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What is the nature of the axioms of Objectivism?

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nzcanadian

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This is the idea that we do not perceive the world directly, but only perceive a representation of the world. Visually, it would mean that you don't see an apple, you see a mental image of an apple which is somehow projected in the brain. I think these guys actually believed that there were little visible "brain spots", and when you heard a sound there would be an actual vibration inside the brain.

Thanks for the summary. So according to representationalism, you only perceive "perceptions", not existents? Sounds like the makings of a Kantian split to me.

I understand that there are modern versions of representationalism that don't seem so silly, except that it intersects with string theory so that lo and behold it turns out that in one of these hidden dimensions, there really are images and sound waves inside the brain, in the 18th dimension.

That's great-- 18-dimensional brain waves. LOL. :P

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Incidentally, String Theory - not really a theory in the physics sense, since it doesn't make any new predictions to be tested. It's more like a hypothesis and, as I understand it, a fairly arbitrary one at that. But the bizarrities of modern physics belong in a different thread.

<Qwertz wanders off in search of the physics thread>

-Q

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This is the idea that we do not perceive the world directly, but only perceive a representation of the world. Visually, it would mean that you don't see an apple, you see a mental image of an apple which is somehow projected in the brain. I think these guys actually believed that there were little visible "brain spots", and when you heard a sound there would be an actual vibration inside the brain. I understand that there are modern versions of representationalism that don't seem so silly, except that it intersects with string theory so that lo and behold it turns out that in one of these hidden dimensions, there really are images and sound waves inside the brain, in the 18th dimension.

Your retinas directly image the world, but they do not perceive. Electric impulses travel to the brain where they are perceived and interpreted into images. When we hear, we don't have anything vibrating inside the brain, but our eardrums do vibrate, which in turn causes the hammer, the anvil, and the stirrup bones in the middle ear to vibrate. The vibration is transferred to the cochlea in the inner ear. The cochlea is lined with sensitive hairs which trigger the generation of nerve signals that are sent to the brain where they are perceived. Our ears are not able to perceive though.

So what does this mean? Do we perceive the world directly or a representation of the world?

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Since that which we see is a combination of both the nature of the perceived object and the nature of our particular perceptive capacities, it's impossible to "directly" perceive reality without the "filter," so to speak. You could thus call it a representation, so long as that's not taken the wrong way.

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LarkLadyInn,

The best way to help you is by first identifying your misunderstanding of "the axioms of Objectivism", in particular the axiom of identity that you use here.

If 1) I am identical with myself.

Wrong. The axiom of identity does not say or suggest this.

2) objective reality is identical with itself.

Wrong again. The axiom of identity does not say or suggest this.

Since these are errors in your identification / application of the axiom of identity, there is no point discussing your confusion any further.

So. Are you able to see why these are not applications or restatements of the axiom of identity?

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Your retinas directly image the world, but they do not perceive. Electric impulses travel to the brain where they are perceived and interpreted into images. When we hear, we don't have anything vibrating inside the brain, but our eardrums do vibrate, which in turn causes the hammer, the anvil, and the stirrup bones in the middle ear to vibrate. The vibration is transferred to the cochlea in the inner ear. The cochlea is lined with sensitive hairs which trigger the generation of nerve signals that are sent to the brain where they are perceived. Our ears are not able to perceive though.

So what does this mean? Do we perceive the world directly or a representation of the world?

If this isnt direct perception, then what would you call 'direct perception'? In other words, what are you using that phrase to mean?

It makes sense to talk about direct perception when, for example, we are comparing the way we gain knowledge of trees and cats to the way we gain knowledge of quarks and the mental images of others (the former are 'perceived directly', while the latter are indirectly inferred from things which we perceive). But when you say that all knowledge is indirect perception, you have removed any real meaning that those words have.

Edited by Hal
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Do we perceive the world directly or a representation of the world?
We perceive the world directly. The fact that sound is transmitted via a medium such as air does not make it "indirect". I think it helps to keep clear on the distinction between sensation and perception.
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If this isnt direct perception, then what would you call 'direct perception'? In other words, what are you using that phrase to mean?

I didn't use the phrase 'direct perception'. The photons bouncing off object in the world enter your eye and are projected in the retina. If you could see inside your eye, you'd actually see an image projected on your retinas. Your retinas are directly measuring this light. After that, it is no longer the light that travels to your brain (where perceiving is done), it's electrical impulses.

An argument could be made for direct perception though if you consider your whole nervous system (including brain, optic nerve, retinas, spinal cord, etc) as one perceiving entity. That is plausible.

It makes sense to talk about direct perception when, for example, we are comparing the way we gain knowledge of trees and cats to the way we gain knowledge of quarks and the mental images of others (the former are 'perceived directly', while the latter are indirectly inferred from things which we perceive). But when you say that all knowledge is indirect perception, you have removed any real meaning that those wors have.

Ok... I see where you're drawing the line. Thanks.

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Wrong. The axiom of identity does not say or suggest this.

Wrong again. The axiom of identity does not say or suggest this.

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 B) 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::

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Black Diamond:

The only thing I see that LadyLarkInn might have not done correctly in the formulation of her statments is perhaps her decision to use the word "with." The proper formulations of Lady's statements should have been "I am identical to myself" and "objective reality is identical to itself" and NOT "I am identical WITH myself" or "objective reality is indentical WITH itself." The words "with" and "to" are very close in meaning, but if you take semantic offense to them because they might not necessarily be exact synonyms, I can understand that. I'm not sure that your disagreement stems from perceived semantic difference between the words "to" and "with" so I'm going to work off from the premise that even if LadyLarkInn had said, "I am identical to myself" that you would still have uttered the same disagreements. Here is why such a position would definitely incorrect if it is indeed the position you truly hold.

Wrong. The axiom of identity does not say or suggest this.
That is actually incorrect. LadyLark is correct when she says, "I am indentical to myself."

The words "I" and "me" have the linguistic property of referring to the same object if both sentences are uttered by the same person.

Thus, "I" and "myself" can be substituted for each other.

Here is an example of a hypothetical dialogue that illustrates this point:

Jack = "Hello, my name is Jack."

Ted = "Hey, Jack, my name is Ted."

Jack = "I really like pie, Ted.

Ted = "Here is some pie, Jack. Help yourself!."

Jack = "Thanks Ted, I'm happy to help myself."

Look at my use of the bolded words.

It should seem clear that from Jack's perspective he can use the words, "I" and "myself" interchangably. If Jack utters the word "myself" and is referring to anyone OTHER than himself, he is using the word incorrectly. If Jack says, "I'm happy to help myself" and he means, "I'm happy to help Sally" then Jack is confusing his identity with Sally which is a bit schizophrenic and destroys any possibility of communicating ideas intelligently.

In fact, the word "myself" is just a pronoun for the any person who uses the word "I" to describe himself.

Here is the defintion of "myself."

Main Entry: my·self

Pronunciation: mI-'self, m&-, Southern also -'sef

Function: pronoun

1 : that identical one that is I -- used reflexively <I'm going to get myself a new suit>, for emphasis <I myself will go>, or in absolute constructions <myself a tourist, I nevertheless avoided other tourists>

Indentity is reflexive.

When LarkLadyInn says, "I am identical to myself" the terms "I" and "myself" refer to the same object (LarkLadyInn).

If you say, "I am identical to myself" then "myself" cannot mean anyone other than yourself.

Person X cannot say, "I'm identical to myself" (where "myself" means "Ted") unless

Person X really IS Ted.

Make sense?

Wrong again. The axiom of identity does not say or suggest this.

Once again, you are wrong and for the same reason.

Look at LadyLark's statement, "objective reality is identical with itself."

Here are 4 sentences that are exactly alike:

1) objective reality is identical to itself.

2) objective reality = itself

3) objective reality = objective reality

4) A is A (or A = A)

Sentence 1 is exactly the same as the axiom of identity (sentence 4) in form and meaning.

The way we go from Sentence 1 to Sentence 2 is by realizing that the indentity sign (also known as the "equals sign") MEANS "is identical to."

If I say 2+ 2 = 4, that means Two units plus 2 units is identical to four units.

You make the jump from step 2 to step 3 by understanding that the word "itself" describes the reflexivity of a labeled object. You can say "Microsoft Office" to connote Object A (which in essence labels Object A "Microsoft Office"). Thus, you can say, "Microsoft Office is itself" or "Microsoft Office is identical to itself" or "Microsoft Office = Microsoft Office." They are all reformulations of the same basic identity axiom (A is A) at work.

Edited by Evan
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LadyLarkInn:

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?

1) Your presuppositions about your own identity were NOT incorrect. I just explained why to BlackDiamond (see above).

2) If you do allow the possibility of A or B (the are really restatements of the same principle in different forms) then you HAVE rejected the axiom of identity.

If you are not identical to yourself, then that translates to "A = -A" which is an outright rejection of the identity axiom.

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.

Your understanding is correct which is why the first would be a bad attempt to answer your possibility.

The definition of identity means that you are exactly equal to yourself in all senses no matter what the sense.

You can't be indentical to yourself in some senses but not all senses.

Lets list some senses that you could be equal or unequal to OTHER people in: height, weight, hair color, bust, and pant size.

If you say that you are indentical to yourself in the sense that you (and yourself) have equal heights, that is true. However if you say that you are indentical to yourself in the area of height but not weight, that is a really silly proposition. You have a set weight at any given time and if we fix the time to 1:59 PM (exactly) you cannot have two different weights at the same time (which would be the only way for you to be unidentical to yourself). If we weighed you at 1:59 PM and the scale spit out 115 pounds and 125 pounds and both measurements happened at the exact same time, we would have to conclude that two objects occupying the same space were weighed (realistically we wouldn't accept such a contradiction, we would just throw out the scale or check its calibration).

In essence, being indentical to yourself in some ways and not others means you are "similar" to yourself which is just a whacky thing to say and totally unjustifiable.

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.)
Restricting the axiom of identity to the logical realm disconnects logic from reality and denies the necessity that logic as a language be capable of describing reality.

A is A is a logical statement. If we confine that to the realm of logic, that denies that there are things in reality that can be substituted in for the variables (like pizza for example...you can substitute it into the logical sentence to say "Pizza is pizza"). You can't find (in reality) an example where one object's given identity contradicts itself. Thus, it is denied in the logical realm as well.

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.

Empirical law. You cannot have an empirical verification of ANYTHING without acknowledging that the things that are being identified (for the purpose of empirical verification) have set identities that are internally non-contradictory.

Let's say that we want to empirically prove the statment 2+2 = 4

If we get two apples and two oranges and want to see if we have a total of four units of fruit , that is an empirical example that demonstrates that the logic of the statement is true in the real world (the argument is sound).

For such an empirical example to serve as a mechanism of determining validity, we must implicity acknowledge that the symbol "2" and the word "Two" refer tothe amount of apples and oranges we have collected.

Denying indentity rejects that anything can be proven empirically (because for empirical proof to actually prove anything, the indentities used within the proof can't change midstream and suddenly refer to different objects).

Without the ability to validate anything, we have no way of separating the phrases "empty logical truism" from "empirical proof." In fact, at that point, they might as well mean the same thing because the terms in the phrases are vacuous.

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Evan, by assuming what you thought i meant, you wasted a lot of space arguing against what i did not say or even think:)

Now. LadyLarkin,

A thing is not identical to itself. A thing IS itself. That's the axiom of identity.

"A is A" is not the same as "A is identical to A".

And no, this is not a matter of semantics; the difference in these formulations lie at the very root of your confusion on this issue. Think about it.

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A thing is not identical to itself. A thing IS itself. That's the axiom of identity.

"A is A" is not the same as "A is identical to A".

Yes, thank you. The problem with changing the axiom from "A is A" to "A is identical to A" is that you open the door to those who would deny the axiom of identity by claiming that two physical objects are never exactly the same.

For example, I might say that a table is a table, but if the statement were changed to a table of type X is identical to table a table of type X (assuming two tables of type X exist), then someone who wishes to deny the axiom (believe me, they are out there) would counter that even if the tables were made in the same factory out of the same type of wood and given the same finish, there will still be small differences that make table X slightly different from the other table X.

I've also heard followers of the Heraclitean view of existence state something to the effect that since change is constant and ever-present, nothing is what it is. In other words, a thing is only that thing for a split second, then it changes - maybe only slightly, but it still changes. Therefore, A is not A. :)

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::smashes head against wall::
*hunterrose gives LarkLadyInn a bandage*

It might be better for us to actually ask LarkLadyInn (odd name :lol: )what was meant, instead of trying to interpret for ourselves :)

That said, so long as the terms "I" and "myself" of "I am identical with myself" refer to the same object, I personally don't see any particularly stressing problem.

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Evan, by assuming what you thought i meant, you wasted a lot of space arguing against what i did not say or even think:)

I made no such assumption.

Here is what I said:

I'm not sure that your disagreement stems from perceived semantic difference between the words "to" and "with" so I'm going to work off from the premise that even if LadyLarkInn had said, "I am identical to myself" that you would still have uttered the same disagreements. Here is why such a position would definitely incorrect if it is indeed the position you truly hold.

So even if LadyLarkInn had used the word "to" instead of "with" you still would have disagreed. Thus, I clearly did NOT waste space because you really DO hold the position that the axiom of identity is not the same as "A is indentical to A." I was working from the assumption that your disagreement was more than an annoyance of Lady's use of the word "with" and that you would put for the SAME disagreements if she had used the more proper word "to" instead. I clearly was correct and that assumption lead me to arguments which were not a waste of space and truly are applicable.

I never argued what you didn't say. I quoted EXACTLY what you said when I responded to it. I was making the assumption that your disagreement wasn't with word choice, but with meaning.

You have further proven me right in your last post where you state:

"A is A" is not the same as "A is identical to A".

My posts were a direct refutation of that very logic. I wasn't sure if you had a problem with the word "with" but you clearly don't because you substite "to" in place of LadyLarkInn's actual word "with."

The entirety of MY last post was a refutation of the "A is A" is not the same as "A is identical to A."

My assumption was correct and I am in no way misrepresenting your position.

btw...the equals sign in philosophy/logic is known as the identity symbol for a reason ;).

Think about that.

Do you really want to argue that "A = A" is not "A is identical to A"when the "=" is the IDENTITY symbol used to express identity? The word in natural language is "identical" to express the property of identity that we express with the symbol "=."

I will come back and address the rest of this later. Right now I'm a bit pressed for time.

Edited by Evan
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What a semantic quagmire. I am going to address Lady Lark Inn (Or perhaps, if she's going to reject the axioms of Objectivism, Lady Larkin?) and hopefully in doing so hit on not only the "Law of Identity" question but also the "Perception" question.

First, when dealing with Objectivism and philosophy in general, it's a poor idea to try to examine one axiom and ignore others. Remember, axioms are statements which are logically irrefutable, and hence, in a sense, irreducable. I would urge you not to consider the axiom of identity without comsidering BOTH consciousness and existence at the same time... if for no other reason than that it makes the definition and articulation of knowledge claims very difficult.

For the purpose of summary, the axioms are as follows:

1) Identity: A=A.

2) Consciousness.

3) Existence: Existence exists.

These three axioms are not at all dichotomous (in fact, they all MUST work in perfect, balanced tandem) and therefore could NEVER produce a dualistic, or I guess in this case trilistic (is that a word, lol?) divide bewteen the self, the perceived, and reality.

As hunterrose said, "Perceiving reality doesn't involve extending beyond oneself per se, simply an interaction between myself and what is perceived."

In other words, consciousness does not *contain* reality, it interacts with it. Nor is your consciousness the thing, particularly, which "contains" you identity; your identity as LadyLarkInn in dependent more on your the amalgam of your conscious/mental, physical, and (for lack of a better term) existential properties.

But just what IS identity? As I've said, it's a seemless, non-dichotomous blend between your ohysical being and your mental/conscious being; it is "you qua you", to coin a phrase.

One thing which identity is EMPHATICALLY NOT is a mathematical "=" sign. Anyone who's had their logic knows this. I studied logic jointly with a mathematics prof and a philosophy prof, and we were jokingly told the following: "If anyone in this class says 'A equals A' instead of 'A is A' when they see the identity symbol '=', we'll not only take a point off your next test, but you'll have to leave the room! So get it right!" This became a problematic threat when one day the math prof slipped and declared, "Alright, on line 2 we've got A equals A..." (We did indeed make him leave the room.) ;)

But I digress. What I mean to say is this: I think everyone here has problematized the statement "A = A" by equivocating a bunch of natural language synonyms with the word "is". Look at all the ways in which we could, if we were being less picky, state that claim in the English language:

A is A

A equals A

A is equivalent to A

A is identical to A

A means A

A is the same as A

A is exactly A

A replicates A

A duplicates A

...etc. ad naseum.

As an English major, I'm concerned with style and meaning. But the other half of me, as a philosophy major, is concerned with precision and implicature.

I think it's more accurate to say that A = A means "A has the identity of A" instead of "A is identical to A". This may be a very minor quibble, but I'd say that positing identity as an adjective makes the logical value of the sentence vague. So, Evan, you were vague.

On the other hand, if you say "A is identical to A *itself*" you properly convey the REFLEXIVE nature of the law A=A. And that works.

But I understand why you all were confused. I think you were actually all *meaning* the same thing from the start, but said it in different (and sometimes poor) ways.

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First, when dealing with Objectivism and philosophy in general, it's a poor idea to try to examine one axiom and ignore others. Remember, axioms are statements which are logically irrefutable, and hence, in a sense, irreducable. I would urge you not to consider the axiom of identity without comsidering BOTH consciousness and existence at the same time... if for no other reason than that it makes the definition and articulation of knowledge claims very difficult.

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.

For the purpose of summary, the axioms are as follows:

1) Identity: A=A.

2) Consciousness.

3) Existence: Existence exists.

These three axioms are not at all dichotomous (in fact, they all MUST work in perfect, balanced tandem) and therefore could NEVER produce a dualistic, or I guess in this case trilistic (is that a word, lol?) divide bewteen the self, the perceived, and reality.

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).

But just what IS identity? As I've said, it's a seemless, non-dichotomous blend between your

ohysical being and your mental/conscious being; it is "you qua you", to coin a phrase.

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?

;)

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You've confused me a bit, LarkLadyInn, but I think I might see your question.

E.g. if I were to use (loosely) "existents exist" as an axiom, and another person replied "non-existents exist," then both being true would make them meaningless statements, and your question might be phrased as how is one proven and the other disproven?

I'm not sure I understand you, but I'll have to look at this more when I get back from work :)

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E.g. if I were to use (loosely) "existents exist" as an axiom, and another person replied "non-existents exist," then both being true would make them meaningless statements, and your question might be phrased as how is one proven and the other disproven?

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.

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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.

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

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.

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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.

Okay, I think I understand that. Let me go back to the identity axiom (since I at least partially agree with "being/exist/existence" being a bit vague... and I think that axiom is easier :) )

Are the axiom of identity (and the others by extension) universally and irrefutably empirically true, or are they merely logical constructs?
Going off the dictionary.com definition of "empirical" as "relying on or derived from observation or experiment," and for the sake of expediency defining "exists" as "to be present under certain circumstances or in a specified place" (also from dictionary.com, not likely the best, but IMO good enough for the moment:)

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.

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.

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

First you say:

The axiom of identity, being logically irrefutable, remains coherent even if not considered directly in relation to the other axioms.

And then you say:

... and this, again, is precisely the reason I bring the the axiom of identity (and both other axioms by extension) under scrutiny.

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.

[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.

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