## What is P and -P?

### What is P and -P?

If (P=P)=(-P=-P) then P=-P through the law of identity which both P and -P share.

If (P=P)≠(-P=-P) then the law of identity is not equal to itself given both P and -P exist through the law of identity.

If (P=P)≠(-P=-P) then the law of identity is not equal to itself given both P and -P exist through the law of identity.

### Re: What is P and -P?

If you have to P so bad, why didn't you go before we left the house?

### Re: What is P and -P?

You're misusing and equivocating '=' multiple times. When you say P = P, what is P? Is it a number? Then the statement is an instance of the law of identity. But if you mean it's a proposition, the '=' has no meaning. You should use <=>, logical equivalence, if and only if. So it's like saying 3 = 3 and 5 = 5, and notating that to (3 = 3) = (5 = 5) and concluding by transitivity of '=' that 3 = 5. That's what you've done here.

Likewise -P. Is that the additive inverse of a number? Or do you mean logical negation?

Likewise (P=P) = (-P = -P). If P is a proposition, then you mean to say T = T but then you should use T <=> T, not '='. Else you'll fall into a transitivity error as you have here.

Your symbology is incoherent, since you go out of your way to use the wrong symbols, or use symbols whose meaning and referents are unclear, and then you use fallacious logic to reach invalid conclusions.

Which is exactly why I respond to you as I do. Now you've gotten a substantive technical reply. Hope you're happy. I'm not, I'm never getting this minute back.

### Re: What is P and -P?

1. P can represent any phenomena be it the number 1, a cat, or a proposition...and yes one proposition can equal another. "A dog ate the food therefore the dog is full" equals "A dog ate the food therefore the dog is full."wtf wrote: ↑Tue Jan 12, 2021 12:32 amYou're misusing and equivocating '=' multiple times. When you say P = P, what is P? Is it a number? Then the statement is an instance of the law of identity. But if you mean it's a proposition, the '=' has no meaning. You should use <=>, logical equivalence, if and only if. So it's like saying 3 = 3 and 5 = 5, and notating that to (3 = 3) = (5 = 5) and concluding by transitivity of '=' that 3 = 5. That's what you've done here.

Likewise -P. Is that the additive inverse of a number? Or do you mean logical negation?

Likewise (P=P) = (-P = -P). If P is a proposition, then you mean to say T = T but then you should use T <=> T, not '='. Else you'll fall into a transitivity error as you have here.

Your symbology is incoherent, since you go out of your way to use the wrong symbols, or use symbols whose meaning and referents are unclear, and then you use fallacious logic to reach invalid conclusions.

Which is exactly why I respond to you as I do. Now you've gotten a substantive technical reply. Hope you're happy. I'm not, I'm never getting this minute back.

2. "=" is undefined and assumed under P=P. "=" can be defined a multitude of ways. The "=" would have to be defined under the law of identity thus showing a self referentiality: "= --> =" or "= <--> =" or etc.

Under these terms "=" is defined through a middle variable as "= p =" where p is defined under "P=P" thus "P=P" is defined through "= P =" and both formulas are required to define the other.

Under these terms a statement such as "Cat is Cat" is defined through "is Cat is" where "is" defines "cat" and "cat" defines "is".

Through this reciprocality of one term defining the other the most accurate way to state an identity is P(p) or just "cat is".

3. The additive inverse of 1 is -1 thus the additive inverse is a negation.

4. P=-P observes + = - through the middle term of P where +P equivocates to -P through P. P is the common middle term through which seemingly opposite phenomenon equivocate. Dually both equivocate through the law of identity as both require the use of the law of identity.

5. An example of P=-P can be observed under the example of a horse in a field. A horse in a field observes specific affects of the horse on the field. Now take away the horse and this absence of horse shows specific effects in the field. The presence and absence of horse both observe specific affects in the field thus necessitating the horse as either present or absent defining the field. The horse form affects the field regardless of whether it is present or absent. Its presence shows an effect. The absence shows an effect. What is common in the presence or absence is the form of the horse itself. Both the horse and absence of horse equivocate through the field which is affected by both.

- Terrapin Station
**Posts:**1855**Joined:**Wed Aug 03, 2016 7:18 pm**Location:**NYC Man

### Re: What is P and -P?

Say what??

No.

If (P=P)=(-P=-P), that would only be because the whole thing in parentheses on the left-hand side amounts to something (such as "true" per one suggestion above) that's the same as the whole thing in parentheses on the right-hand side. You can't take just one segment of the parentheticals and claim that (P=P)=(-P=-P) implies that those segments are equal (or identical, or whatever you're using "=" to refer to exactly).

It would be like saying that since "The man who cuts my hair" has the same denotation as "The man who bought my car last week," because they both refer to Joe Jones, this implies that the denotations of "my hair" and "my car" are identical. Obviously that's not the case.

- Terrapin Station
**Posts:**1855**Joined:**Wed Aug 03, 2016 7:18 pm**Location:**NYC Man

### Re: What is P and -P?

An even simpler analogy to the mistake you're making would be this:

(2+3) = (1+4)

But this doesn't imply that 3=4.

(2+3) = (1+4)

But this doesn't imply that 3=4.

- Terrapin Station
**Posts:**1855**Joined:**Wed Aug 03, 2016 7:18 pm**Location:**NYC Man

### Re: What is P and -P?

Also, what is the following supposed to be saying?

P is standardly a variable representing a proposition. How would that "exist through the law of identity"?

From where are you getting the notion that both P and -P exist through the law of identity?

P is standardly a variable representing a proposition. How would that "exist through the law of identity"?

### Re: What is P and -P?

Both the hair and the car equivocate as property.Terrapin Station wrote: ↑Tue Jan 12, 2021 3:20 amSay what??

No.

If (P=P)=(-P=-P), that would only be because the whole thing in parentheses on the left-hand side amounts to something (such as "true" per one suggestion above) that's the same as the whole thing in parentheses on the right-hand side. You can't take just one segment of the parentheticals and claim that (P=P)=(-P=-P) implies that those segments are equal (or identical, or whatever you're using "=" to refer to exactly).

It would be like saying that since "The man who cuts my hair" has the same denotation as "The man who bought my car last week," because they both refer to Joe Jones, this implies that the denotations of "my hair" and "my car" are identical. Obviously that's not the case.

Using a number line both +1 and -1 are equal lengths from point 0 thus equivocate in these respects.

### Re: What is P and -P?

P requires P=P in order to exist.Terrapin Station wrote: ↑Tue Jan 12, 2021 3:34 am Also, what is the following supposed to be saying?From where are you getting the notion that both P and -P exist through the law of identity?

P is standardly a variable representing a proposition. How would that "exist through the law of identity"?

-P requires -P=-P in order to exist.

### Re: What is P and -P?

1+4 is not the negation of 2+3 however.Terrapin Station wrote: ↑Tue Jan 12, 2021 3:23 am An even simpler analogy to the mistake you're making would be this:

(2+3) = (1+4)

But this doesn't imply that 3=4.

A better analogy would be a glass half full of water and half empty space. Both the empty space and the water equivocate through the glass considering both take shape through the empty glass. Glass is the middle form both the water and empty space take form through. The same applies to the proposition where P is the common middle term amidst +P and -P.

- Terrapin Station
**Posts:**1855**Joined:**Wed Aug 03, 2016 7:18 pm**Location:**NYC Man

### Re: What is P and -P?

(1) They're notEodnhoj7 wrote: ↑Thu Jan 14, 2021 4:55 amBoth the hair and the car equivocate as property.Terrapin Station wrote: ↑Tue Jan 12, 2021 3:20 amSay what??

No.

If (P=P)=(-P=-P), that would only be because the whole thing in parentheses on the left-hand side amounts to something (such as "true" per one suggestion above) that's the same as the whole thing in parentheses on the right-hand side. You can't take just one segment of the parentheticals and claim that (P=P)=(-P=-P) implies that those segments are equal (or identical, or whatever you're using "=" to refer to exactly).

It would be like saying that since "The man who cuts my hair" has the same denotation as "The man who bought my car last week," because they both refer to Joe Jones, this implies that the denotations of "my hair" and "my car" are identical. Obviously that's not the case.

Using a number line both +1 and -1 are equal lengths from point 0 thus equivocate in these respects.

*identical*.

(2) Equivocation is a fallacy when we're doing logic.

- Terrapin Station
**Posts:**1855**Joined:**Wed Aug 03, 2016 7:18 pm**Location:**NYC Man

### Re: What is P and -P?

Repeating that makes it no less nonsensical.Eodnhoj7 wrote: ↑Thu Jan 14, 2021 4:55 amP requires P=P in order to exist.Terrapin Station wrote: ↑Tue Jan 12, 2021 3:34 am Also, what is the following supposed to be saying?From where are you getting the notion that both P and -P exist through the law of identity?

P is standardly a variable representing a proposition. How would that "exist through the law of identity"?

-P requires -P=-P in order to exist.

- Terrapin Station
**Posts:**1855**Joined:**Wed Aug 03, 2016 7:18 pm**Location:**NYC Man

### Re: What is P and -P?

This tells me that you don't understand the term "equivocate."

You need to learn the basics of this stuff before you try to forward arguments about it.