P=P is a Contradiction

[Immanuel Can]

Could you please put your remark into proper context?

We're talking about the law of identity. For that, the mathematics don't even matter. They're an analogy, not a literal demonstration. Logic symbols are not mathematical symbols.

Hope that clears that up.

[Eodnhoj7]

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.

False, the syllogisms presented still are composed of assertions which are true. If I say "the water is wet, and the wetness reflects water present, therefore the water is wet" the assertion of the " "water is wet" is still reflected as a truth value. All contradictions are grounded in truth values thus composed of them.

And as to why circularity is contradictory, I will reiterate:

"One assertion is defined by its relationship to another and with this absence of relation a contradiction occurs given the assertion is absent of contrasting assertions, that result in defintion, therefore leaving it as fundamentally formless in nature.

Absence of form is contradiction considering that which is without form is that which cannot be sensed and this absence of form occurs through the emptiness of circularity."

[Eodnhoj7]

Could you please put your remark into proper context?

We're talking about the law of identity. For that, the mathematics don't even matter. They're an analogy, not a literal demonstration. Logic symbols are not mathematical symbols.

Hope that clears that up.

P=P and 1=1 both reflect a common bond through the equals sign. Logic and math can transition to eachother.

[wtf]

We're talking about the law of identity. For that, the mathematics don't even matter. They're an analogy, not a literal demonstration. Logic symbols are not mathematical symbols.

Hope that clears that up.

Not even remotely. I linked the Wiki page defining the word tautology. The fact is that most tautologies are profound surprises. They're only tautologies after the fact. If you want to say that the law of identity confers no information, that's very different than saying that a tautology doesn't. But you'd be wrong there too. If the law of identity confers no information, why is it regarded as one of the basic laws of logic? After all, "The sky is blue" is not a basic law of logic. I think you are flat out wrong.

You said, and this is a direct quote: "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."

You are clearly saying that BECAUSE the law of identity is a tautology, it adds no information. But I just showed you that tautologies generally add profound information. The analogy would be to say that a sculptor adds nothing new because the statue was already in the rock. Of course some nihilistic philosophers do so argue. Are you one of them? I suppose the drawings on the ceiling of the Sistine chapel were already there before Michelangelo painted them in by the numbers. Coulda gotten a high school kid to do the same work cheaper.

The profound art of human reasoning, art, and even science is to discover the most interesting and surprising tautologies; and to reveal to the rest of us what was already there, if we only knew how to look.

I could pile on the analogies. Special relativity was "already there" in the work of Maxwell, but it took Einstein to elucidate it. Was Einstein's work trivial or adding no new information simply because we can teach a college student to derive it from Maxwell's work?

You may be saying that the law of identity is trivial or provides no new information for reasons OTHER than the mere fact that it's a tautology. If this is the case, please clarify your reasons. Your statement is false as it stands.

[Eodnhoj7]

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.

False a contradiction shows an absence of form through the opposition of phenomena having the inability to connect. This same formlessness is founded in circularity given it is an empty loop. The loop only have value when defined through another loop. A new assertion is what justifies the original assertion by providing definition but with circularity no knew assertion is formed.

Second all contradictions are grounded in truth values. 2+2=5 shows the elements of 2 and 5 as existing as true given they occur through 1 repeating thus a form results. This second element shows circularity as having an intrinsic form through the repetition of a phenomenon.

Thus circularity is both a contradiction and not a contradiction. It is not a contradiction given a form results, it results in contradiction because the form is empty.

[Eodnhoj7]

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.

If "Arab" has no commonalities then what does it point to?

[Immanuel Can]

If you want to say that the law of identity confers no information...

You didn't even read the thread.

I didn't say that. So you're barking up the wrong tree. I'm affirming the law of identity.

"The sky is blue" is not a basic law of logic. I think you are flat out wrong.

hmmm...I'm starting to think you have not the foggiest clue what the "law of identity" is.

The law of identity would only say that if you start a pattern of formal argument with "sky" meaning a particular thing, then "sky" must remain that same thing throughout the entire operation, in order for it to produce any valid logic or sound conclusion.

In maths, this would mean that the value "X" would have to remain whatever specific value it represented in the first line when you reached the third or fifth line. If you had X equalling 6 in line one, it can't turn into 1,002 in line four, or the equation would be ruined, and yield no reliable or informative result.

Essentially, that's all the law of identity is saying.

[Immanuel Can]

... the syllogisms presented still are composed of assertions which are true....

Your phrases don't even make sense.

You don't have anyone doing the "presenting" here, you're not referring to any specific "syllogisms," so Lord only knows why you use the definite article "the," and you don't know that anything is "true" merely because an unarmed entity "asserts" it.

Use grammar, or go away.

[Eodnhoj7]

... the syllogisms presented still are composed of assertions which are true....

Your phrases don't even make sense.

You don't have anyone doing the "presenting" here, you're not referring to any specific "syllogisms," so Lord only knows why you use the definite article "the," and you don't know that anything is "true" merely because an unarmed entity "asserts" it.

Use grammar, or go away.

Learn to read or go away.

An assertion is that which is presented, such as a fact or opinion. All syllogisms are thus composed of assertions. If I say "the water is wet, and the wetness reflects water present, therefore the water is wet" the assertion of the " "water is wet" is still reflected as a truth value. All contradictions are grounded in truth values thus composed of them.

One can have truth values derived from a contradiction as that which composes the contradiction.

The same applies for the contradiction of 2+2=5. It is composed of rational entities, 2 and 5, with these rational entities being rational because they are composed of interlinked parts, in this case 1.


Where circularity is a fallacy is that is is absent of definition, thus justification, given it does not connect to any assertion beyond it. Circularity is an empty loop.

[wtf]

You didn't even read the thread.

I agree that I'm not following the thread. I'm only commenting on this completely false statement that you made:

"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."

Do you agree that you wrote that? It's a direct copy/paste from one of your posts.

It says, plain as day, that P = P is a tautology THEREFORE "... it's utterly uninformative of anything new. It adds no value to our thinking at all."

If you meant to say that P = P "adds no value etc." for some reason OTHER than that it's a tautology, please clarify your intent. As it stands, you're saying that ALL tautologies "add no value etc." and P = P is a tautology THEREFORE etc. But I showed that one of your premises is false, namely that tautologies "add no value etc." On the contrary, tautologies are often surprising and deep.

I didn't say that.

Do you have a cat? Sometimes cats walk across the keyboard and type things in on their own. I see this happen all the time, when people on discussion forums deny their own direct quotes.

hmmm...I'm starting to think you have not the foggiest clue what the "law of identity" is.

I know exactly what it is. And you don't know what a tautology is.

The law of identity would only say that if you start a pattern of formal argument with "sky" meaning a particular thing, then "sky" must remain that same thing throughout the entire operation, in order for it to produce any valid logic or sound conclusion.

I'll retract the sky is blue remark if that will help you to focus on what I'm saying to you.

You asserted the following argument:

Premise1 : P = P is a tautology.

Premise 2: A tautology "adds no value etc."

Conclusion: Therefore P = P adds no value etc.

I falsified premise 2.

Would you care to revise your exposition?

In maths, this would mean that the value "X" would have to remain whatever specific value it represented in the first line when you reached the third or fifth line. If you had X equalling 6 in line one, it can't turn into 1,002 in line four, or the equation would be ruined, and yield no reliable or informative result.

I fail to follow your argument. Please comment on the one quote I'm objecting two, which expands into the valid but UNSOUND syllogism whose premise I just falsified.

Essentially, that's all the law of identity is saying.

Please clarify or retract your claim that: " "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."

What does P = P being a tautology have to do with anything? I just showed that on the contrary to your premise, tautologies are deep, novel, interesting, and important; going back thousands of years and continuing to this very moment.

I agree that I may be MISREADING your unclear statement about the nature of tautologies; in which case I ask only for clarification of your intent. Do you or don't you take my point that tautologies are generally novel and interesting?

[Sculptor]

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.

No.
Indentity is a massively complex topic. And equals signs are never used in such cases.

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

Of course, and it is the only way that an equals sign can be used. But since there is nothing which is a "five" in the world, then it is only useful for mathematical abstractions, and of little use to real things.

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.

What's your point?

[Sculptor]

Yet "Arab" necessitates a common underlying region.

Absolutely NOT.

If "Arab" has no commonalities then what does it point to?

I said it did not point to a region.
Are you saying that an Arab in the USA is not really an Arab?
Are you saying that all Arabs are the same?

[Skepdick]

The "law" of identity is a function: λx.x

Or in its most general form: λx.λ

[raw_thought]

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.

False a contradiction shows an absence of form through the opposition of phenomena having the inability to connect. This same formlessness is founded in circularity given it is an empty loop. The loop only have value when defined through another loop. A new assertion is what justifies the original assertion by providing definition but with circularity no knew assertion is formed.

Second all contradictions are grounded in truth values. 2+2=5 shows the elements of 2 and 5 as existing as true given they occur through 1 repeating thus a form results. This second element shows circularity as having an intrinsic form through the repetition of a phenomenon.

Thus circularity is both a contradiction and not a contradiction. It is not a contradiction given a form results, it results in contradiction because the form is empty.

"A tautology is certainly true, a proposition possibly, and a contradiction certainly not."
Wittgenstein FROM https://readingwittgenstein.blogspot.co ... ction.html
Read some Wittgenstein!

[RCSaunders]

P=P

how is a thing is identical with itself contradictory?

Because of circular reasoning, the beginning is the same as the end. It is arguing identity is a loop which contradicts the standard fallacies.

so, if I say I am me (and no other), that is, quirk is quirk, my self-reference (circular reasoning) is contradictory and -- in fact -- I am not me

ok, then...

You have actually identified the mistake. "quirk is quirk," is correct, "quirk = quirk," would be wrong. It is actually incorrect to say B=B except in algebra, where B is a symbol for a number, because equals means, "has the same value." In all other cases it should be, B is B, which only means B is itself, and not anything else. A thing does not "equal" itself, it just "is" itself. Saying a thing, X "equals" (has the same value as) a thing X implies, illogically, that X is more than one thing, which is where Eodnhoj7 went wrong.