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Russell's Paradox

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n is even iff there exists a k such that n = 2k.

Then definitions of 'odd' that are all perfectly fine:

m is odd iff m is not even.

m is odd iff there exists a k such that n=2k+1.

m is odd iff there exists an n such that n is even and m=n+1.

These all work, not only for natural numbers, but for infinite ordinal numbers as well. However, the concepts of "even" and "odd" are not sensible for infinite cardinal numbers.

m is odd iff there exists an n and a k such that n and k are even and m is between n and k (where 'between' has been previously defined in regard to a previously defined ordering).

Here I think you should say that m is the ONLY number between n and k. Otherwise this will not work.

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Here I think you should say that m is the ONLY number between n and k. Otherwise this will not work.
You're right. That's what I meant. Or, m is between an even n and n++. Actually, I also wanted to come up with the most abstruse definition I could think of (to make the point I was making about the "fungability" of such definitions), but I felt too tired and lazy to do it. Edited by LauricAcid

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These all work, not only for natural numbers, but for infinite ordinal numbers as well. However, the concepts of "even" and "odd" are not sensible for infinite cardinal numbers.
Wait a minute. A limit oridnal is not odd, since no limit oridinal is a successor. But why is a limit oridnal even? For example, what's the n such that omega = 2*n or even n*2 (where '*' stands for ordinal multiplication)? Maybe you mean it works for cardinals but not for ordinals? Because, yes, aleph_0 = 2*aleph_0 (where, this time, '*' stands for cardinal multplication). Right? Edited by LauricAcid

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DISREGARD THE PREVIOUS POST. I wasn't thinking straight. Here's the edit:

I'm rusty on both ordinal and cardinal arithmetic, so please bear with me. I see that every limit ordinal is even (since, for every limit ordinal k, 2*k = k), right? And every infinte cardinal c is even since 2*c = c (where, this time '*' stands for cardinal multiplication), right? So the even/odd dichotomy does not work for cardinals, as you said. But getting back to ordinals, we have to show: for every ordinal k, there is a b such k = 2*b exclusive_or there is a d such that k = (2*d)+1. And that's as far as I'm getting with it until later, 'cause I'm done for the night.

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Wait a minute. Heirarchy. You can't jump the heirarchy. If you extend the theory, then that extension has to be based only on what you've already established. You can bring in anything you like, as its' previously established (from the axioms, what follows from the axioms, and, I would grant, from any directly perceived fact) and does not itself depend on what you're trying to establish. From what principles and concepts that have already established, does it follow that a concept is not correct unless it is necessary? (Aside from, I still don't know by what means you propose we decide whether something is necessary.)

Having a hierarchy does not mean that extending a theory must be based only on the more fundamental facts that have already been established. What it means is that the later knowledge cannot contradict the more fundamental facts. It's not my theory; it's Ayn Rand's, so if you have a problem with her idea (which, admittedly, does not follow directly from the axioms) that one should not form new concepts unless there is some cognitive need for them, talk to her.

If you want my opinion on why she formulated her Razor, I think it stems from her view of epistemology as a practical science--that's pure speculation on my part, though.

Fine. I don't ask that your argument confine itself only to concept formation. Whatever is already established in the theory, up to the point of the principle that concepts must be necessary to be proper, is fair to bring in, and I don't even mean 'up to' as per pages in a book. We can skip around a book and bring in principles developed later in the book, as long as those principles are lower in the heirarchy or logically prior to (or whatever you want to call it and by whatever Objectivist logic you like) the principle being established.
Well, the problem Kyle brought to the table was about whether or not Ayn Rand's theory of concepts was susceptible to Russel's paradox, so the entire theory--all of it--everything she said in ITOE and elswhere on the subject of concepts--is fundamental to this problem.

My purpose in this thread isn't really to prove whether Ayn Rand's later principles follow from the earlier ones, but to show that her theory of concepts, when taken in its entirety does not lead to a contradiction. I have no interest in (nor do I think I'm properly qualified--yet) attempting to do the former, which is basically what you're asking me to do.

What is rationalism is adopting AXIOMS without regard to experience. If the axioms have been adopted with regard to experience, then it is not rationalism to infer from the axioms.

It is rationalism to confine yourself to a deductive proof from any set of axioms, regardless of the nature of those axioms. Most rationalists, historically, did adopt their axioms without regard to experience, but that's a separate issue. There are a great many quasi-Objectivists who adopt certain ideas of Objectivism, with regard to experience, but then apply them rationalistically. Dr. Peikoff has a whole lecture course specifically on this phenomena. ("Understanding Objectivism"--it's very expensive; I don't expect you to buy it.)

If you weren't asking for a deductive proof, then I retract my earlier statemtent, but that is the impression that I got.

Objectivism uses plain old reasoning all the time. Plain old 'if then', 'not', etc. From the very start, through the whole philosophy, there are arguments and inferences based on everyday reasoning forms. The very first paragraph of OPAR is such an argument. Moreover, Objectivism uses plain old reasoning all the time to critique OTHER philosophies and theories.
Well, yeah. Deductive reason works very well for the things it works for, but it isn't the only kind of reasoning, and there are some things that you just can't learn by deduction.

I just noticed that OPAR (pg. 8) uses the term 'validate' to subsume deduction, induction, and direct perception. So, I'm asking what is the validation of the principle that a concept must be necessary for the concept to be correct.

Ayn Rand discusses this in chapter seven of ITOE, "The Cognitive Role of Concepts," the very same chapter where she introduces her aforementioned "razor." I'll warn you though, that she does not show it by a deductive method. Rather, she introspects and tells her observations.

What are the cognitive benefits ONTO THEMSELVES of distinguishing the metaphysically given from the man made?...But that's incorrect. No matter that the odd concept used HAD no cognitive value for one, it does have value once it's been USED in an argument regarding epistemology. Even if we found the concept in the DUMPSTER, if it turns out that the concept has bearing upon one's epistemology, then it is evasion not to face that.

The first thing I want to say is that I don't think I ever said "cognitive value" (I didn't go back and check, so if I did say that, I'll say right now that it was a mistake). What I said was "cognitive significance," which is different from a value judgment.

Secondly, the one point you bring up that does as have real cognitive significance is that forming this concept leads to a contradiction, which is precisely what makes a rejection of the concept warranted, as opposed to your claim that it is arbitrary.

Quite frankly, I'm astonished that you could possibly describe my claim that this concept is invalid (according to Objectivism) as arbitrary, considering the support I have drawn directly from Objectivist literature in favor of my position. At most, what you can claim is that the principles I've referenced are arbitrary, and you're certainly entitled to do that.

I'm not going to attempt to prove that these particular parts of Objectivism are correct. It isn't my purpose in this thread, and I don't fully grasp the validation of them myself--if I were an expert I wouldn't need to be enrolled in OAC, working to become one. What I do fully grasp, however, is that the points I've raise are a part of Objectivism, they are a part of Ayn Rand's theory, and that they cannot be ignored in an attempt to prove that her theory leads to a contradiction.

Edited by dondigitalia

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OK, here we go: http://forums.4aynrandfans.com/index.php?s...indpost&p=13430

Essentiality is a criterion for what to include in a definition of a concept. For specifying a set, there are other criteria: The predicate should be applicable to the base class (you can use the predicate "red" with apples, but you cannot use it with air molecules, since air molecules do not have a color) and decidable for every instance of the base class.

The latter point is important. It makes the infamous "all sets that do not include themselves" invalid as a set specification, because the predicate is undecidable for the set being defined due to circularity.

By "decidable," I meant "meaningful." (Or "falsifiable" if you like; the point is that it must affirm or deny a fact of reality rather than purely depend on its own truth or falsehood.)

So even if you found a valid reason for forming a concept of self-referring concepts--and call it, say "selfcept"--the definition

A selfcept is concept that has itself among its referents

would be inadequate, because it wouldn't tell you whether or not "selfcept" was a selfcept. To make the definition adequate, you would have to include a clause that explicitly specifies whether or not "selfcept" is a selfcept, like:

A selfcept is a concept that has itself among its referents, or is the concept "selfcept."

Problem solved.

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To make the definition adequate, you would have to include a clause that explicitly specifies whether or not "selfcept" is a selfcept, like:

A selfcept is a concept that has itself among its referents, or is the concept "selfcept."

Problem solved.

What in the world? That's a blatantly circular definition. By being circular it NECESSARILY cannot have the "decidability" or "meaningfulness" you insist for concepts. And since you've ended with a circular definition, I won't even bother (at least for now) rebutting the arguments that led up to you making that definition.

(I'll try to catch up to the other posts later. dondigitalia: I didn't mean to put words in your mouth with 'value'. I was just responding to your 'offer to cognition'. By that I took you to mean offering something of cognitive value. But if that is a mistaken understanding of what you mean by 'offer to cognition', then all of my points can rephrased without the word 'value' while it would help also if you said what you mean by 'offer to cognition'. Thanks. I appreciate your amiability and reasonableness in these conversations.)

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What in the world? That's a blatantly circular definition.

You're stuck on symbol-expansion.

A concept definition is not a way of assigning a shorthand symbol for a longer sequence of symbols. The role of a concept's definition is to allow you to decide for each concrete object whether or not it is subsumed under the concept. The second definiton of "selfcept" I provided is suitable for this purpose: Take any object and using the definition you can tell whether or not it is a selfcept. Some examples:

  • Is my computer a selfcept? No, because it is not even a concept; it doesn't belong under the genus provided in my definition.
  • Is the concept "apple" a selfcept? No, because it is not among its own referents; the concept "apple" is not an apple.
  • Is the concept "concept" a selfcept? Yes, because it is among its own referents; the concept "concept" is a concept.
  • Is the concept "selfcept" a selfcept? Yes, because the definition of "selfcept" makes an explicit provision to that effect.

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You're stuck on symbol-expansion.
I have no idea what "symbol expansion" refers to or in what way I am supposed to be stuck in it. I'm using English words and punctuation.

A concept definition is not a way of assigning a shorthand symbol for a longer sequence of symbols. The role of a concept's definition is to allow you to decide for each concrete object whether or not it is subsumed under the concept.
I said nothing about a shorthand symbol for a longer sequence of symbols. We're talking about Objectivism, right? I don't know about the "role" of a definition, but, as far as I understand, for Objectivism, a definition assigns a concrete (a sound or string of letters) to a concept while specifying the essential property that is common to those things that are in the extension of the concept. Also, when you say "each concrete object", what do you mean by "concrete"? Just so that we're on the same page, I'll mention that, as I understand, a concrete is an object of extrospection. The lowest level concepts must be of concretes, thus all concretes, by being built from lower level concepts ultimately reduce to concepts of concretes, but it is not required that all higher level concepts refer directly to concretes or have only concretes in the extension of the concept.

The second definiton of "selfcept" I provided is suitable for this purpose: Take any object and using the definition you can tell whether or not it is a selfcept.
Your putative definition is not a definition, since it is circular, and being circular it does not provide a means of determination that you claim. Moreover, your putative definition needs to be looked at in terms of essentiality (regarding your "explicit provision") and perhaps genus/difference, which you've left unstated. In fact, it is the lack of such form that allows you the freedom to give a circular non-definition.

As to your bulleted list, you blew right past your own putative definition while claiming that you are applying it. You don't account for the second disjunct (what I take to be your vaunted "explicit provision"). In a couple of those list items, you'll find that providing for your "provision" leads the explanation into bizarre involution, as a circular defintion must do. If you doubt me, then go ahead, and provide that "explicit provision" explicitly in each of the bulleted items.

Most important, you've given a circular non-definition, hardly explained as to how it fits the Objectivist method, but your doing so has no bearing upon the correctness of the previously given definition of 'non self-inclusive concept'. And even IF you offered a definition of a DIFFERENT concept that is non-circular and correct yet non-paradoxical, then that still does not make the previously given concept Objectivistically incorrect, unless you can show that the previously given concept fails the criteria of Objectivist concept formation; thus you have not resolved a paradox by simply showing a different concept that is not a paradoxical one. But, as is still unrefuted, the previously given concept proceeds from a given Objectivist concept (viz. the concept "concept") and by differentiating within the genus, finds self-inclusive concepts and non self-inclusive concepts, which differentiation has not been shown to violate any Objectivist principle, especially as Objectivism makes similar dichotomies within a genus as well as, we have no reason to think that Objectivism claims that the vast number of everyday dichotomy-formed concepts are improper.

Edited by LauricAcid

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Having a hierarchy does not mean that extending a theory must be based only on the more fundamental facts that have already been established. What it means is that the later knowledge cannot contradict the more fundamental facts. It's not my theory; it's Ayn Rand's, so if you have a problem with her idea (which, admittedly, does not follow directly from the axioms) that one should not form new concepts unless there is some cognitive need for them, talk to her.
(1) According to Objectivism, knowledge is hierarchical and contextual. But all knowlege is utltimately sourced in perception, of which the axioms and first corollaries are a summary of the most basic truths associated with perception (that we perceive existents or even more fundamentally, we perceive existence, or more fundamentally that existence exists; that for an existent to exist is to exist as itself, different from other existents, with all its properties and acting according to its properties; and that there is a perceiver (a consciousness) to do the perceiving). Or pretty close to that. Right? Now, I would agree with you that one can't derive knowledge just from the axioms, if that is what you are saying. I would agree that asde from the axioms, one continues to look directly at the world to obtain knowledge through direct perception (even as Objectivism explains that the axioms themselves are based on direct perception). Thus, also, that there is a context of knowledge. However, that does not contradict what could not be more clearly propounded in OPAR: All principles are hierarchical. Knowledge that is formulated as principle, not just unrelated perceptions, is all hierarchical. Peikoff goes on about that over at least a few pages in the book. And, actually, I personally might be inclined to be more liberal and allow that there are auxillary axioimatic principles for special enquiries even within philosophy. In that way, I am the one here who is willing to accept a derivation (or reasoned basis, or demonstration, or argument, or whatever you want to call it, even as Objectivism itself uses such rubric) that is less strict than from the Objectivist hierarchy. That is, if we were to hold to strict Objectivistism, I don't see how we could possibly allow that this epistemological principle of not allowing negations in definitions could be gotten other than through the hierarchy, but I'm not even asking for that strictness, as I'm just asking for ANY basis for the principle.

(2) You say the theory is Ayn Rand's, not yours, so we can only refer to her for answers. Okay, but if (emphasis on 'if') we don't find the answers in her writings or in Peikoff's reports of conversations with her, then you've offered a dead end. Uncharitably, one would call it a "blank out" (your blankout, not Rand's since it's not fair to claim lack of an explanation from someone not here to give one), as Objectivists are wont to do regarding such dead ends in the discourse of OPPOSING points of view.

If you want my opinion on why she formulated her Razor, I think it stems from her view of epistemology as a practical science--that's pure speculation on my part, though.
Wait a minute. At least as far as OPAR is concerned, I think you've completely reversed things here. In OPAR, Rand's Razor refers to cutting down philosphies that start in the middle, as opposed to the bottom, of a hierarchy or philosophies that don't have any hierarchy at all. But you are the one here who suggests that not all of the theory need be based on the preceding stages of the hierarchy. So, if Rand's Razor is to be applied, I think it should be applied to your position in this particular regard.

As to epistemology being a practical science, we would then have to ask: Practical to whom and toward what end? I don't want to repeat the mistake of using the word 'value' where you did not intend it, but if practical doesn't mean 'practical toward achieving some goal or value', then I don't know what you mean by 'practical'. So, unless you have some objective criteria of what is practical - and to whom and toward what end - that are not themselves in any way based on the epistemology (for otherwise would be clearly circular), then I don't see how you can objectively claim one concept practial but not another. (Please see my remarks about this earlier.)

Well, the problem Kyle brought to the table was about whether or not Ayn Rand's theory of concepts was susceptible to Russel's paradox, so the entire theory--all of it--everything she said in ITOE and elswhere on the subject of concepts--is fundamental to this problem.
Fine. But so far in this thread it has not been shown that there is anything else in philsophy that dissolves the contradiction. Just claiming that negative based definitions are not allowed is not enough unless we have a basis for that claim and we can explain why Objectivism itself uses negative-based definitions as well as negative-based definitions are vast in everyday concpet making and used even in the discourse of Objectivist (unless, for example, an Objectivist zoologist actually rejects the classification of, for example, invertebrates).

My purpose in this thread isn't really to prove whether Ayn Rand's later principles follow from the earlier ones, but to show that her theory of concepts, when taken in its entirety does not lead to a contradiction. I have no interest in (nor do I think I'm properly qualified--yet) attempting to do the former, which is basically what you're asking me to do.
But you haven't shown that the theory does not lead to contradiction, per the remarks I made in my previous paragraph. The formation of the concept follows proper Objectivist protocol, except possibly on some ban on negative-based definitions. But if negative-based definitions are disallowed then that contradicts that Objectivism uses negative-based definitions. And if a principle against negative based definitions is not part of the hierarchy of principles, then that contradicts the Objectivist principle that all philosophical principles are hierarchical.

It is rationalism to confine yourself to a deductive proof from any set of axioms, regardless of the nature of those axioms.
I don't know that that is true even per the Objectivist definition of 'rationalism'. Of course, a problem is that Objectivism seems to have its own definition of 'deduction' so that I can't even discuss deduction as it is more generally understood without coming up with another word for it. Anyway, whatever you call it - 'deduction', 'demonstration', 'derivation' (as you will find terms such as 'derivation' and 'argument' in OPAR) - I don't know the basis for your claim that a derivation straight from axioms is rationalism, as long as the axioms themselves are based on experience. But, more importantly, I'm not even requiring such a derivation, as I mentioned I just am asking what is ANY argument, that can be from any combination of axioms, principles, facts of experience, deduction or deduction - that negatives are improper for forming concepts.

Most rationalists, historically, did adopt their axioms without regard to experience, but that's a separate issue. There are a great many quasi-Objectivists who adopt certain ideas of Objectivism, with regard to experience, but then apply them rationalistically. Dr. Peikoff has a whole lecture course specifically on this phenomena. ("Understanding Objectivism"--it's very expensive; I don't expect you to buy it.)
Okay, but if the axioms properly adhere to the knowledge of experience, and if the reasoning from the axioms is correct, then please tell me how one can derive an improper conclusion?

If you weren't asking for a deductive proof, then I retract my earlier statemtent, but that is the impression that I got.
Yes, I'm asking for any argument at all - deductive, inductive, from axioms, from added principles, whatever. Then at least we can evaluate that argument as to checking its premises and its reasoning.

Well, yeah. Deductive reason works very well for the things it works for, but it isn't the only kind of reasoning, and there are some things that you just can't learn by deduction. Ayn Rand discusses this in chapter seven of ITOE, "The Cognitive Role of Concepts," the very same chapter where she introduces her aforementioned "razor." I'll warn you though, that she does not show it by a deductive method. Rather, she introspects and tells her observations.
I too think that deduction is not the only source of knowledge (by the way, I'm using 'deduction' as it is generally used).

The first thing I want to say is that I don't think I ever said "cognitive value" (I didn't go back and check, so if I did say that, I'll say right now that it was a mistake). What I said was "cognitive significance," which is different from a value judgment.
Fair enough. But you said "offers cognitively". So I don't know what you have in mind that would be offered other than some value of some sort. But however you wish to formulate that notion is fine with me. I'm not stuck on the word 'value'.

Secondly, the one point you bring up that does as have real cognitive significance is that forming this concept leads to a contradiction, which is precisely what makes a rejection of the concept warranted, as opposed to your claim that it is arbitrary.
(1) We still don't have a definition of "cognitive significance". (2) Even if we had a definition, we don't have an argument that cognitive significance is a requirement (please cf. the points I made about that earlier). (3) Whatever definition might be offered, we would have to see that the concept in question fails, which hasn't been shown (and can't be shown anyway until we have a definition). (4) You're begging the question when you say the concept must be rejected for the very reason that it leads to contradiction as opposed to our checking our premises that allow the formation of the concept and thus entail the contradiction. What you suggests amounts to this: Make it improper to form a concept that would cause a contradiction in the theory. Fine. But now you're adding an axiom to the theory that self-protects the theory from contradiction; thus we could do that for ANY theory, and the defender of any theory could always say, "Well, then just throw out the contradictory parts, but keep everything else." The point with Russell's paradox is that when Russell tapped Frege on the shoulder to say, "Um, well, I hate to break it to you old chap, but...well, your theory is inconsistent", Frege could not turn around and say, "Oh that's not a problem. Just don't allow that there is a set of all sets that are not members of themselves." That set IS allowed by theory. He can't just cherry pick to keep what derivations he likes from the axioms and reject what he doesn't like or what plays a part in the derivation of a contradiction. Rather, he must CORRECT the theory so that contradictions can't be derived. That means he must "check his premises" and look to see where he made a mistake in formulating them. I grant that that is more acute in a formal or mathematical theory. But it still obtains, though in less precise form, in a philosophical theory. Otherwise, any theory at all would be invulnerable from refuation simply by declaring a principle that whatever contradictions are found in the theory are dismissed. Indeed, it is pretty egregious confusion as to heirarchy to just ban what is implied by the lower end of the hierarchy rather than checking lower end premises themselves.

Quite frankly, I'm astonished that you could possibly describe my claim that this concept is invalid (according to Objectivism) as arbitrary, considering the support I have drawn directly from Objectivist literature in favor of my position. At most, what you can claim is that the principles I've referenced are arbitrary, and you're certainly entitled to do that.
I still have to read the passages you cite. But the problem here is that even if Rand says explicitly that we cannot use negatives, then (1) we need to know her REASONING for that, (2) we need to explain why Objectivism itself uses negatives, and (3) we need to explain how Objectivism can avoid the thousands and thousands of everyday concepts that are based on negation (especially, if as you suggest, epistemology is to be practical).

I'm not going to attempt to prove that these particular parts of Objectivism are correct. It isn't my purpose in this thread, and I don't fully grasp the validation of them myself--if I were an expert I wouldn't need to be enrolled in OAC, working to become one. What I do fully grasp, however, is that the points I've raise are a part of Objectivism, they are a part of Ayn Rand's theory, and that they cannot be ignored in an attempt to prove that her theory leads to a contradiction.
Fine. but then see points (1) through (3) in my previous paragraph. Edited by LauricAcid

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Qualification to post 109. I claimed that the concept of non self-inclusive concepts does not violate Objectivist concept formation protocol. However, it is claimed in this thread that there is an Objectivist ban on negation-based formations. My remarks in the above post address that claim.

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Wait a minute. At least as far as OPAR is concerned, I think you've completely reversed things here. In OPAR, Rand's Razor refers to cutting down philosphies that start in the middle, as opposed to the bottom, of a hierarchy or philosophies that don't have any hierarchy at all. But you are the one here who suggests that not all of the theory need be based on the preceding stages of the hierarchy. So, if Rand's Razor is to be applied, I think it should be applied to your position in this particular regard.

Rand formulated two razors, both of which she mentions in ITOE. The one Peikoff refers two is mentioned only in the appendix, and she refers to it as the"original 'Rand's Razor.'" (ITOE, 251) The other is a "razor of concepts." (ITOE, 72)

I still have to read the passages you cite. But the problem here is that even if Rand says explicitly that we cannot use negatives, then (1) we need to know her REASONING for that, (2) we need to explain why Objectivism itself uses negatives, and (3) we need to explain how Objectivism can avoid the thousands and thousands of everyday concepts that are based on negation (especially, if as you suggest, epistemology is to be practical).

I suggest that, until you have read those passages, you refrain from saying that no support has been given.

Secondly, I never said that negatives cannot ever be used. I said that, except in rare cases, they cannot be the proper basis for forming a concept. Rand specifically points out a few of such concepts (such as "nothing" and "non-existence") as examples of "invalid concepts." She also gives an example of a valid concept "absence" which is valid only in reference to the concept "presence," and can only be defined or formed in reference to it--concepts like this are precisely the very rare cases that I was talking about. (The concept of "absence" can be looked at as the fundamental concept-by-negation, as the others are all concepts of a things absence, like "caffeine-free," "non-physical," or "innocent." That does not mean that it is proper to for the concepts of "caffeine-free soda," "non-physical entity," or "innocent man," though--it just means that we have such adjectives to modify proper concepts as a means of describing those phenomena where they occur.)

[EDIT: That parenthetical is to be taken as my own identification, not Ayn Rand's.]

I've given a lot of references to ITOE, and I'm not going to copy them all in here for your convenience. I do request, though, that you stop claiming I haven't given any support for these things or asking for the support, when I've pointed you straight to it. The truth isn't that my claims go unsupported; the truth is that you've either ignored or been unable to look up the support I've given.

Edited by dondigitalia

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A selfcept is a concept that has itself among its referents, or is the concept "selfcept."
Bold mine.

I think LauricAcid is balking at your definition as circular because it uses the word being defined in the actual definition. To quote Wikipedia "A circular definition is one that assumes a prior understanding of the term being defined." Your definition doesn't require one to know what the concept selfcept means, but only that it exists, and so is in fact non-circular.

I was initially of the opinion that adding "or is the concept 'selfcept'" to the previous definition of SRC, in order to get out of a potentially sticky situation, is more or less cheating. Then I recovered a bit and realized that if a definition is incapable of distinguishing whether or not a certain referent fits the definition, then it is in fact a poor definition and in need of revision.

A concept must either be self-refering or non-self-refering, and if the definitions of SRC and NSRC do not allow one to determine which category a certain concept falls into the definitions are at fault and not the Objectivist theory of concepts.

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A concept must either be self-refering or non-self-refering, and if the definitions of SRC and NSRC do not allow one to determine which category a certain concept falls into the definitions are at fault and not the Objectivist theory of concepts.

Exactly.

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Rand formulated two razors, both of which she mentions in ITOE. The one Peikoff refers two is mentioned only in the appendix, and she refers to it as the"original 'Rand's Razor.'" (ITOE, 251) The other is a "razor of concepts." (ITOE, 72)

I suggest that, until you have read those passages, you refrain from saying that no support has been given.

Thanks for the distinction on the two different Rand's Razor's. I don't claim there is not support anywhere given for the negation principle. I'm just saying that no support has been given in this thread, other than to say that Rand said it. I will be looking up the passages you suggest. But in the meantime, unless the argument is so very complex, I don't see why it can't be given in this thread. I'm not demanding or insisting that it be given, but it would help if it were.

Secondly, I never said that negatives cannot ever be used. I said that, except in rare cases, they cannot be the proper basis for forming a concept. Rand specifically points out a few of such concepts (such as "nothing" and "non-existence") as examples of "invalid concepts." She also gives an example of a valid concept "absence" which is valid only in reference to the concept "presence," and can only be defined or formed in reference to it--concepts like this are precisely the very rare cases that I was talking about. (The concept of "absence" can be looked at as the fundamental concept-by-negation, as the others are all concepts of a things absence, like "caffeine-free," "non-physical," or "innocent." That does not mean that it is proper to for the concepts of "caffeine-free soda," "non-physical entity," or "innocent man," though--it just means that we have such adjectives to modify proper concepts as a means of describing those phenomena where they occur.)

[EDIT: That parenthetical is to be taken as my own identification, not Ayn Rand's.]

Thank you. This is at least additional qualification. But I'm not clear whether or not you're saying that Objectivism considers, for example, 'caffeine-free soda' to be a correct concept ( I sense that you're saying it is not). You talk about adjectives. But the principle of fundamentality works just fine in the concept of caffeine-free soda, no less than in the concepts "invertebrate" and, for example, a concept important to Objectivism: "non-human animal". But you say "absence" is okay since it is fundamentally the negation of "presence". But "caffeine-free" is fundamentally the negation of "caffeine-added" within the genus of sodas, just as "non-human" is fundamentally the negation of "human" within the genus of animals. I see no reason why the principle of fundamentality does not apply within a genus (in that sense, what is the genus that "absence" and "presence" are within?), especially given that Objectivism does use concepts by negation within a genus. But I will refresh my memory of ITOE with the passages you suggest. But also, if you reject things like "caffeine-free", or, as you say, only allow rare exceptions, then you'll have made vast parts of everyday concepts to be incorrect, which is fine as long as you're willing to accept that impracticality (as you mentioned practicality). This includes words for concepts not just starting with 'non-', 'a-', 'ir-', etc., but probably thousands and thousands of others. And it would not do to argue that one could find a non-negative definition (IF one could even do that in such cases as "non-human animal") since it is not ensured that such non-negative definitions adhere to the principle of essentiality. Edited by LauricAcid

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Your [Capitalism Forever's] definition doesn't require one to know what the concept selfcept means, but only that it exists, and so is in fact non-circular.
I'm sorry, but that is absurd. He's defining a concept with a word that he's using both to name the concept and to define the concept. That is circular and it is not possible to apply the definition, since to know whether something is a selfcept, one of the clauses is that we check whether that thing is itself the concept "selfcept", which can only be determined by knowing what the concept "selfcept" is, which is what the definition is supposed to tell us. Completely and blatantly circular. Using the definendum in the definiens. Plain bald circularity. It 's beneath debating about. But, on the other hand, if you want to allow such circularity, then great, we'll allow it not just for your special case, but for any other definition. Let's see what kind of epistemologies or theories we get then! Moreover, as I mentioned also, it has not been shown how the proposed definition is an application of the rule of fundamentatlity. And, as I already mentioned, even IF (which it is not) it were non-circular and non-paradoxical, it wouldn't dissolve the paradox of a DIFFERERNT concept. You don't dissolve a paradox just by showing that there is something different that is not paradoxical.

But wow, if one's argument descends to the dregs of using circular definitions (plainly, using the definiendum in the definens), then one is just effacing one's own philosophy. And I really very much doubt that Objectivism looks kindly upon circular definition.

A concept must either be self-refering or non-self-refering, and if the definitions of SRC and NSRC do not allow one to determine which category a certain concept falls into the definitions are at fault and not the Objectivist theory of concepts.
That ignores the arguments I made. The reason the concept of non self-including concept fails to allow determination is that it allows contradictory determination. So the problem is not to say that (after the horse has already left the barn) any concept that has such a contradiction is disallowed, but rather to formulate the rules of concept formation so that such contradictions are blocked by the rules themselves and not by some general rule that says, "except the contradictory ones". The reason is that if you allow such a rule as "except the contradictory ones", then ANY philosophy or theory can use that rule, thus any philosophy or theory, no matter how self-contradictory, can be made right just by saying, "everything is in the theory that follows from the axioms except the contradictions." Edited by LauricAcid

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That ignores the arguments I made. The reason the concept of non self-including concept fails to allow determination is that it allows contradictory determination. So the problem is not to say that (after the horse has already left the barn) any concept that has such a contradiction is disallowed, but rather to formulate the rules of concept formation so that such contradictions are blocked by the rules themselves and not by some general rule that says, "except the contradictory ones". The reason is that if you allow such a rule as "except the contradictory ones", then ANY philosophy or theory can use that rule, thus any philosophy or theory, no matter how self-contradictory, can be made right just by saying, "everything is in the theory that follows from the axioms except the contradictions."

Your argument is ignored because the counter-argument cuts off the discussion before you can get to the place where you would form your argument.

If the definition of a concept does not allow one to determine if a certain existent (or concept) is subsumed by the concept in question, the definition is poor. End of story.

Edited by LaVache

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Your argument is ignored because the counter-argument cuts off the discussion before you can get to the place where you would form your argument.

If the definition of a concept does not allow one to determine if a certain existent (or concept) is subsumed by the concept in question, the definition is poor. End of story.

No, you didn't address what I posted, especially about that if you have such an escape clause, then ANY theory can have it. It is not disputed that the definition is poor. But the point is that you must disallow it on PRIOR grounds than finding it contradictory. You need to have rules for proper definitions that block contradicton causing definitions not by finding out that they are contradicton causing but rather by excluding what it is ABOUT them that CAUSES their inconsistency. You need to make rules that pinpoit the NATURE of correct concept formation so that anything that qualifies by that nature is allowed and all else is excluded. Just saying that a definition must fulfill the criterion of specifying its extension is not enough. You need to give rules that ensure that that criterion is met, else ANY theory could have such a rule and make itself immune from non-referring concepts. And non-conctradictoriness itself can't be the rule, else ANY theory could have such a rule and thus make itself immune from contradiction. Edited by LauricAcid

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That is circular and it is not possible to apply the definition, since to know whether something is a selfcept, one of the clauses is that we check whether that thing is itself the concept "selfcept"

My fellow Objectivists, let us stand in silence and mourn, for the reasoning faculty of LauricAcid is now officially dead. This poor soul is facing the question, "Is the concept 'selfcept' the concept 'selfcept' ?"--and doesn't know the answer.

There is, of course, no such concept as "selfcept," because it makes absolutely no sense to introduce such a concept--but if it ever did make sense, then the concept "selfcept" would be the concept "selfcept" as sure as A is A; if you saw the sequence of letters s-e-l-f-c-e-p-t anywhere, or heard the corresponding sequence of sounds, you would know immediately that the thing you had just observed was the concept "selfcept." Yet our poor braindead friend wouldn't know it; instead, he would be frantically looking for the definition of "selfcept" for assurance. Imagine what a torture it must be to live with such a mind: Even the process of basic nutrition is an excruciating task, for when our identity-challenged acquaintance sees a slice of bread, he doesn't know that it is a slice of bread, but instead has to consult the Encyclopedia Britannica on his bookshelf, but then when he sees his bookshelf, he doesn't know it's his bookshelf, and when he sees the Encyclopedia Britannica, he doesn't know it's the Encyclopedia Britannica! It is a miracle of sorts--a work of extreme coincidence--that a person with such a debilitating disability has been able to log on to our forum and make no less than thirty-six posts in the space of just five days!

I'm sure you'll agree with me that this poor mental cripple deserves some rest, for which reason I have put him on moderator preview for seven days.

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Thanks for the distinction on the two different Rand's Razor's. I don't claim there is not support anywhere given for the negation principle. I'm just saying that no support has been given in this thread, other than to say that Rand said it. I will be looking up the passages you suggest. But in the meantime, unless the argument is so very complex, I don't see why it can't be given in this thread. I'm not demanding or insisting that it be given, but it would help if it were.

It's not that complex, and I did give support, way back at the beginning. You asked for references of what, in the Objectivist theory of concepts gave rise to it, which I also gave. To repeat what I said earlier (since you seem to have forgotten): it follows from the idea of a fundamental characteristic as the one which causes the greatest number of others--characteristic which does not exist cannot be said to cause anything about an existent. I gave two references to support this claim: Rand's explanation of essential characteristics and her discussion of concepts formed on the basis of a non-existent.

But also, if you reject things like "caffeine-free", or, as you say, only allow rare exceptions, then you'll have made vast parts of everyday concepts to be incorrect, which is fine as long as you're willing to accept that impracticality (as you mentioned practicality). This includes words for concepts not just starting with 'non-', 'a-', 'ir-', etc., but probably thousands and thousands of others. And it would not do to argue that one could find a non-negative definition (IF one could even do that in such cases as "non-human animal") since it is not ensured that such non-negative definitions adhere to the principle of essentiality.

I don't reject concepts like "caffeine-free;" in fact, it was my intention to cite that as a legitimate concept-by-negative. What I reject is a concept of "caffeine-free soda." (In fact, as applied to the concepts in this thread, I do not reject the concept of "non-self-referring," but I do reject the concept of "non-self-referring concept.") Those kind of concepts are the rare exceptions. Yes, there are thousands of them, but in comparison to the many, many more thousands of positive concepts, they are relatively rare.

Before I bow out of this discussion (this will be my last post, as my purpose has been met), I will summarize my reasons for rejection of a concept formed on the basis of a non-existent characteristic:

1) The Conceptual Common Denominator. "The units of a concept were differentiated--by means of a distinguishing characteristic(s)--from other existents possessing a commensurable characteristic, a 'Conceptual Common Denominator.'" (ITOE, 41) Attempting to form a concept on the basis of a characteristic some existent does not possess, one is attempting to form a concept on the basis, not of a differentiation between existents possessing a commensurable characteristic, but on the basis of an incommensurability--something which exists and something which doesn't.

2) The rule of fundamentality. "Metaphysically, a fundamental characteristic is that distinctive characteristic which makes the greatest number of others possible; epistemologically, it is the one that explains the greatest number of others." (ITOE, 45) This means that the fundamental characteristic must has some causal efficacy in relation to all of the other characteristics differentiating an existent from the other things sharing its CCD. Aside from the fact that no CCD can exist on the basis a non-existent characteristic, a non-existent characteristic cannot be said to have any causal effect on any of the other characteristics, or anything at all for that matter.

3) Rand's Razor of Concepts. "Concepts are not to be multiplied beyond necessity..." (ITOE, 72) There is no necessity of forming a concept of an existent on the basis of a non-existent characteristic, since "absence" is a valid concept, from which we can abstract the absence of specific things, yielding concepts-of-absence that may be used to modify other concepts in propositions without the need of forming new, invalid concepts.

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If the definition of a concept does not allow one to determine if a certain existent (or concept) is subsumed by the concept in question, the definition is poor. End of story.

My use of the word "poor" was not the best, now that I look back on it. I think incomplete would be much more accurate.

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I'm not sure if this question belongs here. it seems so close that I'm not sure if it is actually being answered and i'm just too dense to see it. In any case i'll put it in my own words and see what i get.

What is the basis of the belief that reason and empericism reflect reality? Can reason be used to prove the validity of reason? Is the objectivist position that reason is self referent, it is its own standard? How is this different from faith being its own standard, the bible is based on god which is based on the bible, etc.? Do objectivists have "faith" in reason?

Now, as I try to explain it to others (probably incorrectly so you should have an incentive to correct me least i lead people astray) the objectivist position is that we know reason reflects reality because it works or seems to work. Our perception of reason and empericism "working" however, relies on our senses (emperical evidence) and reason. Christianity= bible --> god--> bible; objectivism= reason + empericism --> a perception of reality based on reason and empericism --> reason and empericism. I don't see the difference??? I can see how it might be easy to refute a nihilist who rejects reason and his senses altogether (if it came down to it you could just keep slapping him until he acknowledged that this, at least, was real) but what of those who mix and match with faith and reason? are they not happy healthy and productive members of society? is not the emperical evidence of "it works" a result of their system just as it is of the objectivist? What is the basis of the claim that men must live by reason alone if they, in fact, can live just as well with a blending?

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