SpookyKitty

In the first part you are saying that we can have a concept of aboveness even if no things in reality satisfy that relation. And in the second part you are saying just the opposite. Or at least, that's how it appears. How is it possible that the "meaning" of the concept of aboveness is its referents, when, at the same time, you maintain that I'm wrong in thinking that therefore the concept of aboveness is dependent on what actually is or isn't above whatever else? As for the second part, just because everything happens to lie in a 2d plane, does not mean that space is not 3-dimensional, just that everything happens to lie in some 2d plane of a 3d space. Note also, that we have concepts of hyperspace even though no one has ever seen such a thing.

How is this an equivocation on my part? You are the one who is claiming that the concept of "aboveness" is dependent on what things in reality satisfy the relation of "aboveness". A point P does not lie in the given plane if for every point B in that plane, there exists a line PB distinct from every line in the given plane. For such a point, if I have to look up to see it, then it is "above" the plane.

I suppose you mean the claim that a concept can have different sets of referents depending on what is actually the case? If so, consider the concept of "aboveness". Imagine that a book is on a table. Suppose that someone moves the book so that it is under the table? Does your concept of "aboveness" thereby change? Imagine that the world was such that everything lay in the same plane. Nothing would be above anything else, but that does not mean that the concept of "aboveness" would be meaningless.

Yes, I agree.

@New Buddha, Putting a ", period" at the end of something doesn't somehow magically obviate the need for an argument. You have merely restated some of Rand's claims without addressing any of my arguments (or really, any arguments at all). Your mistrust and lack of understanding of logic is your own. That an argument is formalized is not a point against it. Do you seriously doubt mathematics, or something? @Plasmatic, I have no idea what you're even saying in that first big paragrpah of yours. If you or someone else can explain what is being said there, I'll respond. I agree with some of the points you've made about definitions and concepts, but let me address an erroneous claim made by both you and New Buddha (and possibly Eiuol). That is, the claim that the "meaning" of a concept is its referents and also the claim that concepts constitute knowledge. The problem with the meaning of a concept being its referents is that the same concept can have different referents depending on what is actually the case. Take the concept of prime number. We say that x is a prime number if and only if it is greater than 1 and every divisor of x is either x or 1. We say that x divides y if and only if there exists a z such that xz=y. Now, if the rules of multiplication were different, say we had the following alternative rules 1) for all x, x * 0 = x 2) for all x,y, x(y+1) = xy + x. Here's a multiplication table: ----| 0 1 2 3 4 5 6 7 8 9 0 0 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 10 2 2 3 4 5 6 7 8 9 10 11 3 3 4 5 6 7 9 10 11 12 .... It's clear from this table that every natural number divides every number greater than or equal to itself. And that there are no prime numbers. I will now address the claim that concepts constitute knowledge. The reason that they don't is that understanding a statement is not the same thing as knowing it. Concepts only provide understanding, not knowledge. When you have the concept of prime number, you understand the statement "123231314898117 is prime", but you do not know whether or not 123231314898117 is prime.

Hmm... yeah, that should be fixed. Subjects only represent concepts when the subject is a concept. For example, in "Man is a rational animal" can be parsed as "the concept referred to as 'Man' is identical to the concept represented by the predicate 'a thing which is a rational animal'". The reason is that subjects themselves are not necessarily concepts. For example "Jones is a man" is not talking about the concept of "Jones" (assuming such a concept exists), it is about Jones himself. They can. I'm not sure what you mean when you refer to concepts which are true. What's an 'invalid concept', really? I don't think you can simply say that an 'invalid concept' is whatever produces a false statement about some subject, since that's true of virtually every concept. I think it's more helpful to think of concepts as the mechanism of representation and not as the representation itself.

Knowledge only consists of true statements (although more qualifiers might be needed, but at minimum a statement which is known must be true). True statements can be made about unreal things, and false statements can be made about real things.

Sorry to keep doing this to you @Eiuol, but here's a new updated version. I fixed some spelling errors, made a slight modification to definition 6 and axiom 20. Also I added a consistency proof for my axioms as well as an independence proof for them. Huge leaps forward. I really hope I have not misnumbered any sections. objCrit4.pdf

Well that's the first smart question you've asked in a while. No, concepts themselves are not knowledge and they cannot be considered knowledge, period. By themselves, all they do is generate statements about things. They don't decide whether those statements are true or false. That's the million dollar question.

Concepts create knowledge when you combine them with reason and evidence, and obey the laws of logic.

Sure, in the same sense that man 'creates' real things. EDIT: Boom! Pre-emptive strike! I'm ten steps ahead of you in every direction.

If you have nothing intelligent to say, there is no need to pollute the thread with your inane comments.

Make sure you read the second one. It's an updated version.

But I do connect my ideas to "actual" reality. If you actually read the paper you will notice that I am constantly giving concrete examples at almost every step. The error you speak of was certainly not critical. It was trivial. If it was critical I'd have had do to discard the whole argument. My idea is clearly understood by at least me, and the argument as a whole, in my opinion, is actually extremely simple and focused. Your inability or refusal to understand it proves nothing. If there are some parts that aren't clear to you, I'd be happy to explain them. You at least have the opportunity to ask me questions on here. It is already perfectly clear what I mean by 'concept'. The only thing not clear is why you continually make trivial objections such as the meaning of the word 'statement' (in fact, I give a definition of the word 'statement' in the paper itself) and 'phenomenon'. Nothing about that strikes me as wrong at all. The idea that concepts, which are somehow created, cannot also create other things is just silly. Concepts, most critically, are used in the creation of knowledge! Obviously. Why would I give a theory of concept-formation when it is theories of concept formation that my theorizing is supposed to evaluate? --------------------------------------------------------------------------------------------------------------------------------------------------------- How about this, before continuing in your quixotic quest to misunderstand the obvious, why don't you show me that you actually read and understand what I wrote and can follow the argument?

As someone who is objectivish (by which I mean that I, at the very least, take Objectivism seriously enough to consider things from an Objectivist perspective) if not an Objectivist(TM), I certainly would take issue with someone arguing against Rand's theory of concept based on a definition of concept which contradicts Rand's definition. I would be perfectly justified in doing so, because then their argument is circular. Neutrality between me and Rand is not enough. This is not like a legal dispute where a third party can come in to arbitrate. There is no third party. Neutrality is needed to avoid circular reasoning, its not there out of some sense of "fairness". It's a very important and strict epistemological requirement. "Phenomenon" is just "a thing that happens or occurs". A concept, as a mental phenomenon, then, is a thing that happens or occurs in the mind. By "output" I mean that the concept outputs things in the same sense that your computer "outputs" text to the screen. That is, by acting upon some part of the mind. I don't think I should really have to define "statement". Can you not tell that "Mars is red" is a statement? The reason you wouldn't start with a definition like the kind Merriam Webster provides is the same reason that you would never use such a definition in a mathematical, scientific, or serious philosophical work. Dictionaries define words based on a history of usage in an extremely wide variety of contexts. Technical definitions are needed in order to ensure that you use the same meaning of a term consistently in every argument so as to avoid equivocation. You're right that it's really not that difficult to use an opponent's definiton without conceding the validity of it, but in those cases, it is often far too easy to commit the opposite sin and simply assume (often without even knowing it) the negation of your opponent's definition. Then the whole debate devolves into splitting hairs about semantics. What exactly do you mean by 'rationalism'? As I understand it, rationalism is a theory of knowledge that states that all knowledge is ultimately justified by self-evident truths. Where exactly do I argue or even imply such a thing? It seems to me that by 'rationalism' you mean any use of deductive logic at all. Your own example illustrates exactly why you have to carefully define what you're talking about if you are going to seriously talk about it. You have confused the question of the existence of hokobots with the question of what hokobots are. It's the difference between the question "Do eight-legged fish that captain cruise boats to the planet Neptune exist?" and "If hokobots are eight-legged fish that captain cruise boats to the planet Neptune, then are six-legged fish that captain cruise boats to the planet Neptune hokobots or not?" There is no way to answer the second question by examining its "correspondence to reality". As far as I can tell, there is no "internal illogic" in Rand's definition of concepts because, in her theory, a concept is just what the process of concept formation produces, and nothing more. But just because there is no internal illogic doesn't mean your idea can't be wrong. It's the same if I claim that my "car" factory produces cars because that's what a car factory does, and all the while, I'm actually making lamps. Again, that's not rationalism. If you think that it is easy to come up with a definition that meets those two criteria, then I would claim that you don't understand the critera. By 'capture' I mean 'fully and absolutely capture' so that 1) a definitive answer can be given one way or the other whether this or that thing is or isn't a concept and so that there are no obvious counter-examples and 2) ensure that all related ideas (in our case, 'predicate', 'representation', etc.) relate to each other in the appropriate ways. While it may even be true that any dictionary definitions are logically independent of the Objectivist definition, it is not true that logical independence can be proven. The standard of requiring proof of independence is on a whole 'nother level, and absolutely necessary if you want to provide any sort of definitive argument.

I fixed some errors per the above posts. Added another axiom which I figured out I had just assumed without stating. Also finished the independence proof. objCrit2.pdf

@MisterSwig To expand on why I don't care about dictionary definitions: 1. If I had used a dictionary definition, people would inevitably complain that I didn't use Rand's definition. 2. If used Rand's definition, I'm conceding the argument right from the get-go and there's no point in discussing anything at all. 3. Dictionary definitions cannot possibly meet the standard of definition required to unbiasedly evaluate Objectivism. It is essential that the definition of 'concept' 1) capture what people ordinarily mean by 'concept' just like the axioms of arithmetic capture what people ordinarily mean by 'natural number' (even though those axioms are highly technical) 2) be precise enough that a proof of logical independence from the claims of Objectivism could be given.

What part of this is rationalism?

Yes, x is allowed to be a thought in your mind. I'm glad we could reach a point of agreement. Dictionary definitions aren't good enough.

The theorem is supposed be wrong. I don't seriously believe that there is a thing which exists but doesn't exist. It's a reductio. Since the theorem is absurd, it must be that either Claim 20, 21, 22, or axoim 19 is false.

I don't even remember that.

Meh. You can't get anywhere if you first define every word in the dictionary. I think a bright ninth-grader would be able to read the whole paper just fine. Only an idiot would spend a whole six pages trying to be as fair to Rand's theory as possible to then just turn around and misrepresent it, and I am no idiot. If there is a substantial misrepresentation, I'll retract what I said. I spent only the last page discussing Objectivism simply because I wanted to show people what I already had before continuing on for another 20 or so pages. It would be kind of stupid to spend hours and hours of my life to writing a giant technical paper only for the whole thing to collapse due to a simple error I hadn't noticed on page 3. But most importantly, I definitely do not intend to misrepresent Rand's view of concepts. You say: I did not include textual references because I thought my audience would be informed enough about Objectivism to know whether Claim 20 accurately represents Objectivism. I will definitely include textual references in the future. You have a point. I did make a mistake here. But if we drop the qualifier (non-mental), does claim 20 then accurately represent Objectivism? Would you then accept the argument, as in: No, first I establish that the concept "a thing which doesn't exist" exists. Not that there exists a thing which doesn't exist. The distinction is important. The proof still works even if you drop the qualifier 'non-mental'.

You know it would be a lot more helpful and persuasive to point at least one thing that you think is a misunderstanding or an arbitrary assertion. At least then we could have a meaningful discussion about it.

What does that mean, in your own words? I am not critiquing Objectivism via any form of Verificationism. So Objectivism has no epistemology onto itself, but is just a collection of rejections?

"Existence exists" is a statement which refers to the totality of things which exist, yes. Within the statement "Existence" is a subject which does not refer to the concept of existence. But when I say that the concept of "existence" exists, what I'm saying is that Rand's theory of concept claims that such a concept exists. That's an epistemological claim. Since existence is a concept in Rand's theory, then it is definitely something which can be said of other things. As in "This tree exists". That is synonymous with "This tree has existence". I only use the phrasing "has existence" to avoid confusion with the logical modality of "exists". Same thing. "A thing has identity" is synonymous with "a thing is itself". Nowhere do I claim that existence (in any sense) does or does not "have" identity. Indeed I am. If the concepts of existence and identity had no predicates, then they could not form the basis of any knowledge whatsoever. If you maintain that "things that exist but have no identity" is an invalid concept, then you are denying my axiom 19. In that case, you must explain how logic is possible when you can have the concepts A and B but not the concept "A and not B".