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Russell's Paradox

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Kyle

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This was not intended to be a "hijack" or diversion from the original topic, merely a sidenote as I originally mentioned. With that in mind I'll end my part of this segue by reiterating, non-alcoholic beer is contains alcohol, therefore it is not non-alcoholic. It would just as easily and more accurately be described as reduced-alcohol beer, which would be a valid description.
Fair enough. Though, I think that, outside the domain of the scientific laboratory, something does not have to be pure of a substance, down to the very last molecule, to be called free of that substance as it can be understood that 'free' stands for 'virtually free'. And even 'virtually free of' involves negation. It involves saying what a thing lacks within some margin of error.

Anyway, negative definitions abound aside from this point. From strapless bras to invertebrates. Invertebrate. I wonder what negation-free definition one would offer? How would one argue that the essential property of an invertebrate is not that of being without a spinal column? What reasonable definition would one give that does not mention that feature that an invertebrate lacks?

Edited by LauricAcid
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Some of them also refer to concepts. It makes perfect sense to talk about kinds of concepts. Is something a philosophical concept or is it a concept of a particular science? Is something a concept of method or is it not a concept of method? Is something a concept found prevalent among scholars or is it a concept also found prevalent among non-scholars (by the way, 'non-scholar' another negative)? Is it a concept that is talked about a lot or is it a concept that people don't talk about so much these days? Those are all questions as to attributes of concepts themselves. Per Objectivism, concepts are mental entities. Concepts themselves have attributes. One attribute is that of self-inclusiveness. Another attribute is that of not being self-inclusive. Nothing anyone has posted refutes that.

Concepts do have attributes, and they are existents, but concepts are not the ultimate referents of any concept save one. In all other cases, they are ultimate reducible to concretes. The difference between the concept of "concept" and the others is that it is an integration of concepts qua concretes, rather than concepts qua integrations of other concretes.

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(1) You contradict yourself since you defined it in terms of its facility not its "cause". (2) It's still a negative definition. (3) It's an unweidly definition that goes past the essential characteristic to some other characteristic. A mathematician doesn't have to ask, "Hmm, is or is this thing something that allows calculations that a rational number does not?" No, a mathematician wants to get right to the heart of it, "Is this thing a ratio of two whole numbers or not?" Use in calculations is another, separate question, that the engineer or accountant will consider.
In the case of methods, facility is the cause--it is the reason we create methods in the first place. The characteristic is only non-essential when you reject the idea of irrational number as a method rather than a number.

In any event, it's not really fruitful to quibble over the formation and definition of individual concepts--at least it's not something I'm particularly interested in doing.

I grant that a notion being far-flung does not in itself refute the notion. But in the case of irrational numbers, the mathematics works quite splendidly without the far-flung notion that irrational numbers aren't numbers, and that is WHY the notion is far-flung and that is WHY the far-flung notion needs special attention as to its justification.

Well, I told you where you could find such justification. In case you missed it, here's a link.

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Concepts do have attributes, and they are existents, but concepts are not the ultimate referents of any concept save one. In all other cases, they are ultimate reducible to concretes. The difference between the concept of "concept" and the others is that it is an integration of concepts qua concretes, rather than concepts qua integrations of other concretes.
Okay. But it doesn't refute that the concept of non-self including concepts is perfectly fine.
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The two positive characteristics you list aren't anything different from "fully listable."

The big deal with the characteristic of "fully listable" is that it has nothing to do with the concepts themselves. It is a characteristic of sets you have constructed from the concepts. Since the concepts are more fundamental than the sets you constructed from them, characteristics of the sets cannot be fundamental, distinguishing characteristics which form the basis for forming the derivative concepts of NSRC vs. SRC.

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Well, I told you where you could find such justification. In case you missed it, here's a link.
Thank you for that link, but it only offers a way to purchase the justification you claim. I wasn't claiming that he doesn't give his reasons. But if you or someone else understands the argument, perhaps you can convey at least the gist of it. But I understand that posting should not be an obligation, so, of course, only at your convenience.
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I would honestly love to be able to simplify it in a manner that's conducive to a message board, but I'm afraid I just wouldn't even know where to begin. He spends about an hour on the justification in the lecture, so I don't know that I could honestly and convincingly present the whole thing in a few paragraphs. He doesn't spend that long on irrational numbers specifically, but the justification, which invalidates a number of mathematical concepts as they are traditionally defined. Others that he discusses are negative numbers and fractions, as well as geometric concepts such as line, point, and plane, especially line.

Because of the fervor you've shown for mathematics in the past, I would really recommend it to you. Even on the points where I disagree with him (and there are a couple in the section on Physics), his analysis is really very enjoyable.

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The big deal with the characteristic of "fully listable" is that it has nothing to do with the concepts themselves. It is a characteristic of sets you have constructed from the concepts. Since the concepts are more fundamental than the sets you constructed from them, characteristics of the sets cannot be fundamental, distinguishing characteristics which form the basis for forming the derivative concepts of NSRC vs. SRC.

Being fully listable is still a property of the concept because it tells me what kind of set I can build from the concept. Yes, the sets also have properties, but that doesn't preclude the concepts from having properties as well. In fact, the sets couldn't have the properties they have unless they concepts had their properties, so there's obviously a fundamental distinction in the concepts as well.

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Kyle:

The root of the problem seems to be taking a concept to be the same as its extension, and this is a problem because concepts are intensional. A concept is a rule of identification and categorization, i.e. its definition. The rule-nature of concepts is most obvious with many mathematical concepts where the concretes subsumed by the concept have to be generated by a method, but it's actually quite general because concepts are open-ended. If we take a concept like "table", the concretes that the concept subsumes are all of the physical tables existing now or in the past, any created in the future, as well as any mental images or paintings of tables.

Dave Z's point in #52, #80 is important, that concepts aren't sets, and that defining characteristics are not the same as "all characteristics". The equivalent of a Russell-problem for concepts would be an ill-defined concept (one which includes an undefined characteristic or one that includes itself in its definition), and such concepts are invalid. The concept "concept" is not circularly defined, it is a "mental integration of two or more units which are isolated according to a specific characteristics() and united by a specific definition". There may be other thing that you can say about the existents subsumed by a concept, but those things are independent of the concept. A concept will imply, but not include, the characteristics of the concept's referents.

You suggest in #53 that a "listing" can be constructed from the concepts, but I'm not sure that this can be done, since I don't understand the ontology of a listing. The listing at least as you graphically present it would be infinite, so the listing is not an existent. If you consider "listing" to be some kind of method (i.e. the procedure "consider an existent; if it satisfies the rule C1 mark it 1, otherwise mark it 0"), then you would have a concept of "listing" that can exist -- the "listing" is the method, and not the output of the method.

At the risk of belaboring the unit-economy and psychological-prerequisite points, even though you can describe a selection procedure for "self-referring concept", it isn't one (it's a phrase). If for the sake of argument we decide to invent a word "Bnik" to deal with certain things that some philosophers like, then what is the definition of "Bnik"? Is it a well-formed definition? If we had that much, it might help. It seems to me that your NSRC is simply "concept", and it's only the presumption that we have to create a narrower concept than simply "concept" that appears to cause a problem.

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You suggest in #53 that a "listing" can be constructed from the concepts, but I'm not sure that this can be done, since I don't understand the ontology of a listing. The listing at least as you graphically present it would be infinite, so the listing is not an existent. If you consider "listing" to be some kind of method (i.e. the procedure "consider an existent; if it satisfies the rule C1 mark it 1, otherwise mark it 0"), then you would have a concept of "listing" that can exist -- the "listing" is the method, and not the output of the method.

The listing will only be infinite if you have an infinite number of referents in your concepts. Otherwise it will be very large but finite. And as long as it’s finite I can treat it as an output of a method and there should be no problem.

I’ll respond to the rest of your post after I have some breakfast, but I’d like to see your response to this first (if possible) because I think the paragraph I quote underlies the rest of your post.

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The listing will only be infinite if you have an infinite number of referents in your concepts. Otherwise it will be very large but finite. And as long as it's finite I can treat it as an output of a method and there should be no problem.
You're adding "referent" so we have to be careful about what that means. I have not thought about this before, actually, but I think that the (set of) referents of any concept is unbounded. That's certainly true of thinks like table, car, person since the concept refers not just to the actual tables of today, but all past and future tables including representations of table (such as sculptures, drawings, mental images). Let's try the strong form of the claim: the set of referents of any concept is unbounded.
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I address the point you bring up in my first point on full listing - you're right that the concept of tables is unbounded the referents of that concept right now will be fixed. So, instead of a list of all the referents ever, you can construct a list of the current referents. As long as you stick to either the past or the present the referents will be set and you can give a listing.

Edited by Kyle
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He doesn't spend that long on irrational numbers specifically, but the justification, which invalidates a number of mathematical concepts as they are traditionally defined. Others that he discusses are negative numbers and fractions, as well as geometric concepts such as line, point, and plane, especially line.
Thanks, dondigitalia. I've put it on my list to eventually get hold of. Ironically, as far as I know, mathematics doesn't even have a definition of 'number'. As far as I know, the concept of number is only an informal one (and used frequently, such as in the sense of an irrational number being a real number and participating in the real number system) and also in the philosophy of mathematics, but there's not formal definition of 'is a number'.
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I address the point you bring up in my first point on full listing - you're right that the concept of tables is unbounded the referents of that concept right now will be fixed. So, instead of a list of all the referents ever, you can construct a list of the current referents. As long as you stick to either the past or the present the referents will be set and you can give a listing.
Concepts arent fully listable because their extension isnt fixed at any particular point in time in the idealised (mathematical) sense you require; concepts are open ended and can have fuzzy boundaries. There are many objects which the average English speaker would simply be unsure whether to classify as 'chairs' or 'table'. Go out and ask 10 people whether a beanbag is a chair, and youll probably get several 'yes' answers, several 'nos', and several "I dont know, I never thought about that before"s. The same thing applies to tables; if I have a circular piece of wood with no legs that sits on the floor, and I eat off it by kneeling crosslegged in front of it, is this a table? Again, different people will answer in different ways. And these are just basic concepts; when you move into more complex concepts, it gets worse.

In order to form and use the concept of 'table' or 'chair', I dont need to decide in advance whether every single object in the world is or isnt a table or chair; I'm perfectly free to leave the boundaries open and decide things on a case-by-case basis (or even leave them undecided). All I need is a rough knowledge of the essentials of the concept ("tables are for eating off, chairs are for sitting in"), not an absolute (mathematical) decision procedure which can determine through some application of a formal rule whether or not entity X is a table. Hence talking about concepts being 'fully listable' is misleading; theres no absolute fact of the matter whether a listing of the concept 'chair' would include beanbags or toilets. If you want to equate concepts and sets, youre going to need fuzzy set theory.

Edited by Hal
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The equivalent of a Russell-problem for concepts would be an ill-defined concept (one which includes an undefined characteristic or one that includes itself in its definition), and such concepts are invalid. The concept "concept" is not circularly defined, it is a "mental integration of two or more units which are isolated according to a specific characteristics() and united by a specific definition".
But you just assert that self-inclusive concepts are improper; you've not shown that the Objectivist axioms imply that assertion. And the concept "concept" is self-inclusive. Moreover, it has not been shown that the Objecitivst axioms make the concepts of "self-inclusive concept" and "non-self inclusive concept" improper (as I defined them in post 28, though, there I used 'referring' instead of 'inclusive'). Edited by LauricAcid
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Concepts arent fully listable because their extension isnt fixed at any particular point in time in the idealised (mathematical) sense you require; concepts are open ended and can have fuzzy boundaries. There are many objects which the average speaker English would simply be unsure whether to classify as 'chairs' or 'table'. Go out and ask 10 people whether a beanbag is a chair, and youll probably get several 'yes' answers, several 'nos', and several "I dont know, I never thought about that before"s. The same thing applies to tables; if I have a table with no legs that just sits on the floor, and I eat off it by kneeling crosslegged in front of it, is this a table? Again, different people will answer in different ways. And these are just basic concepts; when you move into more complex concepts, it gets worse.

In order to form and use the concept of 'table' or 'chair', I dont need to decide in advance whether every single object in the world is or isnt a table or chair; I'm perfectly free to leave the boundaries open and decide things on a case-by-case basis (or even leave them undecided). All I need is a rough knowledge of the essentials of the concept ("tables are for eating off, chairs are for sitting in"), not an absolute (mathematical) decision procedure which can determine through some application of a formal rule whether or not entity X is a table. Hence talking about concepts being 'fully listable' is misleading; theres no absolute fact of the matter whether a listing of the concept 'chair' would include beanbags or toilets.

Is the position that the concept is actually in a vauge state permanently? Or just that I don't know all of the boundaries at any given time? I had gotten the impression from Rand and from Piekoff that it was the latter.

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Is the position that the concept is actually in a vauge state permanently? Or just that I don't know all of the boundaries at any given time? I had gotten the impression from Rand and from Piekoff that it was the latter.

Well its my position anyway; I'm not entirely sure what Rand would have said and I could be misinterpreting what she meant by 'open-ended'; I dont think she discussed this question explicitly. However, if you dont know the boundaries at any given time, then who does? The writers of the Oxford English dictionary? God?

Edited by Hal
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The traditional view is that you set some criterion - like "four legs, flat top" - and everthing with those properties fits in the extension. According to the traditional view that's just all there is to the word. Rand however, wants the word to extend beyond that. I think this is where Rand and the est of philosophy disagree about the analytic/synthetic distinction. When you think the word's meaning consits entirely in what definition you give it, the concept of analytic truths makes sense. When you don't think that it doesn't.

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Is the position that the concept is actually in a vauge state permanently? Or just that I don't know all of the boundaries at any given time? I had gotten the impression from Rand and from Piekoff that it was the latter.
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.

The traditional view is that you set some criterion - like "four legs, flat top" - and everthing with those properties fits in the extension. According to the traditional view that's just all there is to the word.
What traditional view is that? Aside from extenstion is intension. It is not the common view that words do not have intensions. Edited by LauricAcid
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I address the point you bring up in my first point on full listing - you're right that the concept of tables is unbounded the referents of that concept right now will be fixed. So, instead of a list of all the referents ever, you can construct a list of the current referents. As long as you stick to either the past or the present the referents will be set and you can give a listing.

The current referents of the concept are those of the past and the future. This is a crucial point in Objectivist epistemology. Concepts don't (at present) integrate that which exists right now, and then a year from now, integrate the things which exist then--they are atemporal. The measurement that the specific referents have to exist at some time is retained in the concept, but the specific time is completely omitted. I know of no concept which is an exception to this rule. Once you start talking in terms of the referents which exist right now, instead of all the referent of any era, you are no longer using a concept, but a frozen abstraction.

You might be able to make two categories of concepts: Concepts which, when listed in the form of a set, are fully-listable, and others which are not, but that doesn't mean you have grounds to form a concept. Here is where your nominalism comes into play. You are taking just any old differentiation and trying to make a concept out of it--which is adamantly not the way Objectivism approches concepts.

Ayn Rand put her own spin on Occam's Razor. Rand's Razor is: "concepts are not to be multiplied beyond necessity--the corrollary of which is: nor are they to be integrated in disregard of necessity." (ITOE, 72). You are guilty of the first. There is absolutely no significant cognitive or metaphysical reason to form the concept of "fully-listable concept." Every significant difference you have identified belongs to the sets themselves, so the difference is less fundamental than the concepts themselves. (And they are epistemological differences--there is absolutely no metaphysical difference between sets and concepts, since sets are a particular kind of concept.)

Thanks, dondigitalia. I've put it on my list to eventually get hold of. Ironically, as far as I know, mathematics doesn't even have a definition of 'number'.

That's where he starts. Binswanger talks about that, forms the concept of number, and the rest goes from there.

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.

It's more than just unfamiliar to Objectivists; in the way it's being done here, it's completely rejected by Objectivists. It's an attempt to deduce the properties of concretes from the abstractions, which is the opposite of the Objectivist theory of concepts. In Objectivism, we observe the properties of concretes, and abstract generalizations from them. (Not to say deduction is invalid--it certainly isn't--but it isn't a means of concept-formation.)

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Ayn Rand put her own spin on Occam's Razor. Rand's Razor is: "concepts are not to be multiplied beyond necessity--the corrollary of which is: nor are they to be integrated in disregard of necessity." (ITOE, 72)
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?

There is absolutely no significant cognitive or metaphysical reason to form the concept of "fully-listable concept."
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. Edited by LauricAcid
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What makes a concept necessary?

That depends on the context--what the units of the concept are, their place in the conceptual hierarchy, all sorts of thing. In the context of the particular concept(s) being discussed here, since there is a valid categorization being drawn, in order to validate the concepts, it needs to be shown that the differentiation leads to real consquences in the concepts themselves. So far, all that has been shown is a difference between sets which have been constructed from the concepts.

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?
Yes, one does have to show that they ARE necessary, when called to task to do so. That is the principle of the onus of proof. Broadly, that means showing cognitive significance--that's too broad for you, though. If you're looking for something more concrete, it varies from concept to concept, and it is up to the person claiming cognitive significance to identify the concretes involved. Ayn Rand gives some specific examples in ITOE starting on page 72.

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?

Not necessarily, it depends on how that aligns with our own knowledge of the particular units involved.

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?
Objectivism says a great deal on concepts besides just how they are formed--a great deal. You can't say, prove it from the theory up to this point, but don't bring in anything else from that theory. This discussion is about more than just concept-formation, but the entire Objectivist approach to epistemology, which involves the entire theory of concepts presented in ITOE (aside from just the material on formation), in addition to a number of other articles scattered throughout the Objectivist literature. Objectivist epistemology does not end at concept-formation, nor does it even end at ITOE.

Moreover, it seems like your asking for a deduction from the axioms, which is (as many, many Objectivist intellectuals, including Ayn Rand, have pointed out) a method that is completely incompatible with Rand's theory. It is rationalism.

As to "self-inclusive concept" and "non-self-inclusive concept", there is cognitive reason for them.

What is the reason? What does forming the new concepts offer to cognition that the a concept of "concept" and two other concepts of "self-inclusive" and "non-self-inclusive" don't?

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As long as you stick to either the past or the present the referents will be set and you can give a listing.
So what you have is a method for generating various finite sets (the listings) from a given concept, and then you note that given your algorithm, an SRC cannot be fully listed because an SRC is recursively defined. I've noted that that's invalid, and Dave Z. noted that concepts mean existents and not concepts (again, no recursion). Your approach in #53 seems to be to say that even though it's not necessary to have concepts mean other concepts, it's possible to generate recursive lists that may be mapped to actual concepts. I fail to see how the possibility of defining lists this way has relevance to the validity of concepts.

I question the claim that being fully listable is a property of a concept, in that it seems to depend on a very unconstrained theory of "property". Next week, some guy might have a quarter that he drops, and I might find it walking down the street, which I could then add to 3 other quarters and buy a coke from the 3rd floor vending machine which will turn out, tragically, to be warm. Have I just described a property of the quarter (or the guy)? If so, then don't see the empirical content to the notion of "property".

One fact about the characteristics (properties) that define a concept is that they are inherited by the existents which they subsume -- so if we take "living meat-bag" to be the definition of "animal", then every instance of animal must be a living meat-bag. I haven't seen the definition of "fully listable" that has this property. Not that I think that this full-listing business is productive, but given that concepts are not lists and concepts don't mean concepts (and that concepts are open-ended identifications), I'd like to see your (careful) definition of "fully listable" and how the full-listing of a concept somehow affects the existents covered by the listing (in creating a new property of the existent).

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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?"

Not necessarily, it depends on how that aligns with our own knowledge of the particular units involved.
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.

Objectivism says a great deal on concepts besides just how they are formed--a great deal. You can't say, prove it from the theory up to this point, but don't bring in anything else from that theory.
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.)

The theory proceeds from axioms This discussion is about more than just concept-formation, but the entire Objectivist approach to epistemology, which involves the entire theory of concepts presented in ITOE (aside from just the material on formation), in addition to a number of other articles scattered throughout the Objectivist literature. Objectivist epistemology does not end at concept-formation, nor does it even end at ITOE.
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.

Moreover, it seems like your asking for a deduction from the axioms, which is (as many, many Objectivist intellectuals, including Ayn Rand, have pointed out) a method that is completely incompatible with Rand's theory. It is rationalism.
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."

What is the reason? What does forming the new concepts offer to cognition that the a concept of "concept" and two other concepts of "self-inclusive" and "non-self-inclusive" don't?
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. Edited by LauricAcid
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Next week, some guy might have a quarter that he drops, and I might find it walking down the street, which I could then add to 3 other quarters and buy a coke from the 3rd floor vending machine which will turn out, tragically, to be warm. Have I just described a property of the quarter (or the guy)?
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.
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