The Law of Identity

[attofishpi]

The Law of Identity

Skeppy, as you know I am kind of new to much of this stuff. I am somewhat confused by the concept of the thread title.

My question to google replies:
"The Law of Identity, a fundamental principle in logic, states that anything is identical to itself; meaning "a=a" or for all x: x=x. It's one of the three foundational laws of logic, alongside the Law of Contradiction and the Law of Excluded Middle."

It also stated that "a house = a house"..

This is my confusion since obviously houses come in various forms thus there is a lot of subjective consideration per as to what is a house. Some would say, "that's not a house, that's a bungalow".

Thus, is it only accurate to say: "a house = a house" in the context say, that in computer terms of a variable form: strcmp("a house", "a house") == TRUE?

[Skepdick]

The Law of Identity

Skeppy, as you know I am kind of new to much of this stuff. I am somewhat confused by the concept of the thread title.

My question to google replies:
"The Law of Identity, a fundamental principle in logic, states that anything is identical to itself; meaning "a=a" or for all x: x=x. It's one of the three foundational laws of logic, alongside the Law of Contradiction and the Law of Excluded Middle."

It also stated that "a house = a house"..

This is my confusion since obviously houses come in various forms thus there is a lot of subjective consideration per as to what is a house. Some would say, "that's not a house, that's a bungalow".

Thus, is it only accurate to say: "a house = a house" in the context say, that in computer terms of a variable form: strcmp("a house", "a house") == TRUE?

That's a colloquial misunderstanding. It's a conflation of identity with equality which are distinct notion.

Different houses can be equal in certain respects (both being houses) while still having distinct identities.

strcmp/equality compares the objects contain the same data.
identity compares whether they are the same object in memory e.g whether they exist at the same memory location.

The best way I can explain this is with code.

Take two variables a=house, b=house.

Code: Select all

[1] pry(main)> a = "house"
=> "house"
[2] pry(main)> b = "house"
=> "house"

a is equivalent AND identical to a.

Code: Select all

[3] 
 pry(main)> a == a
=> true
[4] pry(main)> a.__id__ == a.__id__

a is equivalent, but not identical to b.

Code: Select all

[5] pry(main)> a == b
=> true
[6] pry(main)> a.__id__ == b.__id__
=> false

[attofishpi]

The Law of Identity

Skeppy, as you know I am kind of new to much of this stuff. I am somewhat confused by the concept of the thread title.

My question to google replies:
"The Law of Identity, a fundamental principle in logic, states that anything is identical to itself; meaning "a=a" or for all x: x=x. It's one of the three foundational laws of logic, alongside the Law of Contradiction and the Law of Excluded Middle."

It also stated that "a house = a house"..

This is my confusion since obviously houses come in various forms thus there is a lot of subjective consideration per as to what is a house. Some would say, "that's not a house, that's a bungalow".

Thus, is it only accurate to say: "a house = a house" in the context say, that in computer terms of a variable form: strcmp("a house", "a house") == TRUE?

That's a colloquial misunderstanding. It's a conflation of identity with equality which are distinct notion.

Different houses can be equal in certain respects (both being houses) while still having distinct identities.

strcmp/equality compares the objects contain the same data.
identity compares whether they are the same object in memory e.g whether they exist at the same memory location.

The best way I can explain this is with code.

Take two variables a=house, b=house.

Code: Select all

[1] pry(main)> a = "house"
=> "house"
[2] pry(main)> b = "house"
=> "house"

a is equivalent AND identical to a.

Understood - a is a.

..but a is NOT b (different memory locations), am I correct thus far?

I guess my point is - obviously a is a (the same identity)

Two pointers to the same memory address, are they considered identical (per this Law of Identity)?

Outside of computer logic, the claim that a house is a house TRUE to the Law of Identity has me confused, since, ok the term house is a house IS TRUE, but not all houses are identical thus fail the law of identity? That's to say, ONLY the term (the English name for a house) is TRUE, the context of what it actually is is irrelevant?

[Skepdick]

..but a is NOT b (different memory locations), am I correct thus far?

Maybe. They could be one and the same memory location. Or they could be two different memory locations.

Code: Select all

[1] pry(main)> a = "house"
=> "house"
[2] pry(main)> b = a
=> "house"
[3] pry(main)> a.__id__ == b.__id__
=> true

I guess my point is - obviously a is a (the same identity)

Two pointers to the same memory address, are they considered identical (per this Law of Identity)?

Yes.

Outside of computer logic, the claim that a house is a house TRUE to the Law of Identity has me confused, since, ok the term house is a house IS TRUE, but not all houses are identical thus fail the law of identity? That's to say, ONLY the term (the English name for a house) is TRUE, the context of what it actually is is irrelevant?

To say that any noun is "true" is to simply assert the noun.

Is a cat "true"? It's a cat!

[attofishpi]

..but a is NOT b (different memory locations), am I correct thus far?

Maybe. They could be one and the same memory location. Or they could be two different memory locations.

Code: Select all

[1] pry(main)> a = "house"
=> "house"
[2] pry(main)> b = a
=> "house"
[3] pry(main)> a.__id__ == b.__id__
=> true

I guess my point is - obviously a is a (the same identity)

Two pointers to the same memory address, are they considered identical (per this Law of Identity)?

Yes.

Outside of computer logic, the claim that a house is a house TRUE to the Law of Identity has me confused, since, ok the term house is a house IS TRUE, but not all houses are identical thus fail the law of identity? That's to say, ONLY the term (the English name for a house) is TRUE, the context of what it actually is is irrelevant?

To say that any noun is "true" is to simply assert the noun.

Is a cat "true"? It's a cat!

This Law of Identity seems rather pointless to me, or am I missing some important significance?

Of course a noun is a noun and the word "house" is identical to the word "house"..

Did this concept Law of Identity come about due to the advent of digital computers?

[Skepdick]

This Law of Identity seems rather pointless to me, or am I missing some important significance?

Of course a noun is a noun and the word "house" is identical to the word "house"..

Did this concept Law of Identity come about due to the advent of digital computers?

It's not pointless. The very point is that identity is a self-relation. You are only identical to yourself.

When you are being compared to other people to assert that you are "identical" to <insert other person> your identity is being sidelined for some pragmatic convenience. You are identical to Hitler; and you are identical to Mother Theresa are different comparatives.

Identity is uniqueness. In an absolute, ontological sense.

[attofishpi]

This Law of Identity seems rather pointless to me, or am I missing some important significance?

Of course a noun is a noun and the word "house" is identical to the word "house"..

Did this concept Law of Identity come about due to the advent of digital computers?

It's not pointless. The very point is that identity is a self-relation. You are only identical to yourself.

When you are being compared to other people to assert that you are "identical" to <insert other person> your identity is being sidelined for some pragmatic convenience. You are identical to Hitler; and you are identical to Mother Theresa are different comparatives.

Identity is uniqueness. In an absolute, ontological sense.

Ah, thanks..well that makes sense now - outside of the digital sphere.

..eventually I'll start investigating this LEM thang.

[Magnus Anderson]

Did this concept Law of Identity come about due to the advent of digital computers?

Aristotle was the first to formulate it. Back then, there were no digital computers at all, weren't there?

And note that Aristotle didn't call it "the Law of Identity". He didn't use the word "identity" at all. He didn't distinguish between "numerical identity" ( one and the same ) and "qualitative identity" ( the same. ) There was no need to.

He merely said that if a portion of reality exists in a state S, then it exists in that state S.

This means that if an apple is red, that it is red.
And because it is red, it means that it is not not red ( e.g. green. )

It is the Law of Identity that prohibits things from being in multiple different states at the same time.
It is the Law of Identity that makes contradictions unacceptable.

The Law of Non-Contradiction merely explicitly states what is implicitly stated by the Law of Identity.

[attofishpi]

OK. Cheers Magnus.

[anthonypaulrobinson]

A is never anything, but a first letter Uralic-Altaic word.

I know this, because I’m Venetian Iranian.

[Eodnhoj7]

The Law of Identity, one of the fundamental laws of classical logic, states that everything is whatever it is.

It is often expressed as "A is A" and "A = A".

The equals sign represents equality and the two A's are symbols representing one and the same portion of reality.

It is basically saying that every portion of reality is equal, i.e. identical, to itself.

Here in this thread I will present my proof of it and try to address as many fallacious counter-arguments as I can find and cover.

I only do this because there are a bit too many people attacking this law ( and thereby undermining logic. )

1. My Proof
2. "Everything changes" counter-argument
3. "You have to perform a comparison" claim
4. "You have to stop time" counter-argument
5. "You can't compare a thing to itself" argument

If A gains identity by being equal to itself than how does equality have any identity so as to be identitfied as equal?

[Scott Mayers]

It is basically saying that every portion of reality is equal, i.e. identical, to itself.

It merely says that every portion of reality is equal to itself.

Equivocation

Identity is not identical to equality.

See the long fucking thread where you failed to understand this despite numerous explanations.

I only do this because there are a bit too many people attacking this law ( and thereby undermining logic. )

The only person "attacking" this law is you. By erasing the distinction between identity and equality.

Or are you 'equivocating' , Skepdick? (Oh,....and hi. I haven't been here in a long time and am a bit surprised this topic is even still argued.)

For general response to any reader:

I just started reading this thread and so still need to catch up to what anyone is saying here. But I agree with the author of this thread given you cannot even begin to develop a logic without presuming the intent of the 'laws of (any) logic" requires some symbols to reference to some other reality. While 'identity' and 'equality CAN be defined uniquely within any SPECIFIC logic (a 'language'), the POINT of these laws are to assert that one has to be 'consistent' to keep the meaning of the symbols being used constant to itself. That is, the meaning of a symbol at least has to keep the same referent throughout an argument when discussing it. If this wasn't the case, then we could not communicate because we'd be constantly confused at what anything means. The '=' sign is often used but again contextually means LOGICAL identity.

It CAN be possible for another person to use your account here to post. If multiple users argue through your account, this hidden factor is relatively 'variable' but not relevant to those here reading. We just agree in principle that "Skepdick", for instance, will still be the same person speaking unless we run into seriously conflicting arguments that may suggest being suspicious. We 'agree' to the assumption of consistency of the name -- and is probably in our 'acceptance' when signing up here -- such that the author is to be presumed to be the same author of all the posts under our usernames.

A logic CAN be defined to use any symbol for equality and so whether one chooses to express this law using that sign or the more formal sign, "≡" or "=" for 'logical equivalence' is irrelevant. In fact, it is better to use the "=" because whether the symbol refers to an 'address' label (a variable) or to assigning this to constants (such as the particular value of a variable), the actual variable is still a 'variable' and a constant is still a 'constant' at the very least. If I use X[ ] to refer to a variable (or memory location, say), then what it contains as a 'constant' is distinctly different. That is, X[ ] = X[ ] refers to the address or variable named. and "X=X" refers to a constant.

So X[ ] = X[ ] refers to the variable, for instance, and X = X refers to a constant where both of these are still true regardless. I can choose to use X[X] to mean "the variable named 'X' contains the constant value 'X'. And so if I try to say,

X[X] = X[y] ,

...either y = X or this is referring only to the address and not its contents. Math often uses 'dummy' variables to stand in for 'don't-care' type conditions where what you put into the variable or address is irrelevant. The 'equality' is to the address and not its contents in X[ (this is irrelevant)] = X[(so this can differ) ]. We are referring here to the meaning of the address name, not its contents. If we are not allowed to do this, we are prevented to be considered 'logical'.

So X[?] = X[?] and X = X which reduces to whatever symbols that are the same on both sides of the equality symbol. I intentionally picked, "?" as a 'dummy' symbol because it helps get my point across. The law of 'identity' is one about a "logical equivalence" that is still maintained as 'equal' IN MEANING but not necessarily in concepts that can discretely hold different values. So this is easiest to state:

Law of Identity. X = X,

with sufficient universal meaning to all logical systems.This along a couple other laws DEFINES what 'logic' is. You don't have to be 'logical' by refusing to accept this essential property. But then whatever form of 'reasoning' you may try to use without this law is 'indeterminate' in principle. If something changes meaning without being logically consistent how can we possibly make use of it for reasoning.

And ALL other logics, including those that may accept contradictions as a function to indicate a need for changing the mode of logic, still is able to be built up using the initial 'laws of logic" as standard to construct all the other logic systems, including any multivariable ones, on top of it.

[Skepdick]

But I agree with the author of this thread given you cannot even begin to develop a logic without presuming the intent of the 'laws of (any) logic" requires some symbols to reference to some other reality.

That premise is not true. What reality are we referencing when we do symbolic logic? What is the symbol "∃" referencing? Tell me about its idenitty.

While 'identity' and 'equality CAN be defined uniquely within any SPECIFIC logic (a 'language'), the POINT of these laws are to assert that one has to be 'consistent' to keep the meaning of the symbols being used constant to itself.

So what external reality are you referencing to when using the symbol "meaning" ?

That is, the meaning of a symbol at least has to keep the same referent throughout an argument when discussing it. If this wasn't the case, then we could not communicate because we'd be constantly confused at what anything means. The '=' sign is often used but again contextually means LOGICAL identity.

So what's the meaning of symbol "true"; and "truth" and why is it inconsistent? How come we can still communicate true things?

A logic CAN be defined to use any symbol for equality and so whether one chooses to express this law using that sign or the more formal sign, "≡" or "=" for 'logical equivalence' is irrelevant. In fact, it is better to use the "=" because whether the symbol refers to an 'address' label (a variable) or to assigning this to constants (such as the particular value of a variable), the actual variable is still a 'variable' and a constant is still a 'constant' at the very least. If I use X[ ] to refer to a variable (or memory location, say), then what it contains as a 'constant' is distinctly different. That is, X[ ] = X[ ] refers to the address or variable named. and "X=X" refers to a constant.

So X[ ] = X[ ] refers to the variable, for instance, and X = X refers to a constant where both of these are still true regardless. I can choose to use X[X] to mean "the variable named 'X' contains the constant value 'X'. And so if I try to say,

X[X] = X[y] ,

...either y = X or this is referring only to the address and not its contents. Math often uses 'dummy' variables to stand in for 'don't-care' type conditions where what you put into the variable or address is irrelevant. The 'equality' is to the address and not its contents in X[ (this is irrelevant)] = X[(so this can differ) ]. We are referring here to the meaning of the address name, not its contents. If we are not allowed to do this, we are prevented to be considered 'logical'.

So X[?] = X[?] and X = X which reduces to whatever symbols that are the same on both sides of the equality symbol. I intentionally picked, "?" as a 'dummy' symbol because it helps get my point across. The law of 'identity' is one about a "logical equivalence" that is still maintained as 'equal' IN MEANING but not necessarily in concepts that can discretely hold different values. So this is easiest to state:

Law of Identity. X = X,

with sufficient universal meaning to all logical systems.This along a couple other laws DEFINES what 'logic' is. You don't have to be 'logical' by refusing to accept this essential property. But then whatever form of 'reasoning' you may try to use without this law is 'indeterminate' in principle. If something changes meaning without being logically consistent how can we possibly make use of it for reasoning.

And ALL other logics, including those that may accept contradictions as a function to indicate a need for changing the mode of logic, still is able to be built up using the initial 'laws of logic" as standard to construct all the other logic systems, including any multivariable ones, on top of it.

It doesn't matter which symbol you use.

Part of the problem is that "X = X" is an incomplete expression. X=X is ... what? True? False? Chicken? 0.123134? The answer to life the universe and everything?

Here is a perfectly coherent symbolic system in which X = X is NOT True in the Boolean sense.
It evaluates to a random value between 0 and 1.

Code: Select all

class Wut:
    def __eq__(self, other):
        from random import random

        return random()


a = Wut()
In [3]: a == a
Out[3]: 0.7859472786472401

In [4]: a == a
Out[4]: 0.12737171015832338

In [5]: a == a
Out[5]: 0.3313529872436768

Now tell me what it means. And if communication is "impossible" then how am I interacting/communicating with the symbol?

Your theory predicts communication breakdown identity violation. But look - I can generate infinite violations, each one unique, and we're having the most precise communication possible about their distinctness.

The crux is thus: you don't actually have a fixed, identity non-violating referent when you use the symbol "meaning". You are performatively contradicting your thesis.

Communication works without fixed identity-preserving referents. Least you can communicate what you are referring to as "communication".

Foundationalism is identical to infinite regress.

Your problem is two-fold, really. You think meaning is a noun; not a verb. So you fail to recognize that static symbols (those written on paper) don't mean anything - they lack the agency to mean.

Dynamic symbols (like the ones in a programming REPL) have meaning because you can communicate/interact with them.
The question was never "What do symbols refer to?" but rather "How do agents interact meaningfully using symbols?". Meaning is emergent.

So really, you are left holding your cock in your hand because...

1. Logical "laws" are design choices, not universal necessities
2. Alternative logics aren't just possible - they're implementable
3. Communication works across different logical frameworks
4. Identity can be probabilistic rather than Boolean
5. We can reason about and with systems that violate any conception of identity.

[Impenitent]

A is never anything, but a first letter Uralic-Altaic word.

I know this, because I’m Venetian Iranian.

A is the root note of an A chord

-Imp

[Scott Mayers]

But I agree with the author of this thread given you cannot even begin to develop a logic without presuming the intent of the 'laws of (any) logic" requires some symbols to reference to some other reality.

That premise is not true. What reality are we referencing when we do symbolic logic? What is the symbol "∃" referencing? Tell me about its idenitty.

?? The 'symbols' refer to the variables and constants. "∃" is actually a logical quantifier, a type of 'adjective' that adds information about a variable or constant and so not relevant. You CAN define that symbol as a constant of the system.

The identity law is for a STARTING point in many proofs that use the '=' or '==' meanings. Since one can substitute the direct meaning one of the variables, like the right side 'copy' of the symbol, the law is an apriori premise about all the systems that needs no external aposteriori proof.

But given you are just being a dick, whomever "Skepdick" is, are you the same person from post to post? If you don't believe in 'identity' as a default, I have no reason to trust you are consistent as an actual single conscious mind. So should I have to just stop now and not waste further effort because I'd have to repeat constantly repeat myself not knowing if you are the same consistent person in any two posts?

The "x=x" is a definition postulate that is only saying that if I use the letter 'x' in any instance in a PARTICULAR logical argument we have to have an agreement to KEEP the meanings of that symbol constant UNLESS WE INTENTIONALLY CHANGE it within the same argument. You could not even READ this if you didn't default to 'identity' because you need it to remember words and how they are MAPPED one-to-one with their 'definitions'.

I won't be wasting time on this with you given you haven't changed your opinion on this since I've known you in the past....funny given your style and stance indicates this fact too as an 'identity' of one who ironically can't change positions.

To you, "1 = 1" if and only if "1 = 0".

So, no offense, but if you are free to decide to make up whatever rules you want on the fly without AGREEING to be consistent, I cannot DETERMINE anything you say in a 'consistent' fashion and will have to stop if you cannot concede. ('con' + 'sis' '+ 'tent' means "With Same tense or state" which is a single word that sums up what the Identity law is about. ['con' = with, 'sis' = same relative, "tent" = tense] But it could just be my idiocy.

The 'Laws of (all) logic' is just the minimum qualifications used to keep the meaning of 'logic' on par. [Comparable = with the ability to be on equal groundings or 'par'] This is a 'convention', a standard politic used to communicate between two or more people. If we aren't 'consistent' to use the same words mapped to a meaning, then all have to say is, "aaldk foe dfiw fdieoiore iczd tobbi", right?


Another optional expression of the law is 'you may substitute any instance of a symbol with the SAME meaning'. Call it the "substitution law' if you like (some do). OR, you can begin with another equivalence, the double negation:

Given --X, you can equate or substitute this to simply X. [Double Complement]

" X -- X" can mean, X and not-not X. The double negation signs are also represented as "X = X" You may cancel them out if you like so that this becomes, XX, which merely repeats the same symbol and reduces to simply one X.

If this is not sufficient enough for you to draw closure on this topic, I cannot convince you of anything and won't waste any further time, still no offense to you personally.