The Philosophy Discussion Forum

Negation of Classical Identity Laws Using Classical Identity Laws.





I.



1. (P=P) is the law of identity.



2. (-P=-P) is the law of identity.



3. ((P=P)=(-P=-P)) is the law of identity equal to the law of identity.



4. (P=P)=P and (-P=-P)= -P is the law of identity as equal to a singular expression; (P=P) is reducible to P, (-P=-P) is reducible to -P.



5. ((P=P)=(-P=-P)) is reducible to (P=-P).



6. P=-P cannot exist due to the law of non-contradiction however ((P=P)=(-P=-P)) is valid.



7. The law of non-contradiction does not exist if (P=P) exists as (P=P) necessitates ((P=P)=(-P=-P)) which is (P=-P); (P=P) does not exist if the law of non-contradiction exists as (P=/=-P) but (P=P) necessitates ((P=P)=(-P=-P)) which is (P=-P).





8. Either the law of non contradiction exists or the law of identity exists, if not then both exist meaning neither exists, however if one exists and the other does not then both cease due to absence of contrast as with LNC A=-A and without LI A=/=A is valid given the contrast is the mechanic of equality and inequality relative to each.



II



(P=P) observes P as a container for -P thus in arguing for (P=P) it contains (-P=-P). This container is expressed as such:



P is a containment variable. It contains within it a distinction. -P is a distinction, thus P can contain the distinct of -P.



Dually the container is biconditionality as one distinction contains the other by contrast.



-P as a container within a container contains -P as (--P=--P) thus (-P=-P) contains (P=P). Both P=P and -P=-P are containers for each other and are effectively united and equivalent.



As equivalent ((P=P)=(-P=-P)) occurs with this being reducible to P=-P.





Dually both (P=P) and (-P=-P) equate as both expressions of the law of identity; to say ((P=P)=(-P=-P)) is to say the law of identity is equivalent to itself.



P=-P



Examples:





1. "Judas hanged at x time" and "Judas did not hang at x time"; if Judas was standing on a stool with his toes planted while a rope hung around his neck holding up half of his weight he both hanged and not-hanged.



2. One road goes both ways.



3. A square peg equates to a square hole as both are squares.



4. Things exist through change thus the potential state of something must exist within the actual.



5. "We step and do not step into the same rivers; we are and we are not" Heraclitus



6. If all exists as one then opposites must equate to eachother; there is a totality of being thus being is one therefore opposites are one.



7. At an instance of change both the actual and potential are one.



8. Continuous expansion and contraction, thus opposition, at the same time in the same context is a circle.



III.





1. A=A equivocates to A=P as P is just another way of saying A.



2. P=P equivocates to P=A as A is just another way of saying P.



3. A=A equivocates to P=P if A=P.



4. However, A=A and P=P are both distinctly different expressions of the same phenomenon.



5. As distinctly different expressions they are not the same phenomenon as the expression must equal itself under the laws of identity; yet these different expressions equivocate.



6. Equivocation thus can mean many things and as such is self-negating as one degree of equivocation is not equal to another degree of equivocation.

Eodnhoj7 wrote: ↑Tue Jun 09, 2026 10:32 pm Negation of Classical Identity Laws Using Classical Identity Laws.

I.

1. (P=P) is the law of identity.

2. (-P=-P) is the law of identity.

It seems to me that you've made an error at this second step. While this would be true for any number P, it is not true for non-numbers. The law of identity states that 'everything is what it is' and 'is not what it is not'. That does not mean that everything that is 'not P' is the same. My cat is identical to my cat. But my dog (which is 'not my cat') is most certainly not identical to my table (although it is also 'not my cat').

But I've probably misinterpreted what you are saying here, which is inevitable given that most of what you post here is without any commentary or explanation to help your readers understand, so your thought process is pretty opaque to me, as I'm guessing it also is to most of us here.

His fatal error is in #4

thomyum2 wrote: ↑Wed Jun 10, 2026 6:04 pm

Eodnhoj7 wrote: ↑Tue Jun 09, 2026 10:32 pm Negation of Classical Identity Laws Using Classical Identity Laws.

I.

1. (P=P) is the law of identity.

2. (-P=-P) is the law of identity.

It seems to me that you've made an error at this second step. While this would be true for any number P, it is not true for non-numbers. The law of identity states that 'everything is what it is' and 'is not what it is not'. That does not mean that everything that is 'not P' is the same. My cat is identical to my cat. But my dog (which is 'not my cat') is most certainly not identical to my table (although it is also 'not my cat').

But I've probably misinterpreted what you are saying here, which is inevitable given that most of what you post here is without any commentary or explanation to help your readers understand, so your thought process is pretty opaque to me, as I'm guessing it also is to most of us here.

If the second step is an error than -P is not an identity and cannot be asserted as an identity in the law of non-contradiction.

phyllo wrote: ↑Wed Jun 10, 2026 6:11 pm His fatal error is in #4

The error of you argument is the lack of one.

It was an observation, not an argument.

phyllo wrote: ↑Thu Jun 11, 2026 3:34 am It was an observation, not an argument.

It was an observation, not an argument can be said likewise.

Anyone can claim "right" or "wrong". No definition behind it just leaves a tautology.

The text has been test multiple times, against multiple AIs. The simple truth is that your response only proves human intellect becoming obsolete.

AI says that (P=P)=P evaluates to P

IOW, the identity law would be ((P=P)=P)=P which evaluates to True

Eodnhoj7 wrote: ↑Thu Jun 11, 2026 9:46 pm

phyllo wrote: ↑Thu Jun 11, 2026 3:34 am It was an observation, not an argument.

It was an observation, not an argument can be said likewise.

Anyone can claim "right" or "wrong". No definition behind it just leaves a tautology.

The text has been test multiple times, against multiple AIs. The simple truth is that your response only proves human intellect becoming obsolete.

So what is your reply to the point that thomyum2 made? And what do you mean when you posit that

Dually both (P=P) and (-P=-P) equate as both expressions of the law of identity; to say ((P=P)=(-P=-P)) is to say the law of identity is equivalent to itself.

I mean, I don't see how (P=P) = (not the case P=not the case P). It sounds like you're making a logical mistep somewhere, though my logic is rusty these days.

p=red
blue is not the case p
green is not the case p

blue does not equal green
(but you can't prove a negative - which ironically is a negative claim itself)

-Imp

Impenitent wrote: ↑Fri Jun 12, 2026 7:27 pm p=red
blue is not the case p
green is not the case p

blue does not equal green
(but you can't prove a negative - which ironically is a negative claim itself)

-Imp

That definitely seems to be the misstep. I'm just not remembering how purely symbolic logic works. So I can't point to a mathematical (or logical) term for the error other than to say that not the case P does not necessarily = not the case P. But since symbolic logic cannot contradict reality and remain true, and blue and green are both not red, but blue and green are not identical, your explanation probably sums the error up better than terminology would.

P is True or False

phyllo wrote: ↑Fri Jun 12, 2026 9:12 pm P is True or False

P=P is the law of identity.
True and false are subject to LI, if not then they have no identity.

Gary Childress wrote: ↑Fri Jun 12, 2026 3:56 pm

Eodnhoj7 wrote: ↑Thu Jun 11, 2026 9:46 pm

phyllo wrote: ↑Thu Jun 11, 2026 3:34 am It was an observation, not an argument.

It was an observation, not an argument can be said likewise.

Anyone can claim "right" or "wrong". No definition behind it just leaves a tautology.

The text has been test multiple times, against multiple AIs. The simple truth is that your response only proves human intellect becoming obsolete.

So what is your reply to the point that thomyum2 made? And what do you mean when you posit that

Dually both (P=P) and (-P=-P) equate as both expressions of the law of identity; to say ((P=P)=(-P=-P)) is to say the law of identity is equivalent to itself.

I mean, I don't see how (P=P) = (not the case P=not the case P). It sounds like you're making a logical mistep somewhere, though my logic is rusty these days.

P=P is LI.
-P=-P is LI

LI = LI as LI.

I mean, I don't see how (P=P) = (not the case P=not the case P). It sounds like you're making a logical mistep somewhere, though my logic is rusty these days.

P=P evaluates as True

-P=-P evaluates as True

(P=P)=(-P=-P) evaluates as True since it's the same as True=True