The Law of Identity

[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

Well yes obviously A can mean different things in the abstract, we agree what we use the symbol for (doesn't have to refer to anything).

[Logik]

When we speak about the laws of thought - I don't have to agree to anything with anyone. How I think and in what language/alphabet I think is my business and my business alone.

The symbol means whatever I want it to mean. The point of identity is to maintain coherence. Avoid equivocation.
Ensure that things are interpreted consistently. Avoid conflating things. It's self-discipline for a thinker like an exercise routine is self-discipline for an athlete.

The "laws" of thought are training wheels. That's it. Or maybe padded walls - I don't know.

Once you develop the self-discipline you are allowed to break the rules. Because you understand what they are (false authorities) and what they are for (to prevent you from making errors). Evolution did a good job getting us where we are, but the human mind is capable of much MUCH more.

[Eodnhoj7]

When we speak about the laws of thought - I don't have to agree to anything with anyone. How I think and in what language/alphabet I think is my business and my business alone.

The symbol means whatever I want it to mean. The point of identity is to maintain coherence. Avoid equivocation.
Ensure that things are interpreted consistently. Avoid conflating things. It's self-discipline for a thinker like an exercise routine is self-discipline for an athlete.

The "laws" of thought are training wheels. That's it.

Once you develop the self-discipline you are allowed to break the rules. Because you understand what they are for. They prevent you from making errors. Evolution did a good job getting us where we are, but the human mind is capable of much MUCH more.

The symbol meaning whatever you want it to mean observes the "I" fundamentally equivocating to the symbol itself as an extension of the observer.

[Logik]

The symbol meaning whatever you want it to mean observes the "I" fundamentally equivocating to the symbol itself as an extension of the observer.

Nauraly. Language is self-expression of one's thought.

Symbol-manipulation is what distinguishes man from animals.

[Logik]

Perhaps Aristotle knew what he was doing all along. Set down a LAW, an imaginary prison for one's mind and the rebellious human spirit will take care of the rest...

At least, that's the only way I can give him any credit for his "blunder".

[Logik]

X = 1

There. identity.

X means 1. For the time being and within this context. X means 1.
It doesn't mean 2. or 3. or 4. or 6.

It means 1.

X = 2

There. Identity.

X means 2 now. It USED to mean 1 in the paragraph above, but I redefined it. We are in a new context now.
In this context X doesn't mean 1, or 3, or 4 or 6.

it means 2.

X = 3

There. identity.

X means 3 now. It USED to mean 1 and 2 in the paragraphs above, but I redefined it. We are in a new context now.
In this context X does not mean 1 or 2, or 4 or 6.

It means 3.

X = []

There. Identity.

X means "empty set now". It USED to mean 1, 2 and 3 in the paragraphs above. But I redefined it. We are in a new context now.
In this context X does not mean 1,2,3,4 or 6.

It means []

X = FlipFLop()

X means flip flop now. It USED to mean 1,2,3 and [] in the paragraphs above but I redefined it. We are in a new context now.
In this context X does not mean 1,2,3,4,, 6 or [].

It means FlipFlop()

It is a flip flop. It behaves like a flipflop. Which MEANS - it behaves like a wave. 1 one second. 0 the next. True. False. True. False.

Behaviourism....

When you ignore time you get trapped in the illusion of ontology. You speak about what things ARE rather than what things DO.

[Arising_uk]

And X=X means the abstraction of all of the above?

[Logik]

And X=X means the abstraction of all of the above?

It means nothing.

According to wikipedia it's supposed to signify "a rose is a rose is a rose is a rose".
Say it 100 times it makes no difference. If A represents a rose then saying:

A

Is sufficient. No need to re-affirm it.

A = A means nothing. It conveys no new information

[Scott Mayers]

"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?

That is why I used the example below of a joke. Humor is a significant factor of humanity. It is based one's clever capacity to "trick" ourselves by breaking the rules of consistency. It if a function of all the arts. If we were perfectly logical, we'd not be able to be tricked. Although I disagree with the over-stereotyped science fiction concern against the robots or cyborgs, etc, there is truth to the nature of normal solid-state electronic computers to be able to replicate the full range of emotional content because emotions (including all sensations to some degree) rely on a relatively INDETERMINATE environment. The logic of biochemistry for animals requires adapting to the indeterminate variable experiences though variable environments.

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"?

The form of the genus/specie definition, important in the logical defining of terms, would treat the class, "animals", as the parent or genus class to which a cat belongs to. The expression, "A cat is an animal." is at least true as it assigns the meaning of cat to be at least IDENTIFIED as some animal.

In computers, most higher-ordered languages simply use the "=" as this type of operator:

x = 2

...but reverses the order. "2" is assigned to the class variable, "x", where "x" doesn't require being only "2". Another way to express this to see the relationship, is

Let x represent some Number.
Then if x = 2, 2 is the particular Number in x.

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.

The word "identity" is being treated broadly by you and logik here. This is 'tricking' YOU because you assume the meaning of it in one context should be universal when there are more than one meaning. The error you guys are making is to interpret the "Law of Identity" to be imposed by Aristotle's use of the verb "are" or "is" as this law when that particular law is only the 'equality' type relationship, NOT the 'assignment' type.

Why require [a law of identity] when it seems it already applies?

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

Because it defines what is minimally accepted in formal logic using language that expresses things linearly.

x = x

means the symbol, x, variably standing for any proposition, term, constant, or variable, remains constant in meaning through an argument. That is, you cannot use different meanings of homonyms or synonyms, variants of different parts of language uses (like noun or verb). You have to agree to keep what you use "consistent" and why this law is important. You both BREAK this law when YOU expect that law to be REQUIRED to fulfill the different meanings of "identities" used in specific instances of logic, like that the symbol for equality I demonstrated as "=" for this law, would require being interpreted as "==" in computers so as not to confuse it to mean an assignment operator in higher order languages.

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.

The words we use to symbolize something we define is ARBITRARY. So you can technically define the symbol, "true", to be assigned to the constant, 0, in computers. If this is used, then the word's human meaning doesn't fit with the particular computer's normal use of the Boolean, "true", that is actually assigned as "true" = 1.

"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

That is precisely what it means. The word "law" is used for the static meaning. It is a "rule" in that this means the PRACTICE of logic, as though is were a game's rule we agree to when we play the game called, "logic".

What became questioned in the field of logic was to how the rest of the laws were to apply when you can have more than just binary truth values. Reality does permit the contradiction, "x & not-x", because you can have say, three values = {0, 1, 2} to some system.

If given x = 0, both "1 = not-x " and "2 = not-x" in this case. If I then ask you if "x = not-2", you'd assert this true. But "1 = not-2" also. So I might replace the not-2 in "x = not-2" with "1" and have "x = 1", If I now replace the "1" in that to "not-x", we have,

x = not-x.

This is still 'consistent' but is a logic of three values and why the question about consistency arose in the first place. But the problem is about a confusion in the meanings of "=" that differ. The three apriori laws are about the 'truth' value of the logic systems themselves. In other words they assume a prior postulate to all logic systems with those three laws. The problems raised for others is that this 'game' of logic doesn't permit the multivalued versions yet we can see they still have RATIONALITY. Thus, such a system based only on these restrictions of consistency, cannot define all rational systems without treating the meaning of logic restricted to those laws. The contention is that some think we require KEEPING those laws and then say that "logic" being defined as requiring those laws by most, must treat the other forms of reasoning as "non-logical" OR extend the meaning of "logic" to have other initial rules. Consistency is always one that is kept but the other two, "The law of the Excluded Middle" or the "Law of non-contradiction" can be changed to form new kinds of 'logic.'

[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

Everything you listed are concrete.

Whoa.
In "A = B", the object A is abstract. It is represented by the symbol "A", which is concrete.
In "The cow is in the stable", the object cow is concrete because a particular and real object is meant. It is represented by the symbol "cow", which is also concrete, like "A" was.
In "A cow is a mammal", the object cow is abstract because not one particular real object is meant. It is represented by the same symbol "cow", which is still concrete because the symbol used is a particular and real object although what it stands for isn't. The symbol will be said "abstract" in reference to its object.

Concrete "A"s are themselves.

Each thing is itself whether it's concrete or not.

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

Two letters A on the page are identical (or: the same) on the face of it, i.e. one "A" looks like the other "A".
They are the same but they are not the same things, since they will be at different places.
What matters here, though, is that each "A" is itself, irrespective of the fact that two "A"'s are identical.
So, the fact that two "A"'s are identical because they look the same seems irrelevant here.

If the letter A is used to represent an object, then it represents an object A, which is indeed abstract simply because no real object is identified.
However, two letters A may both be used to represent an object and may well not represent the same object, because representation is contextual. One "A" may represent, say, a set, while the other "A" may represent, say, a relation. The following sentence is perfectly acceptable: If the object A is a set then it may be empty, but if the object A is a relation then it may be transitive. Two "A"'s, different objects.
What matters here is that the context should show whatever we need to know to understand what object is meant.

However, all this is only relevant to the issue of equivocation and more generally, clarity. That's still completely irrelevant to the Law of Identity. It's not because you make sure you're not equivocating that any object A is itself. The object A, like any other thing, abstract or not, will be itself irrespective of whether we equivocate when referring to it.
EB

[Scott Mayers]

By the way, I have a book I'm about to read called, "Abel's Proof" by Peter Pesic. Abel's proof is an older proof about unsolvability. Specifically, Abel's proof was about showing how the solutions to polynomial expressions with a degree of five or more to a single variable was unsolvable. It relates to all of this. I read the back cover and discovered that he wrote another book called,

"Seeing Double: Shared Identities in Physics, Philosophy, and Literature"!! (MIT Press, 2002) by Peter Pesic.

I think this would be a good and relevant read for this topic.

[Logik]

Here is a question: why does thought need to have any "laws" ?

[roydop]

Do you realize that you are trying to prove your own existence, when it is self evident?

This results in infinite redundancy and delusion.

You will find true self in/as thought free Awareness. Then all of this nonsense stops.

[Speakpigeon]

"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".

That is precisely what it means. The word "law" is used for the static meaning. It is a "rule" in that this means the PRACTICE of logic, as though is were a game's rule we agree to when we play the game called, "logic".

Yet, it's been called a law for a very long time.
If it wasn't, in fact, a law, don't you think people would have noticed?
And is it not the case that it is indeed a law and not just a rule?
If you think it's just a rule against equivocation, please name one thing that is not itself.
EB

[Atla]

Whoa.
In "A = B", the object A is abstract. It is represented by the symbol "A", which is concrete.
In "The cow is in the stable", the object cow is concrete because a particular and real object is meant. It is represented by the symbol "cow", which is also concrete, like "A" was.
In "A cow is a mammal", the object cow is abstract because not one particular real object is meant. It is represented by the same symbol "cow", which is still concrete because the symbol used is a particular and real object although what it stands for isn't. The symbol will be said "abstract" in reference to its object.

Obviously. Okay then not everything you listed was concrete.

Each thing is itself whether it's concrete or not.

Fundamentally yes. But we can for example talk about a single abstract object, referred to by multiple A letters.

Two letters A on the page are identical (or: the same) on the face of it, i.e. one "A" looks like the other "A".
They are the same but they are not the same things, since they will be at different places.
What matters here, though, is that each "A" is itself, irrespective of the fact that two "A"'s are identical.
So, the fact that two "A"'s are identical because they look the same seems irrelevant here.

If the letter A is used to represent an object, then it represents an object A, which is indeed abstract simply because no real object is identified.
However, two letters A may both be used to represent an object and may well not represent the same object, because representation is contextual. One "A" may represent, say, a set, while the other "A" may represent, say, a relation. The following sentence is perfectly acceptable: If the object A is a set then it may be empty, but if the object A is a relation then it may be transitive. Two "A"'s, different objects.
What matters here is that the context should show whatever we need to know to understand what object is meant.

Obviously.

However, all this is only relevant to the issue of equivocation and more generally, clarity. That's still completely irrelevant to the Law of Identity. It's not because you make sure you're not equivocating that any object A is itself. The object A, like any other thing, abstract or not, will be itself irrespective of whether we equivocate when referring to it.
EB

Then I don't know what else this Law of Identity is supposed to be about. Things are themselves, not something else, which is 100% obvious, self-evident, isn't this the "law"?