P=P is a Contradiction

[Eodnhoj7]

1. The laws of identity.... contradictions where P=-P.

Just wrong.

Then prove it. P=P is circular thus exists as a fallacy. It derives this fallacious state through an absence of progressive linear reasoning where one assertion is justified by its divergence to a new assertion. Justification is derived from one new assertion progressing to another.

[Sculptor]

So if P doesn't equal P, what does equal P?

I think P is equal to wee.
As when I take a P I tend to wee

At last, philosophy we can apply to real life.

Are you taking the P???

[Sculptor]

P=P is circular reasoning given the same assertion made in the beginning is the same as in the end. P=P is thus a contradiction.

Nope
Whilst it is true that no two Ps can ever be the same, the expression is not saying that.
So
P=P is true
whilst
one P = another P is false

That other P is still a P.

Even Peas in a Pod are not identical.

The P exists recursively thus necessitates the P existing in multiple states.

Only in your mind

As existing in multiple states, through recursion, one P differentiates from another. An example of this would be a single person's identity changing across a span in time. The person in x time and space is not the same person in y time and space yet a common underlying bond of identity repetition is unavoidable. The person is both equal and not equal to him or herself simultaneously.

So you know something about peas. So what?

[Immanuel Can]

P=P is circular.

A cat is a cat. That's circular. It's not untrue. It's just uselessly true. It only becomes a fallacy if it is offered as an argument. But nobody is offering P=P as an argument, except you. So the only possible fallacy there is your own.

[Eodnhoj7]

P=P is circular.

A cat is a cat. That's circular. It's not untrue. It's just uselessly true. It only becomes a fallacy if it is offered as an argument. But nobody is offering P=P as an argument, except you. So the only possible fallacy there is your own.

The fallacy of circularity defines an argument by what it is not linear. That argument is rational all the way up to its circularity in which case the premise is repeated in the conclusion thus reflecting an absence of divergence to a new assertion. The absence of divergence to a new assertion thus results in an absence of analysis resulting in a new truth value. This fallaciousness is derived from an absence of progressive linear reasoning where one assertion is justified by its divergence to it's new assertion, justification is derived from one assertion progressing to another.

So while the premise and conclusion, or the beginning and end of the assertion are true, an absence of truth value occurs because of the absence of justification of the assertion through another assertion. 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 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.

[Immanuel Can]

The fallacy of circularity...circularity.

A circular and empty response.

[Harbal]

Are you taking the P???

Of course I am; this thread deserves nothing less.

[Sculptor]

P=P is circular.

A cat is a cat. That's circular. It's not untrue. It's just uselessly true. It only becomes a fallacy if it is offered as an argument. But nobody is offering P=P as an argument, except you. So the only possible fallacy there is your own.

No two cats are the same. All cats are unique.
"Cat" is just your subjective convenience.

[Immanuel Can]

No two cats are the same. All cats are unique.

Not the point.

[Eodnhoj7]

P=P is circular.

A cat is a cat. That's circular. It's not untrue. It's just uselessly true. It only becomes a fallacy if it is offered as an argument. But nobody is offering P=P as an argument, except you. So the only possible fallacy there is your own.

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.

[Eodnhoj7]

The fallacy of circularity...circularity.

A circular and empty response.

So while the premise and conclusion, or the beginning and end of the assertion are true, an absence of truth value occurs because of the absence of justification of the assertion through another assertion. 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 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.

[Immanuel Can]

So ...circularity.

The only two words you got right.

[Sculptor]

No two cats are the same. All cats are unique.

Not the point.

Why?

[Sculptor]

A cat is a cat. That's circular. It's not untrue. It's just uselessly true. It only becomes a fallacy if it is offered as an argument. But nobody is offering P=P as an argument, except you. So the only possible fallacy there is your own.

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".

[Immanuel Can]

No two cats are the same. All cats are unique.

Not the point.

Why?

Because 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 mid-sentence.