Russell's Paradox

Metaphysics and Epistemology
21

What is an “anti-realist”?

A big simplification would be: You’re an anti-realist about X if you don’t think X is a part of reality. You’re a realist about X if you think it is.

When I say that I’m an anti-realist about reference it means that I don’t think words really “refer” to anything. That’s not to say that there’s no difference between appropriate and inappropriate uses of words – no one thinks that “hello” refers to anything but there are still inappropriate uses of it – but there’s no fact of the matter as to what “tree” refers to.

Note that I’ve just listed the cliff-notes version here. My full theory isn’t really open to what probably seem like easy replies. Also, note the anti-realism thesis and the Russell’s paradox are unrelated – attacking one isn’t the same as refuting the other.

What purpose are you pursuing by joining an Objectivist forum?

One of my professors (who happens to be an objectivist) used Rand’s theory of concepts in an argument against Scalia’s approach to constitutional law. I have an interest in drawing out a contradiction in Rand’s notion of concepts because I want to help Scalia – if her notion of concepts is internally inconsistent then it can’t be used as a foundation for arguments against Scalia. I brought my Russell argument here, then, A) to make sure that there wasn’t something I was missing and B ) to give people who like objectivism a chance to point out flaws in my argument.

Also, I have a passing interest in objectivism generally. You guys seem like reasonably intelligent people and I thought that this would make for an interesting conversation (which it has).

22

You don’t need to make sets part of your ontology to get a paradox – the paradox is a logical paradox, not a metaphysical one.

My knowledge of Russell is marginal at best, so I won’t discuss his paradox directly, but:

It is right here that an Objectivist would (or at least should) reject your argument. Logic is useful only as a means of gaining and validating knowledge, and knowledge is always knowleddge of reality. On what grounds do you separate logic from metaphysics in this way?

When I say that I’m an anti-realist about reference it means that I don’t think words really “refer” to anything. That’s not to say that there’s no difference between appropriate and inappropriate uses of words – no one thinks that “hello” refers to anything but there are still inappropriate uses of it – but there’s no fact of the matter as to what “tree” refers to.

lol, this is exactly the view I was going to attempt to unearth at the heart of your arguments, but it seems you’ve already done it for me. :thumbsup:

Are you aware of the grounds on which Objectivism rejects this view of concepts? Is there a reason you say anti-realism instead of nominalism?

23

My knowledge of Russell is marginal at best, so I won’t discuss his paradox directly, but:

It is right here that an Objectivist would (or at least should) reject your argument. Logic is useful only as a means of gaining and validating knowledge, and knowledge is always knowleddge of reality. On what grounds do you separate logic from metaphysics in this way?

I’m not necessarily seperating the two - I’m just pointing out that my argument doesn’t need any particular commitment to sets. Rand’s view is logically inconsistent - I think that has implications for metaphysics.

lol, this is exactly the view I was going to attempt to unearth at the heart of your arguments, but it seems you’ve already done it for me. :thumbsup:

Are you aware of the grounds on which Objectivism rejects this view of concepts? Is there a reason you say anti-realism instead of nominalism?

“Anti-realism” is the standard academic term. I don’t recall the reasons Rand gives for rejecting the view - I suppose I could look them up - but even if my view is false, Rand’s view won’t become consistent.

24

Okay let me see if I can figure this out…

In refercence to Kyle’s SRC:

His sentence is self-referring, indeed. It is an artifact of the sentence structure. The notion of a concept of “concept” is not. Try diagramming the sentences. Try to more clearly explain what a concept of a concept is and the paradox will be eliminated. Let me break down the sentence.

THE SUBJECT

By definition:

The concept “concept” = = concept

Just like:

The concept “paradox” = = paradox

ENTER THE PREDICATE

It follows then:

The concept “concept” is one self referring concept. = = Concept is one self-referring concept.

“Concept is one self-referring concept” is a meaningless sentence. Let’s try replacing concept with its definition:

A mental device that refers to a set or group of sets is one self referring concept.

A mental device that refers to a set or group of sets is one self-referring mental device that refers to a set or group of sets.

Take out self-referring:

A mental device that refers to a set or group of sets is a mental device that refers to a set or group of sets.

A is A. Who knew?

Where’s the (even indirect??) paradox?

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The concept “concept” = = concept

If ‘= =’ stands for ‘is equal to’, then the above is incorrect. There is no such thing as concept, just as there is no such thing as dog. There are dogs and there is the concept of dog, but there is no entity that is dog. There are concepts and there is the concept of concept, but there is no entity that is concept. So, in the sentence “The concept of concept equals concept”, the third use of the word ‘concept’ is meaningless.

26

Ayn Rand defines “concept” as follows:

“A concept is a mental integration of two or more units which are isolated according to a specific characteristic and united by a specific definition” - (Introduction to Objectivist Epistemology, p. 10)

She goes on to explain that the process of concept formation involves abstraction of certain attributes of the units being conceptualized. For example, when forming the concept “chair”, we mentally isolate the attributes of the units (different chairs), such as having a surface and a type of support. After isolating the essential attributes of chairs, we are able to integrate all such units into the concept “chair”.

Notice that a concept can be formed with two or more units. We can form a concept of chair based on perception of only a few units, without seeing the rest of the chairs in the universe. What the concept “chair” describes are the attributes essential to “chairness”, not the chairs themselves. We can later see an object that fits the definition of chair and identify it using our previously-formed concept “chair”, but this new chair was not necessary to form the concept “chair” in the first place.

Hence, the definition that concepts are “mental devices referring to sets” is misleading and is the root of Kyle’s error. We form concepts from two or more units. We form the concept “concept” (call this C) from two or more existing concepts (the units). Before we form, and during the process of forming C, C does yet not exist. Therefore, we cannot use C as one of the units to form C (an obvious absurdity). When forming C, we use existing concepts, say X, Y, and Z, as the units from which to abstract.

To summarize, the concept “concept” only refers to every existing concept in the way that the concept “chair” refers to every existing chair (a reference to shared attributes, not to the set of chairs as such). And just as the concept “chair” can be formed without reference to every chair in existence, the concept “concept” can be formed without reference to every concept in existence, and therefore without reference to itself. The phrase “self-referring concept” is meaningless under a proper understanding of the process of concept formation.

27

To summarize, the concept “concept” only refers to every existing concept in the way that the concept “chair” refers to every existing chair (a reference to shared attributes, not to the set of chairs as such). And just as the concept “chair” can be formed without reference to every chair in existence, the concept “concept” can be formed without reference to every concept in existence, and therefore without reference to itself. The phrase “self-referring concept” is meaningless under a proper understanding of the process of concept formation.

When a man first integrates the concept “chair” from two chairs he happens to observe the concept he has integrated still refers to every chair that exists, has existed, and will exist.

Lets say he has not observed a particular chair (for the record it is blue, slightly tacky, and exeptionally confortable). His concept of “chair” still refers to that unobserved chair.

So just because a man integrates the concept “concept” without personal reference to every concept in existence doesn’t mean that what he has integrated fails to refer to the concept “concept.”

I would also like to point out that it is extremely difficult to form any sort of florid prose when talking about self-reference :thumbsup:

Edit: I left an important bit of the concept “concept” concept concept concept sentance out, and have added it in so the sentance now makes sense…whether or not it rolls off of the tongue is a completely different issue.

28

Spano, accepting your explication of Objectivism and your terminology in this regard, whatever did or did not exist previously, by this time, the concept “concept” does exist as a mental entity, and is one of the entities that fits the definition of ‘concept’. So there is at least one concept that has the attribute of fitting the definition of the word used to define that concept. So those concepts that are isolated according to the attribute of fitting the definition of the word used to define those concepts are united by the definition of ‘self-referring concept’: An entity is a self-referring concept if and only if the entity is a concept and fits the definition of the word used to define that concept. And there are concepts that are not self-referring concepts. And ‘non-self-referring concept’ is defined: An entity is a non-self-referring concept if and only if the entity is a concept and is not a self-referring concept. So there is the concept “non-self-referring concept”. Now, either the concept “non-self-referring concept” is a self-referring concept or it is not a self-referring concept. If it is a self-referring concept, then, since it is the concept “non-self-referring concept”, it fits the definition of ‘non-self-referring concept’ so it is a non-self-referring concept, so it is not a self-referring-concept. If it is not a self-referring concept, then it fits the definition of ‘non-self-referring concept’, so, since it is the concept “non-self-referring concept”, it is a self-referring concept.

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Marnee:

THE SUBJECT

By definition:

The concept “concept” = = concept

Just like:

The concept “paradox” = = paradox

ENTER THE PREDICATE

It follows then:

The concept “concept” is one self referring concept. = = Concept is one self-referring concept.

“Concept is one self-referring concept” is a meaningless sentence.

You’re equivocating here with the word “concept” – when you use it the first time you’re using it as (something like a) proper name but when you use it the second time you use it as a natural kind term. For example:

The concept “concept” = = C

C is one self referring concept.

Note that this sentence does make sense, but it says the exact same thing as the sentence you claim is unintelligible. Notice that I can also do the same thing with the concept of paradoxes:

“Paradox is about paradoxes” as opposed to “the concept “paradox” is about paradoxes.”

LauricAcid & LaVache:

Am I to understand that you agree with me?

30

One of my professors (who happens to be an objectivist) used Rand’s theory of concepts in an argument against Scalia’s approach to constitutional law. I have an interest in drawing out a contradiction in Rand’s notion of concepts because I want to help Scalia – if her notion of concepts is internally inconsistent then it can’t be used as a foundation for arguments against Scalia.

Ah, well now we know where you are and who she is. I guess since I don’t know this argument of hers against Scalia, I don’t know how to help you (not that I actually want to – I want to show you that she is right and Scalia is wrong). I would caution that even if you uncover some kind of problem in the theory of concepts, that won’t automatically invalidate Smith’s argument (whatever it is) against Scalia – you’d have to show that the point that you’re making is actually relevant to her argument.

You asked, btw, about the multiple referents of “Dogs bark” – that refers to multiple tokens of “dog” and multiple events of barking. The referent of such a proposition is an event, and that one states a universally quantified dog / barking-event relation.

Now that I understand your argument a bit better, I think I see the basic issue: I didn’t initially understand what you meant in talking about a concept referring to itself. Your blue-eyed blonde example was simply the wrong kind of example because it’s a conjunction of properties. An example of what is forbidden is a “concept” whose members are sets of random integers (or other random collections), because they have no non-self referential definition. But in addition, concepts are claimed to have a special status, that they are aspects of human cognition. That means that the ability to give a formal characterization of a collection does not assure that it could ever be a concept. In differentiating a broader class such as “concept”, you might indeed be able to define a class of “self-referring concepts” (thanks for the examples – the brain just refused to work there), but the complement is not automatically a concept. The claim then would be that NSRC is not a possible concept, because the things that you mean by NSRC have no identifiable properties in common. Similarly, in the real of numbers “non-13” does not define a concept, for colors “non-chartreuse” is not a concept, and so on.

Obviously the question to ask is “then how do I know what the possible concepts are?”, and the answer is “undertake a huge study of human cognition”. The basic claim of the Objectivist theory of concepts is that units subsumed under a single concept have to have defining properties that identify those units as being subsumed under concept A and not B, and that those properties are grounded in perception. The specific claims that Objectivists would make about those defining properties are not philosophical per se, they are scientific. But also note that a concept must be represented as a linguistic symbol (see the discussion of unit-economy in ITOE ch. 7). A test of whether a particular “concept” can be formed, according to psychological criteria, would be whether a single symbol (word, in English) can be successfully used to capture the referents. This is an “actual use” criterion – not whether you can say “Well, let’s call that R”, but rather can it be benerally used by speakers of English. That’s not a question that can be decided a priori. People can certainly understand the idea “all concepts, except those whose definition would subsume that particular concept”, but that doesn’t make the idea a concept, anymore that “Dogs bark” is a concept.

31

“Anti-realism” is the standard academic term. I don’t recall the reasons Rand gives for rejecting the view - I suppose I could look them up - but even if my view is false, Rand’s view won’t become consistent.

Perhaps I misunderstood what you were trying to say in your initial description of your anti-realist views, but I have never heard “anti-realism” used in the way you described. Everywhere I’ve seen it used it refers to the denial of an objective reality as such (a metaphysical position), rather than the epistemological view that our concepts don’t have an objective basis in reality, which is what I thought you were saying.

EDIT: Perhaps my initial intention in asking you why you chose “anti-realist” as opposed to “nominalist” will be more clear if I rephrase it: Do you deny the existence of reality, or do you accept that there is an objective reality, but deny that concepts have an objective basis in reality?

You’re right that your own views don’t have anything to do with the consistency of Ayn Rand’s, but it does help facilitate discussion to know exactly where you are coming from.

32

In differentiating a broader class such as “concept”, you might indeed be able to define a class of “self-referring concepts” (thanks for the examples – the brain just refused to work there), but the complement is not automatically a concept. The claim then would be that NSRC is not a possible concept, because the things that you mean by NSRC have no identifiable properties in common. Similarly, in the real of numbers “non-13” does not define a concept, for colors “non-chartreuse” is not a concept, and so on.

This is (kind of) where I was headed, although in a somewhat more roundabout way, since I’m not sure this presents a problem to Kyle’s position, given his anti-realist and/or nominalist views (whichever it is he meant). (Of course, it is a huge mistake to accept that this paradox is a problem in Objectivism, and use integrations that could not be classified as concepts under Rand’s theory.)

In essence, what NSRC amounts to is an attempt to arbitrarily integrate existents into a concept based on something they’re not. Under that principle I could have a concept that unites me, my tv, the Blockbuster down the street, the Sun, Jupiter’s Great Red Spot, and Alpha Centauri into a concept of things that aren’t on Pluto–or any number of other completely arbitrary groupings.

33

Everywhere I’ve seen it used it refers to the denial of an objective reality as such (a metaphysical position), rather than the epistemological view that our concepts don’t have an objective basis in reality, which is what I thought you were saying.

In the context where it came up, he was being an anti-realist w.r.t. reference. So I suppose that would mean that words don’t really refer to things, and sets don’t really refer to other sets. I don’t know what it would actually mean for reference to be unreal; and there are various problem with the referential theory of meaning. I just don’t know how the concept of “reference” or “referring” can be unreal. But I’m a thorough-going unimaginative realist, so I’ll wait to see what Kyle says anti-realism w.r.t. reference refers to.

34

David Odden:

Ah, well now we know where you are and who she is. I guess since I don’t know this argument of hers against Scalia, I don’t know how to help you (not that I actually want to – I want to show you that she is right and Scalia is wrong). I would caution that even if you uncover some kind of problem in the theory of concepts, that won’t automatically invalidate Smith’s argument (whatever it is) against Scalia – you’d have to show that the point that you’re making is actually relevant to her argument.

I’m really very impressed. How did you identify Professor Smith from what I said?

But in addition, concepts are claimed to have a special status, that they are aspects of human cognition. That means that the ability to give a formal characterization of a collection does not assure that it could ever be a concept. In differentiating a broader class such as “concept”, you might indeed be able to define a class of “self-referring concepts” (thanks for the examples – the brain just refused to work there), but the complement is not automatically a concept. The claim then would be that NSRC is not a possible concept, because the things that you mean by NSRC have no identifiable properties in common. Similarly, in the real of numbers “non-13” does not define a concept, for colors “non-chartreuse” is not a concept, and so on.

You have to be careful with the word “compliment” here – the compliment of the even numbers could be the odd numbers (if we’re restricting our domain to the integers) or it could be thing like Pluto, chairs, myself and my dog (if we’re not restricting the domain at all).

I think you’re right that the compliment of a set won’t work as a compliment if we’re not restricting the domain. Nonetheless, there seem to be lots of examples where we use the compliment of a concept in a restricted domain to form another concept. So, for example, the concept of the even numbers is defined by all of the numbers that yield an integer when divided by 2. We get the concept of the odds from the numbers we can’t do this with. The concept of the primes (this is probably my best example) comes is the compliment of the numbers that be can be divided cleanly by something other than 1 or itself. Outside the numbers, the concept “non-violent criminal” is the compliment of “violent criminal” when we restrict the domain to criminals.

And so, yes, if I took the compliment of SRC without restricting the domain I’d end up with a collection including Pluto, trees, and doors. But as long as I restrict the domain to concepts NSRC doesn’t seem any different than the concept of primes.

Obviously the question to ask is “then how do I know what the possible concepts are?”, and the answer is “undertake a huge study of human cognition”. The basic claim of the Objectivist theory of concepts is that units subsumed under a single concept have to have defining properties that identify those units as being subsumed under concept A and not B, and that those properties are grounded in perception. The specific claims that Objectivists would make about those defining properties are not philosophical per se, they are scientific. But also note that a concept must be represented as a linguistic symbol (see the discussion of unit-economy in ITOE ch. 7). A test of whether a particular “concept” can be formed, according to psychological criteria, would be whether a single symbol (word, in English) can be successfully used to capture the referents. This is an “actual use” criterion – not whether you can say “Well, let’s call that R”, but rather can it be benerally used by speakers of English. That’s not a question that can be decided a priori. People can certainly understand the idea “all concepts, except those whose definition would subsume that particular concept”, but that doesn’t make the idea a concept, anymore that “Dogs bark” is a concept.

We seem to be using the term NSRC without much of a problem. Also, remember that some terms only come into common use after they’ve been introduced for the purposes of a math book – for example, the term “truth value” was popularized by Frege. So while I think you make a good point, I don’t think it invalidates NSRC.

David Zornek:

Perhaps I misunderstood what you were trying to say in your initial description of your anti-realist views, but I have never heard “anti-realism” used in the way you described. Everywhere I’ve seen it used it refers to the denial of an objective reality as such (a metaphysical position), rather than the epistemological view that our concepts don’t have an objective basis in reality, which is what I thought you were saying.

Do you deny the existence of reality, or do you accept that there is an objective reality, but deny that concepts have an objective basis in reality?

I believe in a mind independent, physical world, but I deny that there’s any “deep” connection between our understanding of the world (i.e. the concepts we use, logic, etc.) and the world itself. I think that, for Darwinian reasons, the way we perceive the world generally matches up well with the physical reality, but language, color, logic, etc. are all human creations.

35

Ayn Rand defines “concept” as follows:

“A concept is a mental integration of two or more units which are isolated according to a specific characteristic and united by a specific definition” - (Introduction to Objectivist Epistemology, p. 10)

Thanks for that. I thought I was missing something and should have double checked my reference material.

36

I’m really very impressed. How did you identify Professor Smith from what I said?

Perhaps you are unaware, but Tara Smith is something of a household name among Objectivists. I’m guessing Dave checked your profile and saw UT Austin and made the connection based on the fact that she has done a lot of speaking recently on judges. At least that’s how I figured it out.

I think you’re right that the compliment of a set won’t work as a compliment if we’re not restricting the domain. Nonetheless, there seem to be lots of examples where we use the compliment of a concept in a restricted domain to form another concept. So, for example, the concept of the even numbers is defined by all of the numbers that yield an integer when divided by 2. We get the concept of the odds from the numbers we can’t do this with. The concept of the primes (this is probably my best example) comes is the compliment of the numbers that be can be divided cleanly by something other than 1 or itself. Outside the numbers, the concept “non-violent criminal” is the compliment of “violent criminal” when we restrict the domain to criminals.

In the case of numbers, there are actual characteristics shared by odd numbers (or prime numbers) that are the objective basis for forming the concepts–the basis is not the lack of a characteristic, i.e. an integration based on what they are not. (I will identify those positive characteristics if asked, but it shouldn’t be necessary really.)

In the case of your “non-violent criminal” vs. “violent criminal,” the first thing I would say is that neither is a concept. You have one concept (criminal), which you are modifying by two other concepts (non-violent and violent). In the face of an objective concept of “crime,” there would be no possibility of distinction between the two, since there would be no such thing as a “non-violent criminal.” In other words, the entire distinction rests on a bad concept.

Taking a concept of a thing, and combining it with a concept of one or more qualifying concepts does not necessarily yield a new, delimited concept.

And so, yes, if I took the compliment of SRC without restricting the domain I’d end up with a collection including Pluto, trees, and doors. But as long as I restrict the domain to concepts NSRC doesn’t seem any different than the concept of primes.

The big difference is that one is based on characteristics which exist, the other is based on the non-existence of a characteristic. Objectivism rejects (except in very rare cases) the forming of concepts based on the lack of a characteristic(s), which is why this “NSRC” thing isn’t a problem for Rand.

P.S. Thanks for clarifying your views on whether or not there really is a world out there. It’s helpful to know exactly how far down your differences from Objectivism go.

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is true just in case the referent of “trees” is in fact green. But if “trees” doesn’t refer then (1) can’t be true or false. You can, if you want, then, say that “concept” doesn’t refer, but its hard to say sentences which use the word are “true” in that case. And if that’s the case, a lot of sentences in IOE have no truth value.

Its not clear what the word ‘refer’ means in this particular context. To go back to the memory example, I can make claims which are true or false about my memories (eg that I can remember a red lego car from my childhood), and even develop a theory of scientific psychology which explains how memories are formed. But none of this depends on (or implies) the claim that there is a queer set of objects called ‘memories’ which somehow live inside a person’s head/mind and constitute the referents of this term. The word ‘memory’ has a use within the English language and it is a useful tool for explaining certain aspects of human cognition. However, to treat it as a term which refers directly to mental objects seems a misleading way of viewing things.

The same thing applies to concepts - we can talk sensible about concepts being formed, but to view the concept of ‘tree’ as being some kind of psychic object which exists inside the human head in a similar sense to how pictures of trees exist inside art galleries is nonsense.

38

Now that I understand your argument a bit better, I think I see the basic issue: I didn’t initially understand what you meant in talking about a concept referring to itself. Your blue-eyed blonde example was simply the wrong kind of example because it’s a conjunction of properties. An example of what is forbidden is a “concept” whose members are sets of random integers (or other random collections), because they have no non-self referential definition.

(…)

Obviously the question to ask is “then how do I know what the possible concepts are?”, and the answer is “undertake a huge study of human cognition”. The basic claim of the Objectivist theory of concepts is that units subsumed under a single concept have to have defining properties that identify those units as being subsumed under concept A and not B, and that those properties are grounded in perception.

What does ‘possible concept’ mean here? You seem to be making a descriptive claim, that it is somehow impossible for humans to form these kind of concepts. But I doubt that this is true, and it would require some kind of psychological evidence to support it. From my understanding of Rand’s discussion of invalid concepts, she wasnt intending to make a psychological claim about what it was possible for humans to do - she was making a normative statement about what they should do. She didnt say that it was literally impossible for humans to form disintegrated concepts like “blonde haired people over 6 foot tall”, just that doing so was a bad idea from an epistemological standpoint. When we say that a concept is invalid, we dont mean that a person cant form it, we mean that he shouldnt form it because it has no objective basis in reality.

edit: you even said in another thread when discussing the concept formation of children that “[the child] will generally classify the world in bizarre ways orthogonally related to the concepts formed by the people around him”. I would guess that some of these bizarre classifications are more arbitrary and disintegrated than “blonde people over 5 foot tall”, so there is no real question of psychological impossibility here.

In the case of your “non-violent criminal” vs. “violent criminal,” the first thing I would say is that neither is a concept. You have one concept (criminal), which you are modifying by two other concepts (non-violent and violent). In the face of an objective concept of “crime,” there would be no possibility of distinction between the two, since there would be no such thing as a “non-violent criminal.” In other words, the entire distinction rests on a bad concept.

Isnt this, as bottom, just the statement that the English language does not currently have a single word for ‘violent criminal’? In a different language where there was a single word for each of these categories (violent vs nonviolent), I dont think there would be any ground for denying that these were valid concepts.

You could make a strong argument that the concept ‘criminal’ is itself invalid, since the set of actions which you have to perform in order to be a criminal have nothing objective in common - they are grouped together simply because our government has arbitrarily declared that they should be illegal. A tax-evader has nothing in common with a murderer, and a cannibas user has nothing in common with a rapist. And yet, these people are all ‘criminals’. The distinction ‘violent criminal’ vs ‘non-violent criminal’ probably comes a lot closer to capturing the objective distinction between ‘rights-violator’ and ‘non-rights-violator’ than does ‘criminal’ and ‘not criminal’ (the majority of ‘non-violent crimes’ shouldnt be crimes).

The big difference is that one is based on characteristics which exist, the other is based on the non-existence of a characteristic. Objectivism rejects (except in very rare cases) the forming of concepts based on the lack of a characteristic(s), which is why this “NSRC” thing isn’t a problem for Rand.

I dont think that you could given a language-independent account of the distinction between a characteristic and its lack. For instance, we could say that ‘humourous’ is a valid concept which describes certain types of sentences, but that ‘lacking humour’ isnt a valid concept because it is just the absense of humour. But this is just a way of speaking peculiar to the English language rather than being anything particularly deep or metaphysical. Language X could have a word, say “chrand” which they use to describe non-humourous sentences. And they would then describe humourous sentences by saying that they “lacked chrand”. So, in their language, “chrand” (=‘not-humourous’ in English) would be the predicate, and “humourous” would be defined as being ‘the absence of chrand’. Hence speakers of this language would be entitled to say that ‘humour’ isnt a valid concept, since its defined entirely by the lack of a particular characteristic (chrand).

A more realistic example would be something like ‘innocent’. Is this a valid concept? Well it intuitively seems so, but only because English happens to have a single word for it. However, innocent just means ‘not guilty’. If the English language didnt have the word ‘innocent’ and we instead used ‘not guilty’ to describe innocent people, you could make an argument that ‘innocence’ isnt a valid concept because its just the absence of guilt. This sort of thing is entirely relative to the language under consideration, and whether it happens to use a single word to desribe something instead of the negation of an opposing term.

39

So, for example, the concept of the even numbers is defined by all of the numbers that yield an integer when divided by 2.

I’m skeptical about this, because odd numbers are defined (positively) as numbers with a remainder of 1 when divided by 2. A prime number is any positive integer with only two positive integer factors (which would be 1 and N). The claim is not that there are no concepts which also happen to be the complement of another concept, but rather that this is an accidental fact, and they can be described in terms of what they are.

We seem to be using the term NSRC without much of a problem. Also, remember that some terms only come into common use after they’ve been introduced for the purposes of a math book – for example, the term “truth value” was popularized by Frege. So while I think you make a good point, I don’t think it invalidates NSRC.

Well, of course you can write up anything you want and turn it in. I’m just suggesting that you not ignore what the Objectivist theory of concepts is, in constructing an argument against Smith’s argument against Scalia. The main points that need to be emphasized are (1) the inter-relatedness of various components of the theory, so you can’t detach the Objectivist theory of concepts from the Objectivist theory of logic, (2) concepts are psychological because Objectivism is a realist epistemology, (3) concepts have a special status in Objectivist psycho-epistemology in being conventionalised and economical condensations of knowledge, which are represented and stored as single symbols thus different from phrases and ptopositions, (4) arbitrary propositions cannot stand as antecedents in a valid deduction. You’re implicitly claiming “we may not have a term ‘Blort’ that refers to NSRC but I’m betting that we could”. I’m explicitly claiming that we can’t, because NSRC is not a valid concept.

I believe in a mind independent, physical world, but I deny that there’s any “deep” connection between our understanding of the world (i.e. the concepts we use, logic, etc.) and the world itself. I think that, for Darwinian reasons, the way we perceive the world generally matches up well with the physical reality, but language, color, logic, etc. are all human creations.

How is that different from realism? Is it just in the use of the word “deep”?

40

the complement is not automatically a concept

One partition of beers is between alcoholic and non-alcoholic. One partitionof concepts is between self-referring and non-self-referring. In fact OPAR (as I recall, I don’t have the book here) mentions that ‘the metaphysical’ is defined as ‘non-man made’ (perhaps someone would quote the passage to establish exactly the formulation), in which case not only is some domain (such as beers or concepts partitioned) but the domain of EVERYTHING is partioned, very much to the contrary of your insisting that this be disallowed.

The formulation in my post 28 stands unrefuted.