Then what would be the correct wording?
P=P is a Contradiction
Re: P=P is a Contradiction
Re: P=P is a Contradiction
Yet "Arab" necessitates a common underlying region.Sculptor wrote: ↑Wed Sep 16, 2020 11:34 amNo 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".
 Immanuel Can
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Re: P=P is a Contradiction
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.
Re: P=P is a Contradiction
No, what would be the correct way of wording how circularity is a fallacy.Immanuel Can wrote: ↑Wed Sep 16, 2020 4:55 pmSorry...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.
 Immanuel Can
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Re: P=P is a Contradiction
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.
Re: P=P is a Contradiction
But ALL cats are different cats because no cat can be the same cat as an other..Immanuel Can wrote: ↑Wed Sep 16, 2020 1:58 pmBecause the statement isn't about different cats.
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 midsentence.
Re: P=P is a Contradiction
Absolutely NOT.Eodnhoj7 wrote: ↑Wed Sep 16, 2020 4:52 pmYet "Arab" necessitates a common underlying region.Sculptor wrote: ↑Wed Sep 16, 2020 11:34 amNo 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".
 Immanuel Can
 Posts: 9680
 Joined: Wed Sep 25, 2013 4:42 pm
Re: P=P is a Contradiction
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.
Re: P=P is a Contradiction
But an equals sign is about equivalence. Since no two things are the same P=P is false.Immanuel Can wrote: ↑Wed Sep 16, 2020 10:27 pmI 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.
 Immanuel Can
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Re: P=P is a Contradiction
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.

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Re: P=P is a Contradiction
if it is so stable, put a horse in it
Imp
Imp
 henry quirk
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Re: P=P is a Contradiction
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!

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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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Re: P=P is a Contradiction
Quite right.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.
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.
Re: P=P is a Contradiction
In the mathematical theory of rings (which includes the integers, rationals, real, and complex number systems), we have the tautologyImmanuel 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.
(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.