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.
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Mon, 2006-06-19 05:25
First off, I found you through all the sites on INTP. Stayed up the whole night reading, researching, and taking more tests to see if I'd consistantly get INTP. I did. Gotta say, the descriptions were pretty spot on and it's refreshing to see another person who thinks as much (if not more) as me! Okay, down to business.The way I perceived your meaning of (A is A) is that there are two distinct and separate A's, even if both of them are supposedly identical, right? What if we're talking about only one A, instead of two identical A's? It's like saying "I am me." Surely that cannot be faulty in logic. The trouble, however, is that it does not give us any new information. It seems like saying "I am me," even though it is not wrong per se, is still pretty pointless. But I found it interesting that you used the word "copy."The word "identical" is an adjective, describing the characteristics of something. The word "copy," however, although is an adjective as well, implies action/verb. Something can be identical, but no action is required for that. Not so with "copy." For a copy of anything to exist, it is necessary for the action of "copying" to have preceded it. Therefore we end up with two very different context when we change the wording.To say (A is identical to A) or (A is identical to itself) or [A is identical to a separate but identical A (which does not mean the 2nd A was created/copied from the 1st A)] is not at all the same as saying (A is A) using the "copy" approach as I took from what you wrote.I think we should expound on what we mean when we attribute "unique" to a concept. If we are just talking about a physical representation of Concept A, ie: the Sphere, in a physical sense, I see no reason why there cannot physically be two Spheres, identical. Both of those Spheres would still be unique, it seems to me, as the Concept of Spheres still seperates and "identify" both of said Spheres from other physical representations of Concepts like Cubes or Pyramids. So if we're talking physically, I see no problem even if we "copy" Sphere B from Sphere A, because Concept measurement does not go into physical measurements. But I think you're talking conceptually.Conceptually, I'll have to say the argument you presented only worked due to the inherent faulty vocabulary usage, messing with the context. A Concept is a Concept right? I don't think there can be multiples of the same Concept, kind of like the Forms that Socrates and Plato talk about right? Even if there are multiple, identical Concepts, they do not have to be "copies," which implies "being copied." But I still hold that a Concept, by definition, must be singular because there can be only one. It cannot be copied because it is not physical. So it seems like you took "copy, copying, to copy" which is a physical property and applied it to something that is conceptual. That, logically, cannot work.It's 6:00am here and I haven't slept yet, so please let me know if what I wrote makes sense only in my sleep deprived mind. =) I look foward to your response.
Mon, 2006-06-19 12:49
Thanks for your comment. I agree in part. Regardless of what I wrote above, here is what I would argue now: The map is not the territory. As you point out, I can say that something is identical with itself, assuming I like wasting my breathe. So what? A good example is to say that identity is identical with itself. What could that possibly mean? It doesn't.
The same holds for A = A or any such similar assertion. In what conceivable sense is the letter A equal to itself written again? Only potentially in the sense that one A looks like another. Yeah, okay, but it isn't identical in a number of other ways, like in that each A is several pixels apart, that each occupies separate physical memory addresses inside your computer, and that we're using at least two different monitors. And if you can't say that something is identical with itself in every respect, then it simply isn't identical. It's similar, but not identical, and we shouldn't muddy the definitional waters needlessly. It is identical in one sense or another, but not in every sense, which makes the identity partial. Can I say that something is partially identical with itself? Do I like wasting my breathe?
What if I didn't write it twice? What if I merely spoke it? What if my lips moved and sounds came out that we recognize as designating the first letter in the English alphabet? Does that get us anywhere? Nope. Hearing. Seeing. Feeling. Tasting (as in the case of a certain soup product my sister ate practically every day for years). It's all the same. Any sensory experience that leads us to knowing that A = A will prove the assertion to be something other than a statement of identity.
All that aside, the fact is that people use identity to mean similarity all the time. Identity effectively means similarity. They're synonyms.
Also, we who wish to uphold and revere the English language as a meaningful means of communication should stop saying that A is identical to B. It isn't. A is identical to A, but only questionably, in only a small, insignificant, and utterly wasteful sense.