The Law of Identity

[Logik]

You know what..... I may have to backtrack here. Because I tried to do what I THOUGHT was impossible and yet - I succeeded.

To my own surprise Python didn't explode. I guess id() is not a fundamental

https://repl.it/@LogikLogicus/OverrideIdentity

Code: Select all

IDENTITY: 0 = 0: False
IDENTITY: 1 = 1: False
IDENTITY: 2 = 2: False
IDENTITY: 3 = 3: False
IDENTITY: 4 = 4: False
IDENTITY: 5 = 5: False
IDENTITY: 6 = 6: False
IDENTITY: 7 = 7: False
IDENTITY: 8 = 8: False
IDENTITY: 9 = 9: False

[Speakpigeon]

"The law of Identity" is a logical apriori assumption or agreement to what one means minimally about what is considered logical. For any given concept, symbol, or referent, if given some concept referenced by a label, say X, it is related to the concept referred by it uniformly by the label, X, wherever it is used.

You think people don't usually comply with the Law of Identity in everyday speech?

As to the expressions of the form, xRy
The R represents the relationship of the symbol x on the left, to the symbol y on the right. If we want to define some R as something such that some meaning of x is assigned to y, such that the meaning of y identifies with x as being uniquely referring to the same meaning by either force or comparison, then we call that R an Identity relationship of y to x.
A definition that uses a symbol on one side, usually the left, IDENTIFIES the meaning of something more explanatory on the other.
"Cat" is "an animal" [meaning, a cat is identified (at least) as an animal]; but "animal" is-not "a cat"

How exactly does writing "A cat is an animal" assigns meaning to the term "cat"?

It is an agreement of those opting to play a game to follow the exact same rules with the same meanings shared rather than to arbitrarily confuse or change the meaning of the words or symbols used arbitrarily.

I would say that "Law of Identity" is a very strange name to use to do what you suggest here. I would call it a rule, not a law, just like you don't have the law(s) of football or the law(s) of chess but rules.
So, unless you can justify your perspective, I don't think I'll buy it.

Why require this when it seems it already applies?

Exactly. This is the crucial point here and you dismiss it much too quickly.

It doesn't apply if people do not DEFINE their TERMS in a philosophical debate and is often the reason FOR disagreement.

According to this, if anyone uses the word "true" first to mean true and then to mean false within the same argument, then the law of identify is falsified?!
Please clarify.

"to find one's head and shoulders on a beach" =?= "to find one's Head & Shoulders™ on a beach."

I believe the Law of Identity means something a bit deeper than a redundant injunction not to equivocate.
If that was what it meant, we would call it "Rule against equivocation" or some such. And we do have it in logic. It's called the "fallacy of equivocation".
EB

[Logik]

If that was what it meant, we would call it "Rule against equivocation" or some such. And we do have it in logic. It's called the "fallacy of equivocation".

If you recognize the equivocation fallacy then why do you overload the meaning of "=" ?

Why does it mean identity AND equality?

[Speakpigeon]

In set theory, they define their first law, often called "extension", to define what it means when one uses the symbol "=" EXTENDED from first order logic's use of the implication and biconditional symbols, → and/or ↔:

Law of Extension
For any classes A and B,
(A = B) means (A → B) and (B → A)

This is set theory's logical identity law regarding the system itself. It tells you what "=" means as a rule to agree to remain consistent throughout as a minimum.

It seems to me that "(A = B) means (A → B) and (B → A)" has no relation to the Law of Identity. The Law of Identity asserts that for all things, the thing is identical to itself, sometimes formalised as "For all x, x = x", or "For all x, x ≡ x".
EB

[Logik]

It seems to me that "(A = B) means (A → B) and (B → A)" has no relation to the Law of Identity. The Law of Identity asserts that for all things, the thing is identical to itself, sometimes formalised as "For all x, x = x", or "For all x, x ≡ x".
EB

Equivocation. If you use ≡ to mean "identity" then you can't ALSO use it to mean "material equivalence".

One symbol - one meaning!
Two meanings - two symbols.

[Atla]

Concrete things are themselves. And abstract things like two "A"s are identical.

[Logik]

Concrete things are themselves. And abstract things like two "A"s are identical.

Nope.... https://repl.it/@LogikLogicus/OverrideIdentity

"identity" is meaningless in the abstract. You are pre-supposing that things have some integer-value.
Integers-types have integer-value. Cat-types don't have integer-value.

Set-theoretic error

[Atla]

Concrete things are themselves. And abstract things like two "A"s are identical.

Nope.... https://repl.it/@LogikLogicus/OverrideIdentity

An unrelated computer program

"identity" is meaningless in the abstract.

It's not

You are pre-supposing that things have some integer-value.

I haven't

Integers-types have integer-value. Cat-types don't have integer-value.

Didn't mention types or integer-values.

Set-theoretic error

Nope

[Logik]

Concrete things are themselves. And abstract things like two "A"s are identical.

Nope.... https://repl.it/@LogikLogicus/OverrideIdentity

An unrelated computer program

"identity" is meaningless in the abstract.

It's not

You are pre-supposing that things have some integer-value.

I haven't

Integers-types have integer-value. Cat-types don't have integer-value.

Didn't mention types or integer-values.

Set-theoretic error

Nope

Checkmate. https://repl.it/@LogikLogicus/Python-3-7

Code: Select all

A = 1
А = 2
print(A)
print(А)
print(A == А)
print(id(A) == id(А))
print(A + А)

Code: Select all

1
2
False
False
3

[Atla]

Nope.... https://repl.it/@LogikLogicus/OverrideIdentity

An unrelated computer program

"identity" is meaningless in the abstract.

It's not

You are pre-supposing that things have some integer-value.

I haven't

Integers-types have integer-value. Cat-types don't have integer-value.

Didn't mention types or integer-values.

Set-theoretic error

Nope

Checkmate. https://repl.it/@LogikLogicus/Python-3-7

Code: Select all

A = 1
А = 2
print(A)
print(А)
print(A == А)
print(id(A) == id(А))
print(A + А)

Code: Select all

1
2
False
False
3

Another unrelated computer program.

I've never seen a programming language where a variable can have two different values at the same time. And we also know that you are a pathetic fraud, a liar.

So obviously there must be some trick somewhere. I converted your two A's to ASCII and got different results.

Your first A is ASCII 64 and your second A is ASCII 208 144.

If I rewrite your program using only one kind of A, the program gives the expected result:

2
2
True
True
4

Checkmate..

[Logik]

Concrete things are themselves. And abstract things like two "A"s are identical.

So obviously there must be some trick somewhere. I converted your two A to ASCII and got different results.

So much for your theory..... eh?

[Atla]

Concrete things are themselves. And abstract things like two "A"s are identical.

So obviously there must be some trick somewhere. I converted your two A to ASCII and got different results.

So much for your theory..... eh?

Different ASCII codes are different, not identical. You won't refute the law of identity using a simple cheat.

[Logik]

Different ASCII codes are different, not identical. You won't refute the law of identity using a simple cheat.

But I am refuting it. I am showing you that 2 or 2000000000000000 As can have a different meaning.

Because identity is a notion entirely divorced from symbols (language).

Identity is information. https://en.wikipedia.org/wiki/Physical_information

In a general sense, the information of an entity is that which resolves the uncertainty of its properties. It answers the question of what that entity is, and can thus be considered that which specifies the existence of that entity and the nature of its properties, which themselves are also entities. The answer that information performs the function of is divorced from any and all types of language.

[Speakpigeon]

Concrete things are themselves.

Sure, but the question is, what that's supposed to mean.

And abstract things like two "A"s are identical.

"A"'s are not abstract things at all. An "A" is the letter A written on a piece of paper or on your display right now in the very expression ""A"'s" that we use to talk about "A"'s here. Very concrete. You can count them and measure their size even.
Two "A"'s are definitely not identical in that they are not the same "A". They are identical as to their form but not as to their locations on the paper, which is why we will say there are two "A"'s to begin with.
So, "A"'s are letters A used here and there and are in effect different things although they are instances of the same character A since they have the same form.

The abstract thing you may be talking about will be A's, not "A"'s.
Two A's, however, are not in general the same thing either.
Two "A"'s in two different papers will probably be different things. And two A's in the same paper may well not be the same thing either.
We only have a small set of symbols we can use, so the same symbol may well have to be used to refer to different things. So, two A's may be two different things although not necessarily.

Seems this has little to do with the Law of Identity.
EB

[Atla]

Concrete things are themselves.

Sure, but the question is, what that's supposed to mean.

And abstract things like two "A"s are identical.

"A"'s are not abstract things at all. An "A" is the letter A written on a piece of paper or on your display right now in the very expression ""A"'s" that we use to talk about "A"'s here. Very concrete. You can count them and measure their size even.
Two "A"'s are definitely not identical in that they are not the same "A". They are identical as to their form but not as to their locations on the paper, which is why we will say there are two "A"'s to begin with.
So, "A"'s are letters A used here and there and are in effect different things although they are instances of the same character A since they have the same form.

The abstract thing you may be talking about will be A's, not "A"'s.
Two A's, however, are not in general the same thing either.
Two "A"'s in two different papers will probably be different things. And two A's in the same paper may well not be the same thing either.
We only have a small set of symbols we can use, so the same symbol may well have to be used to refer to different things. So, two A's may be two different things although not necessarily.

Seems this has little to do with the Law of Identity.
EB

Everything you listed are concrete.

Concrete "A"s are themselves. Abstract "A"s are (seen as) identical.