What is the basis for reason? And mathematics?

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Skepdick
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### Re: P=P is a Contradiction

Immanuel Can wrote: Tue Sep 29, 2020 3:27 pm Well, that's what you imagine. And that's fine. You have a right to be wrong.
Given which "wrongness" axiom?
Immanuel Can
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### Re: P=P is a Contradiction

Skepdick wrote: Tue Sep 29, 2020 3:44 pm
Immanuel Can wrote: Tue Sep 29, 2020 3:27 pm Well, that's what you imagine. And that's fine. You have a right to be wrong.
Given which "wrongness" axiom?
You allege you don't accept axioms. So I guess there's no telling you.

But it's the right to freedom of conscience. That gives everybody a right to be wrong.
Skepdick
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### Re: P=P is a Contradiction

Immanuel Can wrote: Tue Sep 29, 2020 5:48 pm You allege you don't accept axioms. So I guess there's no telling you.
How does me not accepting any axioms prevent you from telling me the axioms you have accepted?
Immanuel Can wrote: Tue Sep 29, 2020 5:48 pm But it's the right to freedom of conscience. That gives everybody a right to be wrong.
You'll have to explain how you are using the word "wrong"...
Immanuel Can
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### Re: P=P is a Contradiction

Skepdick wrote: Tue Sep 29, 2020 5:52 pm You'll have to explain how you are using the word "wrong"...
Factually incorrect. Or not corresponding to reality.
Skepdick
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### Re: P=P is a Contradiction

Immanuel Can wrote: Tue Sep 29, 2020 6:31 pm Factually incorrect. Or not corresponding to reality.
So you have asserted that my real state of mind doesn't correspond to my real state of mind?

That's a rather neat trick! Are you a mind-reader?
Immanuel Can
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### Re: P=P is a Contradiction

Skepdick wrote: Tue Sep 29, 2020 6:56 pm
Immanuel Can wrote: Tue Sep 29, 2020 6:31 pm Factually incorrect. Or not corresponding to reality.
So you have asserted that my real state of mind doesn't correspond to my real state of mind?
No, that the delusions in your state of mind are telling you things that are not real.

And on that note, the scintillating content of this exchange is beginning to put me to sleep.
wtf
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### Re: P=P is a Contradiction

Immanuel Can wrote: Sat Sep 26, 2020 10:47 pm Sorry. I have no idea what you're foaming on about.
Can only be willful blindness. Or blatant refusal to take responsibility for your own quoted text.

We're done, I'm sure we agree on that. Nice chatting with you.
wtf
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### Re: P=P is a Contradiction

Immanuel Can wrote: Sun Sep 27, 2020 1:56 pm P.S. -- It occurs to me, after the fact, that I may have to point out (or perhaps explain for the first time, if you didn't happen to know already) that "P" in logic stands for either "premise" or "predication." Thus it is not at all the same as a mathematical placeholder like "X" or "Y." It refers to a specific linguistic utterance, rather than to mathematical formulation or quantity.
Are you as arrogant and ignorant an asshole as this remark makes you out to be?
Immanuel Can
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### Re: P=P is a Contradiction

wtf wrote: Sun Oct 04, 2020 5:02 am
Immanuel Can wrote: Sat Sep 26, 2020 10:47 pm Sorry. I have no idea what you're foaming on about.
Can only be willful blindness. Or blatant refusal to take responsibility for your own quoted text.
Sorry, wtf. I literally don't know what you're talking about. You have this maths point you seem to want to make. I have no such point. Go ahead and make your point as much as you wish. I frankly don't see it impinges in any way on the law of identity. But hey, whatever floats your boat.
Averroes
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### Re: P=P is a Contradiction

Immanuel Can wrote: Sun Sep 27, 2020 1:56 pm P.S. -- It occurs to me, after the fact, that I may have to point out (or perhaps explain for the first time, if you didn't happen to know already) that "P" in logic stands for either "premise" or "predication." Thus it is not at all the same as a mathematical placeholder like "X" or "Y." It refers to a specific linguistic utterance, rather than to mathematical formulation or quantity.
Everything is just wrong with the paragraph just quoted above. It shows that you not only do not know about logic and mathematics, but you don't know history as well. I understand that such a paragraph would greatly irritate a mathematician and make him lose his cool. But we still have to educate people about such an important subject as logic and mathematics.
Immanuel Can wrote: Sun Sep 27, 2020 1:56 pm"P" in logic stands for either "premise" or "predication." Thus it is not at all the same as a mathematical placeholder like "X" or "Y."
The letter "P" is exactly a mathematical placeholder or as we say in sentential logic, a sentential/propositional variable . This "P" is not because of the "p" in "premise" and "predication"! It could be any other letter of the alphabet, it doesn't matter in logic. We could have chosen "Q" or "R" or even "X" or "Y" as is done to differentiate between different sentential variables(or placeholders) in compound sentences for example.

A note on predication though is that we do not use just the letter "P" in referring to predication in modern logic, but we use the mathematical notation of a mathematical function, something like "P(x)". And the notation of a mathematical function is used because this is exactly how predication is construed in logic, ie a sentence is construed as a truth function. As a refresher to what a function is in mathematics, I quote Wikipedia:
• In mathematics, a function is a binary relation between two sets that associates every element of the first set to exactly one element of the second set.
A function is a process or a relation that associates each element x of a set X, the domain of the function, to a single element y of another set Y (possibly the same set), the codomain of the function. It is customarily denoted by letters such as f, g and h. https://en.m.wikipedia.org/wiki/Function_(mathematics)
And this contruing of a sentence/utterence as a truth function was the revolution that Frege introduced into logic which ushered the age of modern logic.
Now, such an intricate relation between logic and mathematics should not be surprising because Frege himself was a German mathematician (a professor in mathematics), and his aim was the continuation of the work of the mathematization of logic which was started by an English mathematician namely George Boole who had previously succeeded in the algebraization of the logic of Aristotle. Ubiquitous algebra as we all know was discovered by the Muslim mathematician Al-Khwarizmi. And today the power and usefulness of algebra in any field of study cannot be overstated.

Anyway, all this is very basic knowledge for mathematicians. When you say things like the above quoted paragraph of yours, which is just compound ignorance, then well, many will lose their cool. And understandably so! The mathematization of logic was an important achievement of centuries of intellection, and no one wants to see that have the same fate as Italian mathematician Galileo and have us fall back into the Western Dark Ages.
Immanuel Can
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### Re: P=P is a Contradiction

Averroes wrote: Sun Oct 04, 2020 4:12 pm A note on predication though is that we do not use just the letter "P" in referring to predication in modern logic, but we use the mathematical notation of a mathematical function..
Sigh.

Nobody's denying that P can be used in maths. It can also be used in science, in poetry, and in the making of pepper pots and parking signs....but so what?

In something like ¬ P (P∧¬P), it does not have a mathematical meaning. It refers to a "proposition." Likewise, in a syllogism like:

P1: X ➙ Y
P2: Y ➙ Z
∴ C: X ➙ Z

It stands for "premise."

The subject in hand was not at all mathematics. Why anybody brought it in, I don't know. It was logic. And in particular, the subject at the time was the law of identity.
Averroes
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### Re: P=P is a Contradiction

Immanuel Can wrote: Sun Oct 04, 2020 4:25 pm Nobody's denying that P can be used in maths. It can also be used in science, in poetry, and in the making of pepper pots and parking signs....but so what?
That's the beauty of mathematics, it can be used everywhere, in science, in the making of pots, in engineering, in agriculture, in the making of pepper, in computer science, in the recent field of AI. You just name it and the list goes on!
Immanuel Can wrote:In something like ¬ P (P∧¬P), it does not have a mathematical meaning.
Now, "¬ P (P∧¬P)" is not a well formed formula (wff) in the language of sentential logic (LSL). In other words, in the language of sentential logic it is the same as a word salad, ie it is nonsense. In that sense, it could be construed as not having a meaning in propositional logic. But "P∧¬P" on the other hand is a wff and it is understood in LSL as a contradiction and thus have a meaning. It's meaning is expressed through a truth-table or truth function for the compound sentence "P∧¬P".
Immanuel Can wrote:It refers to a "proposition." Likewise, in a syllogism like:

P1: X ➙ Y
P2: Y ➙ Z
∴ C: X ➙ Z

It stands for "premise."
This was your initial confusion I addressed in my previous post. The "P1" and "P2" is of a different mathematical nature than the "P" in "P∧¬P". Here P1, P2 and C are metalogical variables. These are different mathematical objects than the "P" in "P∧¬P". You still could use other symbols than P1, P2 or C. By convention, Greek symbols are used to denote metalogical variables.
Immanuel Can wrote:The subject in hand was not at all mathematics. Why anybody brought it in, I don't know. It was logic. And in particular, the subject at the time was the law of identity.
Nowadays logic is a branch of mathematics.
Immanuel Can
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### Re: P=P is a Contradiction

Averroes wrote: Sun Oct 04, 2020 5:00 pm The "P1" and "P2" is of a different mathematical nature than the "P" in "P∧¬P".
No, in what I was talking about, neither has a "mathematical" nature. They both have a linguistic nature. That's the real point.

You could write either as "premise one" and "premise two," and have exactly the same meaning. Likewise, in Aristotle's law of non-contradiction, written in symbols as ¬ P (P∧¬P), it's a linguistic placeholder, not a mathematical one.

Again, the subject matter was the law of identity. It was linguistic, not mathematical.
Skepdick
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### Re: P=P is a Contradiction

Immanuel Can wrote: Sun Oct 04, 2020 5:09 pm
Averroes wrote: Sun Oct 04, 2020 5:00 pm The "P1" and "P2" is of a different mathematical nature than the "P" in "P∧¬P".
No, in what I was talking about, neither has a "mathematical" nature. They both have a linguistic nature. That's the real point.

You could write either as "premise one" and "premise two," and have exactly the same meaning. Likewise, in Aristotle's law of non-contradiction, written in symbols as ¬ P (P∧¬P), it's a linguistic placeholder, not a mathematical one.

Again, the subject matter was the law of identity. It was linguistic, not mathematical.

Mathematics is a language.
Logic is a language.
Last edited by Skepdick on Sun Oct 04, 2020 5:34 pm, edited 2 times in total.
Immanuel Can
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### Re: P=P is a Contradiction

Skepdick wrote: Sun Oct 04, 2020 5:29 pm
Immanuel Can wrote: Sun Oct 04, 2020 5:09 pm
Averroes wrote: Sun Oct 04, 2020 5:00 pm The "P1" and "P2" is of a different mathematical nature than the "P" in "P∧¬P".
No, in what I was talking about, neither has a "mathematical" nature. They both have a linguistic nature. That's the real point.

You could write either as "premise one" and "premise two," and have exactly the same meaning. Likewise, in Aristotle's law of non-contradiction, written in symbols as ¬ P (P∧¬P), it's a linguistic placeholder, not a mathematical one.

Again, the subject matter was the law of identity. It was linguistic, not mathematical.