What is the nature of the axioms of Objectivism?

[dondigitalia]

LarkLadyInn-

Are you aware that Objectivism rejects the split between a priori and a posteriori knowledge entirely?

[LarkLadyInn]

Yes, it does. If there are no existents, then what exists?

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.")."

Also, in Objectivism, the axiomatic concept "existence" is not synonomous with "state of being or existing." It's "everything which exists," which includes the state of being.

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?

[LarkLadyInn]

LarkLadyInn,

First you say:

And then you say:

When you bring the axioms "under scrutiny", do you mean scrutiny by logic? i suspect so. So, how are you bringing what you have identified as being "logically irrefutable" under (logical) scrutiny? If logic is unable to refute something (as you yourself say), then it (logic) CAN NOT be used for scrutinising that thing, yes?

So - before i continue with this interesting discussion, i want to know what we are using to "scrutinise" the axioms, LarkLadyInn. Thanks.

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.

][To help you again, notice that you say you want to find out if the axioms are EMPIRICALLY true. But "empirically true" is itself meaningless without the axioms being true - this is the very meaning of their identity as axioms.] But first answer the other question above.

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?

[blackdiamond]

LarkinLadyInn,

I'm not sure any more what you mean by "attacking a straw man". You make statements, someone points out something (perhaps a contradiction - or an apparent contradiction) from those statements - and you just accuse them of "attacking a straw man" without showing EXACTLY how it is "a straw man" they are attacking. Can you at least acknowledge the contradictions inherent in some of your arguments (with themselves or with objectivism) as pointed out by others before just attacking them for attacking a "straw man"?

Begining from your starting formulation of the identity axiom, you made an error which was fundamental (by using the term 'identical') and I pointed out that your confusion lies right there (as in, you do not understand the basics of the subject matter itself that you are 'scrutinising'). But your errors have continued and you do not want anyone to point them out, apparently, because they are just "straw men".

Even in your last post, you do make some fundamentally fallacious statements, but i do not know any more if they are worth pointing out. For example,

Since I can imagine an existence without existents (e.g., an empty space), it does not defy logic that no existents exist.

.

This is called "primacy of consciousness", larkin, an error you would have been familiar with if you had actually read the subject you are analysing. Just because you can imagine something does not mean "it does not defy logic".

The point i am driving at is this: you do not understand the axioms themselves and what they really mean; until you do, your question (and scrutiny) itself will be wrong. When you do, you will see why your question is wrong - and the light will shine through!

[LarkLadyInn]

LarkLadyInn-

Are you aware that Objectivism rejects the split between a priori and a posteriori knowledge 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.

[B. Royce]

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

It would help to restate 1) and 2): If 1) I am identical with myself, and 2)each thing in reality is identical with itself; or, if each thing that exists is what it is, how is it that some things (including me) are able to be aware of other things? The problem in your formulation was that you spoke of yourself as a concrete, but of reality as a floating generality.

[DavidOdden]

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.

Well, how do you explain your response "Since I can imagine an existence without existents (e.g., an empty space), it does not defy logic that no existents exist"? This is a nonsensical statement, from the perspective of Objectivist epistemology. So there are two reasonable inferences that can be made based on your own words. One is that you are unaware of the argument that your statement is founded on an incoherent, anti-Objectivist epistemology, and that is not an uncommon problem (belief in the analytic / synthetic false dichotomy is extremely common so if you were ignorant of Peikoff's refutation of the distinction, then I for one would not blame you for that, nor, I think, would others here).

The other possibility is that you are aware of that fact, and you reject Peikoff's argument and Objectivist epistemology. Which is it? This isn't an attack, this is just a question.

[Hal]

What does it mean to imagine that 'no existents exist'? What are you actually doing in your mind's eye while you do this? When I try it, the best I can do is to imagine an indeterminate black patch of space, with the words "nothing is in here!!!" written underneath.

I think that when doing philosophy, people are often too quick to assume that they can imagine/understand things. The fact that a group of words seem to form a grammatically correct English sentence isnt enough to ensure that they actually make sense.

Edited February 11, 2006 by Hal

[Nate T.]

LarkLadyInn,

Saying something like "non-existents exist" is contradictory. To treat your counterexamples:

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.

Leaving the false analytic/synthetic split aside, there's a problem here: space is defined by reference to existents (say, the distance from one entity to another, or some suitably defined coordinate system). If nothing exists, therefore, there can be no such thing as "space" (indeed, there can be no such thing as any concept!) Hence, there is no such thing as a space devoid of existents.

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 [...]

The only way you can talk about something yet to be created is if you know about that kind of thing to begin with. If there is an entity which you know will come into existence but has not yet done so, it simply does not exist. However, there is nothing contradictory in saying that it will exist, but it does not now.

[...] or when I speak of something in a negative sense (e.g., "Billy's not here. Billy was never born.")."

One can imagine all sorts of things (unicorns, gremlins, etc.) without any of them actually corresponding to anything in reality. Nonetheless, one's conception of such imaginary or mythical constructs do exist, as conceptions. The fact that one's imaginations do not correspond to reality is not a contradiction-- it is, in fact, an affirmation of the primacy of existence.

[hunterrose]

Did you agree with my identity validation (as more than merely a logical contruct,) LarkLadyInn?

So the question isn't just how one or another axiom can to be proved, but whether it is provable at all.

For the sake of the discussion, do you accept observation as a basis for the empirical verification of axioms?

"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."

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?

Assuming (until you say otherwise) that you accept that the identity axiom (as used in my prior post) as provable, would it be correct to say that your position on the existence axiom is that it is too vague/unprovable unless "exists" is defined properly?

I'm taking for granted that the definition used for my identity response won't necessarily be suitable for the existence axiom, but if your question is whether an axiom is provable (instead of whether the three axioms are "trilistic,") then I suppose it's not necessary, for the purposes of your argument, that we immediately reconcile the definition to simultaneously apply to all axioms.

[LarkLadyInn]

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.

[Hal]

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.

Imagining an empty space doesnt imply that youre imagining an existence without existents. Also, how do you know that the space you are imagining is really empty? There might be (eg) quantum fields and vacuum fluctuations in it which you just cant see!

Edited February 11, 2006 by Hal

[LarkLadyInn]

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

LarkLadyInn,

Saying something like "non-existents exist" is contradictory. To treat your counterexamples:

Leaving the false analytic/synthetic split aside, there's a problem here: space is defined by reference to existents (say, the distance from one entity to another, or some suitably defined coordinate system). If nothing exists, therefore, there can be no such thing as "space" (indeed, there can be no such thing as any concept!) Hence, there is no such thing as a space devoid of existents.

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.

The only way you can talk about something yet to be created is if you know about that kind of thing to begin with. If there is an entity which you know will come into existence but has not yet done so, it simply does not exist. However, there is nothing contradictory in saying that it will exist, but it does not now.

That something does not yet exist doesn't mean I can't speak of it meaningfully; I can plan for its creation.

One can imagine all sorts of things (unicorns, gremlins, etc.) without any of them actually corresponding to anything in reality. Nonetheless, one's conception of such imaginary or mythical constructs do exist, as conceptions. The fact that one's imaginations do not correspond to reality is not a contradiction-- it is, in fact, an affirmation of the primacy of existence.

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?

[LarkLadyInn]

It can be observed that identity is present under certain circumstances e.g. your computer monitor is of a certain height and color. I can say that mine is grey and 2.25 ft (making up) high - or I could be even simpler and say that it is not black and is taller than 3 inches. For identity to not be present, in the second case my monitor would also have to be black, and not be taller than 3 inches. Assuming one accepts observation to be an "empirical" basis, then identity, interpreted in its most basis sense, is irrefutably (and universally?) empirically true. Empirical qua experiment, no, since I suppose an experiment would require the existential possibility of non-identity.

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.

OTOH I'm not sure if it's a part of your point, but I suppose you could consider (what I assume to be) the corollary statement "non-identity doesn't exist" to be a logical construct, in the sense that (natch) such a statement can neither be observed nor the result of an experiment. Though such a statement can certainly be proved logically.

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).

IMO this is indeed not limited in such a way. Could you give an example of one of these interpretations?

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.

[RationalBiker]

[the preceding three paragraphs are just my opinion. I don't need a lot of useless commentary on it, everyone.]

Keep in mind, when you post something on this forum (or any forum for that matter), the responses you get may have absolutely nothing to do with what you want or need. If you don't like your ideas being challenged, you may find you are in the wrong place. Aside from that, you are insulting people by saying their commentary is "useless". If you think a comment is useless, attack the comment with logic and reasoning by explaining why it's useless. I would venture to say that most users are not concerned with what you find to be "F-ING IRRITATING".

[Evan]

Begining from your starting formulation of the identity axiom, you made an error which was fundamental (by using the term 'identical')

NO. That is NOT a problem.

LarkLadyInn didn't just use the word "identical," she used the phrases "identical to myself" and "identical to itself."

As long as you have the phrase "identical to" and you use that phrase in conjunction with a word that has extra built in reflexivity (himself, herself, itself, myself, theirselves, etc), you have NO problems in formulation.

There is NO semantic or formulaic difference between saying:

1) Tom is identical to himself

2) Tom = Tom

3) Tom is Tom

They are all the same.

Saying Tom is identical to Tom is a little sketchier because simply using the phrase "identical to" DOES leave open the possibility of imprecision.

However, LarkLadyInn never just used "identical to" by itself.

So long as "identical to" is used in conjuction with a word that specifies the reflexive nature of the object in question (himself, herself, etc) then there is no problem whatsoever.

A = A is a statement in First Order Logic (FOL). In natural language, we call the "=" the identity symbol because it expresses a reflexive identity relationship.

Saying "identical to" in natural language to describe the relationship the identity symbol ("=") specifies is only out of line if you don't add in a conjoining words that specifies the extra reflexivity. The conjoining words are needed, and when they are used in conjunction with "identical to" theynullifies the original problem you and Gags had with potential vagueness and imprecision that would result if you only used "identical to" in place of the identity symbol. I agree that "identical to" wouldn't suffice to describe a relationship like Clark Kent = Superman because that sets up Clark Kent and Superman as two distinct objects which sort of goes against Liebnit'z law (the idescernability of identicals).

It makes more sense to say, "The identy of Clark Kent is identical to the identity of Superman" instead of just "identical to."

However, this is all moot because LarkLadyInn DID use those conjoining words (itself, and myself) in her initial formulations.

You really need to quit rehashing the same arguments that have been already addressed.

Edited February 12, 2006 by Evan

[hunterrose]

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.

No, "X is identical to itself" might be a derivative of "identity exists," but that would be a broader statement than the bare-bones Objectivist axiom. The example doesn't need the monitor to be identical to itself, strictly speaking.

Such [an axiom,]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).

This is what you meant by universally true? I wasn't sure, so I left that alone at first. I grant that the identity axiom is generally interpreted much more universally than I've used it, and "everything that ever has or ever will exist is/was identifiable in every one of its properties" is much, much more difficult to empirically prove. Such an axiom would indeed likely require a logical proof, in addition to empirical evidence IMO.

[The "baseline" identity axiom's proof]strikes me as a logical proof rather than an empirical one.

So long as I can look at something and recognize one of its properties as being of quality Y (or even easier and as previously, as not being of quality Z) then the axiom is true, at the least, in this most basic interpretation. This would be an empirical proof, instead of (or as well as) a logical one, wouldn't it? If not, what would qualify as an empirical proof?

At any rate, I think you have to agree that "identity exists," as defined in the basic sense, is provable, whereas it's negation would be falsifiable. It's admittedly not nearly as meaningful as its broader use, but I would nonetheless argue that there is very good reason for choosing this "identity exists" over "identity does not exist" as an axiom.

One example would be Dialetheism, a paraconsistent logic which accepts some contradictions as true.

I checked the link, though admittedly a lot of it went over my head. I don't think that it could junk a baseline "identity exists." And as for a broader interpretation, to use the link's example (a man standing in a doorway and the property of "in the room,") it could be argued that "in the room" and "not in the room" are not contradictory values (as used on Wiki.) You might be right that such could prove an axiom to be invalid, but I think it's more likely that this kind of thing only works by looking at situations in unusual (and more important, potentially invalid) ways.

[DavidOdden]

I think that when doing philosophy, people are often too quick to assume that they can imagine/understand things. The fact that a group of words seem to form a grammatically correct English sentence isnt enough to ensure that they actually make sense.

This is a fundamental fact that seems to have eluded many quite respectable philosophers. Any time I see someone basing an argument on the assertion "you couldn't imagine X", I cringe at their lack of imagination.

[Hal]

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.

That's a misleading way of phrasing things. The point of paraconsistent logics isnt to accept contradictions as true - its to create a system which doesnt fall apart the minute you get a contradiction. In classical logic, having an inconsistent system is catastrophic because it allows you to prove anything whatsoever (since anything follows from a false statement). But this is very unrealistic: humans are generally able to function perfectly well even if they believe contradictory things - the error is isolated to some degree. Hence paraconsistent logics (once which 'fail gracefully' like humans do) can be useful when designing reasoning agents (eg robots) which function in real world environments and might pick up errors by mistake. Its not a case of saying 'contradictions are good!' or 'lets throw out identity!' - its a pragmatic decision to accept that some contradictions are likely to occur in reasoning, and to prepare accordingly.

Theres a decent article on platostanford about paraconsistent logic which gives a fuller explanation than wikipedia, along with describing the motivations:

The development of paraconsistent logic was initiated in order to challenge the logical principle that anything follows from contradictory premises (...) Let L be a relation of logical consequence, defined either semantically or proof-theoretically. Let us say that |= is explosive iff for every formula A and B, {A, ~A} |= B. Classical logic, intuitionistic logic, and most other standard logics are explosive. A logic is said to be paraconsistent iff its relation of logical consequence is not explosive.

...

A most telling reason for paraconsistent logic is the fact that there are theories which are inconsistent but non-trivial. Clearly, once we admit the existence of such theories, their underlying logics must be paraconsistent. Examples of inconsistent but non-trivial theories are easy to produce. An example can be derived from the history of science. (In fact, many examples can be given from this area.) Consider Bohr's theory of the atom. According to this, an electron orbits the nucleus of the atom without radiating energy. However, according to Maxwell's equations, which formed an integral part of the theory, an electron which is accelerating in orbit must radiate energy. Hence Bohr's account of the behaviour of the atom was inconsistent. Yet, patently, not everything concerning the behavior of electrons was inferred from it. Hence, whatever inference mechanism it was that underlay it, this must have been paraconsistent.

etc Edited February 12, 2006 by Hal

[blackdiamond]

LarkLadyInn didn't just use the word "identical," she used the phrases "identical to myself" and "identical to itself."

As long as you have the phrase "identical to" and you use that phrase in conjunction with a word that has extra built in reflexivity (himself, herself, itself, myself, theirselves, etc), you have NO problems in formulation.

EVAN,

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.

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.

You really need to quit rehashing the same arguments that have been already addressed.

So, i should accept your 'address' as logically true just because YOU have ALREADY addressed it, sir? Okay.

[blackdiamond]

As for LarkLadyInn, it seems clear to me that she - i will assume it's a she - has no respect for the minds of the people she is debating against. She believes that they somehow just want to focus on some small, peripheral statements that she makes incidentally (she wrongly brands this "attacking a straw man"), when the fact is that those statements betray her lack of understanding of the very basic elements of the subject she is trying to 'dissect'. Helping her see these errors could lead her to resolve the confusion she has on the issue.

She describes the arguments of the people she is seeking intellectual discourse with as "F-ING irritating", and "useless" ("i don't need a lot of useless commentary, everyone"), etc. I for one judge her as not worth my time/consciousness unless she is willing to apologise for her attitude.

[DavidOdden]

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.

Since there is no divide at all, I can't imagine what you mean by saying that you think it's one of degree. Peikoff says, p. 94 "Objectivism rejects the theory of the analytic-synthetic dichotomy as false—in principle, at root, and in every one of its variants". Since Objectivism rejects contradiction, you cannot embrace the AS dichotomy without rejecting Objectivism. That's all well and fine, but you cannot expect anyone to join you in rejecting Objectivism "for the sake of the argument".

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.

This is really a large part of Peikoff's paper, so it appears to me that you don't understand the paper in the first place. The thing is, this is actually the central point of the conversation. In fact, ASD starts with an example of precisely this type -- the philosophy professor separating reality and logic in denying the logical possibility of coercive monopolies under capitalism. The quotes from Wittgenstein and Ayer p. 94, asserting the unreality of logic, are directly addressed to this point.

The concept "logical possibility" is identical to "factual possibility", i.e. there is just "possibility". Something is possible if there is evidence to support the conclusion, and not definitive evidence to reject the conclusion, but still not anywhere near enough evidence to be certain that it is true. If you have some evidence that there exists a space devoid of existents, then it is possible. That means, since you're asserting that it is logically possible for there to be such a space, then you do in fact have some evidence that it is so. What is that evidence? Of course, if you don't understand the concept "logically possible" and how it is identical to "factually possible", then because of this error in your understanding of logic, it's easy to see how you would make this error.

It appears to me that your anger over people focusing on this particular point is caused by the fact that you don't get understand that logic and fact are not autonomous, and this this is one of the 6 most important things to understand about Objectivism. It is not a trivial error on your part, it is a fundamental error, which needs to be corrected. It's roughly analogous to a creationist telling a bunch of evolutionary biologists "All I'm saying is that god created the earth in 6 days and he created man on the 6th day, but that's not important, now let's talk about the history of man and his relation to other species".

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.]

But you plainly do reject Objectivist epistemology (in saying you don't take it at face value, that can only sensibly mean "I reject it at face value"). I think you may have misunderstood the purpose of this forum. This is not a general philosophy forum for any and all whacko beliefs, this forum is specifically designed for exploration of Objectivism. You don't actually have to personally believe in Objectivism, you just have to understand it well enough to know what constitutes acceptance and what constitutes rejection. There are plenty of people here who don't agree with Objectivism, but they are able to make the distinction between using the forum as a springboard for disseminating anti-Objectivist viewpoints (which will land you in trouble), and entering into an informed discussion of matters relevant to Objectivism. In other words, it is not logically possible for there to be a space devoid of existents, unless you're willing to argue that such a thing does exist. If you don't accept that then you should stop making the false assertion that there's a difference between the logically possible and the factually possible. You should stop saying things like that there are statements which are logically provable but can't be verified empirically, because there are no such statements. You can always say "I have no idea whether there exists a space devoid of existents". Or, you can try again to understand Objectivism.

[Nate T.]

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

How can divorcing logic from fact and divorcing existence from identity be irrelevant to a discussion about metaphysics? These are basic things you must understand about the Objectivist metaphysics if you are going to ask questions about it. If you are here to simply disagree with Objectivist metaphysics, I suggest you read the Forum Rules. In any case, you ought to work on your manners.

Also, I don't know how else to explain to you that space is a meaningless term if nothing exists, so I'll stop trying.

That something does not yet exist doesn't mean I can't speak of it meaningfully; I can plan for its creation.

Of course; I've already conceded that it will exist. But you don't get to assume that it exists now. Remeber, the whole point of bringing this up was to give counterexamples to "nonexistents do not exist." Something that does not yet exist does not exist. Just because you're referring to it does not mean it exists. As such, this is not a counterexample to "nonexistents do not exist".

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'.".

Referring to "keys that are not on the table" is a reference to keys that exist, but which are not on the table. As such, those keys exist, and by your manner of speaking you're introducing extra information about them through the dependent clause "that are not on the table." The keys aren't in a 'mode of nonexistence' or anything. However, if you were to say "the keys which aren't anywhere," you would be spouting nonsense, since keys are material and hence have a location. In any case, "the keys that are not on the table" are somewhere, so they are not "nonexistents that exist."

[DavidOdden]

Also, I don't know how else to explain to you that space is a meaningless term if nothing exists, so I'll stop trying.

I don't know if this will help, but I'll give it a try. There are two ontologies of space: it's a thing which is everywhere (like "the ether"), or it's a relationship between things that exist. If space is an absolute entity that exists independent of particles, it would still be an existent, presumably the only existent, but it would exist. In that sense, space without existence is a contradiction. If space is relational, i.e. it is the time-space relation between some two particles, then that particular space is meaningful only with respect to those particles. If there are no particles, the "space" relationship between particles also doesn't exist.

[Nate T.]

I don't know if this will help, but I'll give it a try. There are two ontologies of space: it's a thing which is everywhere (like "the ether"), or it's a relationship between things that exist. If space is an absolute entity that exists independent of particles, it would still be an existent, presumably the only existent, but it would exist. In that sense, space without existence is a contradiction. If space is relational, i.e. it is the time-space relation between some two particles, then that particular space is meaningful only with respect to those particles. If there are no particles, the "space" relationship between particles also doesn't exist.

That's a good way to think about it-- thanks!