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  1. 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.
  2. 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. 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."
  3. 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. 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.
  4. I refreshed my memory by reading several synopses and articles about the film. So I grant that Teddy was a particularly scummy murderer. But I don't see how an Objecivist could find virtue in Leonard's decision to deceive himself that Teddy is John G. What Leonard did was to choose, with full, and even spoken aloud, moral comittment to what he knows to be a grave falsehood. And his purpose in doing that was not to right any wrongs but rather to leave himself a clearer field in which to continue his ritual of remembering, searching, and killing, as this ritual is what gives his life meaning, even as he himself calls it the "structure" of his life. Now that Teddy is gone, ANYONE can become Leonard's next John G. Whenever Leonard likes, all he has to do is jot some falsely implicatory note and then have it tatooed on himself so that he can repeat the ritual of "remembering", finding, and killing. And it seems to me that the auteur of the film is clear to draw Leonard as a very sick menace. At the end of the film, Leonard, in order to "test" the reality of the external world, closes his eyes for several seconds while he is driving. By so doing he puts his prerogative to be impetuous with life and death above the safety of anyone else, not to mention his own safety, and while pumping himself up about this "structure" for his life, which is the "structure" of being a self-decieving murderer. But most of all, at that once crucial moment with the license plate, he chooses to define his ethics, and it is the ethics of lying to oneself.
  5. 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.
  6. (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. 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.) 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). 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. 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. 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? 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. I too think that deduction is not the only source of knowledge (by the way, I'm using 'deduction' as it is generally used). 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'. (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. 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). Fine. but then see points (1) through (3) in my previous paragraph.
  7. 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. 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. 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.
  8. 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.)
  9. 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.
  10. 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?
  11. 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.
  12. Sure you have. It's one of the properties extremely far from the essential property. But it's still one of the properties of the quarter that it was dropped by that guy and used by you to buy a warm cola from the 3rd floor vending machine; and it is a property of the guy that he dropped the quarter that etc. Just because they are properties far down the scale from essential doesn't make them not properties.
  13. I asked, "Every time you or Rand or anyone else forms a concept, should the rest of us not recoginize that your concept is proper until you've shown its necessity?" I don't know what you mean by the alignment of knowledge with particular units (I guess you mean that knowledge must ultimately reduce to knowing concrete facts). But I sense that your answer is that, depending on that factor, one can grant the correctness of a concept without having seen that it is necessary. But if you say that only concepts that are necessary are correct, then I just don't see how you can know that a concept is correct without knowing that it is necessary. 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.) 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. 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. Whatever you call it, if you don't call it 'deduction', then 'induction' or 'Objectivist logic' or whatever, I'm just asking how does the principle of necessity follow from the axioms with what's already been established from the axioms and even with whatever empirical facts you want to add. What is the reasoning? Just plain old reasoning or Objectivist reasoning or whatever. 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. 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. I wrote, "As to "self-inclusive concept" and "non-self-inclusive concept", there is cognitive reason for them." Probably quite like what concepts such as "stolen concept" and "floating abstraction" are meant to offer. They identify flaws in concept formation and in theory making. The concepts of "self-inclusive concept" and "non-self-inclusive concept" are intermediate concepts toward probing for a flaw in having a concept of concept. Now, you may respond that that only shows that those odd concepts only have an ad hoc purpose and thus don't have cognitive benefit ONTO THEMSELVES, thus are not correct concepts. But that requires showing that benefit onto itself, not just benefit as an intermediate step, is required for correct concept formation. What are the cognitive benefits ONTO THEMSELVES of distinguishing the metaphysically given from the man made? No doubt, the distinction is extremely useful since we can use it to see all kinds of important philosophical ramifications and even to guide us in our lives. But those are consequences of the distinction, not in the distinction itself. And, "non-self inclusive concepts" is a concept that also has philosphical ramifications, particularly as to the consistency of holding a concept of concepts. To reject that as having cognitive benefit, one must give some NON-ARBITRARY reason for doing so. Moreover, the cognitive benefits of concepts need not be limited to grave philosophical and important practical concerns. For that matter, what is an important practical concern? Practical for WHOM? If I'm studying mathematics as a hobby, for the enjoyment of finding out what other people have thought of and the enjoyment of working out abstract problems, then I may find the concept of "non-self including concept" to have great cognitive value as it provides comparisions with Russell's paradox and with all kinds of questions and matters of conversation in philosophy, mathematics, logic, AI, and computer science. Now, if SOMEONE ELSE finds no cognitive value in that, then so be it. But then there are lots of concpets that someone else has that are of no cognitive value to ME. To a stamp collector, there is cognitive value in having concepts about certain kinds of stamps. That's of no cognitive value to me. To a tanning booth proprietor there's cognitive value in distinguishing differnt tanning methods. That's of no cognitive value to me. Now, one could say, "Well, your concept of "non-self-including concept" may have value to you, but it doesn't to me, so I don't have to worry about the ramifications for the Objectivist concept "concept"." 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.
  14. What makes a concept necessary? What makes Rand's concepts necessary, or your concepts necessary? What do you mean by 'necessary' in this context? It has not been shown that the concepts "self-inclusive concept" and "non-self-inclusive concepts" are not necessary. Does one then have to show that they ARE necessary? What does showing that require? Every time you or Rand or anyone else forms a concept, should the rest of us not recoginize that your concept is proper until you've shown its necessity? Moreover, even after defining what it means to form concepts unnecessarily, if one is to ban unnecessary concept formation, then one needs to show how that ban follows from Objectivist axioms and the Objectivist statement of concept formation, up to definition by conceptual common-denominator (with the fundamental questions about that that I raised but are yet unanswered). Objectivism says how a proper concept is formed, through identification of attributes, differences, definition, et. al. Where is the derivation that then what can be done through this process must be done out of necessity? What constitutes a "significant reason"? What is a "metaphysical reason"? As to "self-inclusive concept" and "non-self-inclusive concept", there is cognitive reason for them.
  15. See, you're not distinguishing between the concept and its extension. To hone your arguments here you need to read ITOE and OPAR. Anyway, your 'listable' tack is distracting from your basic argument. It's bogging you down while it offers little attraction to Objectivists as it just adds a construction, not familiar to Objecitivist ways of looking at things. The self-inclusive/negation convolution is already suspicious to Objectivists. I don't think you'll gain acceptance for your argument by adding yet another odd seeming construction. What traditional view is that? Aside from extenstion is intension. It is not the common view that words do not have intensions.
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