LarkLadyInn

This strikes me as a logical proof rather than an empirical one. You seem to be saying that the monitor has all and only its own properties, therefore it is identical to itself, which is a tautology. I'm not sure whether saying "non-identity doesn't exist" adds any extra semantic problems, but, yeah, I'm saying that there are statements (axioms) that are apparently logically provable but can't be verified empirically. Or rather that such a statement, insofar as it can be shown to be true empirically, cannot be determined to be at all true in every case or entirely true in any case (except in a purely logical context). Sure. One example would be Dialetheism, a paraconsistent logic which accepts some contradictions as true. Of course, if I'm correct, one could just as easily interpret an axiom to be definitely true, definitely false, neither, or ambiguously true and false (as one might interpret the Liar Paradox, for instance), so it's certainly not limited to contradiction.

I don't know what is provoking people to attack this particular argument which I just used in passing in a reply and is now utterly irrelevant to the discussion, but it's F-ING IRRITATING. Anyway Let's be clear about some things. I never said that there is such a thing as a space devoid of existents, nor did I say that there might ever be one, or that there might have ever been one. I said it's not logically impossible that such a thing exists. Space is not defined by reference to existents. Spatial relationships, of which space is the form, are defined by reference to existents. Space is the possibility of those relationships, and it's not contradictory to imagine the possibility of nothing-in-particular. It's just nothing. That something does not yet exist doesn't mean I can't speak of it meaningfully; I can plan for its creation. This doesn't even address the idea in my example. I never said anything about anything imagined existing in reality or corresponding to anything existing in reality. I did say that we may speak meaningfully of things that do not exist. Take, for example, the keys that are not on the table. Their meaningfulness lies in my inability to use them. I cannot take the keys from the table. And yet I'm apparently able to refer to them meaningfully in some sense; "The keys are not here. The keys are here in the mode of 'not'.". Keep in mind that I'm not arguing for the meaningfulness of the nonexistence of impossible objects, but only of possible objects in possible situations. "The keys could be on the table, but they've been misplaced." It could have been otherwise. Does anyone care to explain how the analytic-synthetic distinction fits in with this?

After some thought I've decided that Peikoff's paper on the subject is hardly a refutation, and I reject it outright as such, adding that I do not believe the true divide between analytic and synthetic is an absolute one, but rather one of degree. I don't believe there's any fundamental disagreement between Peikoff's views and mine, simply because I reject the distinction only in an absolute sense just as Peikoff does, and I do not believe he would object my stance. Or, at any rate, I don't believe our positions are mutually exclusive. So, I don't reject objectivist epistemology, but I don't take it at face value either. [the preceding three paragraphs are just my opinion. I don't need a lot of useless commentary on it, everyone.] Could you or someone quickly explain how "Since I can imagine an existence without existents (e.g., an empty space), it does not defy logic that no existents exist" defies objectivist epistemology? btw, I don't want to make a big conversation out of this since it's not an important part of the discussion.

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.

You're fighting straw men, too, blackdiamond. It's a waste of my time and yours. You are obviously trying to confuse the issue by accusing me of circular reasoning, but that is completely unjustified if you just look at what I've already said in my last post: "There just doesn't seem to be any good reason for choosing an axiomatic statement such as 'being is' over (the apparently equally axiomatic) 'being is not.' The meaning of 'being' in the most general sense is just too vague to place it in one or another such category without losing all meaning." (btw, I left out 'a priori' without changing the meaning of the argument) And that's how I'm scrutizing them logically, by acknowledging a fundemental antinomy in axioms. In order to respond to this directly, I would have to have already answered the question for which I'm here seeking an answer. I'm apparently being accused of circular reasoning again. So, In order to respond appropriately, I'll have to restate my question in a new form: Is it the case that "empirically true" is meaningful if and only if the axioms are true?

You haven't presented an argument, and this really isn't even an important part of the discussion, but I guess I'll answer your question anyway. First, I didn't deny that existents exist, I said it was not logically necessary that they do. Since I can imagine an existence without existents (e.g., an empty space), it does not defy logic that no existents exist. Plus, as I said in my last post, "There are, in fact, some senses in which I could meaningfully speak of non-existents as existing, such as when I speak of something yet to be created, or when I speak of something in a negative sense (e.g., "Billy's not here. Billy was never born.")." 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?

Well, it doesn't defy logic that there may be existence with no existents, so the example you use doesn't quite have the power of an axiom. There are, in fact, some senses in which I could meaningfully speak of non-existents as existing, such as when I speak of something yet to be created, or when I speak of something in a negative sense (e.g., "Billy's not here. Billy was never born."). But to answer your question, there just doesn't seem to be any good a priori reason for choosing an axiomatic statement such as "being is" over (the apparently equally axiomatic) "being is not." The meaning of 'being' in the most general sense is just too vague to place it in one or another such category without losing all meaning. So the question isn't just how one or another axiom can to be proved, but whether it is provable at all.

The axiom of identity, being logically irrefutable, remains coherent even if not considered directly in relation to the other axioms. Indeed, it implies the other axioms, so it is irrelevant that I did not explicitly state the relation of the axiom of identity to the others. The axioms openly state a three-way divide, if only among the axioms themselves. But even if it does not directly divide the self, the consciousness, and reality, then this tripartite division, belonging to the axioms and being therefore fundamental to our logic and understanding, implies such distinctions universally at least. Whether this divide is one which actually exists in some sense or whether it is merely a logical construct is essentially the entire problem at hand, and this problem cannot simply be brushed away. Unless one ignores the fact that logic is incapable of a reductive description or explanation of the world, the "perfect, balanced tandem" construct of which you speak must be confined to a purely logical or purely extralogical existence in order to maintain its irrefutability. But, in either case it's utterly meaningless (in the purely logical case because it is a tautology, and in the purely extralogical case because it is a contradiction.) And if the "perfect, balanced tandem" construct is not limited in such a way, the dissonance between our logic and the "logic of the world," so to speak, means that there can be some interpretations of the axioms in which they are false (paraconsistent logics are capable of this, for example). I agree. But that I am "me qua me" says absolutely nothing about me, and this, again, is precisely the reason I bring the the axiom of identity (and both other axioms by extension) under scrutiny. So I must ask again: Are the axiom of identity (and the others by extension) universally and irrefutably empirically true, or are they merely logical constructs?

The general consensus seems to be that my problem misses something important about the axiom of identity and it's implications because my presuppositions about my self-identity(1) and metaphysical self-identity(2) were misinformed, but that only raises more questions: If we allow even the possibility that a) I am not identical with myself, or that objective reality is not identical with itself, then have we not denied the universality of the axiom identity? I can see only two ways in which to meet this question. The first is by rejecting the law of bivalence (in this case that something must be either 'self-identical' or 'non-self-identical') so that I can maintain that I am identical with myself in some senses and not in others. Unfortunately, this seems to deny the axiom's universal undeniability, and my understanding is that the axiom cannot be denied. The second is by denying that the axiom of identity is an empirical law and restricting it to the purely logical realm. But in this case the axiom has been reduced to the level of a mere tautology and means nothing (and it is also the case that the tautology, having no content, may be reinterpreted in such a way that it is false.) These problems may be generalized to obtain a new question: For it to be universally true and undeniable, what must be the ontological status of the axiom of identity? In other words, is the axiom of identity an empirical law or an empty logical truism, and why? Of course if it's neither then the original metaphysical problem still stands. ::smashes head against wall::

It seems inevitable that the axioms of Objectivism lead one to a metaphysical problem analagous to that of the relationship between mind and body. If 1) I am identical with myself, 2) objective reality is identical with itself, and 3) I am conscious of objective reality, then how can I account for my being conscious of objective reality without either admitting that I extend beyond myself to include objective reality (thereby denying the axiom of identity) or admitting representationalism (thereby denying my relation to the world and by extension the validity of the axiom of consciousness)? In other words, what is my relation to the external world if the world and I exist independently of each other? "My philosophy, Objectivism, holds that: 1. Reality exists as an objective absolute—facts are facts, independent of man's feelings, wishes, hopes or fears. [...]" -Ayn Rand, Introducing Objectivism