangeable, and to call maths a "language" is to mistake a metaphor for a reality. It's not actually a "language": it's a universal code for quantities.
You are saying mathematics and linguistics are different and not interchangeable. And I am not disagreeing with that. I am only adding that mathematics and linguistics are compatible and not mutually exclusive, otherwise mathematical linguistics would not exist. You previously said:
Immanuel Can wrote: Mon Oct 05, 2020 3:11 am No, it's either a mathematical placeholder OR a linguistic one. It's not both.
May I ask you whether you still consider linguistic and mathematics to be incompatible and mutually exclusive? If so how do you account for the actuality of mathematical linguistics?

Immanuel Can wrote: Mon Oct 05, 2020 2:46 pm
Alright, I read what you wrote. May I now please ask you whether you consider the sequence of strings/symbols "¬(P∧¬P)" to be part of natural language or not?

No, it's not strictly part of natural language. No natural language contains it,
Thank you for replying to my question. Indeed, we agree here. "¬(P∧¬P)" is a statement in the Language of Sentential/Propositional logic and not of any natural language. I call English, French, Arabic and others, natural languages because this is how they are called in the field of logic, and recently in AI.

Immanuel Can wrote: Mon Oct 05, 2020 2:46 pm And unlike, say, a sentence in English, it lacks the syntactic-grammatical and cultural elements required of English.
LSL or Propositional logic has a syntax and grammar.

Immanuel Can wrote: Mon Oct 05, 2020 2:46 pm Instead, it contains both placeholders for concepts, such as "¬" and mathematical symbols, like brackets, and linguistic placeholders, such as "P." But "P" there is not algebraic. It stands for "proposition." It's linguistic. So symbolic logic is neither purely maths nor purely linguistics: it's an artificial hybrid, designed to try to impose mathematical precision on linguistic contents.
As I said, that "P" in "¬(P∧¬P)" be linguistic is not an issue for me given that "¬(P∧¬P)" is an LSL statement and also given the existence of mathematical linguistics as a field of study. What I find problematic is that you say it's not algebraic. This is putting your point of view to be in direct opposition to how mathematicians have been construing it for more than a century! You will find references to verify this claim in many places. I chose the Wikipedia entry for "Propositional Formula" under the sub-heading "An algebra of propositions, the propositional calculus" as evidence for my claim:

Wikipedia:
  • An algebra (and there are many different ones), loosely defined, is a method by which a collection of symbols called variables together with some other symbols such as parentheses (, ) and some sub-set of symbols such as *, +, ~, &, ∨, =, ≡, ∧, ¬ are manipulated within a system of rules. These symbols, and well-formed strings of them, are said to represent objects, but in a specific algebraic system these objects do not have meanings. Thus work inside the algebra becomes an exercise in obeying certain laws (rules) of the algebra's syntax (symbol-formation) rather than in semantics (meaning) of the symbols. The meanings are to be found outside the algebra.

    For a well-formed sequence of symbols in the algebra —a formula— to have some usefulness outside the algebra the symbols are assigned meanings and eventually the variables are assigned values; then by a series of rules the formula is evaluated.

    When the values are restricted to just two and applied to the notion of simple sentences (e.g. spoken utterances or written assertions) linked by propositional connectives this whole algebraic system of symbols and rules and evaluation-methods is usually called the propositional calculus or the sentential calculus.

    While some of the familiar rules of arithmetic algebra continue to hold in the algebra of propositions (e.g. the commutative and associative laws for AND and OR), some do not (e.g. the distributive laws for AND, OR and NOT). https://en.m.wikipedia.org/wiki/Proposi ... l_calculus

Wikipedia:
  • Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations between propositions, including the construction of arguments based on them. Compound propositions are formed by connecting propositions by logical connectives. Propositions that contain no logical connectives are called atomic propositions. https://en.m.wikipedia.org/wiki/Propositional_calculus

You are saying that "P" in "¬(P∧¬P)" is not algebraic but the writers of the aforementioned Wikipedia entries are saying it is algebraic. Do you wish to comment on this discrepancy between you and the Wikipedia writers? If so, do you think they got it wrong and that they don't know what they are talking about? If this be the case, they and all other mathematicians who think likewise should be informed immediately as they are misguiding a lot of people. What do you say? I will now let you answer if you so wish.
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Re: P=P is a Contradiction

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Averroes wrote: Mon Oct 05, 2020 9:40 pm
Immanuel Can wrote: Mon Oct 05, 2020 2:46 pm Actually, it is. Mathematics is a universal code system. It works the same in all languages and cultures. "Natural languages," as you call them, do not. That's one of the big differences between linguistics and mathematics. They are not interchangeable, and to call maths a "language" is to mistake a metaphor for a reality. It's not actually a "language": it's a universal code for quantities.
You are saying mathematics and linguistics are different and not interchangeable. And I am not disagreeing with that.
Fair enough.
I am only adding that mathematics and linguistics are compatible
Well, whether that's right depends on whether by "compatible" you mean, "able to get along," or "the same thing." Yes to the former, no to the latter, of course.
May I ask you whether you still consider linguistic and mathematics to be incompatible and mutually exclusive?
I didn't say either. I said "different," and that maths is not a natural language...to which you replied, "I am not disagreeing with that."
Immanuel Can wrote: Mon Oct 05, 2020 2:46 pm And unlike, say, a sentence in English, it lacks the syntactic-grammatical and cultural elements required of English.
LSL or Propositional logic has a syntax and grammar.
If you use those terms in the most general way, so do all codes. But when you get that metaphorical, you could also speak of them being "languages." But they don't have the same kind as "natural languages" do. Hence the distinction.

But I grow bored of this, and care to invest no more effort into the topic. We have moved too far away from the law of identity for this to have any relevance to me.

However, for your peace of mind, I note your disagreement, or rather, your partial agreement. And there the matter shall rest.
Last edited by Immanuel Can on Mon Oct 05, 2020 10:50 pm, edited 3 times in total.
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Re: P=P is a Contradiction

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Skepdick wrote: Mon Oct 05, 2020 7:58 pm Because they haven't figured out how to unify both fields through linguistics?
I'll answer A. and you at the same time, since he raises all the issues you do, and more. See above.
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Re: P=P is a Contradiction

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Immanuel Can wrote: Mon Oct 05, 2020 10:15 pm We have moved too far away from the law of non-contradiction for this to have any relevance to me.
You haven't moved at all... you continue to be as confused as you always were.
Immanuel Can wrote: Mon Oct 05, 2020 2:46 pm
Alright, I read what you wrote. May I now please ask you whether you consider the sequence of strings/symbols "¬(P∧¬P)" to be part of natural language or not?

No, it's not strictly part of natural language. No natural language contains it,
"¬(P∧¬P)" is the Law of non-contradiction.

You can't even agree with yourself whether you are agreeing or disagreeing.
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