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How can they be derived from observation? We dont 'know' the law of identity yet, how can we possibly derive either it or anything else?

A baby observes that his mother is his mother, his fist is his fist, his crib is his crib, milk is milk, etc. That's how he learns identity.

When he wills his hand to move, then sees his hand moving, then observes it batting the mobile over his crib, he learns that he can cause his own actions and that is actions can affect the external world. He learns causality.

Later, when he starts to abstract and integrate, he occasionally comes up with a contradiction which, when he tries to apply the contradiction to reality, he observes that one of his premises was incorrect. That's how he learns non-contradiction.

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A baby observes that his mother is his mother, his fist is his fist, his crib is his crib, milk is milk, etc.  That's how he learns identity.

So the baby does all this without knowing any principles of logic? If we distinguish between 'knowledge-that', and 'knowledge-how', the baby has 'knowledge-how' to identify things, but not knowledge of what he is doing? Then when he gets older he is able to identify what he is doing, and formulate it as a formal principle (the law of identity)?

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Spearmint: “How can logical principles be derived from observation? Logical principles are necessary to do the deriving in the first place, this argument is going to descend into circularity...”

You’ve identified a major sticking point with the notion of identity as a foundational concept derived from observation. If identity is one of the foundations of all knowledge, and all knowledge derives from observation, one is justified in wondering how it is possible to derive the notion of identity without circularity.

The problem is primarily one of logical rather than psychological priority. There are few solutions to this conundrum. One is to suppose that identity is somehow given in perception, but this runs up against Rand’s claim that perception is an automatic, purely physiological process. Another is to suppose that the mind derives identity from observation, but if the notion of identity is also presupposed in all knowledge, this leads to circularity.

A third is to posit that identity is arrived at independently of observation, but where observation is the occasion of such understanding, but this is the a priori justification that Rand also rejects.

So that leaves unexplained just how Rand justifies her axiomatic concepts in a way that doesn’t fall into one of these three categories.

E

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So the baby does all this without knowing any principles of logic?

He doesn't have to know logic because reality IS logical. Around age 5 - 7, when he goes beyond the perceptual level and begins to abstract from abstractions, he can come to conclusions that contradict reality. Then he has a reason to learn the rules of logic explicitly, and he learns them from observing reality.

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Spearmint: “How can logical principles be derived from observation? Logical principles are necessary to do the deriving in the first place, this argument is going to descend into circularity...”

You’ve identified a major sticking point with the notion of identity as a foundational concept derived from observation. If identity is one of the foundations of all knowledge, and all knowledge derives from observation, one is justified in wondering how it is possible to derive the notion of identity without circularity.

It isn't and that is not a problem. It only goes to demonstrate the axiomatic status of identity. Axioms are inescapable.

What is more, it is IMPOSSIBLE to DENY true axioms without USING them in the denial -- something Aristotle called Reaffirmation through Denial and Ayn Rand called the Fallacy of the Stolen Concept. That is what distinguishes a true axiom from an idea which isn't an axiom. A bogus axiom can be denied without accepting it.

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Betsy: “What is more, it is IMPOSSIBLE to DENY true axioms without USING them in the denial -- something Aristotle called Reaffirmation through Denial and Ayn Rand called the Fallacy of the Stolen Concept. “

Try denying the claim “unicorns exist” without using the concepts in the denial. An axiom is merely a convenient starting point in an argument. The undeniability of a statement tells us nothing about its truth or otherwise. In order to discover that, we need to subject the statement to scrutiny and analysis. But of course that sort of procedure unavoidably appeals to other knowledge, and thus fatally undermines the claimed fundamental nature of the Objectivist axioms.

If “existence exists” means something like “that which exists, exists” or “some things exist”, fine, few people will argue with that. But in itself it tells us nothing about the world or what sort of things exists, or how they exist. Nor is it possible to spin off a series of necessary truths from such a statement.

E

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Try denying the claim “unicorns exist” without using the concepts in the denial. An axiom is merely a convenient starting point in an argument.

You are misunderstanding the issue once again. It is not their mere "use". It is the presupposition of their *truth* which is implicit in any attempt to deny them. And the axioms are not mere conveniences. They are the base and logical starting point of all knowledge and the presupposition of all knowledge, i.e. if they are not true then nothing is nor could be.

Look, this discussion is becoming tiresomely endless and you are evidently making no effort to grasp anything that is being said. At this point you are just wasting our time. If you genuinely wish to understand the Objectivist position on this, and many other issues, you must read ITOE and OPAR. If all you are interested in is intellectual game-playing than you most certainly have come to the wrong place. In any event, speaking for myself, I have no interest in pursuing this with you further.

Fred Weiss

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Betsy: “What is more, it is IMPOSSIBLE to DENY true axioms without USING them in the denial -- something Aristotle called Reaffirmation through Denial and Ayn Rand called the Fallacy of the Stolen Concept. “

Try denying the claim “unicorns exist” without using the concepts in the denial.

More precisely, it is impossible to deny true axioms without assuming the axioms are true in the denial.

As for the creatures you say exist, where are they? Show me some evidence.

An axiom is merely a convenient starting point in an argument. The undeniability of a statement tells us nothing about its truth or otherwise.
Sure it does! What is it about certain statements that MAKES them undeniable? That's an important thing to know.

In order to discover that, we need to subject the statement to scrutiny and analysis. But of course that sort of procedure unavoidably appeals to other knowledge, and thus fatally undermines the claimed fundamental nature of the Objectivist axioms.

Prove it!

If “existence exists” means something like “that which exists, exists” or “some things exist”, fine, few people will argue with that.
Existentialists?

But in itself it tells us nothing about the world or what sort of things exists, or how they exist. Nor is it possible to spin off a series of necessary truths from such a statement.

So? If you want to learn about the world, LOOK at the world. If you find a contradiction, it means you made a mistake. Keep looking.

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Fred: “You are misunderstanding the issue once again. It is not their [axioms] mere "use". It is the presupposition of their *truth* which is implicit in any attempt to deny them.”

Presumably, what you are saying here is that “existence exists” is a self-evident truth claim about the world. If so, it would need to be justified by some empirical evidence. Merely claiming undeniability does not constitute sufficient empirical evidence. Since evidence of this type is required to justify the statement, this calls into question its axiomatic status, since its truth would depend on something more primary, such as a sense datum or other knowledge.

I think I do understand what Objectivists are claiming in their appeal to their axiomatic concepts, but I’m not convinced that they are either axiomatic or concepts. But I’m happy to agree to disagree.

E

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Betsy: “More precisely, it is impossible to deny true axioms without assuming the axioms are true in the denial. As for the creatures you say exist, where are they? Show me some evidence.”

In regard to the truth of axioms, see my post to Fred above. I have made no claim for existence of “the creatures” you refer to, that is, unicorns. As for evidence, the same question could be asked regarding the truth of the claim that “existence exists”. Since Rand claims that all knowledge ultimately derives from sense experience, this axiom should rest on some sense datum. But in that case what is primary or foundational is the sense datum, not the statement “existence exists”, which therefore cannot be axiomatic, given that axioms cannot be subject to further analysis.

I assume this is why Rand falls back on her undeniability claim, but implicit in that claim are several assumptions, for example that all philosophical claims are necessarily about the external world. That may well be the case, but even so, it would also negate the axiomatic status of a statement such as “existence exists”, since its meaning would be dependent on a particular theory of concepts. In that case, it could not be a fundamental, primary claim.

E

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I think I do understand what Objectivists are claiming in their appeal to their axiomatic concepts, but I’m not convinced that they are either axiomatic or concepts.

Then why did you say in

http://forum.ObjectivismOnline.com/index.p...indpost&p=41941

"The timid should take heart that Objectivism is indeed alive and well. And those lacking in imagination, those who cannot envisage a world founded on Objectivist principles, need only open their eyes to the best that Objectivism can offer. It’s yours for the taking."

If you have read ITOE then surely you know the importance to her philosophy that Ayn Rand placed on axiomatic concepts. How do you praise "Objectivist principles" while denying the axiomatic base and conceptual form of those principles? Were you being disingenuous back then?

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Stephen asked: “How do you praise "Objectivist principles" while denying the axiomatic base and conceptual form of those principles?”

The context of the thread in question was about whether any countries at the moment have a fully laissez-faire government and capitalist economy. The answer, of course, is no. But I was pointing out, I guess in a rather opaque way, that despite this lack, an Objectivist community of sorts does exist, on forums such as this and in various real-world organisations and clubs.

So my comments were not about Objectivist principles as such, but rather an observation about the ontological status of Objectivism. I was drawn to make the comments because I have seen that a common theme among some Objectivists, especially the younger ones, is an impatience to realise the ideals embodied in “Atlas Shrugged”.

What this attitude fails to realise is that such ideals are already being embodied as we speak, among those who proclaim themselves as Objectivists. In that sense, it’s not necessary to try to imagine a future world of Objectivism, all one need do is observe the current situation to gain an idea of what that future might hold.

E

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Since Rand claims that all knowledge ultimately derives from sense experience, this axiom should rest on some sense datum. But in that case what is primary or foundational is the sense datum, not the statement “existence exists”, which therefore cannot be axiomatic, given that axioms cannot be subject to further analysis.

For anyone that is unsure how to answer yet another of Eddie's arbitrary arguments against Objectivism, I'll post this one for your benefit:

Existence, identity and consciousness are concepts in that they require identification in conceptual form. Their peculiarity lies in the fact that they are perceived or experienced directly, but grasped conceptually. They are implicit in every state of awareness, from the first sensation to the first percept to the sum of all concepts. After the first discriminated sensation (or percept), man's subsequent knowledge adds nothing to the basic facts designated by the terms "existence," "identity," "consciousness"—these facts are contained in any single state of awareness; but what is added by subsequent knowledge is the epistemological need to identify them consciously and self-consciously. The awareness of this need can be reached only at an advanced stage of conceptual development, when one has acquired a sufficient volume of knowledge—and the identification, the fully conscious grasp, can be achieved only by a process of abstraction.
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Bowzer wrote (quoting Ayn Rand): “Existence, identity and consciousness are concepts in that they require identification in conceptual form.”

The meaning of this is unclear. If existence, identity and consciousness are concepts, it follows that they must be explicated as concepts. It’s not clear why Rand would want to reiterate this.

“Their peculiarity lies in the fact that they are perceived or experienced directly, but grasped conceptually.”

Here Rand seems to be telling us that the axiomatic concepts are perceived or experienced directly, even though elsewhere she claims that all concepts must be formed by a specific method. That aside, how is it possible to directly perceive or experience a concept, which is a non-material entity?

“They are implicit in every state of awareness… After the first discriminated sensation (or percept) man’s subsequent knowledge adds nothing to the facts designated by the terms “existence, “identity, “consciousness…”

What is the “they” referred to here? Is it the concepts themselves, or the referents of the concepts? Presumably, it’s the referents of the concepts, which seem to be certain “facts” of reality. A related and important point is one that has been touched on earlier: is the “first discriminated sensation (or percept)” logically prior to awareness of the axioms, or are the axioms logically prior to percepts? In other words, are perceptions logically dependent on the axioms, or vice versa?

Unfortunately, this passage does nothing to clarify Rand’s axiomatic concepts. It’s not at all clear when she is referring to reality and when to the contents of her mind, since she fails to make a clear distinction between the two.

What she seems to be claiming in this passage is that we directly perceive a “fact” called “existence”, whereas consistency with her epistemology would require Rand to claim that such knowledge is an inference derived from experience.

E

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Bowzer wrote (quoting Ayn Rand): “Existence, identity and consciousness are concepts in that they require identification in conceptual form.”

The meaning of this is unclear. If existence, identity and consciousness are concepts, it follows that they must be explicated as concepts. It’s not clear why Rand would want to reiterate this.

Existence, identity and consciousness are axiomatic concepts which are implicit in any and every act of awareness from an infant's first days. Everything and anything perceived is what it is and every act of being aware of it is consciousness of reality. Any knowledge is an implicit acceptance of these axiomatic concepts.

They are not explicit concepts until and unless a person, usually as an adult, conceptualizes what has been implicit in all his previous cognition.

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Betsy: “Existence, identity and consciousness are axiomatic concepts which are implicit in any and every act of awareness from an infant's first days.”

And how do you know this? Are the axioms derived from and justified by the infant’s every act of awareness, or do these acts of awareness presuppose the axioms?

E

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And how do you know this? Are the axioms derived from and justified by the infant’s every act of awareness, or do these acts of awareness presuppose the axioms?

The axioms are IMPLICIT in the infant’s every act of awareness AND these acts of awareness presuppose the axioms.

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Betsy; “The axioms are IMPLICIT in the infant’s every act of awareness AND these acts of awareness presuppose the axioms.”

If the acts of awareness presuppose the axioms, this implies that the axioms are logically prior to such acts, that is, a priori. If this is not the case, the alternative is that the axioms are a matter of reasoned inference derived from observation. If so, what observations lead you to these conclusions?

E

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Betsy; “The axioms are IMPLICIT in the infant’s every act of awareness AND these acts of awareness presuppose the axioms.”

If the acts of awareness presuppose the axioms, this implies that the axioms are logically prior to such acts, that is, a priori.

Wrong implication.

The acts of awareness are all awareness of REALITY. The axioms are the rules by which reality operates. Therefore, awareness of reality IS awareness of the axioms.

If this is not the case, the alternative is that the axioms are a matter of reasoned inference derived from observation. If so, what observations lead you to these conclusions?

Every single one of them.

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Betsy: “The acts of awareness are all awareness of REALITY. The axioms are the rules by which reality operates. Therefore, awareness of reality IS awareness of the axioms.”

Here you have conflated mind and matter, in a way that implies some form of idealism. In doing so, you have also appealed to the direct apprehension of abstractions, or what Rand would call “intrinsicism” or “mysticism”.

This is a very long way from Rand’s explicit metaphysics and epistemology, but it’s not hard to see why Objectivism should slip into idealism or rationalism. Rand aims to provide an axiomatic foundation for all knowledge, but these concepts cannot be formed via the method outlined in her theory of concept formation, which she otherwise claims must always be used to form concepts.

In other words, Rand’s epistemological theory cannot account for its own foundations. This fact must cast a major question mark over her epistemology.

E

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Betsy: “The acts of awareness are all awareness of REALITY. The axioms are the rules by which reality operates. Therefore, awareness of reality IS awareness of the axioms.”

Here you have conflated mind and matter, in a way that implies some form of idealism. In doing so, you have also appealed to the direct apprehension of abstractions, or what Rand would call “intrinsicism” or “mysticism”.

This is a very long way from Rand’s explicit metaphysics and epistemology, but it’s not hard to see why Objectivism should slip into idealism or rationalism. Rand aims to provide an axiomatic foundation for all knowledge, but these concepts cannot be formed via the method outlined in her theory of concept formation, which she otherwise claims must always be used to form concepts.

In other words, Rand’s epistemological theory cannot account for its own foundations. This fact must cast a major question mark over her epistemology.

Apparently, you disagree with me and Ayn Rand.

At this point, I'll leave it to the readers of this thread to sort out the various arguments made thus far and decide who is making sense and who is not.

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... but these concepts cannot be formed via the method outlined in her theory of concept formation, which she otherwise claims must always be used to form concepts.

What you actually mean is that you are unable to grasp both the method and meaning.

In other words, Rand’s epistemological theory cannot account for its own foundations. This fact must cast a major question mark over her epistemology.

Your own lack of understanding is the only actual fact. And, your lack of understanding is a reflection on you, not on Ayn Rand or on her theory of concept formation.

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Posted by Eddie

Betsy: “The acts of awareness are all awareness of REALITY. The axioms are the rules by which reality operates. Therefore, awareness of reality IS awareness of the axioms.”

Here you have conflated mind and matter, in a way that implies some form of idealism. In doing so, you have also appealed to the direct apprehension of abstractions, or what Rand would call “intrinsicism” or “mysticism”.

This is a very long way from Rand’s explicit metaphysics and epistemology, but it’s not hard to see why Objectivism should slip into idealism or rationalism. Rand aims to provide an axiomatic foundation for all knowledge, but these concepts cannot be formed via the method outlined in her theory of concept formation, which she otherwise claims must always be used to form concepts.

Betsy did not conflate mind and matter, you are failing to grasp the unique nature of the very few axiomatic concepts that there are. It is an implicit awareness of the most fundamental facts. It is not the equivelent of perceiving a table and grasping "tablehood" as if there is a "tablehood" in the table, and a "doghood" in the dog like the Aristotilian theory of essence in naive realism. Nor is it akin to the plato's Idealism.

The axiom existence is not a tag on every existent as your accusation implies.

Also, there is a distiction between how the axioms stand in the minds of every man whether he has heard of them or not, and a philosopher (or student after they've been discovered and articulated) discovering and making explicit these concepts. In the former instance, these are there and he relies upon them in order to think and live, and ultimately succeeds to the extent that he does not go against these fundamental rules. In the later they are discovered and formed in the same way the normal concepts are formed but on a radically expanded scale. It is no small wonder that it took thousands of years before all of them were discovered.

But, understand that they were already there-implicitly-even the philosopher that grasped them for the first time (Aristotle for two of them btw).

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Betsy: “Apparently, you disagree with me and Ayn Rand. At this point, I'll leave it to the readers of this thread to sort out the various arguments made thus far and decide who is making sense and who is not.”

This has been a lengthy exchange, so it’s probably a good idea to wind it up. In order to clarify my understanding of the axiomatic concepts, below is a summary of the way I interpret Rand’s method of concept formation, and how it impacts on these concepts.

Previously, you said that the axiomatic concepts are implicit in all “acts of awareness”, and that awareness of reality IS awareness of the axioms. Presumably, this means that each individual perception/experience of objects in the external world is also the perception/experience of the referents of the axioms.

If so, the perception of an individual object, such as a table, would also be the perception of existence, that is, real existence. But since existence is not obviously a perceptual object, it’s not clear how one could have such a perception. In that case, it doesn’t seem possible that the axiomatic concept that refers to this real existence could become present in the mind merely via the perception of objects.

On Rand’s epistemology, the concept existence should be formed by the method outlined in ITOE, that is: perception, differentiation, similarity, unitisation, definition, word. To take her example of the concept “table”, the essential perceptual characteristic -- a certain shape -- is abstracted from the process of perception/differentiation/similarity of at least two examples. This characteristic, or unit, then forms the basis of a definition.

But it’s not clear how this procedure would apply to the formation of the axiomatic concepts, since perception is always of particular objects and their particular characteristics, not general abstractions such as “existence” and “identity”.

That is the issue that I think needs to be resolved in order to support the claim that the axioms are derived from perception/experience rather than in some other way.

E

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Thoyd Loki: “…you are failing to grasp the unique nature of the very few axiomatic concepts that there are. It is an implicit awareness of the most fundamental facts…they are discovered and formed in the same way the normal concepts are formed but on a radically expanded scale.”

If it is the case that the axiomatic concepts are formed in the same way that normal concepts are, perhaps you could provide an account of the way that you form these concepts, according to the method that Rand outlines when she forms the concept “table” in ITOE. That is, one begins with the perception of an object, and then moves on to differentiation between objects, then similarity, unitisation and so on.

E

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