What is the nature of the axioms of Objectivism?

[Evan]

BlackDiamond:

OR to put it another way, the concept 'identical' depends on the concept 'identity' whereas 'identity' does not depend on 'identical'. A is A is simply a restatement of the concept 'identity,' but not of identical (to or with whatever) - which requires 'identity' to be conceptually valid before you can ever use it.

The concept of something being identical and the concept of identity are the same. For anything to have a given and fixed identity (for anything to be "A" for example) it has to be isolated as being ONLY the thing that it is. That itself is a comparison. It is called "the indiscernability of identicals" aka "Leibniz' Law" and it is also axiomatic.

The concept of identity rests on the fact that anything WITH an identity must be identical to itself. Also formulated as "A =A."

Your claim that identical somehow rests on identity and not vice versa is unwarranted. Identity and identical work together hand in hand.

You can't have the concept "identity" without reflexivity (which is formulated as "identical to itself.").

to say something is IDENTICAL with/to something (even if that something is itself) is to make a comparison. But before you can even compare anything, you must (implicitly or explicitly) accept the axiom of identity to be true. You must accept that something "IS" something before you state if anything is "identical" to anything, even itself.

When you say that something IS something, you are making a claim about existence. Existence exists (the axiom of existence) and that means that for anyone to postulate that X "IS" that there is something that can be talked about. All of the axioms work together. Before you can say anything IS , you must accept that it has a fixed identity (identity implies reflexivity which is what is meant when you say "A is identical to itself" ). If identity was NON-reflexive andf you pointed to an object and said, "That is A" then that would imply that "A" could share all of the properties as "-A." A wouldn't be identitical to itself at that point...it could be identical to a variety of things (even things that were contradictory to its nature).

However, you are forgetting the other two axioms. For something to "be" it must have an identity, it must exist, and there must be something to perceive the existence of an object (something that perceives the identity of an object...as existence IS identity).

If you say, "Tom is identical to himself" that doesn't mean there is a comparison. It means "Tom is who he is" which is to say, "Tom exists and he has a specific identity that isn't contradicting itself."

When you say "A =A" that also necessarily means "A does NOT = -A."

For A to have any meaning or rather...for the identity symbol to have any meaning, A must have reflexive identity. A must be identical to itself.

That comparision is forced by the nature of identity. By simply switching terms to "A IS A" you don't get away from the fact that for A to be A and ONLY A, it must also not be -A, B, C, or a pepperoni pizza.

To declare that "A is A" requires the acceptance of the fact that A has a definite identity that cannot be contradictory which means that the necessary comparison is built into the reflexive and symmetric nature of the FOL formulation of the statement ("A=A").

-E

Edited February 14, 2006 by Evan

[dondigitalia]

Sure. I don't think I implied anything otherwise, and I don't know what you're trying to tell me. Maybe you could explain what you mean a little more?

The reason I thought it might be necessary to point out what "existence" is in Objectivism is because I inferred from your comments that you might be operating from the "state of being" concept. For instance, when you used the idea of something that has not yet been created as an example of a non-existent. In Objectivism, the concept of "existence" subsumes everything which has existed, currently exists, or will exist in the future--that is what is meant by a concept being "open-ended."

Also, the idea of existence without existents is a contradiction. A non-existent is something which does not exist, and is not subsumed under the concept of existence.

Dave Odden's explanation of the "empty space" problem can suffice as my own, as I agree with it entirely.

Dondigitalia, both of your posts lack arguments entirely and are only attacking straw men. I won't keep defending myself against such vague, indirect attacks.

For one, how can my posts lack argument entirely and attack a straw man? Attacking a straw man would mean I was arguing against a false position, so you're saying that I'm both arguing and not arguing.

A true description of my posts is that they lacked any argument whatsoever. This is because its pointless to pose an argument without first determining the context of your opponents position. I'm not sure if you are aware of these aspect of Objectivism and reject them, or are completely unaware. I'm not making attacks, so don't bother defending.

Both of my posts were entirely valid. The first for the reasons I have already explained, the second, because that dichotomy is popping up all over the place in your posts. I was unsure if you realized how irrelevant it all is in the face of Objectivism. If you do realize, and reject it, then why are you here, posting on a forum dedicated to the exploration of a philosophy you reject?

I do not make indirect attacks. Ever. I find that to be highly dishonest and am offended that you would (groundlessly) make that assertion. A question is not an attack. If I'm attacking your ideas, trust me, it will be abundantly clear that I'm doing so. Check my post history; I'm sure you will find that the behavior you are mistakenly ascribing to me would be extremely out of character.

Edited February 14, 2006 by dondigitalia

[Nate T.]

For instance, when you used the idea of something that has not yet been created as an example of a non-existent. In Objectivism, the concept of "existence" subsumes everything which has existed, currently exists, or will exist in the future--that is what is meant by a concept being "open-ended."

Is there a place in the literature I can find a reference to this (in IOE, say)? This doesn't seem right to me-- I thought that existence is that which exists now. That is, if some entity no longer exists or does not yet exist, it doesn't exist (though you could say it existed or it will exist, respectively, but that's not the same thing). If this is wrong, would you explain why?

[dondigitalia]

Is there a place in the literature I can find a reference to this (in IOE, say)? This doesn't seem right to me-- I thought that existence is that which exists now. That is, if some entity no longer exists or does not yet exist, it doesn't exist (though you could say it existed or it will exist, respectively, but that's not the same thing). If this is wrong, would you explain why?

The open-ended nature of concepts is discussed in ITOE, on pages 17-18, 26-28, 65-69, 98-100, 147, and 257-258.

In OPAR, page 5, Peikoff says, "[Existence] subsumes...everything which is, was, or will be."

It seems as though you are making the exact mistake I was trying to point out, which is equating the axiomatic concept "existence," with the concept which means: state of existing or being, a form of the verb "to exist." This is not the way Ayn Rand used the term. She used it in a manner that was synonomous with "universe." Sort of a collective noun subsuming all particular existents.

[Nate T.]

The open-ended nature of concepts is discussed in ITOE, on pages 17-18, 26-28, 65-69, 98-100, 147, and 257-258.

In OPAR, page 5, Peikoff says, "[Existence] subsumes...everything which is, was, or will be."

It seems as though you are making the exact mistake I was trying to point out, which is equating the axiomatic concept "existence," with the concept which means: state of existing or being, a form of the verb "to exist." This is not the way Ayn Rand used the term. She used it in a manner that was synonomous with "universe." Sort of a collective noun subsuming all particular existents.

Okay, so to summarize, we have to be sure not to equate the referents of the concept "existence", which does refer to everything that exists, has existed or will exist, from the referents of the verb "exist" (present), whose referents are those things that exist now as opposed to in the past or in the future. We have to do this because of the open-ended nature of concepts: one's conception of "red" would be in constant flux if the referents of "red" were just the red things that have existed up until now, negating the purpose of concepts in the first place. Right?

So to be precise, one would say that some entity that does not yet exist but will "does not exist, but is still in the universe?" Something about that still seems wrong, but it may be due to the technical use of the term "universe" in this context.

[dondigitalia]

Okay, so to summarize, we have to be sure not to equate the referents of the concept "existence", which does refer to everything that exists, has existed or will exist, from the referents of the verb "exist" (present), whose referents are those things that exist now as opposed to in the past or in the future. We have to do this because of the open-ended nature of concepts: one's conception of "red" would be in constant flux if the referents of "red" were just the red things that have existed up until now, negating the purpose of concepts in the first place. Right?

Even the referents of the verb "to exist" include those of the past and future, regardless of the grammatical tense of the verb. That is the open-ended nature of concepts. If we say "existed" the referents still include those things of the present and future, viewed from the perspective that they will have, at some point, ceased to exist.

The reason its so crucial to draw a distinction between the axiomatic concept "existence" and the non-axiomatic concept "state of being" is because one subsumes all the characteristics of all existents, whereas the other subsumes only one characteristic of all existents.

So to be precise, one would say that some entity that does not yet exist but will "does not exist, but is still in the universe?" Something about that still seems wrong, but it may be due to the technical use of the term "universe" in this context.

Even universe isn't fully interchangeable with existence. It's just the concept that comes the closest to existence in scope. I used it because it's the same concept Ayn Rand used in the Appendix of ITOE in explaining what she meant when she said "existence." But even then, she just said that it is "in a certain way, close to the concept 'universe,'" rather than saying they were the same.

[Bold Standard]

It is Descartes' theory of knowledge, so I think it would be half of what Kant was spewing out in his epistemology (not that I understand Kant, or that he can be understood).

It's my understanding that representationalism or sensualism was actually Hobbes' theory of knowledge, and that Descartes devised his epistemology primarily to avoid Hobbes' conclusions-- although they both end up being trapped in conciousness. But Descartes maintained that ideas are derived primarily from innate ideas, rather than any kind of origin in experience, as Hobbes put forth.

Representationalism was developed further by Locke, and rejected by Berkeley and Hume. By the time Kant came along, sensations really weren't considered a representation of reality anymore. The pretense of the two resembling each other had been dropped, for the most part, and would continue to be denied with greater consistency by subsequent moderns.

[DavidOdden]

It's my understanding that representationalism or sensualism was actually Hobbes' theory of knowledge, and that Descartes devised his epistemology primarily to avoid Hobbes' conclusions-- although they both end up being trapped in conciousness.

I wasn't aware of that historical precedent, but I see at least one source that does root what is now called representationalism in Hobbes' Leviathan. Though I must say, I didn't read the paper and couldn't possible evaluate its historical credibility. I suppose the point would be not who first came up with the idea or the seeds of the idea, but who popularized it, which is the sense I had in mind by saying that it was Descartes' theory.

[blackdiamond]

If identity was NON-reflexive andf you pointed to an object and said, "That is A" then that would imply that "A" could share all of the properties as "-A." A wouldn't be identitical to itself at that point...it could be identical to a variety of things (even things that were contradictory to its nature).

Evan,

are you saying that you can not have something which is identical to something else? You seem to be creating a false dichotomy between "identical to itself" and identical "to a variety of things" (other things besides itself).

You said in the above quote,

"A wouldn't be identitical to itself at that point...it could be identical to a variety of things (even things that were contradictory to its nature)."

Well, what makes you say it WOULDN'T be identical to itself at that point? 'itself' would still be just one of the things it would be identical to even at "that point".

Something you seem to be sneaking into the meaning of "identical with itself" is the idea of "identical with itself and nothing else" - but those two statements do not mean the same thing.

(By the way, this is a discussion of Ayn Rand's ideas - not Leibnitz's ideas - these are not 'identical'!)

[blackdiamond]

By the way, Evan. Could you also make up your mind whether you think 'identical' involves comparison or not? Your statements in quotes below do not sound like you have your mind made up:

The concept of something being identical and the concept of identity are the same. For anything to have a given and fixed identity (for anything to be "A" for example) it has to be isolated as being ONLY the thing that it is. That itself is a comparison.

If you say, "Tom is identical to himself" that doesn't mean there is a comparison. It means "Tom is who he is" ...

For A to have any meaning or rather...for the identity symbol to have any meaning, A must have reflexive identity. A must be identical to itself.

That comparision is forced by the nature of identity.

[Nate T.]

Even the referents of the verb "to exist" include those of the past and future, regardless of the grammatical tense of the verb. That is the open-ended nature of concepts. If we say "existed" the referents still include those things of the present and future, viewed from the perspective that they will have, at some point, ceased to exist.

I see, so the referents of the verb "will exist" is all existents that ever were, are, or will be that at one point in time did not exist but at a later point did? In other words, the measurment being omitted here is not that of "does not exist now (at present) but will", but that of "does not exist at one point in time but exists at a later point in time"?

Wow, this is making my head spin. Although now that I think about it, that's how it has to be. Otherwise, the referents of the verb "will exist" would change as soon as something started existing that didn't exist before.

The reason its so crucial to draw a distinction between the axiomatic concept "existence" and the non-axiomatic concept "state of being" is because one subsumes all the characteristics of all existents, whereas the other subsumes only one characteristic of all existents.

Namely, that of existing?

Even universe isn't fully interchangeable with existence. It's just the concept that comes the closest to existence in scope. I used it because it's the same concept Ayn Rand used in the Appendix of ITOE in explaining what she meant when she said "existence." But even then, she just said that it is "in a certain way, close to the concept 'universe,'" rather than saying they were the same.

What is the difference between "universe" and "existence," then? When I read IOE, I thought that Rand was using them as synonyms.

[Evan]

(By the way, this is a discussion of Ayn Rand's ideas - not Leibnitz's ideas - these are not 'identical'!)

The axiom of identity as stated by Ayn Rand (A =A) is not Ayn Rand's idea in any sort of original sense. The originality Ayn Rand has in terms of that "starting point" (axiom) is where she "goes with it" so to speak. Ayn Rand's originality is not in the formulation of "A is A" as the axiom of identity (which she had nothing to do with) but rather the philosophical implications she made by analyzing the already existing axiom. Aristotle and Leibnitz' came WAYYYYYYYYYYY before Ayn Rand. The original question that LarkLadyInn posted was a question of formal logic that arose in her mind that spun out of the Objectivist epistomology. The requires that we analyze both formal logic and Ayn Rand's original extensions that arose from her position.

Your problem with LarkLadyInn articulating "A=A" was a logical problem. You said that such a formulation was incorrect.

To prove you wrong in the realm of logic, I'm free to use other axioms (like Leibniz's to show how stating "A is identical to itself" is NOT an incorrect statement of that axiom because the axiom itself is stated in the terms of formal logic and translated into natural language.

Thus, we have to analyze what identity really means in logical terms. Ayn Rand didn't add anything new to that definition as far as I know, so I think it is safe and fair to discuss formulation issues in strictly logical terms.

By the way, Evan. Could you also make up your mind whether you think 'identical' involves comparison or not? Your statements in quotes below do not sound like you have your mind made up:

All I mean is that a comparison is sort of forced by extension if you decide to look at it that way, but it isn't necessitated in the moment.

When you say that A = A, that also means A is not = to -A and A is not =B (and any other variable that aren't A). That essentially sets up the possibility to compare A with any other variable and also forces you to reject all of those false alternatives. The only thing that can be identical to A , is A.

are you saying that you can not have something which is identical to something else? You seem to be creating a false dichotomy between "identical to itself" and identical "to a variety of things" (other things besides itself).

That is exactly what I'm saying. I don't see any false dichotomy. The only way something can be identical to " a variety of things" is if the two (or more) objects in question are only identitical in a given property.

For example, in logic we can say:

Height(George) = Height(Tim)

That (in natural language) translates to : "George's height is identical to Tim's height."

If you wanted to specify the identity of a property and how the property itself has many units that fall under its umbrella, you could say something like this:

5'10" is an element of {height} where {height} is the vertical measurement of any object.

Thus, the specific measurement (5'10") is one part of the greater set (height). You could add a subset to 5'10" to specify people that are only belong to the set of 5'10" as well.

The point I'm trying to make is that two objects can only be identical to each other in terms of properties.

A =A is NOT such an instance. The way that we know we are dealing with two objects in terms of a class of properties (like height, weight, etc) is if we specify those properties with predicates. By introducing predicates into FOL, you can talk about more than one object by comparison.

The simple term A =A cannot be a comparison of two different entities or units.

There is nothing you can substiute in for "A =A" that would somehow lead you to believe you were comparing two separate and distinct units.

any statement of the sort: "Tom = Jerry" forces us to come to the conclusion that Tom and Jerry both name the same object.

Something you seem to be sneaking into the meaning of "identical with itself" is the idea of "identical with itself and nothing else" - but those two statements do not mean the same thing.

Erh. Give me an example of something that is identical to itself but is also identical with something else then.

I argue that you cannot do it, thus I'm not "sneaking in" anything. I believe those two statements to say the same thing.

If I point to the stick of deodorant on my desk and call it "A" and I say, "A is identical to itself" that is 100% true. It is only fully identical to itself. That stick of deodorant is ONLY identical to itself. It cannot be identical to ANY other stick of deodorant unless you are comparing properties like, "Shape(A) =Shape(."

Edited February 16, 2006 by Evan

[dondigitalia]

What is the difference between "universe" and "existence," then? When I read IOE, I thought that Rand was using them as synonyms.

She does use them as synonyms, but synonyms don't usually have the exact same meaning.

Universe refers to the 3-dimensional physical universe we live in, whereas existence could refer to any hypothetical universe. Since this physical universe is the only one which exists, it's generally ok to use the terms interchangeably in most contexts, but the concept "existence" does not necessarily mean anything physical.

It could be said that "universe" is a scientific concept, but "existence" is a metaphysical one.

Wow, this is making my head spin. Although now that I think about it, that's how it has to be. Otherwise, the referents of the verb "will exist" would change as soon as something started existing that didn't exist before.

Either that or you'd have a frozen abstraction.

[blackdiamond]

1.

The point I'm trying to make is that two objects can only be identical to each other in terms of properties.

What else does an object have besides its properties? Can you describe for me what you get when you strip an object of its properties? Nothing. Comparison is always about properties - even when you do compare it with 'itself.'

So, if two objects have the same properties, then those two objects are IDENTICAL. Since identical applies ONLY to properties (unless you can show otherwise), a thing that is identical to itself is also only identical "in terms of properties". Therefore, something that is "identical to itself" can also be identical to something else.

"A thing is itself" or "A is A" does not have the same problem.

2.

Erh. Give me an example of something that is identical to itself but is also identical with something else then.

I argue that you cannot do it, thus I'm not "sneaking in" anything. I believe those two statements to say the same thing.

Evan, are you saying that the term 'identical' never (or should never) refers to to two distinct objects? The first part of your statement ("give me something that is identical to itself") is irrelevant by your logic since everything is identical to itself, but when you add "that is also identical to something else", all you are saying is that 'identical' can never be used in any way except in the axiom of identity (as you formulate it). Isn't this a new invention of the use of this very common term which always assumes distinction (and therefore implies comparison)? You have gone from saying you CAN use 'identical' on only one thing (without comparing it with something else) to saying that in fact identical can ONLY be used on one thing (identical to itself) and never to distinct objects?

Is all this from Leibnitz?

[Evan]

What else does an object have besides its properties? Can you describe for me what you get when you strip an object of its properties? Nothing.

I buy that.

Comparison is always about properties - even when you do compare it with 'itself.'

I also buy this.

So, if two objects have the same properties, then those two objects are IDENTICAL.

They are only identical in terms of the properties that they both share.

If I point to a stick of deodorant (object A) and then point to an iPod (object , those objects can only be said to be identical in terms of *some* properties, but clearly not *all* properties.

If two objects have exactly equal properties in every respect, then they aren't two objects (according to Lebniz' law). Keep in mind that one of the properties that must be equal is the fact that they occupy the same time and space.

Since identical applies ONLY to properties (unless you can show otherwise), a thing that is identical to itself is also only identical "in terms of properties".

Why the emphasis on "only?" As you yourself stated, an object is only an object due to its properties. If you strip it of those properties, NOTHING remains. The concept of identity itself must therefore apply ONLY to properties.

Therefore, something that is "identical to itself" can also be identical to something else.

An object that is identical to itself can only be identical to another distinct object in some of its properties but not all of its properties.

For example...the famous wine glasses example.

Let's say there is a wine glass factory that makes wine glasses (duh...lol). The machines are calibrated so that every wine glass that comes out is exactly the same size and shape.

In such a case, holding up two wine glasses and saying, "Wine glass A is identical to wine glass B" is logically incorrect if for no other reason than they are made up of different molecules/atoms and clearly don't occpuy the same space.

In logical language, if you say:

A = A

A = B

B = C

__________

Therefore A =C

That is logically valid. It is also logically sound. However, we must conclude that A, B, and C all name the same objects. For example, you can call Superman by the same Superman, Clark Kent, or Kal-El.

All of them refer to the same thing.

However, if you tried to claim that I (Evan) was somehow identical to BlackDiamond that would look like this sentence:

Evan = BlackDiamond.

Evan and Blackdiamond clearly do not name the same objects.

Thus, despite the fact that I am identical to myself and you are identical to yourself....we are not necessarily identical to each other. The only way you and I could be identical is in "some" respects (one or more ways but not ALL) . Maybe you and I share the same height? Maybe we weigh the same?

In those cases, you must specify the property that you are labeling as "identical" between the two objects.

As I said before, you must use predicate relationships like:

Height(Blackdiamond) = Height(Evan)

In that case, Evan and Blackdiamond are clearly distinct entites...however if you go back to:

Evan = Blackdiamond

from that sentence, we must conclude that Evan and Blackdiamond name the exact same thing.

There are only two ways something can be identical in natural language according to Merriam Webster's online dictionary (Refdesk.com) and these also in agreement with FOL.

Here is the definition:

Main Entry: iden·ti·cal

Pronunciation: I-'den-ti-k&l, &-

Function: adjective

Etymology: probably from Medieval Latin identicus, from Late Latin identitas

1 : being the same : SELFSAME <the identical place we stopped before>

2 : having such close resemblance as to be essentially the same <identical hats> -- often used with to or with

The difference between one and two is clear. One refers to Clark Kent = Superman.

Two refers to something like the two wineglasses that share a close resemblance. Ask yourself though, what IS a close resemblance? For something to resemble another object, it has to share identical visual properties (size, shape). In such a case where someone (in natural language) is talking about identical hats, the fact that he is using the plural form of the word "hats" automatically gives us the context to work with the second definition. Same thing when hold up two wine glasses from that factory and we say, "Those wineglasses are identical."

When you use "identical" to talk about similarities, you are using it to talk about some properties being the same. In such cases, the nature of the subject (the fact that you are talking about two or more distinct objects) would naturally lead you to specify plurality in your language or indicate it visually.

If I'm standing in front of you and I pull two wineglasses off of the assembly line and say to you, "Wine glass A is identical to wine glass B" then by nature of what I'm displaying to you, you obviously must understand that I'm talking about identity in terms of comparing properties of two distinct objects. Your mind clearly cannot fool you into thinking I'm talking about one object when I'm clearly holding two.

By the same token, if I say, "My two hats are identical to each other" the phrase "my two hats" automatically cues you into the fact that you are talking about two distinct objects and the visual/spatial properties that they have in common.

As such, saying A is identical to A doesn't confuse anyone that we are talking about two different objects because you are using the same symbol and word to describe the same thing.

Evan, are you saying that the term 'identical' never (or should never) refers to to two distinct objects?

No, that isn't what I'm suggesting. However, if you are using the word to specify two distinct objects, you MUST say what properties you are talking about (like saying, "Evan's height is identical to Blackdiamond's height") as well as name your objects separately (Evan and Blackdiamond).

You have gone from saying you CAN use 'identical' on only one thing (without comparing it with something else) to saying that in fact identical can ONLY be used on one thing (identical to itself) and never to distinct objects?

No no no. You can have things that are identical in some ways but not ALL ways. For example, if you and I can have identical heights, weights, and eye colors.

Here is your initial statement:

Something you seem to be sneaking into the meaning of "identical with itself" is the idea of "identical with itself and nothing else" - but those two statements do not mean the same thing.

Object A can only be fully 100% identical to itself. Object A can never be fully identical to Object B unless Object B is another name for the same object.

When you say an object is identical to itself it means that it is ONE object that has a set of properties that make it one distinct object.

Thus, when I point at my stick of deodorant and call it A, it is separate and distinct from YOUR stick of deodorant. Each of our sticks is 100% identical to itself, but they are not 100% identical to each other. They might have *some* identical properties, but they can never be fully identical to each other without being one object.

"A thing is itself" or "A is A" does not have the same problem.

It isn't a problem to begin with though.

An object that is identical to itself (as all objects must be) can also be identical to another object only in terms of some (but not all) properties. That isn't a problem because in such cases when you use the word identical, you must also label those properties and the fact that you are talking about two objects.

Thus, there can never be any confusion about meaning.

Tell me how you can be confused about whether or not we are dealing with one or 2 objects when I formulate "A is A" as "A is identical to A."

Do you really read, "A is identical to A" and think that somehow I'm comparing two sticks of deodorant to each other in terms of properties or do you think that I'm talking about one stick simply BEING itself?

If there really is genuine confusion on your part, please explain how you get from, "A is identical to A" (A is identical to itself) to "A is identical to some other separate and distinct object" (A and B have identical properties).

The fact that objects can have identical properties is NOT a problem. It is part of the nature of what it means to have identity. Identities are made up of parts (properties). Some of those parts might also be present in other distinct objects. That isn't any sort of problem, it is simply how reality is.

When you say that "A thing is itself" you don't know that the things that make the thing what it is aren't also shared in some identical quantity with another object. You cannot get around that fact.

Ayn Rand said, "existence IS identity." When you say, "A thing is itself" the word "is" denotes existence. It also must denote identity and identity is made up of component properties that make an object what it is when it exists. Such component properties might be found in equal quality and quantity in other separate objects. Simply saying, "A thing is itself" doesn't get around that.

Edited February 17, 2006 by Evan

[blackdiamond]

There are only two ways something can be identical in natural language according to Merriam Webster's online dictionary (Refdesk.com) and these also in agreement with FOL.

Here is the definition:

Main Entry: iden·ti·cal

Pronunciation: I-'den-ti-k&l, &-

Function: adjective

Etymology: probably from Medieval Latin identicus, from Late Latin identitas

1 : being the same : SELFSAME <the identical place we stopped before>

2 : having such close resemblance as to be essentially the same <identical hats> -- often used with to or with

Evan,

neither definition 1 or 2 is similar to the way you are using the word 'identical'.

In definition 1, there is still a comparison between two distinct 'things' (or occasions, instances, etc). The example given - "the identical place we stopped before" - is comparing the place at two different times (hence the word 'before'); using time as the reference point, it is established as being the IDENTICAL place as before (comparisons are not just in space, but can also be in time). Identical always implies some distinction.

As i said before, unless you want to completely change the meaning of the word 'identical', you can not use it without the comparative aspect of it as essential to your usage. And comparison necessarily implies at least two distinct things (differentiated in time or space or any other dimension).

If you are going to use the word 'identical' like that, you might as well say "A is like A" and call that a correct formulation of the identity axiom. You can argue that there are no two things that are really 'alike' except a thing with itself. But that is changing the meaning of the word 'like' or 'alike' which always involves some distinguishing aspect. It always involves two or more distinct objects or percepts or concepts.

The fact that objects can have identical properties is NOT a problem. It is part of the nature of what it means to have identity. Identities are made up of parts (properties). Some of those parts might also be present in other distinct objects. That isn't any sort of problem, it is simply how reality is.

I know it is not a problem for things to be identical, but it should be a problem to you, with respect to your current formulation of the identity axiom. If you say 'a thing is identical to itself' and you also say 'a thing can be identical to another thing', then your first statement has no significance. You do get that, don't you?

When you say that "A thing is itself" you don't know that the things that make the thing what it is aren't also shared in some identical quantity with another object. You cannot get around that fact.

No, i can not get around that fact and neither do i want or need to for my formulation to work as the identity axiom. This is because "A is A" (or a thing is itself) is simply a fact about any object that i choose to isolate from other objects by my perception, or by any number of properties that i chose to focus on (differentiation and integration) as the basis of my identification. So, a thing can have the same properties as another thing, but i can still identify it as a thing (alone) or i can identify it generically with the other thing(s) it is identical with in any number of properties, etc.

I think Ayn Rand / Peikoff agrees with me on this score, in his/her analysis of definitions and their role in epistemology. You might want to check that out.

[Evan]

I'm bowing out of this debate. For all intents and purposes, I'm fine conceeding that A is identical to A can be reformulated to "A is A" or "should" be reformulated. Carry on with whatever fruitful discussions you wish to pursue. .

[blackdiamond]

I'm bowing out of this debate. For all intents and purposes, I'm fine conceeding that A is identical to A can be reformulated to "A is A" or "should" be reformulated. Carry on with whatever fruitful discussions you wish to pursue. .

May the force be with you, Evan.

[Evan]

May the force be with you, Evan.

[Andrew Joseph Sandberg]

In other words, what is my relation to the external world if the world and I exist independently of each other?

You do not exist independently from existence. You are a consciousness- therefore conscious of reality. Your consciousness depends on something to be conscious of. Not to mention the fact that you exist. Something which exists cannot exist independently from existence.

Edited January 1, 2007 by Andrew Joseph Sandberg