thomtg

Breaking out from another topic, I would like to discuss a point Ted makes:

[...]

[...] I find Rand's theory of human nature rationalistic. We are not rational (animals) whose every value descends top down from our intellect and will, but (rational) animals whose values develop from our most basic urges upward as we learn to integrate and harmonize them and pursue longer term goals in the same way we come to understand more abstract concepts. [...]

I don't see Ayn Rand's theory of human nature to be rationalistic at all. Our being rational animals is only the essentialized summary of our human nature, not the full enumeration of our faculties. If understood this way, Rand's theory conforms exactly to your interpretation of human sexuality, which, if I understand correctly, goes as follows:

1. that human beings are omnisexual in like manner as being omnivorous in appetite;
   
2. that urges, or needs, are determined from species-level capacities or potentialities which are discoverable biologically;
   
3. that preferences (or attractions, tendencies, dispositions) develop naturally through individual refinements in like manner as being left-handedness or ambidextry; but
   
4. that desires, or wants, to satisfy such needs are volitionally chosen (in the form of values) with the optional aid of morality; and therefore,
   
5. that those sexual acts in a sex life which are derived from a rational guidance (on a standard of life) are moral. Additionally therefore,
   
6. that sexual identity (e.g., heterosexuality/straight, homosexuality/gay-lesbian, transexuality, bisexuality, etc.) is a postmodernist anti-conceptual package-deal development.
   

Given Rand's theory of concepts and her theory of human nature, including the nature of emotions, I find her meta-ethics to be based on perceptual experience and scientific knowledge. If so, I see no difference in your approach and hers.

[...]

Here are 3 videos of Derren Brown that strike dead center in the issue of words, concepts and referents. Unfortunately embedding has been disabled by YouTube for all three videos, but the links work fine.

[...]

When I think of taking the insights of Clotaire Rapaille and adding them to the NLP techniques Derren Brown, I see a very powerful union that would need more than just a good idea to penetrate.

If anyone is interested in trying to figure out how philosophy influences large groups of people in practical terms, the actual mechanism, and why people can hear a good idea and even agree with it, but still adhere to irrational traditions, I have no doubt that the answer is on this path.

Michael

I just saw the three short videos. (The fourth is too long to search for the particulars.) I am skeptical of all three as representative of whatever theory Derren Brown tries to illustrate.

In the first and second videos, we are not told how many subjects he had videotaped before he chose the ones he now presents to us. In the third, he includes one of three subjects who wasn't duped by his verbal sleights. I'll grant that the tricks he does may work on those lulled into a state of non-alert or distraction, but that is all I can draw from what is shown.

If there is a moral to the anecdotal evidence, it is that one's level of focus is key to one's thriving in life, especially in civil society.

Here is another source corroborating Ellen's list that Prof. B is indeed Allan Gotthelf. Stephen Boydstun writes:

[...]

Allan Gotthelf mentioned to me that he had an exchange with Rand in which she addressed the question of whether such phrases are concepts, that is, whether they designate a concept. Here is the exchange, from the Appendix to ITOE, page 177:

Gotthelf: I want to get clearer on the distinction between a concept and what you call a qualified instance of a concept [ITOE 23, 71]. How would you classify stationery supplies in that regard?

Rand: That is a qualified instance of a concept; it is used as if it were a concept, but it is a compound concept.

Gotthelf: What would turn it into a concept?

Rand: If we had a special word for it.

Gotthelf: Just as the phrase Conceptual Common Denominator became a concept by reducing it to CCD.

Rand: Yes, that’s right.

Gotthelf: If the phrase stationery supplies became, in effect, one unit—if you hyphenated it, so to speak, then it would become a concept?

Rand: That’s right.

[...]

That makes the answer definitive to my original query (Post #20) that it was Allan Gotthelf, not Harry Binswanger, who asked Ayn Rand how she came upon her theory of measurement-omission in the 1940s. (ITOE "Concluding Historical Postscript" 307)

Thanks, everyone.

Every time I use "swan" and "white," I mean all instances of swans and all instances of whiteness, and I mean them the same way each time. I cannot do that with "this." There isn't any universal reference to it. If I use "this" in a sentence, I don't mean all instances of whatever items close to me or to the context for all times and places, past, present, and future. I only mean this item one time, here, in this context, and nothing else. Each evocation of "this" stands for and corresponds one-to-one to a concrete

Sorry, no. When you say "I was bitten by a white swan" you are most emphatically not refering to all instances of swans and all instances of whiteness.

I will grant you that there is a difference between deictic concepts and concepts of kinds. Nouns are concepts of entities andd substances. Adjectives are concepts of qualities. Verbs are concepts of states and of actions. Prepositions are concepts of (usually physical) relationship. Conjunctions are concepts of logical relation. And deictics are concepts of contextual reference. I still fail to see both the validity and the point of denying that deictics are concepts at all.

No, the sentence still makes use of the meanings of "white" and "swan" universally. It is only due to the article "a" that syncategorematically reduces their combined universality to a smaller subset. Unless you know a specific swan by name or by deictic means, the equivalent sentence is, "Some white swans bit me." Regimented into logical form, it is clear that "whiteness" and "swans" continue to be referenced universally: Ez(Wz & Sz & Bza) where a==Ted.

Why do I want to make the point of denying deictics to be concepts? Because their denial explains better other aspects of cognition. For example, why is "This statement is false" a meaningless grammatical construction? On the thesis that deictics were concepts, the explanation would have to show why the unit-contents of the involved concepts in the subject term fail to be empty. (E.g., "So and so are statements and are this.") I counterclaim that this cannot be done. On the other hand, if deictics are not concepts, the explanation involves showing it to be a concrete existent whose resultant thoughtmaking production fails to produce a concrete reference (for the subject term of the grammatical construction).

[...]

So, "this" cannot be a concept.

Why not? When "this" is used, there is something more specific it refers to. The referent could be a concrete, such as "this tree", or it could be a concept, such as "this theory."

When so referred as this concept of "swan" or that concept of "whiteness" or the theory of induction, the concepts and theory referred are actually mental concretes. The words "this," "that," and "the" may be considered adjectives from a grammatical perspective, but they themselves contribute no content to the thought fragment. That is, although the phrases "these swans" and "black swans" have the same grammatical structure, "these" doesn't modify "swans" in the same way as "black" does. The difference can be seen when regimented thusly: "So and so are swans and are black" vs. "So and so are swans and are the (or these or this)." Swans can be instances of blackness or whiteness, but they cannot be instances of the-ness or these-ness or this-ness.

[...]

"This/these" still does express a kind, an item or items close to the speakers, or close in the speech context. Numerator and denominator are similar concepts, they apply in the context of an expression of a fraction, but there is no natural class of denominators such that one can go purchase one at walmart or find one in a drawer at the smithsonian. Neither "this" nor "denominator" expresses a natural kind, such as spider or noble gas. Deictics require extant conscious minds for their existence in a way that amniote vertebtrates do not. Deictics are concepts of consciousness in Rand's terms. Again, a concept, but just a different kind of concept.

Rand emphatically does not say that conjunctions or prepositions don't correspond to anything in reality. They just don't correspond to entities as entities. "With oxygen and fuel and a source of ignition one gets combustion, but without oxygen there is none" is a statement with very real reference. You can't just omit or arbitrarily change the conjunctions there, they have real import.

Since you haven't defined syncategoremata (I understand the implications of the greek, but have not used the word myself before) I can't say whether you have or haven't answered my question; If deictics are not concepts, what are they. So please be more explicit.

A symbol is either a sign or a signal. If a word, being a visual-auditory symbol, does not denote a concept, then it must denote a concrete. Since syncategoremata are words that don't denote concepts, therefore they denote concretes in a conceptual method of cognition. Deictics like "this" and "these" denote concretes in such a method to form certain propositions.

Your comparison of "this" to "denominator" relies on their being in relationships. To that extent, "denominator" is indeed a natural concept; it is a concept of quantities in a ratio relationship. A comparable concept is "husband." By your analysis, husbands don't exist as "natural" kind. Yet, when we consider human beings in marriage relationships, husbands can be found to be the men in these relationships.

"This," on the other hand, is different. In every instance of the use of the word "denominator," the same set of referents are meant. This is not the case with "this." Each instance of "this" refers to a different "item or items close to the speakers, or close in the speech context." We can generalize from an introspective perspective that "this" appears to be relational to the speaker or speech context, but this generalization is once-removed from actual speech. This is second-intention generalization. Rand's concepts of consciousness arise from this sort of introspective generalization.

Every time I use "swan" and "white," I mean all instances of swans and all instances of whiteness, and I mean them the same way each time. I cannot do that with "this." There isn't any universal reference to it. If I use "this" in a sentence, I don't mean all instances of whatever items close to me or to the context for all times and places, past, present, and future. I only mean this item one time, here, in this context, and nothing else. Each evocation of "this" stands for and corresponds one-to-one to a concrete.

So, "this" cannot be a concept. It symbolically denotes a concrete that somehow enables the speaker to form a thought about a concrete. Similarly, all other syncategorematic words denote concretes that enable a conceptual being to form rational thoughts. Because "with" is a preposition, a concept denoting relations, it is not a syncategorematic word in your example. "And," on the other hand, is a syncategorema. "A boy and a girl went up the hill to fetch a pail of water." The three propositions formed are about a boy, a girl, and their action together. "And" has no category of its own; instead, it enables the speaker and reader to form a complete thought comprising the three propositions. Its effect is in the use of thoughtmaking, not in the content of the thought.

On a TV interview (perhaps an old Phil Donahue Show, first visit), a questioner asked Ayn Rand a question from a questionable source of authority. I don't remember the exact question, but it goes in paraphrase: "I used to read Atlas Shrugged and believed in capitalism, but since then my economics professors tell me otherwise. Why do you still believe in capitalism?" Rand's reply was to dismiss the question. It was asked in bad faith.

If I understand Rand's refusal correctly, I conclude that it is all right to question Rand's belief in capitalism, but it is not fine to frame it prefixed within discredit and from a mutually unrecognized authority. A question is asked in bad faith whenever the questioner has failed to pass judgment on a claim but then gone on to ask a question based on the claim. I call it the "stolen-question fallacy."

The stolen-question fallacy is a species of the complex-question fallacy, which in turn is a species of the fallacy of begging the question. The questioner in the TV show above already presumed capitalism to be false; any reply from Rand would have no effect on that as a foregone conclusion. Rand was correct and rightly so to dismiss the question. (See ARA 132-133 for more examples of such improper questions.)

I interpret Ted's argument as following this principle. There are points in Rand's writings that can be questioned (parodied, criticized, etc.), but they can be done without a layer of preachy, cynical muck whose purpose is to elevate the muckraker as some sort of authority. Repeating this critic's blog entry serves no purpose but to dignify it in civilized dialog. It properly belongs in dark places or maybe not anywhere.

I believe that if one follows this principle consistently, one may readily detect a current attempt to discredit Rand's legitimate critics. By having a book, say, PARC, written and legitimized, it becomes easy for an authority simply to point any innocent reader to it to dismiss Rand's critics. How many of us, having known its existence but prior to having read PARC, thought perhaps that we might have been mistaken in our prior assessments of the individual Brandens' writings? Now imagine the thousands of new readers every month who are introduced to Ayn Rand's writings, and imagine the sheer amount of intellectual work they need to do to integrate her ideas. It is thus not farfetched to imagine PARC standing as a convenient division of intellectual labor for the new readers. And if they have not mastered their own psycho-epistemological style for independent thinking, it is very likely that many, if not most of them, will commit the stolen-question fallacy and dismiss Rand's legitimate critics based on PARC's mere existence. The more people repeat PARC or debate Rand's story within the framework of PARC, the more legitimate PARC will appear, at the expense of discrediting legitimate dialogs about Rand's ideas, her life, and her philosophical legacy.

[...]

My all-time favorite serial was with the fourth doctor. Having visited Gallifrey and having brought aboard a young Time Lady as apprentice, the Tardis crew got trapped in the parallel universe E-Space that they ended up having to leave behind the apprentice woman. At the end, a male companion asked the Doctor whether she (the woman) was going to be all right in E-Space. The Doctor said, "Yes, of course, she will be. After all she is a Time Lord." That, I thought, was classic.

The episode you're referring to is Warrior's Gate. I have about half of the episodes from the Leela thru the Romana days taped on VCR but do not have that episode. The BBC would realize a lot of revenue if theu would stream their videos with commercials on the internet, but they'd rather not, apparently. You can watcht the losty episode Shada as well as a new episode, Scream of the Shalka done as animation here at the BBC.

Thanks, Ted. That's the story, and Romana is her name. I just checked, and the BBC has just brought it to DVD! :yes:

[...]

http://en.wikipedia.org/wiki/Doctor_Who

http://en.wikipedia.org/wiki/Doctor_(Doctor_Who)

Tom Baker as the Fourth Doctor

I remember watching back-to-back episodes of Doctor Who on Saturday mornings on PBS. That's how I got interested in the TV series.

I like the third and fourth doctors best. I never did watch the prior doctors, since at the time I had a bias against B&W TV shows, especially British subsidized ones. Shows of the fifth and sixth doctors were short-lived in syndication, so I did not watch them as much. I did not like the seventh doctor--he looked too plump and fastidious--and the storylines often turned mystical. Even though the syndication continued on, I stopped watching the series after that turn.

My all-time favorite serial was with the fourth doctor. Having visited Gallifrey and having brought aboard a young Time Lady as apprentice, the Tardis crew got trapped in the parallel universe E-Space that they ended up having to leave behind the apprentice woman. At the end, a male companion asked the Doctor whether she (the woman) was going to be all right in E-Space. The Doctor said, "Yes, of course, she will be. After all she is a Time Lord." That, I thought, was classic.

Thomas, if "this" is not a concept, then what is it? A percept? A phrase? A proper noun? There seems little point to me in denying that it is a concept, just a member of a special class of concepts, one based not on the expression of natural kinds (which suffer definition by genus and species) but of deixis. Rand touched very briefly on concepts of conjunctions like "but" and "and" in ItOE. She calls these words concepts, and I take it from your attitude here that you would not. But that seems a matter of terminology, and if you wish to deny that deictic words are concepts it is up to you to say what they are.

Meanwhile, keep in mind that not all concepts are definable by genus and differentia. (E.g. existence.) Also, the fact that we use the word "the" or "a" obligatorily in English is not a proof of circularity of definition. Russian has the word "this" but it does not have the word "the" and you can define "this" easily enough in a grammitical sentence of Russian. I am not really interested in picking such nits. It is quite obvious that you can define the word this, and that it is a concept, just not a concept of kind.

Isn't concepts of kind the only kind of concepts? "The," "a," "if," "and," and "but" are syncategorematic words. Yes, Rand thinks conjunctions are "special concepts," but she admits that they don't correspond to anything in reality. (ITOE 37d) So I would say that Rand here is alluding to something entirely new. That is, whether syncategoremata are concepts is an open question. "This" in my view counts as a syncategorema. Syncategorematic words are certainly needed "in a conceptual method of cognition." (ITOE 11a)

My hunch is that Thom means the word 'this'. It is only defined with examples of usage. It has no clear set of referents. It is indexical or deictic. My hunch is that Thom thinks a 'concept' has a clear set of referents.

Merlin is correct, as I have mentioned on other threads, words like "this" and "that" as well as pronouns such as "I" and "mine" are deictic, the indicate another referent within the context of a certain speech act. "This" is certainly a concept. Its specific referent is the previously mentioned object, fact or phrase within a discourse. E. g., "Unemployment is high, and this is something we should all lament." In this phrase, the referent of "this" is (the fact that) unemployment is high. Or, "this" can simply mean the object nearer the speaker. I like this (dress, car, etc.,) but I don't like that.

Just like the word this, the pronoun I is radically contextual. Its referent is the speaker in a speech act. When Ted Keer says "I" the pronoun refers to Ted Keer. When you (the listener or adressee in this speech act) say "I" the reference is entirely different. This does not mean that "I" is not a concept. It is just a special kind of concept.

The confusion is that these deictic pronouns referents are radically context dependent, whereas common nouns refer to classes of things and proper nouns refer to specific individuals or collectives. The definition of the common noun bachelor is not context dependent in the way that the definition if "this" is. Yet even the concepts of common nouns need contextual specification when the statement is not a universal claim. Most presidents are a mixed bag, but this one is an unmitigated disaster.

If "this," "that," and pronouns were to denote concepts, then Ayn Rand would be correct in her universal judgment that S1 ("Every non-proper-name word is a symbol that denotes a concept")--unless David Kelley had in mind some other words that didn't denote concepts. Since I do not think Kelley uses the quantifier "most" in his statement for false modesty, I conclude that there are words that don't denote concepts, and "this," "that," pronouns, and other deictics are my candidates for such words.

Now Ted is claiming that "this" is "certainly" a concept and can be defined. If this turns out to be the case, then the second part of my conclusion is wrong, but the first part is still valid. Either Rand is correct, or else Kelley is.

So, is "this" a concept? Ted defines the denoted concept as "the previously mentioned object, fact or phrase within a discourse." Is this a valid verbal definition? Does it have a genus and differentia? Does it name the essential characteristic(s)? Does it narrow down the referents and delimit their broadness? Does it avoid circularity? Does it avoid vague language?

If a child can understand the word "this," then I would suggest that a definition of its concept--if there were one--would use language a child can understand. The statement of definition above it seems to me uses some obscure words. What is "discourse"? What does it mean to be "within a discourse"? And what does the word "mentioned" mean in the statement? Could some other clearer words or phrases be used?

I cannot help but think that the above statement is circular. That "the" in the statement seems to point deictically to "this." It's like "the whatever" is equivalent to "this." In this sense, we haven't come closer to understanding what "this" is. We have merely described its indexicality.

Along with the immediately above objection, I think the "whatever" part to be highly interesting. The statement names intrinsic objects, objective facts, and linguistic phrases as candidates to be grouped together for being indexed. This is a highly heterogenous grouping. Alternatively, it could be too narrow a grouping. For example, I can use "this" to refer to a false statement.

I certainly agree that the statement does describe a primary function of the use of "this," so in a sense we have identified an essential characteristic. The question remains though as to what it is that has this characteristic. What is the genus of the "this" if it were a concept?

Ted suggests that the words "this," "that," "these," and "those" are related to pronouns in their being "radically contextual." This suggests that perhaps their genus is "pronoun." "Pronoun" is defined as words which can be used in place of other noun words or phrases. But this we already knew: "this" is a word. The question is, does it denote a concept? And more generally, if "this" is a pronoun, do pronouns denote concepts? "Pronoun" it would seem is a concept of second intention. Thus, it is an open question as to whether the individual words here-called pronouns are concepts.

An example Ted cites is the pronoun "I": "Just like the word this, the pronoun I is radically contextual. Its referent is the speaker in a speech act. When Ted Keer says 'I' the pronoun refers to Ted Keer. When you (the listener or adressee in this speech act) say 'I' the reference is entirely different. This does not mean that 'I' is not a concept. It is just a special kind of concept." We have extrospective concepts and introspective concepts. We have concepts that divide up objective and subjective reality. In what sense are these concepts "special"--if they are concepts? As opposed to what other kinds of concepts are they different?

Deictic pronouns are said to be "radically context dependent." What does this mean? Does it mean that that which you refer is not the same as that which I refer? But isn't this tantamount to saying that what is true for you is not the same as what is true for me? If I grant you the fact that deictic pronouns are indeed radically context dependent, then something has to be resolved such that my truth and your truth must be the same truth. The only way out, as I see it, is to resolve that deictics aren't concepts.

[...]

We moved to Lynchburg last month. We never owned a home before. It is a splendid place for me to study and write. My library is glass on three sides. My books fan out behind me. There are trees out every window of the house. We have about two acres, so many birds, an otter, chipmunks, rabbits, and squirrels. The Blue Ridge Mountains are near. I am happy.

PS (a day later)

Just now a deer walked out of the woods and across the front yard.

You should take some pics of the glass library to decorate your new corner.

So THIS is what we have: common nouns, proper nouns and THIS.

--Brant

How about this: concept helpers. This (thing). Above (the rim). Blue (sky).

--Brant

No, Brant, I see "above," "blue," "throw," "selfishly" as words denoting concepts respectively of a relationship, an attribute, an action, a quality of a property. What they aren't is that they aren't classified by your categories.

Thomas, forgive me, but you sound a bit like

here. What word are you talking about?

I think this is the word: this. I am somewhat perplexed; it is defined in any dictionary. Hey, Thom. Help us out here. Did you leave something out?

--Brant

I think you are right, Ted. This is funny! And yes, Brant and Merlin, that is the word I meant. No, I did not leave anything out although I thought I had underlined it with some BB code. (There is supposed to be another photo image as well, but I don't see it either.)

Notice that the dictionary entries don't define it; the entries are all parenthetical. The absence of a concept may explain partly the variability of meaning, which Ted ably illustrated in "The Opposite of Nothing ..." (Post #155).

It used to be considered as common knowledge that all swans were white. Then when Australia was colonized, black swans were discovered in 1790.

Does this mean the commonsense knowledge about swans before that time was invalidated by the discovery? Does it mean every advance in science must be acknowledged as a setback to common sense? According to Ayn Rand (ITOE 67b-c), the answer is, No. While the meaning of our concept "swan" remains the same, the statement "all swans are white" in the present context is falsified only because our knowledge about swans have been extended. Does it imply that those who asserted the statement before the discovery were wrong? No, they were not wrong or erroneous, just ignorant. Was the statement true then but false now? No. It was always false, but people were objective and rightfully so in believing it true.

I make reference of this discovery to highlight the common phenomenon regarding knowledge acquisition and to highlight an ignorance of judgment in Ayn Rand's ITOE on account of a little-known, recent discovery. On page 10 of ITOE, Rand writes: "Every word we use (with the exception of proper names) is a symbol that denotes a concept, i.e., that stands for an unlimited number of concretes of a certain kind." This is statement of the logical form "every S is P"--an empirical universal statement waiting to be "falsified." Though its utterance prior to having knowledge (e.g., here) is not erroneous, I believe it is falsified. The statement, let us call it S1, "Every non-proper-name word is a symbol that denotes a concept," is false.

(Perhaps my saying about Rand's judgment being a judgment from ignorance, is also inexact. It may simply be a case of simplification on her effort at presenting her theory of concepts gradually, on the basis of her spiral theory of learning. Nevertheless, I contend that in the widest context of man's knowledge, S1 is false.)

Why do I believe this? Merely taking it as a hypothetical scenario, what if anything must the state of a man's knowledge be altered in order for him to come to or accommodate this as a truth? The meaning of the concept "word" in S1 has not changed. Nor has the concept "concept" per Rand's four definitions changed. (ITOE 10b, 13c, 31d, 83d) Every Objectivist still knows what the word "word" means. (ITOE 11b) And the word "mean" still means the same. (ITOE 20a, 40b, 237) What has to change is for there to be a discovery of the existence of a word that does not denote a concept.

David Kelley, a more knowledgeable epistemologist than Rand, acknowledges: "One of the major functions of language is to divide the world up into categories. Except for proper names, most words stand for groups of things." (TAOR 1st 9, my emphasis) What is the black swan of S1? And if it does not stand for groups of things, for what in reality does it symbolically stand?

The word I have in mind is this . (The Random House College Dictionary, Revised Edition, 1367a) This word is not a concept. Notice that it is not even definable. Since it is not a concept, the open question is, what is it?

I think that Rand provides for the means of answering this last when she describes the psycho-epistemological role of proper names in a language: "Proper names are used in order to identify and include particular entities in a conceptual method of cognition." (ITOE 11a) What else does our conceptual method of cognition require besides particular entities and universal groups of things? The basic answer depends on an introspective understanding of what human cognition is. Several chapters in ITOE are devoted to its discussion.

By the way, the existence of these words--and there are many--implies a fundamental re-interpretation of the linguistic notion of the sign.

[...]

Dr. Ross’ remarks include the following:

“Number is not a technical term; it is an everyday word. Wave too. If specialists want to use these terms, or others, in a technical way to denote something other than what the man in the street denotes by them, specialists must keep in mind that they are doing this. When I specify and define the concepts with which such words are associated as simple English words, I adhere to two criteria. One is based on the need to communicate; the definition must coincide as much as possible with common usage. The other is based on objectivity; the concept must conform to our cognitive need to ‘cut reality at the joints’. . . .

[...]

There are many different levels of mathematical education among laypersons. My Mom’s second husband was born into a cattle ranching family and went to school only through the third grade. He was a paratrooper in North Africa and in Italy during WWII, and after the war he returned to ranching. I found him perfectly intelligent to talk to. He had a good memory, kept up on current affairs, knew some fine points of theology, and could do the arithmetic necessary for raising and selling cattle.

He had zero, the positive integers, some arithmetic operations, and dollars-and-cents. That was enough. Those span to a natural joint. There are some other kinds of numbers that he had never heard of, numbers known to more educated people. He would not have known about negative integers or irrational numbers, let alone real numbers. Most people I know outside of engineering and the sciences don’t know what is a real number. Their education in mathematics did not go that far, and their work and life does not require they know about such numbers. Their numbers end at another natural joint.

As we construct these numbers from zero and the positive integers on up to the reals, at which joint should the name number stop when talking to laypeople? Which laypeople?

David mentioned that he thought mathematicians have done an excellent job in forming their classifications: natural number, integer, positive real number, and complex number. This suggests he thinks it is fine for mathematicians to think of complex numbers (that is what they call them) as numbers in the ways mathematicians usually do. They show that the real numbers R are a field in the sense of abstract algebra (and whisper to trusting laypersons, “Hey, the reals are a kind of field”). They show that the Cartesian space RxR is a field and that no higher Cartesian product spaces of R such as RxRxR are a field. They then show that the complex number system C is a field, having the same addition operation as the field RxR, but having as well a multiplication operation. RxR has no multiplication operation, and that might seem an inferior way of being, but C, unlike R, lacks the order properties. Give them each a ribbon.

Were one to learn what a real number is and what being a field is, I bet one would learn something about real numbers when learning that it is a field. Then one could get a better grasp of the relationship between real numbers and complex numbers.

The cuttings of the mathematicians are at sensible joints. If a layperson wants to learn about more numbers than he presently knows about, let him. If a layperson wants to insist that the numbers they know about are the only numbers there are, let him. In any event, the epistemology of mathematics does not depend on the public relations of mathematicians with laypeople.

David’s definition of a wave would not be accepted by any of my physics professors and is not accepted by me. His definition is at first brush a definition of the concept of an important subclass of the class wave in media. Electromagnetic waves, of course, are waves sometimes in media, sometimes not—but enough on that already (Objectivity V2N6, 143–48).

I think David Ross is not advocating that the epistemology of mathematics be dependent on the public relations of mathematicians with the man on the street. What he is advocating is merely what Ayn Rand has stated in the ITOE workshop. (ITOE 237) Specifically, a concept, such as "number," should have the same identical meaning for the man on the street as for the mathematician. The latter may know more than the former--not by means of inductive evidence but by sheer deductive integration--but that is the extent of the difference.

Now granted that your mother's second husband may not have used or thought of negative numbers or irrational numbers, his concept of "number" would admit them, in my view, to be numbers. Given the opportunity to observe that aspect of reality, his limited understanding of numbers should still "pick out" numbers from reality. I may not have seen every kind of birds there is, but I should think that what I mean by "bird" should mean the same as what is meant by an expert ornithologist.

This is basically a criterion of objectivity in mathematics.

But as I understand your objection, you want to make out the distinction that mathematicians understand numbers radically differently and cannot be held down to the same meaning of "number" as held by laypeople, that the former may at will define "number" compositionally as "field" to allow for the inclusion of "complex numbers" and presumably "vectors." (See Ross's remark, p. 104, here not quoted).

To me, this is a prescription to corrupt mathematics. Mustn't a concept mean the same for all time and place, past, present, and future--even if its definition changes contextually? It is not a matter of public relations but a matter of unit economy that the concept "number" must mean its open-ended units, including those not yet discovered, and only those units. To allow mathematicians to take liberties at changing the meaning of "number" is to admit that knowledge of reality at one level cannot transition gradually to a new level--that scientific war is a fact of reality--that every advance in science calls for the destruction of old knowledge. (ITOE 67)

Finally, I find David's definition of waves (p. 106) to be exceptionally clear. It is not a subject of any public relations to win over physics professors; it is merely an accurate identification of some existents in reality that may be studied in more depth by physicists. What you have stated at Objectivity V2N6, 143–48 about the history of "the wave model of light" is at best a metaphorical use of "wave," not wave per se, if "wave" is to be understood to mean identically by anyone in or out of physics.

By the way, thanks for the insight to the behind-the-scenes struggles of editors.

[...]

I have publically corresponded with him about the issue [in BioShock] and I'm happy to post it here if you would like some evidence.

The irony is BioShock has been some of the best publicity Objectivism has ever had. I'd rather have publicity from a sympathetic not-really-critic than from a loathesome hater of all we stand for (for instance, Alan Moore's character "Rorschach" in Watchmen). Some of my friends have actually began reading Atlas Shrugged because of BioShock.

Yes, please do post any. I am curious about the game.

I didn't know, but happy birthday just the same.

Rich, Brant, et al. -- My testimony should indicate why Obama took the Census out of the Commerce Dept. and brought it right into the White House. Why would they care about a relatively obscure part of the government? Because they mean to do serious mischief with the numbers!

I have always tried to be levelheaded in my comments about politics and to avoid overblown rhetoric. But I've worked for 25 years in D.C. and I tell you that Obama and his crew are the most serious threat to freedom in many generations. They are moving systematically—one step here, another there—to centralize power in Washington and re-create America in the image of their socialist vision.

But the socialists in the past were upfront about their aims and willing to argue their own points of view seriously if erroneously. By contrast, the Obamaites are doing it with a new kind of Orwellianism. They are manipulating facts and appearances in order to feed Americans who want to deluded themselves plausible sound-bites in support of Obama policies which they declare are "not socialist, just temporary measures." This is post-modernism manifest in politics! And so many Americans, who are victims of government schools, leftist media, and cultural attention deficit disorder, simply cannot connect one impression or sound-bite with another.

Consider: About a month ago, after Obama had created out of thin air several trillion dollars in new spending, he then declared, with his voice that seems to lull the weak-minded into an even more catatonic state, that budget deficits are a serious problem that must be dealt with. The reporters in the room did not laugh out loud. Americans did not bombard their Congressmen with calls and letters asking "Are you people for real?"

I do believe that there are still enough semi-sound Americans who will wake up if we keep explaining to them what is happening. And I believe that the key to the future of freedom is found, among other places, in the young people who love the products of technology, who still see their lives as potentially exciting adventures, and perhaps who voted for Ron Paul.

I just read your testimony from your Cato days. The four questions you raised and answered are still relevant today. It is amazing to me that this perspective is not understood and appreciated.

By the way, what's with the sudden move, moving upstairs from 425? I have always thought that your being adjacent to the IBD branch office is a great plus.

[...]

The basic idea of post-modernism (real post-modernism) is basically one of aperspectivism. It means that the associative and causal network chains of thinking in our head are unique and different among men just as definitions may vary. Below is Ken Wilber's take of post-modernism. [...]

"The fact that meaning is context-dependent... means that a multi-perspective approach to reality is called for. Any single perspective is likely to be partial, limited, perhaps even distorted..."

But in good and healthy post-modernistic fashion, I think there are gems in both modernism and postmodernism. No single perspective is 100% accurate.

[...]

Against Immanuel Kant's attempt to invalidate our knowledge of reality, Ayn Rand writes in For the New Intellectual:

"His argument, in essence, ran as follows: man is limited to a consciousness of a specific nature, which perceives by specific means and no others, therefore, his consciousness is not valid; man is blind, because he has eyes--deaf, because he has ears--deluded, because he has a mind--and the things he perceives do not exist, because he perceives them."

Because our perception of reality is perspectival, it is therefore invalid? And you take this "aperspectivism" to be compatible with Objectivism?

This quotation, by the way, is also cited by Rand herself in ITOE, Ch. 8. "Consciousness and Identity," p. 80. I guess she wanted to make doubly sure readers take it seriously.

This entry is a trackback cross-reference to a discussion on "The Opposite of Nothing ..." at Post #292 about your subsection "Superordinates and Similarity Classes" in Post #4.

[...]

[...] That broad genus does not yield a commensurable dimension between shape and shininess. I think we agree on that (see the subsection "Superordinates and Similarity Classes" here. On this we are in contradiction of Rand's essay (ITOE 23), but in oral exchange, she seemed to lean our way at this high level of genus (ITOE 275-76).

[...]

[...]

As for the reference to ITOE 23, I do not think my view of commensurable characteristics in forming intensive qualified instances of a concept contradicts Ayn Rand's. [...]

Stephen,

Because we are comparing my view to your view about whether they match and whether the one or the other contradicts Ayn Rand's view, I am placing my comments here (rather than at where your article is posted).

I think your conception of strength of a solid as a superordinate concept is flawed ontologically. (See the subsection "Superordinates and Similarity Classes" here.) If so, your claim that Rand's supposition--that there is always some same, common measurable dimension supporting the conceptual common denominator for any superordinate concept--is false, is invalidated.

Let us first compare yours with a conception of shape of a solid as a superordinate concept. The species of shape may include cube, tetrahedron, sphere, etc. The species of strength according to the subsection may include "[h]ardness, fatigue cycle limit, critical buckling stress, shear and bulk moduli, and tensile strength."

As I understand it, a concrete referent when classified abstractly in a superordinate concept must fall under one and only one subordinate concept. A bowling ball when classifed in terms of its shape is considered as a sphere. It cannot be a sphere and cube at the same time. By contrast, the strength of the bowling ball--i.e., its " resistance to degradations under stresses"--can be various and simultaneously classified under your concept strength in all the "species." That is, when asked what is the shape of the bowling ball, I can only give you one answer. But from your view about its strength, you will give me no less than five simultaneous answers. Your answers can only mean there is an error on the superordinate-subordinate relation of classification. It is an ontological error.

As I see it from my current reading of ITOE, what your proposal is doing is an attempt to classify categories on the basis of incommensurables. Going back to shape, what would be the equivalence of this attempt? Shape as a superordinate concept would instead have for subordinates, for example, vertex, edge, area, volume, etc. On this basis, I cannot blame you for seeing these concepts as not having anything commensurable that may somehow be subclassed under shape.

The error is in not conceptualizing that attributes such as shapes and strengths of solid objects may themselves be discovered metaphysically to have attributes--that attributes too have identities. Entities such as solid objects are not the only aspects of reality that can be identified conceptually. As Ayn Rand states, a definition of a concept of some existents encompasses not only their distinguishing essential characteristic but all their characteristics, including those not yet discovered. (ITOE 27a-b, 42b, 65d) Although the shape and strength of a bowling ball are not the entity ball but merely its attributes, shape and strength can be individually discovered to have many other characteristics in themselves, and among which only one or few distinguishing characteristics will be stated in their definitions.

If nothing else, the ontological error may have affected your identification of "nothing."

Thom,

Nothing is no thing at all. I do not see how it can be a species of anything with identity. Absence has identity, consistent with your remarks, in the sense that particular possible existents can be found absent. But as with possibility, so absence; they have specific connections to some of existence. Not so with nothing.

I thought that positive state and privation were the principles of contrariety and contraries. Contrariety is a type of relation that permits comparisons to be made, the fundamental contraries are positive state and privation, and this fundamental one is the principle and cause of all others. (I’m taking this from a fourteenth century Dominican, whom I happen to be studying at this time. He takes himself to be true to Aristotle, but maybe not all Aristotelians have shared his understanding of these relationships.)

I was thinking of greenness as something one could obtain from brownness by removing some pigments that make up the latter. I was thinking of the shiny surface as restricting the angles of scattered light in comparison to the angles from the dull surface. I agree, however that the contrast of the shape of the leaf with the shininess of one side of the leaf is not a contrast along a common genus, other than the genus attribute (of a leaf in this case). That broad genus does not yield a commensurable dimension between shape and shininess. I think we agree on that (see the subsection “Superordinates and Similarity Classes” here. On this we are in contradiction of Rand’s essay (ITOE 23), but in oral exchange, she seemed to lean our way at this high level of genus (ITOE 275–76).

I cannot go your way on two sides of an issue in contradiction having an opposition that has a commensurable dimension, specifically the goal of truth shared by both sides. That is like the leaf, were it taken as the commensurable dimension of all its attributes. The attributes are radically dependent on the particular entity, but I would not take the opposition of shininess of the entity and shape of the entity to be opposition along a commensurable dimension. The opposition of contradictories seems even less likely to be an opposition along a commensurable dimension: at least an entity can have shape and shininess at the same time. Not so with the sides of a contradiction.

Rand’s conception of mathematics as the science of measurement is a classical one, and it remains a good first approximation. But mathematics has progressed and expanded. There are parts of mathematics that are not measurement theory. Even the part of mathematics known as measure theory (Lebesque integration, etc.) is not theory of measurement. It would be a watering down of the concept of measurement to the point of uselessness to take all of mathematics to be theory of measurement. (We physics folks—at least the children of Physics at Chicago—do not refer to mathematics as a science, but as a theoretical discipline. We are referring to the same discipline as those who follow the ancient tradition of calling mathematics a science.) Rand’s measurement-omission analysis of concepts has punch only because she there uses measurement in a sufficiently narrow sense to be saying something substantial and novel. Rand’s knowledge of mathematics and measurement theory was limited. It is my understanding that she was trying to learn more about them. I should mention that very important discoveries in theory of measurement were made a few years after her death. I learned the pertinent mathematics for her measurement analysis of concepts. My essay “Universals and Measurement” is Chapter 2 to her Chapter 1.

I’ll rest now.

Stephen,

It is too bad you don't want to continue with the thread's discussion, which I think is only beginning to get interesting.

On the chance you feel like continuing in the future, ...

I wonder why "nothing" cannot according to you be a species of anything with identity. If "nothing" is a word and if it is not a proper name, what do you think it is? And if you define it (whatever it is or isn't), would you define it ostensively or with a verbal definition? And if it's with the latter, what is the genus?

---

According to Aristotle, positives and privatives are oppositions of a different kind from oppositions of contraries. (Categories Ch. 10, GBWW1952) Paper cup sizes, such as small, medium, large, can be said to be contraries to each other; and for the extremes, small and nonsmall cups are also contrary opposites. In no way is each cup size a privation of the other cup sizes. Contraries cannot be in the self-same singular subject. A 7-11 cup is either small, medium, or large. Positives and privatives, by contrast, may have reference to the very self-same singular subject. At one time someone was blind and now she sees.

---

As for the reference to ITOE 23, I do not think my view of commensurable characteristics in forming intensive qualified instances of a concept contradicts Ayn Rand's. I will study your view in the cited post after my biweekly study group meeting. Meanwhile you may peruse my understanding of qualified instances of a concept here.

---

When I previously cited contradiction as an example of opposition that shares a standard unit, I meant that on either side of this relation each must be at least a proposition. That is the standard unit from which contradiction can be judged.

Thom,

You proposed, in #244 , classifying nothing under the derivative concept absence, which is a privative. What do you mean by the qualification "derivative"?

A magnolia leaf is greener and shinier on the light-catching side of the leaf than on the under side. The opposition of greenness to brownness and the opposition of shininess to dullness are plausible privative oppositions. But the opposition of shape of the leaf to the shininess of the leaf is simply difference, and it is labored to squeeze flat difference into a privative opposition. (Compare with paragraphs 58 in the "Analytic Constraint" subsection of Genesis.)

Further, it seems natural to take all privative oppositions to be types of difference-relations; while it seems contrived to take all difference-relations to be types of privative opposition. A or not-A, exists or not, these are straightforwardly difference-relations.

In #241 you remarked that "anything that is utilized [sic] by man can be counted (i.e. measured), not just entities." It is true that things besides entities can be counted; events can be counted. But counting is not the only type of measurement, and the type of measurement appropriate to a given magnitude structure is determined by that structure. Counting is the form of measurement known as absolute measurement. There are others (A, B, C).

On whether zero and the imaginaries are numbers, I go with the mathematicians. There is a history of the discipline of mathematics, and it has its splendid reasons.

In addition to histories of mathematics, I can recommend The Nature of Mathematical Knowledge by Philip Kitcher and Naturalism in Mathematics by Penelope Maddy.

Stephen,

What do I mean by "derivative" in my classification of "absence"? I mean by the qualification that the concept "absence" cannot be formed without having first formed the concept "presence." Here is Ayn Rand's explanation: "One can arrive at the concept "absence" starting from the concept "presence," in regard to some particular existent(s); one cannot arrive at the concept "presence" starting from the concept" absence," with the absence including everything." (ITOE 58c) In my view, both "zero" and "nothing" are species of "absence"--the former in regard to quantity, the latter in regard to everything.

---1

I disagree that the pair greenness and brownness, and the pair shininess and dullness are privative oppositions. They are contraries, not privative oppositions. Separately, I consider the shape of the leaf and the shininess of the leaf as incommensurables; they are different at the basic level, but they are not related in any opposition. An opposition presumes a commensurable standard of unit. (For example, a contradiction is an opposition in which the relata share the standard unit of truth.)

I do agree, however, that the difference relation is more fundamental than the positive-privative opposition.

---2

The links you give in ROR show that there really are other forms of measurement. Would you agree with Rand that mathematics is the science of measurement?

---3

Speaking of math, I too would defer to mathematicians to determine whether zero and imaginaries are numbers--provided that they adhere to proper epistemological criteria of mathematical knowledge. David Ross, for instance, is a mathematician who takes a stand on an epistemological standard that disqualifies imaginaries as numbers. Is his standard the same as other mathematicians' in your Post #279 (above) and Post #286? I think not. If not, which set of criteria is proper for mathematics? The answer can only be provided by epistemologists, not mathematicians. (ITOE 78b, also root post and my Post #198)

The present question is whether "zero" is a quantity or an absence of any quantity. The second choice is the one found in dictionaries. (Merlin's Post #188) And given my understanding of positives and privatives, just as blindness pertains not to the eye but to the state of privation of someone with eyes, so "zero" pertains not to a quantity but to the absence of any quantity.

---

On a related point, recall that I implied in #244 that a privative is a pole/relatum in an oppositional relation. I also stated that absence (and presence by implication) is categorized as a relation in Aristotle's categories. What in reality is this absence relation? This is a question of ontology that should pique anyone with interests in "zero" and "nothing."

[...]

I interpret Ayn Rand's culling of the excerpts from her novels as an effort to be more serious about philosophy. She definitely knew she was going to write more, but she first wanted to separate out from her extant writings what were about reality and what were about re-creation of reality. Any journalist, engineer, politician, or academic henceforth could quote her ideas from FTNI instead of from some "mere" novel. So FTNI is like a nonfictional packaging wrapper, wrapping the best of the best of the state of philosophy at the time. And the title essay "FTNI" does a great job wrapping up the whole history of Western Civilization.

As for the history of Western Civ, I'd strongly, most strongly, suggest Isabel Paterson's god of the machine.

As a matter of fact, I have read Isabel Paterson's book, and I agree with Ayn Rand's review of it: If you take out all the gratuitous references to God and the Christian religion, the book is a gem. It gives the reader a framework for understanding that the entity "State" has causal identity--like a machine--and not something amorphous. I can clearly remember her assessment that the Constitution Amendment 17 is a machine breaker.