Tossing Around A Tautology

What follows is intended to provoke discussion and deepen understanding, not to express personal views. I have an answer to what follows, and it will suffice to say that I side with Rand as a matter of "common sense," in context with her intentions, but I want to hear your thoughts. Perhaps, this problem has been widely covered by Objectivists and put to rest years ago, but I have seen it nowhere outside Hegel. I arrived at Hegel's conclusion independently, without his influence, before knowing his conclusion or his argument.

That essential qualification out of the way, I challenge you to find a flaw. If any of you are familiar with symbolic logic, then, perhaps, we could discuss it at that more formal and precise level and achieve better results.

One final note: I expect some to unthinkingly react with, "Why not?" That is not a sufficient refutation, and one who reacts in this way obviously has no interest in probing beneath the surface of popular discourse. Respect your mind. Don't react. Respond.

UK

Short version:
The Law of Identity states that a thing is identical to itself. This is famously written as A = A. However, all things, by which we mean mental constructs, have properties that enable us to identify them for what they uniquely are. This being true, A has a property of being a copy of itself, which necessarily happens twice, making each copy also an original. Each original is a copy of an identical original. Since nothing can be both an original and a copy of itself, A = A is invalid. Therefore, the Law of Identity is invalid.

Long version:
The Law of Identity states that (p ↔ p) or (A is A). This law can be regarded as a statement composed of three parts, "A," "is," and "A." The first part, "A," is a signifier for a possible concept. A concept is possible if it can be identified as an abstract mental construct that is distinct from all others by virtue of its unique set of properties. For example, a sphere can be defined as a real or imaginary, round, three-dimensional object. Thus, "sphere" is a concept that contains several properties. Those stated are "real or imaginary," "round," "three-dimensional," and "object." Likewise, each of these properties is itself a concept as defined by its unique set of properties.

The second part of this statement, "is," denotes equivalence between the first and third parts. Here, equivalence refers to a concept, so that "is" more precisely states, "is identical in concept to." In short, this part designates that the first part, "A," is identical to the third part, which is also named "A."

When considered independently, the third part of this statement, "A," is a signifier for a possible concept. However, when considered dependently, that is, apart from the statement of (A is A) and the relation of each part to the whole, this part refers to another instance, or copy, of the first part. The distinction between independent and dependent assignment is found within the second property's denotation, which, as mentioned, equates the first part with the third.

Thus, the statement of (A is A) can be written, "A is a concept that is identical to a copy of itself." When stated in this way, one question immediately arises. That is, if a concept is distinct from all others by virtue of its unique set of properties, the concept of number is also a concept, and the concept of "A" can be copied, then is "A" identical to a copy of itself? One must consider that "A" in the first instance contains another property, that of "the ability to be copied," and that "A" in the third instance also contains this property by virtue of being equated to the former in concept in the second part. However, one must also consider that "A" in the third instance contains the property of "copy of 'A' in the first instance," such that it contains now a different property than "A" in the first instance. Briefly stated, the second "A" is different from the first "A" in that the former is a copy of the latter, while the first "A" is different from the second "A" in that the former is able to be copied as the latter.

However, another question arises. If the first "A" is a different concept than the second "A," then how can the second be a copy of the first? The first part of the Law of Identity is not identical to the third part, which means that the second part is false and that, as a result, the entire statement is also false. Therefore, the Law of Identity does not represent a universal, self-evident truth.
(Edited by UberKuh
on 3/17, 10:46am)

Post 1

Friday, March 17, 2006 - 10:56am

UberKuh, There are similarities and differences between the parts of Reality "A" and the parts of Reality "A". When a person says they are equal, they are only referring to the similarities. Relationships can be equal, or the same relationship can exist when comparing many parts of reality. The bounds of the relationships are kinda continuous or "fuzzy", and some people use different bounds than others.

Post 2

Friday, March 17, 2006 - 2:37pm

UberKuh: The statement "A is A" is not the same as "A = A". As you note, "A = A" assumes that there is a copy of A. "A is A" means that A is A and nothing else. Nothing else, even a copy, has all the qualities of A, and that includes location.

Sam

Post 3

Friday, March 17, 2006 - 3:07pm

A part of Reality is itself, for example: "A". Isn't that more clear than "A is A"?

Post 4

Friday, March 17, 2006 - 5:22pm

Being a fan of Hofstadter, I prefer the term isomorphic. These are provocative responses, to which I will respond when I can give them due attention.

Post 5

Saturday, March 18, 2006 - 3:38pm

'UberKuh':

As soon as I got to the 'short version' part saying...

...all things, by which we mean mental constructs [really? what you mean 'we'? nm], have properties that enable us to identify them for what they uniquely are. This being true, A has a property of being a copy of itself...[etc.]

      ....all I saw was equivocational word-game playing, and I thereby lost interest in reading any further.

      Right off the bat, here, 'we' have a mental construct of A that 'uniquely' identifies it for what it is...yet it has a contradictory-to-uniqueness property (not 'we' ascribing such to it, of course) of also being a copy of itself; uh, huh.

     So much for its uniqueness, I guess.

     And, is the 'copy' supposed to itself also have any uniqueness (hmmm. it's a 'copy', not the 'original', I guess)? Unclarified, methinks purposefully. --- But, here's the kicker: is the copy of the (original?) 'copy' the same or different from...A? AND, does the copy-Of-the-'copy' itself possess any uniqueness?

     And we didn't even finish your paragraph about the 'short version'!

      I grant there's much that can be discussed and is worth discussing (shades of Theseus' ship and Bones McCoy's complaints about 'beaming' a la The Fly), if not discoverable amongst the constellation of concepts re the terms original/copy/duplicate/unique/same/clone/etc not all of which are inherently synonomous; but, Ubee, as *you've* phrased the prob, such are word-game probs and  nothing more.

     Before you try to dare others into deep waters, try to be...less careless...in the opening waves of your challenges.

LLAP
J:D

Post 6

Saturday, March 18, 2006 - 8:55pm

John, if you did not read my full post, then your comments are trivial and that should be obvious. All I can tell you at this point is that you are missing the point.

Post 7

Sunday, March 19, 2006 - 10:49am

Uberkuh, interesting name. I assume you're German, and what's interesting is your manner of approaching ideas, which is squarely in the tradition of the German rationalists. You need a little of that old British empiricism! ;-) Seriously, you need to look at reality at bit more, and ask yourself, is existence self-contradictory, or does it conform to the law of identity? Is an existent whatever it is and nothing else? because if it isn't, then no clear reasoning about it is possible, and you are doomed from the very outset to fail in your quest for a non-contradictory answer. In other words, you cannot question the law of identity and expect to arrive at an answer either way without presupposing the law of identity, the very thing you're questioning. If the law isn't true, then neither is any answer that you arrive at concerning its truth. You conclude your argument by stating, "Therefore, the law of identity is invalid." But observe that the concept of "validity" depends on the law of identity. Without the law of identity, the concept of 'validity' itself would have no meaning, and the law could not be identified as "invalid." In short, your argument commits the fallacy of the stolen concept, because it assumes a standard -- validity -- that is based on the law of identity.

But let me address the specifics of your argument, because there is another very common logical fallacy that is behind it and is responsible for whatever plausibility it has. You write,

The Law of Identity states that a thing is identical to itself. This is famously written as A = A. However, all things, by which we mean mental constructs, have properties that enable us to identify them for what they uniquely are. This being true, A has a property of being a copy of itself, which necessarily happens twice, making each copy also an original.

When we say that A has the property of being a copy of itself, what we mean is that it is possible to make a copy of it, not that there is a copy of it. But is this true? Does every existent have the property of being able to be copied? No, not necessarily, unless you can show that there is a way to do it. Can the universe be copied? I doubt it. In any case, this is an empirical question. It cannot be rationalistically deduced in the way that you are attempting to do. And even if it could, the copy wouldn't be identical to the original in every respect, because it would occupy a different place than the original. It is therefore impossible to make a perfect copy of something -- a copy that is identical to the original in every respect. So, to say that the copy is "identical" to the original does not reflect the same meaning of "identical" that is expressed by the law of identity itself. In the latter sense of "identity," a thing is itself. A is A. At any rate, you then draw the following conclusion:

Each original is a copy of an identical original.

No, not "identical" in the relevant sense!

Since nothing can be both an original and a copy of itself, A = A is invalid. Therefore, the Law of Identity is invalid.

Again, "A = A" (if it is intended as a statement of the Law of Identity) means "A is A; it does not mean that there's an A and then a copy of A, which is not the original A.

In short, the argument you're making trades on the fallacy of equivocation; it equivocates on the meaning of "identical," which can mean either that one thing is the same as another, or that one thing is the same as itself. The law of identity refers only to the latter meaning. This was essentially Sam Erica's point, which I've expanded on a bit by identifying the fact that your argument commits the fallacy of equivocation, which is what gives the argument its plausibility.

- Bill

Post 8

Sunday, March 19, 2006 - 12:17pm

which is what gives the argument its plausibility.

Its seeming plausibility......

Post 9

Sunday, March 19, 2006 - 12:30pm

In short, the argument you're making trades on the fallacy of equivocation; it equivocates on the meaning of "identical," which can mean either that one thing is the same as another, or that one thing is the same as itself. The law of identity refers only to the latter meaning. This was essentially Sam Erica's point.

Well, yeah. There cannot be two identical existents. To be so they must have exactly the same attributes. Two existents cannot occupy the same location at the same time and location is an attribute.

Sam

Post 10

Sunday, March 19, 2006 - 3:07pm

"Mathematics is a language plus reasoning; it is like a language plus logic. Mathematics is a tool for reasoning." - Richard Feynman

"What is truth, that we cannot know it." - Charles van Doren

Math is the most precise language we have. Feynman suggests that math helps us understand natural language. This is precisely why symbolic logic was invented. Words, alone, do not seem up to the task of discovering truth. They commonly lead to such problems as equivocation.

As everyone seems to have noticed, on a "common sense" level, identical essentially means "very similar" or "approximate." In other words, the word identical in natural language means "nearly identical" when we break down its underlying logic. Some of you, like Dean who have written software or worked extensively with operating systems like UNIX, will know that this word could also be identified as a reference, alias, or link. You can link from one thing to another, and modifying one can affect the other, making them each, in effect, identical to the other. Yet, each is stored in a different place on your computer's hard drive and, therefore, cannot be said to be exactly identical.

I understand what promulgators like Aristotle and Rand are saying, but both are philosophers searching with logic for truth in its most precise form, and so neither would accept the surface of a problem if there is evidence of something lurking underneath. What you do not see is far more intriguing than what you do see, if you want to see at all. So, what I am basically asking here is, "Is natural language sufficient to understand reality?" Can it map, one-to-one? No one has shown why I should not interpret the word identical in its most exact and logical form. In fact, by arguing that I should not interpret it this way, your words are telling me that that those same words are insufficient to know reality beyond mere approximation.

Thank you, everyone, for your feedback.

UK

Post 11

Sunday, March 19, 2006 - 6:39pm

UberKuh:

No one has shown why I should not interpret the word identical in its most exact and logical form. In fact, by arguing that I should not interpret it this way, your words are telling me that that those same words are insufficient to know reality beyond mere approximation.

I am arguing that one should and must interpret the word, "identical" in the most rigorous way possible for any sort of meaningful discussion on this forum.

Firstly, it is not possible to verify if two physical existents are identical. The mere act of observing them changes them, as we all know by the Heisenberg Uncertainty Principle. If they are to be identical every atom and particle comprising the entity must have the same velocity and relative position. Moreover, the two detectors must also be identical to each other. Furthermore, all environmental impacts must also be identical � and this would include all radiation impinging on the two objects. The temperature of the ambient atmosphere (if it is present) would have to be the same and, of course, this means that the velocity of the molecules would have to be the same. Extending this argument this to its logical conclusion implies that the universe would have to bear the same relationship to each object, which is clearly impossible (i.e. appealing to "common sense").

If two objects are identical they must continue to be identical. If the environments were not also identical then one object would decay or change differently than the other.

Another way of looking at it would be to consider the two detectors (which have to be identical). Some sort of pulse of zero or one could indicate whether an object was in a positive or negative state. If both pulses were the same then they would be determined to be identical. The detectors would have to be equal distances from their respective object so that there were no communication delays. This, together with my arguments above, leads to the conclusion that there must be a plane of symmetry midway between the two objects that extents to infinity. Common sense and observation tells us that there is no such plane of symmetry that divides the universe.

Post 12

Sunday, March 19, 2006 - 8:12pm

Now, this gets interesting. Sam, to support your opinion, which I share, that "one should and must interpret the word, 'identical' in the most rigorous way possible for any sort of meaningful discussion on this forum," you say that "it is not possible to verify if two physical existents are identical." (Btw, this begs the question of what's meaningful.) In other words, you are saying that at the deepest level of our current understanding about reality, we cannot verify the Law of Identity (thus, giving Hegel the upper hand).

Consider Schrodinger's Cat. Until it is observed, it is both dead and alive (A is and is not A, where A is "dead" or A is "alive"). Once the wavefunction collapses and the cat's state is observed, it becomes either dead or alive (A is A).

So, you are saying that A might or might not be A, but, for our purposes of discussing if A is A, we can conclude that A is A. In a twisted way, this sounds like something a Functionalist might say in that our ends justifies our means. What else can one do, right?

For starters, one can, as we agree, be rigorous about using logic. One can ask, is it possible to prove that A is A using logical or mathematical symbology? To preclude formal and semi-formal languages from reality is shortsighted. All languages must be allowed in a discussion of ultimate truths corresponding to objective reality. So, including all languages at our disposal for gaining knowledge about reality (a sort of "total epistemology" if you will), does the Law of Identity hold true? Can it stand the test of reality? Sam, you seem to be saying no, but, given what I just wrote, I would like to hear your response.

UK

Post 13

Sunday, March 19, 2006 - 9:22pm

UberKuh:

In other words, you are saying that at the deepest level of our current understanding about reality, we cannot verify the Law of Identity

No. I am saying that we can't prove that two supposedly identical object are, in fact, identical and I think I have demonstrated that for them to be identical they would have to:

1. Occupy the same location � (impossible)
2. Have exactly the same environment to the limits of the universe � (impossible)
3. Be mirror images of themselves across an infinite plane �(impossible)

If I am wrong you should be able to demonstrate it by symbolic logic or any other formalism.

Your proposition is that if there can be two identical existents then the Law of Identity is invalid (A is not A). I have shown that there cannot be identical existents whether or not one can validate it by observation.

Post 14

Sunday, March 19, 2006 - 9:52pm

UberKuh wrote:

I understand what promulgators like Aristotle and Rand are saying, but both are philosophers searching with logic for truth in its most precise form, and so neither would accept the surface of a problem if there is evidence of something lurking underneath. What you do not see is far more intriguing than what you do see, if you want to see at all. So, what I am basically asking here is, "Is natural language sufficient to understand reality?" Can it map, one-to-one?

The short answer is: yes. Natural language enables one to conceptualize and categorize reality, which one is aware of through the evidence of one's senses.

No one has shown why I should not interpret the word identical in its most exact and logical form. In fact, by arguing that I should not interpret it this way, your words are telling me that that those same words are insufficient to know reality beyond mere approximation.

Nonsense! Who said that you shouldn't interpret the word "identical" in the most exact and logical form?! Certainly not I. I simply said that the word can be used in two different ways, depending on the context -- that "identical" can mean either that one thing is the same as another, or that one thing is the same as itself. The law of identity refers only to the latter sense. Although "identical" can be used in either of these senses, there is nothing inexact or illogical about either of them. It is just as exact and logical to say that one thing is identical to another (if it is) as it is to say that one thing is identical to itself. The meaning of "identical" in the first sense simply refers to a range of similarity as against a background of difference. For example, one apple is identical to another apple as against an orange, pear, banana, etc. One Gala apple is identical to another Gala apple as against a Macintosh apple, Pippen apple or Delicious apple, etc. There is nothing inexact or illogical about this use of "identical." Given the relevant context, it is perfectly exact and logical -- just as exact and logical as saying that a particular apple is identical to itself. But the law of identity, which says that a thing is itself, would employ only the latter usage.

- Bill

Post 15

Sunday, March 19, 2006 - 11:09pm

Sam,

I must have misunderstood you. I thought you said that the deepest level of reality that we can study using the strictest logic is the quantum level, where indeterminacy reigns. Were that the case, then my analysis should hold and the Law of Identity would not for all possible truths (i.e., ways of seeing truths). But I understand you to be clarifying your opinion that, although we cannot verify that "two physical existents are identical," this does not affect our conscious application of the Law of Identity.

All I can say here without repeating myself too much is that I disagree that the concept of identity should not apply to all contexts. And not to sound like a sycophant, but I probably need to clarify that my disagreement does not mean I disagree with Rand's interpretation of this law. She was more or less using it to get across an important point, namely, that reality is noncontradictory.

As an aside, if any of you have read George H. Smith's book, Atheism: The Case Against God, would you agree that Smith, being a fan of Rand, seems to employ another important aspect of Rand's concern with identity, that to be something is to be something specific? He uses this exact argument to show that the concept of God is self-contradictory, thus, precluding the existence of God.

Bill,

Like I told Sam, all I can say is that I disagree that the concept of identity should be limited. For ordinary, day-to-day needs, it works, but as an epistemological discussion, I think we've scratched the surface.

UK

Post 16

Monday, March 20, 2006 - 6:08am

A couple of weeks ago, in a discard bin on campus, I found a picture book from Time/Life called Ice Ages. Hegelian phenomenology would not explain human survival though the last million years.

Before we can light a fire to save our sorry frozen asses, we first must define what we mean by "fire." Is it always the same fire, or is it a different fire? If it is a different fire, will it have the same nature as the nominally "same" fire might have had in an arbitrarily "previous" (however defined) moment. I point out that so-called "common sense" tells us that if we built a fire in a shallow pit surrounded by rocks, we could stay warm all night in this cave. Yet, if fire has a different nature from moment to moment, might it not leap out of the pit and burn us all to death? Suppose, really, that a fire is a "copy" of "itself." In that case, by morning, there might be a flock of fires in here. That could be a problem.

We are here today to discuss this because our ancestors did not, and thus, with mere common sense, survived glaciers.

Carl Sagan said that it is wrong to disparage "savages" as being "primitive." He called them true scientists. On the thin edge of survival, they have to live rationally and objectively, understanding the evidence of their senses and logically drawing the correct conclusions -- or else they die. We, however, have the luxury of self-imposed idiocy.

(Edited by Michael E. Marotta on 3/20, 6:12am)

Post 17

Monday, March 20, 2006 - 6:42am

Michael:

Carl Sagan said that it is wrong to disparage "savages" as being "primitive." He called them true scientists. On the thin edge of survival, they have to live rationally and objectively, understanding the evidence of their senses and logically drawing the correct conclusions -- or else they die.

Thanks, Carl Sagan was perceptive.

Sam

Post 18

Monday, March 20, 2006 - 9:11am

Michael, I have not argued that our everyday understanding of identity should not be regarded as a given. I have not argued that one should question the conscious organization of visual perception. I have granted, several times now, that our everyday awareness of identity is useful, for psychological as well as physical reasons. You seem to think that everyone's points before yours are missing the point, but the fact is that you are missing my point of the entire discussion, and to call my interest in discussing this a result of "self-imposed idiocy" is, itself, a laughably ironic case of "self-imposed idiocy" for you not reading or, if you have, trying to understand.

UK

Post 19

Monday, March 20, 2006 - 10:02am