Negation of Classical Identity Laws Using Classical Identity Laws.

[Gary Childress]

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.

The law of identity is that anything referred to equals itself. It doesn't mean that the law of identity itself is equal to "P=P", and then you can plug it into symbolic logic using logical/mathematical notation to prove that not the case P = not the case P is equal to P=P. Thte law of identity is a pre-step to symbolic logic necessary to make logic itself work. It is outside of the equations. "P" is a placeholder for a "something", and a "something" does not equal all somlethings except in a semantic sense. A cat is a thing. A dog is a thing. A cat does not = a dog. Something = something, referring only to the word itself, not referring to what the word indirectly represents. Or think of Doberman and Collie. Both are Dogs (both are "things") but they are not equivalent to each other. They are not the same thing.

I wish I could remember symbolic logic well enough to give an answer in symbolic logic; however, your statement "(P=P)=(not the case P=not the case P) is clearly a flawed argument, as the example of Dog and Cat easily demonstrates.

Or is your point to say that the law of identity itself cannot be trusted? For example, "Napoleon, the leader of France" maybe is not the same as "Napoleon, the General", in a sense. They are not logically identical terms. But they can be made logically identical with the right notations. For example if we both agree that "Napoleon was both a leader of France and a General" then we could subsitute the two separate terms "Napoleon, the leader of France" and "Napoleon, the General" with "Napoleon who was both the leader of France and a General" We must both agree to the statement and then when we both agree we can plug it into a logical argument to see what we come up with. But it's important to get the terms identical in order for the law of identity to work in logic. And if two things are not the same thing, then they are not the same thing according to the fundamental premise that P=P. Meaning the same P = the same P.

[thomyum2]

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.

I don't know what you mean by this. The law of identity and the law of non-contradiction are two different things. The law of non-contradiction asserts nothing about identity.

The law of identity only applies to singular terms. As per my, and Inpenitent's, examples, 'not P' (assuming that's what you mean by '-P') is not a singular term because 'not P' encompasses any number of things which are not identical to P. So (-P=-P) does not correctly represent the law of identity as you have stated in the second step.

[Gary Childress]

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.

I don't know what you mean by this. The law of identity and the law of non-contradiction are two different things. The law of non-contradiction asserts nothing about identity.

The law of identity only applies to singular terms. As per my, and Inpenitent's, examples, 'not P' (assuming that's what you mean by '-P') is not a singular term because 'not P' encompasses any number of things which are not identical to P. So (-P=-P) does not correctly represent the law of identity as you have stated in the second step.

Hmm. I didn't think that maybe he was mixing the law of non-contradiction with the law of identity. But now that you mention it and judging from his quote, it does look (at first glance to me) that maybe he is.

[Eodnhoj7]

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.

I don't know what you mean by this. The law of identity and the law of non-contradiction are two different things. The law of non-contradiction asserts nothing about identity.

The law of identity only applies to singular terms. As per my, and Inpenitent's, examples, 'not P' (assuming that's what you mean by '-P') is not a singular term because 'not P' encompasses any number of things which are not identical to P. So (-P=-P) does not correctly represent the law of identity as you have stated in the second step.

If the law of non-contradiction asserts nothing about identity then A=/=-A requires A and -A as having no identities thus there is no LNC.

LNC requires A=A and -A=-A if A=/=-A where at the meta level it is revealed as (A=A)=/=(-A=-A)....which also simultaneously points out the LI is not equal to itself.

Also if LNC is to have identity it is subject to LI as LNC = LNC, but previously it was shown the LI =/= LI under the context of LNC.

The laws consume themselves.

[Eodnhoj7]

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.

I don't know what you mean by this. The law of identity and the law of non-contradiction are two different things. The law of non-contradiction asserts nothing about identity.

The law of identity only applies to singular terms. As per my, and Inpenitent's, examples, 'not P' (assuming that's what you mean by '-P') is not a singular term because 'not P' encompasses any number of things which are not identical to P. So (-P=-P) does not correctly represent the law of identity as you have stated in the second step.

Hmm. I didn't think that maybe he was mixing the law of non-contradiction with the law of identity. But now that you mention it and judging from his quote, it does look (at first glance to me) that maybe he is.

Read my response to him.

[Eodnhoj7]

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

If true equals true, as (P=P)=(-P=-P) and P and -P are expressed respectively as P=P and -P=-P then (P=P)=(-P=-P) reduces to P=-P and LNC fails.

[Gary Childress]

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.

I don't know what you mean by this. The law of identity and the law of non-contradiction are two different things. The law of non-contradiction asserts nothing about identity.

The law of identity only applies to singular terms. As per my, and Inpenitent's, examples, 'not P' (assuming that's what you mean by '-P') is not a singular term because 'not P' encompasses any number of things which are not identical to P. So (-P=-P) does not correctly represent the law of identity as you have stated in the second step.

If the law of non-contradiction asserts nothing about identity then A=/=-A requires A and -A as having no identities thus there is no LNC.

What do you mean by -A? Do you mean -A = (not the case A), or are you creating something you are calling "negative A"?

[Eodnhoj7]

I don't know what you mean by this. The law of identity and the law of non-contradiction are two different things. The law of non-contradiction asserts nothing about identity.

The law of identity only applies to singular terms. As per my, and Inpenitent's, examples, 'not P' (assuming that's what you mean by '-P') is not a singular term because 'not P' encompasses any number of things which are not identical to P. So (-P=-P) does not correctly represent the law of identity as you have stated in the second step.

If the law of non-contradiction asserts nothing about identity then A=/=-A requires A and -A as having no identities thus there is no LNC.

What do you mean by -A? Do you mean -A = (not the case A), or are you creating something you are now calling "negative A"?

If A and -A have no identity under the LI, then LNC is saying nothing as there ks not identity.

At the meta-level A=/=-A is (A=A)=/=(-A=-A). If not then the A and -A in A=/=-A have no identities and LNC is self-negated as saying nothing.

If they do have identities, as (A=A)=/=(-A=-A) then LI is not equal to itself and LNC collapses because LI collapses

[Gary Childress]

If the law of non-contradiction asserts nothing about identity then A=/=-A requires A and -A as having no identities thus there is no LNC.

What do you mean by -A? Do you mean -A = (not the case A), or are you creating something you are now calling "negative A"?

If A and -A have no identity under the LI, then LNC is saying nothing as there ks not identity.

At the meta-level A=/=-A is (A=A)=/=(-A=-A). If not then the A and -A in A=/=-A have no identities and LNC is self-negated as saying nothing.

If they do have identities, as (A=A)=/=(-A=-A) then LI is not equal to itself and LNC collapses because LI collapses

So for concrete example [Cats do not = non cats] is the same as [(cats = cats) does not = (non cats = non cats)]? Is that what you are saying?

[Eodnhoj7]

What do you mean by -A? Do you mean -A = (not the case A), or are you creating something you are now calling "negative A"?

If A and -A have no identity under the LI, then LNC is saying nothing as there ks not identity.

At the meta-level A=/=-A is (A=A)=/=(-A=-A). If not then the A and -A in A=/=-A have no identities and LNC is self-negated as saying nothing.

If they do have identities, as (A=A)=/=(-A=-A) then LI is not equal to itself and LNC collapses because LI collapses

So for concrete example [Cats do not = non cats] is the same as [(cats = cats) = (non cats = non cats)]? Is that what you are saying?

What I am saying is under LNC LI=/=LI, I am also saying Under LI A=-A as both are LI. The laws self-consume under there own application and the laws have to be applied to themselves if they are to have an identity.

[Gary Childress]

If A and -A have no identity under the LI, then LNC is saying nothing as there ks not identity.

At the meta-level A=/=-A is (A=A)=/=(-A=-A). If not then the A and -A in A=/=-A have no identities and LNC is self-negated as saying nothing.

If they do have identities, as (A=A)=/=(-A=-A) then LI is not equal to itself and LNC collapses because LI collapses

So for concrete example [Cats do not = non cats] is the same as [(cats = cats) = (non cats = non cats)]? Is that what you are saying?

What I am saying is under LNC LI=/=LI, I am also saying Under LI A=-A as both are LI. The laws self-consume under there own application and the laws have to be applied to themselves if they are to have an identity.

1) So the law of identity does not = the law of identity according to the law of non-contradiction? Is that what your conclusion is?

2) And A is = to not the case A according to the law of identity?

Is that what you are saying?

Both statements #1 and #2 seem blatantly false as far as I can tell. So if your statements #1 and #2 are false, then what is your argument? There must be more to it than that.

[Eodnhoj7]

So for concrete example [Cats do not = non cats] is the same as [(cats = cats) = (non cats = non cats)]? Is that what you are saying?

What I am saying is under LNC LI=/=LI, I am also saying Under LI A=-A as both are LI. The laws self-consume under there own application and the laws have to be applied to themselves if they are to have an identity.

1) So the law of identity does not = the law of identity according to the law of non-contradiction? Is that what your conclusion is?

2) And A is = to not the case A according to the law of identity?

Is that what you are saying?

Both statements #1 and #2 seem blatantly false as far as I can tell. So if your statements #1 and #2 are false, then what is your argument? There must be more to it than that.

And how can you tell? I do not see a counter argument about the application of identity laws on identity laws.

I see an empty assertion.

So lets break it down:

Does A=/=-A require A=A and -A=-A?

[Gary Childress]

What I am saying is under LNC LI=/=LI, I am also saying Under LI A=-A as both are LI. The laws self-consume under there own application and the laws have to be applied to themselves if they are to have an identity.

1) So the law of identity does not = the law of identity according to the law of non-contradiction? Is that what your conclusion is?

2) And A is = to not the case A according to the law of identity?

Is that what you are saying?

Both statements #1 and #2 seem blatantly false as far as I can tell. So if your statements #1 and #2 are false, then what is your argument? There must be more to it than that.

And how can you tell? I do not see a counter argument about the application of identity laws on identity laws.

I see an empty assertion.

So lets break it down:

Does A=/=-A require A=A and -A=-A?

How can I tell what? That statements #1 and #2 (which you made in the post above mine) are false? Are you saying they aren't false?

[Eodnhoj7]

1) So the law of identity does not = the law of identity according to the law of non-contradiction? Is that what your conclusion is?

2) And A is = to not the case A according to the law of identity?

Is that what you are saying?

Both statements #1 and #2 seem blatantly false as far as I can tell. So if your statements #1 and #2 are false, then what is your argument? There must be more to it than that.

And how can you tell? I do not see a counter argument about the application of identity laws on identity laws.

I see an empty assertion.

So lets break it down:

Does A=/=-A require A=A and -A=-A?

How can I tell what? That statements #1 and #2 (which he made in the post above mine) are false? Are you saying they aren't false?

If you want an answer then answer the question:

Does A=/=-A require A=A and -A=-A?

[Gary Childress]

And how can you tell? I do not see a counter argument about the application of identity laws on identity laws.

I see an empty assertion.

So lets break it down:

Does A=/=-A require A=A and -A=-A?

How can I tell what? That statements #1 and #2 (which he made in the post above mine) are false? Are you saying they aren't false?

If you want an answer then answer the question:

Does A=/=-A require A=A and -A=-A?

Perhaps it does. I don't have the logic skills anymore to run it through symbolic or predicate logic. But what the OP is saying seems to be that if A does not = (not the case A) [the law of non-contradiction] and at the same time A = A [the law of identity], that there is some kind of contradiction there between those two axioms. Do you see the contradiction? I don't.