Equal but not identical.

[TuringAI]

There is a fine conceptual difference between 'identical' and 'equal'. The proof is that when we say "this is identical to that" we are saying they refer to the same thing, IE, they share an identity, whereas when we say 'this is equal to that' we are positing a weaker form of identity, IE they share certain properties which are essential in this context. Imagine someone claiming that 'man and woman are identical' versus someone else claiming 'man and woman are equal'. Clearly the former is false, since a man and a woman are anatomically distinct. However, the latter is true, since both a man and a woman possess the same fundamental rights, IE the right to life, liberty, property, and pursuit of happiness, all apply the same to one as they do the other.

I know that that had already been covered but I want to ask something. Does this necessarily mean that an object, which necessarily undergoes constant change through time in terms of nonessential properties, remains equal to itself through time but is not identical, since identical refers to all aspects of an existent whereas equal requires context, including the context in which a conscious entity is observing it?

If a stone falls from a height, it is 'the same' in a sense when it was up there as it was when it is down here, but various things have happened to it even apart from its movement. Microscopic changes have occurred that do not change the conceptual identification of the object but which change its structure in terms of fine differences. IE pieces may have flown off during its fall time, and the position of all of its constituent parts may be slightly off WRT their position earlier, et cetera.

My question is this: is this a proper understanding of the law of identity? Is identity narrow in scope or is it broad? That's what I'm asking.

[Mindy]

The determinate state of affairs you describe is impossible. If time passes, change occurs. That means everything changes in terms of external relations to whatever marked the passage of time. So the specific distinction you posit between "identity" and "equal" doesn't exist.

If the Universe naps, we don't know about it. Without inviting Parmenideic or Heraclitic distortions here, we understand that there is a certain, constant "noise" in the universe, Brownian motion, at the least. So, the fact that a given stone is constantly enjoying the internal changes of Brownian motion is just part of its identity. It is a characteristic of all matter, (Above absolute zero.) Uncountable numbers of external relations have changed, as it fell, but that fact, too is entailed by existence in the Universe. So those changes don't count as differences in the stone's identity.

Of course, no two things are identical. But they can be identical in various ways. Even the judgment that a thing is identical with itself implies two observations to be judged, or else it is not a judgment at all. (And two observations means two points in time, or two perspectives, with the alterations in at least external relations those necessitate.) So "identical" requires a context as much as "equal" does.

The law of identity is something altogether different, though. "A is A" is not a comparison. It says: existence is identity. It says that being is being a certain way. It is a denial that matter and form can be separated except by mental abstraction. It proves moot the question of what holds a thing's characteristics and traits and properties all together. What is the existing thing that they characterize? A is A keeps us from making a slew of philosophical errors.

-- Mindy

[A is A]

There is a fine conceptual difference between 'identical' and 'equal'. The proof is that when we say "this is identical to that" we are saying they refer to the same thing, IE, they share an identity, whereas when we say 'this is equal to that' we are positing a weaker form of identity, IE they share certain properties which are essential in this context. Imagine someone claiming that 'man and woman are identical' versus someone else claiming 'man and woman are equal'. Clearly the former is false, since a man and a woman are anatomically distinct. However, the latter is true, since both a man and a woman possess the same fundamental rights, IE the right to life, liberty, property, and pursuit of happiness, all apply the same to one as they do the other.

I know that that had already been covered but I want to ask something. Does this necessarily mean that an object, which necessarily undergoes constant change through time in terms of nonessential properties, remains equal to itself through time but is not identical, since identical refers to all aspects of an existent whereas equal requires context, including the context in which a conscious entity is observing it?

If a stone falls from a height, it is 'the same' in a sense when it was up there as it was when it is down here, but various things have happened to it even apart from its movement. Microscopic changes have occurred that do not change the conceptual identification of the object but which change its structure in terms of fine differences. IE pieces may have flown off during its fall time, and the position of all of its constituent parts may be slightly off WRT their position earlier, et cetera.

My question is this: is this a proper understanding of the law of identity? Is identity narrow in scope or is it broad? That's what I'm asking.

Identity is broad, not narrow. Identity includes what a thing becomes. Don't confuse identity with identical. You seem to be doing that. Men and women possess identical rights because they have the same identity: a rational faculty. But men and women do not have equal rights. What each achieves in life is different. If I have a job because of a contractual agreement, another person does not have an equal right to that job. But everyone has identical rights: they may have the job upon entering into a contractual agreement with the employer. I have a right to my house; you do not.

When an object changes, it clearly does NOT remain equal to itself. Nor does it remain identical. Equal implies a quantitative relationship. Identical is more of a qualitative relationship. Identity is an abstract concept about the nature of the entities and their relationships.

Edited July 28, 2010 by A is A

[DavidOdden]

There is a fine conceptual difference between 'identical' and 'equal'. The proof is that when we say "this is identical to that" we are saying they refer to the same thing, IE, they share an identity, whereas when we say 'this is equal to that' we are positing a weaker form of identity, IE they share certain properties which are essential in this context.

I dispute this claim, factually and philosophically. I am identical to myself in the strong sense, and there is no context in which one would ever say "This is identical to that". In order to say that and have a "this" and a "that", there would have to be two distinct things. Which means they are not the same thing. The problem is the term "identical". I suggest you identify real contexts where "identical" can be used naturally. You're approaching the matter in a deductive fashion, without even identifying a correct higher-level principle. In fact, "identical" is identical to "equal" in all relevant (semantic) respects.

So obviously, your other questions miss the mark. One important fact about "identical" and "equal" is that they both refer to a dimension of measurement. A pole that weighs a kilo is identical / equal in weight to a sphere that weights a kilo, and not identical / equal in shape. No two things can be identical / equal, context-free. Two poles can be identical/equal in weight and diameter-length ratio but not identical in length; or they can be identical/equal in all three yet distinct in color. No two leptons can be exactly identical in all respects (as I believe you know).

[aleph_0]

Take the scenario where one person borrows another's book, accidentally destroys it, buys her friend a new copy, and says, "Sorry, but this is the same edition as yours and everything, they're identical, hope you don't mind." That's a natural context and natural use of the word, in which "identical" does not imply quantitative identity.

[DavidOdden]

Take the scenario where one person borrows another's book, accidentally destroys it, buys her friend a new copy, and says, "Sorry, but this is the same edition as yours and everything, they're identical, hope you don't mind." That's a natural context and natural use of the word, in which "identical" does not imply quantitative identity.

I suppose you're helping him some, but "contexts" means "a number", not just one. He's not going to get anywhere in seeing the equivalence of "identical" and "equal" just given one example where a sentence can be uttered without explicitly stating the non-omitted measurement. I don't understand your point about "quantitative identity". Neither "equal" nor "identical" are terms referring just to numeric values.

[dream_weaver]

Take the scenario where one person borrows another's book, accidentally destroys it, buys her friend a new copy, and says, "Sorry, but this is the same edition as yours and everything, they're identical, hope you don't mind." That's a natural context and natural use of the word, in which "identical" does not imply quantitative identity.

Two books may be indistinguishable from one another at a glance.

In your example, one book was destroyed, the other is still intact. Your 'quantitative identity' was invoked utilizing the modifier 'same edition'.

[aleph_0]

"Numerical identity" in philosophical contexts, just means that two things are exactly the same thing in every possible sense of the word--like how Mohammad Ali is Cassius Clay. They are numerically identical, not just qualitatively in this way or that.

I was just giving an example of how, in some context, the word "identical" can be used to be mean something like an emphatic "really really similar". I don't think the English language fully specifies a distinction or equivalence between "identical" and "equal". If you are to use them respectively to signify specific distinct concepts, you just need to state which concepts you intend to signify.

[dream_weaver]

"Numerical identity" in philosophical contexts, just means that two things are exactly the same thing in every possible sense of the word--like how Mohammad Ali is Cassius Clay. They are numerically identical, not just qualitatively in this way or that.

I was just giving an example of how, in some context, the word "identical" can be used to be mean something like an emphatic "really really similar". I don't think the English language fully specifies a distinction or equivalence between "identical" and "equal". If you are to use them respectively to signify specific distinct concepts, you just need to state which concepts you intend to signify.

Two indistinguishible items, such two postage stamps, appear in all respects to be identitcal. Yet they will always bear a relationship to one another. Two lines passing through one point with the same vector would not only be indistinguishible, but for all practical purposes, identical.. The English language is only as precise as it is applied.

[DavidOdden]

"Numerical identity" in philosophical contexts, just means that two things are exactly the same thing in every possible sense of the word--like how Mohammad Ali is Cassius Clay. They are numerically identical, not just qualitatively in this way or that.

Muhammad Ali is not "exactly the same thing in every possible sense" as Cassius Clay. The former refers to his life post-conversion. What you're thinking of is "the same in all important, essential respects", and his silly flirting with Nation of Islam is non-essential. BTW "numerical" is not the right term to use. "Numerical" refers to numbers. "Human", "rational" etc. are not numbers.

I don't think the English language fully specifies a distinction or equivalence between "identical" and "equal". If you are to use them respectively to signify specific distinct concepts, you just need to state which concepts you intend to signify.

So are you claiming that the words "identical" and "equal" are not even words of English? If they are words of English, then either they refer to the same things (they are identical / equal) or they do not refer to the same things. But you're saying that it is not the case that they are equal, or not equal. Do you have an opinion on the identity / equality of being burned and not burned, or whipped and not whipped?

[aleph_0]

Muhammad Ali is not "exactly the same thing in every possible sense" as Cassius Clay. The former refers to his life post-conversion. What you're thinking of is "the same in all important, essential respects", and his silly flirting with Nation of Islam is non-essential. BTW "numerical" is not the right term to use. "Numerical" refers to numbers. "Human", "rational" etc. are not numbers.So are you claiming that the words "identical" and "equal" are not even words of English? If they are words of English, then either they refer to the same things (they are identical / equal) or they do not refer to the same things. But you're saying that it is not the case that they are equal, or not equal. Do you have an opinion on the identity / equality of being burned and not burned, or whipped and not whipped?

They are exactly the same entity, so while Ali carried the name Cassius for more than a decade, they are actually numerically (and qualitatively, in every way) identical. For every property of Ali, that property is true of Clay and vice versa. Even the statement "Cassius Clay is trivially the same person as Mohammad Ali" is true, even if there was a time (arguably, the exact instant when he changed his name) when not everybody would have agreed to the statement, but that is merely due to not understanding what is being communicated by the statement.

And no, I am not claiming the words are not English, but that the English language--aside from any specialized English jargon in some contexts of discussion, like in philosophy--does not determine whether the two are identical or distinct. The words only have the meaning that common English speakers understand them to communicate. It would be absurd to think that these words had their meaning before anybody spoke English, and that the development of English was a discovery of some objective fact rather than the creation of a language by agreeing upon what certain words will signify. And so when these words entered the English language, in whatever primitive form they might have had, deriving from Latin and possibly whatever else, the English-speaking community might not have had any kind of agreement upon whether they were distinct and in what ways. We can compare it to the state lines of Virginia when the colony was formally established--whether one particular square foot of land actually belonged to Virginia or not, was not entirely determined since the boundaries were not specified with that kind of detail. Likewise, the exact boundaries of what "identical" might mean or not mean is largely understood in most colloquial contexts by English speakers, even though border cases and matters of detail were not entirely determined. That doesn't mean reality is under-determined, so in any reasonable meaning of "equal" or "identical", I would deny that being burned and not burned are equal. I have a T-shirt with the Avicenna quote, and I stand by it. And in it.

[Mindy]

Two indistinguishible items, such two postage stamps, appear in all respects to be identitcal. Yet they will always bear a relationship to one another. Two lines passing through one point with the same vector would not only be indistinguishible, but for all practical purposes, identical.. The English language is only as precise as it is applied.

Actually, there are not two lines as you describe. There is only one such line, though you could draw it, re-draw it, describe it, refer to it, etc. many times.

-- Mindy

[dream_weaver]

Actually, there are not two lines as you describe. There is only one such line, though you could draw it, re-draw it, describe it, refer to it, etc. many times.

-- Mindy

Yes. They would be the same, one, line.

[aleph_0]

Lines are just sets of points, so if we're talking about lines in R² then a line is just {(x, y) in R x R | y = ax + b, a in R, b in R} and so if two lines share the same vector and any particular point, then they are the same line. Otherwise, they are distinguishable.

[Mindy]

aleph_0, on 28 July 2010 - 05:00 PM, said:

"Numerical identity" in philosophical contexts, just means that two things are exactly the same thing in every possible sense of the word--like how Mohammad Ali is Cassius Clay. They are numerically identical, not just qualitatively in this way or that.

Response from DavidOdden:

Muhammad Ali is not "exactly the same thing in every possible sense" as Cassius Clay. The former refers to his life post-conversion. What you're thinking of is "the same in all important, essential respects", and his silly flirting with Nation of Islam is non-essential. BTW "numerical" is not the right term to use. "Numerical" refers to numbers. "Human", "rational" etc. are not numbers

Response to DavidOdden's post:

"Numerical identity" is a term of art, meaning that the referents of two references are numerically one, they refer to the same entity. That is, I believe, your sense of "identical."

-- Mindy

[DavidOdden]

They are exactly the same entity, so while Ali carried the name Cassius for more than a decade, they are actually numerically (and qualitatively, in every way) identical. For every property of Ali, that property is true of Clay and vice versa.

Such as "his name", and his religion. Thus you're saying that the difference in name (or religion) is not important enough to recognize. Thus they are identical in all important ways, not "in every possible sense".

The words only have the meaning that common English speakers understand them to communicate.

Ah, okay, the Lowest Common Denominator social-construct theory of meaning. So that means that "numerical identity" doesn't mean "that two things are exactly the same thing in every possible sense of the word", since that's not when many or most people understand the words to mean, and the fact that you used that expression when it doesn't mean what you had in mind was a mistake on your part. By your understanding of meaning, I suppose the meaning of "numerical identity" would be "having the same numeric value (of some quantifiable attribute)".

[aleph_0]

Such as "his name", and his religion. Thus you're saying that the difference in name (or religion) is not important enough to recognize. Thus they are identical in all important ways, not "in every possible sense".

In all important and unimportant ways. Mohammad Ali and Cassius Clay have the same name(s).

Ah, okay, the Lowest Common Denominator social-construct theory of meaning. So that means that "numerical identity" doesn't mean "that two things are exactly the same thing in every possible sense of the word", since that's not when many or most people understand the words to mean, and the fact that you used that expression when it doesn't mean what you had in mind was a mistake on your part. By your understanding of meaning, I suppose the meaning of "numerical identity" would be "having the same numeric value (of some quantifiable attribute)".

No, "numerical identity" means what I said, because we (philosophers, and philosophers communicating with non-philosophers) have come to denote this in speech, and we communicate that we mean this, whenever there is confusion.

Numerical identity just means being the same in every possible sense.

[DavidOdden]

In all important and unimportant ways. Mohammad Ali and Cassius Clay have the same name(s).

Since the entity with the name "Muhammad Ali" is the same entity as the one that had the name "Cassius Clay", and it is obvious that "Muhammad Ali" and "Cassius Clay" are not the same strings, then I am left to decide between one of two conclusions. 1: perhaps you had a stroke recently or 2: you intended to say something entirely different from what you did say, but then I can't guess what that might be.

[aleph_0]

The entity with the name "Mohammad Ali" is the same entity as the one that had the name "Cassius Clay" and also had the name "Mohammad Ali". These are not the same strings, because both people (i.e., that one person, who is Muhammad Ali, and who is Cassius Clay) had both names. Perhaps I should have noted that some people have more than one name, since your confusion seems to be stated in the form, "This person was associated with this string, that person with that string, (enthymeme: and clearly an individual may only be associated with one string), thus they are different people in some way."