What is the basis for reason? And mathematics?

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Eodnhoj7
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### Re: P=P is a Contradiction

Immanuel Can wrote: Wed Sep 16, 2020 4:21 am
Eodnhoj7 wrote: Wed Sep 16, 2020 3:27 am So ...circularity.
The only two words you got right.
Then what would be the correct wording?
Eodnhoj7
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### Re: P=P is a Contradiction

Sculptor wrote: Wed Sep 16, 2020 11:34 am
Eodnhoj7 wrote: Wed Sep 16, 2020 3:26 am
Sculptor wrote: Tue Sep 15, 2020 10:50 pm

No two cats are the same. All cats are unique.
"Cat" is just your subjective convenience.
Yet the same forms of hair, tail, teeth, etc. repeat so there are common factors. The cat is both equal to a cat and not equal at the same time.
No all those things are also unique. Just because you have no interest in the difference does not change the fact that they all occupy distinctly different places in space/time, and that each hairs is comprised of a difference number of molecules.
To a higher being, maybe cat and dog are the same thing - just part of the biological scum on an otherwise pristine planet.
All things are unique. Lack of uniqueness is about degrees of interest and the ability to ignore differences. It is a human trait. "All Arabs are the same".
Yet "Arab" necessitates a common underlying region.
Immanuel Can
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### Re: P=P is a Contradiction

Eodnhoj7 wrote: Wed Sep 16, 2020 4:51 pm
Immanuel Can wrote: Wed Sep 16, 2020 4:21 am
Eodnhoj7 wrote: Wed Sep 16, 2020 3:27 am So ...circularity.
The only two words you got right.
Then what would be the correct wording?
Sorry...I can't salvage for you an argument that doesn't even make grammatical sense. I wouldn't know how to do it if I tried.
Eodnhoj7
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### Re: P=P is a Contradiction

Immanuel Can wrote: Wed Sep 16, 2020 4:55 pm
Eodnhoj7 wrote: Wed Sep 16, 2020 4:51 pm
Immanuel Can wrote: Wed Sep 16, 2020 4:21 am
The only two words you got right.
Then what would be the correct wording?
Sorry...I can't salvage for you an argument that doesn't even make grammatical sense. I wouldn't know how to do it if I tried.
No, what would be the correct way of wording how circularity is a fallacy.
Immanuel Can
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Joined: Wed Sep 25, 2013 4:42 pm

### Re: P=P is a Contradiction

Eodnhoj7 wrote: Wed Sep 16, 2020 4:56 pm No, what would be the correct way of wording how circularity is a fallacy.
Circularity only produces a fallacy if it is offered as the basis of a syllogism or argument, as you have done.

Circularity, as a phenomenon, produces a truth...but only a trivial or recursive one.

That's the right way to understand it.
Sculptor
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### Re: P=P is a Contradiction

Immanuel Can wrote: Wed Sep 16, 2020 1:58 pm
Sculptor wrote: Wed Sep 16, 2020 11:30 am
Immanuel Can wrote: Wed Sep 16, 2020 2:58 am
Not the point.
Why?
Because the statement isn't about different cats.
But ALL cats are different cats because no cat can be the same cat as an other..
It's about the fact that a cat is, so to speak, "what it is," and must remain so throughout a rational operation, or the operation goes wrong. That's what the law of identity entails.

In other words, it's not a claim about all cats on he basis of one. It's a claim about one cat and its "identity" so long as we continue to form arguments about that one cat.

It's as if "Sculptor" were used to refer to you at the beginning of a message, but by the end referred to Auguste Rodin. The statement thus formed would have no conclusion, because the identity of the referent had changed in mid-sentence.
Sculptor
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### Re: P=P is a Contradiction

Eodnhoj7 wrote: Wed Sep 16, 2020 4:52 pm
Sculptor wrote: Wed Sep 16, 2020 11:34 am
Eodnhoj7 wrote: Wed Sep 16, 2020 3:26 am
Yet the same forms of hair, tail, teeth, etc. repeat so there are common factors. The cat is both equal to a cat and not equal at the same time.
No all those things are also unique. Just because you have no interest in the difference does not change the fact that they all occupy distinctly different places in space/time, and that each hairs is comprised of a difference number of molecules.
To a higher being, maybe cat and dog are the same thing - just part of the biological scum on an otherwise pristine planet.
All things are unique. Lack of uniqueness is about degrees of interest and the ability to ignore differences. It is a human trait. "All Arabs are the same".
Yet "Arab" necessitates a common underlying region.
Absolutely NOT.
Immanuel Can
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Joined: Wed Sep 25, 2013 4:42 pm

### Re: P=P is a Contradiction

Sculptor wrote: Wed Sep 16, 2020 8:34 pm
Immanuel Can wrote: Wed Sep 16, 2020 1:58 pm Because the statement isn't about different cats.
But ALL cats are different cats because no cat can be the same cat as an other..
I say again: it's not about DIFFERENT cats. It's about what rationally has to be said about ONE cat.

It's about IDENTITY. It doesn't at all draw any comparisons to others in the class.
Sculptor
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### Re: P=P is a Contradiction

Immanuel Can wrote: Wed Sep 16, 2020 10:27 pm
Sculptor wrote: Wed Sep 16, 2020 8:34 pm
Immanuel Can wrote: Wed Sep 16, 2020 1:58 pm Because the statement isn't about different cats.
But ALL cats are different cats because no cat can be the same cat as an other..
I say again: it's not about DIFFERENT cats. It's about what rationally has to be said about ONE cat.

It's about IDENTITY. It doesn't at all draw any comparisons to others in the class.
But an equals sign is about equivalence. Since no two things are the same P=P is false.
Immanuel Can
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Joined: Wed Sep 25, 2013 4:42 pm

### Re: P=P is a Contradiction

Sculptor wrote: Wed Sep 16, 2020 10:39 pm But an equals sign is about equivalence.
That depends. If the sign on the far side of an equals sign is exactly the same as that on the near one, then it's merely about identity.

Essentially, it's saying "a five is a five." Which might be trivial, but is also true.

But since we're talking about the law of identity, an "equals" sign is not involved at all. What's involved is the question of the identity of ONE THING. The law simply says it must remain stable. That's all.
Impenitent
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### Re: P=P is a Contradiction

if it is so stable, put a horse in it

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

Impenitent wrote: Thu Sep 17, 2020 12:03 am if it is so stable, put a horse in it

-Imp
A horse is a horse, of course, of course
And no one can talk to a horse, of course
That is, of course, unless the horse is the famous Mr. Ed!
raw_thought
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Location: trapped inside a hominid skull

### Re: P=P is a Contradiction

P=P is a tautology not a contradiction. Tautologies are always true and so say nothing. Contradictions are the opposite. They are always false. For example suppose I say, " It will rain today or it wont." True in all cases and tells me nothing about the weather.
Immanuel Can
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Joined: Wed Sep 25, 2013 4:42 pm

### Re: P=P is a Contradiction

raw_thought wrote: Thu Sep 17, 2020 12:36 am P=P is a tautology not a contradiction. Tautologies are always true and so say nothing. Contradictions are the opposite. They are always false. For example suppose I say, " It will rain today or it wont." True in all cases and tells me nothing about the weather.
Quite right.

P=P is also a tautology. The fault is not that it is wrong, or tells a lie; it's that even if true, it's utterly uninformative of anything new. It adds no value to our thinking at all.
wtf
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### Re: P=P is a Contradiction

Immanuel Can wrote: Thu Sep 17, 2020 2:11 am

P=P is also a tautology. The fault is not that it is wrong, or tells a lie; it's that even if true, it's utterly uninformative of anything new. It adds no value to our thinking at all.
In the mathematical theory of rings (which includes the integers, rationals, real, and complex number systems), we have the tautology

(a+b)^2 = a^2 + 2ab + b^2

According to you, it's "... utterly uninformative of anything new. It adds no value to our thinking at all." Yet every student is required to learn it, be able to derive it from the distributive law, and apply it on sight. Not only that, more advanced students are taught its generalization to arbitrary exponents as the binomial theorem, another tautology. It took Newton to discover the most general form of the binomial theorem. Are you saying Newton wasted his time on a triviality? If it was so trivial, why did nobody ever notice it before?

Could you please put your remark into proper context? In what way is the binomial theorem "utterly uninformative of anything new?" The Pythagorean theorem is true in every model of Euclidean geometry, making it a tautology. Would you call it "... utterly uninformative of anything new. It adds no value to our thinking at all?" On the contrary, it's the basis of the distance formula in analytic geometry and vector calculus. Many generations of students have struggled to internalize it. No undergraduate engineer or physics student can graduate without thoroughly internalizing it.et you say it adds no new information.

A tautology is simply a proposition that is true in every possible interpretation, or model, of an axiomatic system. Therefore virtually all mathematical theorems, including the ones not yet discovered, are tautologies. Thousands of years of mathematical practice show that your claim is false.

https://en.wikipedia.org/wiki/Ring_(mathematics)

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

https://en.wikipedia.org/wiki/Tautology_(logic)
Last edited by wtf on Thu Sep 17, 2020 3:38 am, edited 4 times in total.