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David Hume wasn't always such a sceptic about induction. Indeed, he described three of (so-called) Mill's methods before Mill did. See Bk I, Part III, Sec. XV of his Treatise of Human Nature - Rules by which to judge of causes and effects. He described there the method of agreement, the method of difference, and the method of concomitant variations.

I grant you've supplied some evidence that Rand considered the differentia but not the genus as the essence. However, the last quote says the essence distinguishes these units from all other existents within the field of man's knowledge. I take this to say the essence includes the genus, too. Was she inconsistent? Arguably so. In any case, I think that the genus is part of the essence, too, and Aristotle would probably have agreed. "For if a definition is an expression signifying the essence of the thing and the predicates contained therein ought also to be the only ones which are predicated of the thing in the category of essence; and genera and differentiae are so predicated in that category: it is obvious that if one were to get an admission that so and so are the only attributes predicated in that category, the expression containing so and so would of necessity be a definition; for it is impossible that anything else should be a definition, seeing that there is not anything else predicated of the thing in the category of essence" (Topics VII, 3).

She goes on, btw, to say that the essence "may be altered with the growth of man's knowledge." I don't think she'd have considered animality to distinguish humans from "all other existents within the field of a man's knowledge." (I don't agree with her theory of a concept having an "essential" characteristic -- or with quite a bit else in her theory of concept formation. I'm here just pointing out that I think, on her own terms, she wouldn't have considered "animal" "essential" in her meaning to the concept "man" (human).) Ellen Why don't you think she'd have considered animality to distinguish humans from non-animals such as plants and non-living things? I did only a brief search and did not find her explicitly endorsing the species-genus model of definition, but think she endorsed it implicitly. So I agree with MSK's last point in #219. Distinguishing is evident on two levels in the genus-species model. The genus distinguishes the members (animals in the case of 'man') from non-members in general. The species (rationality in the case of 'man') distinguishes the members from non-members within the genus. P.S. Rand explicitly uses the genus-differentia model of definition on p. 41 of ITOE (2nd ed.). I take it as equivalent to the genus-species model.

The criticism fails. The relevant definition of man is "rational animal". The animal part is essential, too, and encompasses DNA and respiration.

Indeed. After all it's just a matter of definition of the word "true"/"truth", and I don't see why we should use a different word for mathematical statements. The statement "2 + 2 = 4" is not a true statement but a correct statement? Seems rather awkward to me. Of course there is a difference between a mathematical truth and truth as correspondence to reality, which is related to the difference between analytic and synthetic statements, but I have no problem with that distinction... I don't know if this is a response to what I posted earlier or Ellen Stuttle's latest. Regardless, I have not said nor do I hold that all mathematical statements should be considered correct but not true. Some, such as 2 + 2 = 4, are true. It is empirically demonstrable, i.e. it corresponds to reality. By the way, I took Brant Gaede's remark to be about what I wrote about a bit of Atlas Shrugged. Would he have said the same if my example had been 'God created the world in 6 days and rested on the 7th'? This is correct per the Bible, but it is fiction.

I see that Stephen Boydstun responded to your first question. I have not developed it further. Besides some propositions in mathematics, being correct but not true applies to fiction. 'Hank Rearden had an affair with Dagny Taggart in the novel Atlas Shrugged' is true. 'Hank Rearden had an affair with Dagny Taggart' is neither true nor false, but correct. I was also going to point you to Stephen Boydstun's piece about Ruth Milliken and truth theory, but he beat me to it.

Ellen, You are correct. There is a missing "not." Aaarrrggh! (At myself.) Hopefully other readers will take it to be a typo, too. It is fairly evident from the rest of what is said about Popper.

Stephen, Thanks for the reference to the book by Newman. I looked for it on Amazon and found another book that looked even more interesting -- Bare Facts And Naked Truths: A New Correspondence Theory Of Truth by George Englebretsen. Both this book and Newman's are pretty expensive. Englebretsen is also the author of Something To Reckon With: The Logic of Terms, which is about Fred Sommers' term logic. I read it a few years ago and liked it.

I think Rand subscribed primarily to the correspondence theory of truth. However, there are some elements of the coherence theory of truth in her position, and this sounds more like one of them. Daniel, I realize you are extremely eager to dismiss anything Ayn Rand said as banal verbalism, but you could have noticed the difference between her two similar phrases simply by reading her next sentence: "you have used all of the knowledge available to you and have not indulged in any evasion." As for the banality that Ba'al raises, I suggest caution. It comes mighty close to "no truth w/o omniscience." For anyone interested I address the coherence theory of truth in Volume 1, Number 5 and the Objectivist theory of truth in Volume 1, Number 6 here: http://objectivity-archive.com/

I didn't ask you if numbers are subject to the rules of arithmetic, which is what you answered for 6. I asked if you did any addition, subtraction, multiplication, and division. Clearly you did not.

Admittedly, she did not say it was a definition. Nowhere to my knowledge did she say this or that is a definition of mathematics. Maybe it's only a description. But I think that the above is the best candidate for her definition. How do you know it's a definition? Maybe it's only a description. Suppose you measure a stick and find it's 6 inches long. Did you do any addition, subtraction, multiplication, and division? I'm not trying to denigrate Rand. I wouldn't expect Rand, who studied no math beyond middle-school algebra, to give a good definition.

Here is my working definition. mathematics -- the study of number, space and structures that can be quantified, and their abstractions and generalizations. Rand's definition -- the science of measurement -- is far too narrow. It doesn't even include arithmetic! This is a half-truth. Topology is about both metric and non-metric spaces.

No, ^ meant exponentiation or "to the power of", as in some computer languages. Context!

Apology accepted. It's really quite simple. Let x and y be any real numbers, x not 0. (x^y)/(x^y) = x^(y-y) = x^0. Clearly (x^y)/(x^y)= 1. Hence, x^0 = 1.

I made the distinction in #315. The former seems especially important in the cognitive development of a child. Dimensionally specific similarity comes later. Your last sentence is pretty sweeping, but Rand's similarity examples in ITOE were the latter kind.

Really? So two objects could not be similar while not being perceived? What about a cause-and-effect relationship? Is it also just "in here" and not "out there"?

I note a significant shift in position here. First similarity could not be perceived, then it's "in the perception". Maybe in a few more days, he will say that objects can be similar, even while not being perceived.

I don't believe it's as big a problem for humankind as Rand portrayed it in "For the New Intellectual", that the fate of mankind rests upon the solution. (I'd say ethics is far more important.) Many people form concepts quite well without being able to articulate how they do it. However, I do think the problem of universals is a genuine and interesting one for philosophy (and cognitive science). Also, I don't believe Popper called it a "non-problem" (in Objective Knowledge). He rather thinks the nature of concepts less important than propositions and theories. You say that similarities do exist in reality and we have ways of recognizing them (shaped by evolution). I don't believe that's in dispute here. The dispute is more about how we recognize them. Much of the rest of your post is about the reliability of perception. That's an interesting topic, but not what we have discussed so far on this thread. What brought me into it was whether similarity is perceptual or conceptual or both. Of course, the line or bridge between them is not so clear and on the frontier of cognitive science.

Thanks to MSK for introducing "perceptual judgment" to the thread. Brendan used "mental judgment" with regard to similarity w/o making a perceptual-conceptual distinction, though I'm inclined to think he meant "conceptual judgment" since he has objected to similarity being perceived. MSK also brought up David Kelley's Evidence of the Senses, giving Kelley's definition or description of "perceptual judgment" on pp. 208-9. Also relevant is pp. 221-2 (hb) where Kelley says: Kelley thus says that the identification of any object as a particular kind of thing or having a particular quality involves a judgment -- which could be implicit -- that it or the quality is similar to other particular things or qualities one has perceived. He doesn't, however, compare adult humans to infants or other species , and Brendan chose not to respond to my introducing perception by infants and eagles. This is a fascinating subject, at least to me. I call comparison the basic act of knowledge. I wrote a long article about similarity, now on the web here Pursuit of Similarity thanks to Stephen Boydstun. Here are a couple of quotes especially relevant to this thread. "Conceptualism comes down on the side of resemblance as being the ontological basis of general ideas" (p. 59). "Another broad distinction is between global and dimensional similarities. The former means similarity at an overall level and is dimensionally nonspecific. Linda Smith suggests that dimensionally nonspecific relations are experimentally and developmentally prior to an emerging knowledge system. Objects are originally perceived holistically, without being decomposed into separate dimensions. ... As adults we are inclined to think that similarity of parts is logically prior to overall similarity. But logical priority does not equal chronological priority" (p. 126). I repeat my two questions to Brendan. (Anyone else is welcome to chip in.) Does an infant make a judgment that mommy now is the same person seen hours earlier? Must an eagle make some sort of judgment that the hare it sees today is similar to the hare it preyed on earlier? What sort of judgment in each case?

Robert Campbell, Can you elaborate on, or be more specific, about #44? I have the Signet paperback 35th edition of AS, and I don't see anything about "moral perfection" in "About the Author". Also, where in OPAR?

No. I said "much better" and what followed because this forum is allegedly Objectivist with Ayn Rand's picture and name in the header. And repeating what I said in my prior post, "I fail to see how it [your article or essay] reflects your understanding (or misunderstanding ) of Rand's meaning of 'moral perfection'."

What essay? If you mean #1 in this thread, I fail to see how it reflects your understanding (or misunderstanding) of Rand's meaning of "moral perfection". You address it barely or not at all. Hardly. Rand's meaning of "moral perfection" is basically a relentless effort at unbreached rationality. Rationality clearly includes making value choices consonant with moral principles. I didn't say "high degree, not highest degree." If anything, I'd take "relentless" and "unbreached" as meaning "highest degree." Did I say she was sloppy? No, I said she used a common term ("perfection") in an uncommon way.

Technically speaking, that's correct. I unwittingly repeated Brendan Hutching's misuse. However, the point of my sentence still holds.

I haven't researched all Rand said about it. However, I read Tara Smith's "Ayn Rand's Normative Ethics", and Smith writes that for Rand moral perfection is simply unusual consistency in abiding by one's moral principles day in, day out (p. 237). Smith cites Rand: "Moral perfection is an unbreached rationality -- not the degree of your intelligence, but the full and relentless use of your mind, not the extent of your knowledge, but the acceptance of reason as an absolute" (Atlas, p. 1059). Citing but not quoting Peikoff, Smith writes: "[M]oral perfection, in its essence, consists in a single policy: the commitment to follow reason." This is another case of Rand using common words in uncommon ways. It's no surprise that it leads to misunderstanding and controversy. In the more common meaning of "perfection", Rand's meaning is an extraordinary striving for perfection, not its achievement. MSK makes a good point with the distinction between temporary and permanent. Even with the common meaning, a student can get a perfect score on a test w/o getting a perfect score on every test. Even in Rand's sense one can be morally perfect for several months or years w/o being so one's entire life. However, I do think it would much better for MSK to find out what Rand meant by the term before writing an entire article about it using the common meaning of "perfection." Of course, one can probably find those who claim Rand was "morally perfect" her entire life, while not understanding what Rand meant by the term, and mixing ordinary meanings of "perfection" with it.

I used "instance" to mean a single case of similarity, especially one that is perceived. What's crucial is whether or not more than perception is always required. You (seem to) say 'yes'; Rand and I say 'no'. Suppose somebody shows you side-by-side two identical or nearly identical leaves from the same tree. Do you need a "mental judgment" to say they are similar? Before saying 'yes', consider the images on your retina and the neural processing that's going on. The processing of two distinct parts - the two leaves - of the visual field is undoubtedly similar. In other words, similarity is a given by perception in this case. In Rand's length example, the similarity requires a little more selective focus, but the similarity really there and perceived. I take that to be her point, and that similarity is not an a priori concept, which is in effect what you have argued. If she had used for her example three pencils identical except in length, less selective focus is required. Nothing more than selective focus, i.e. attention, is required in many cases. If you hold that more than perception and selective focus -- some kind of mental judgment -- is required, then I submit you must hold that for infants and other species as well. Does an infant make a mental judgment that mommy now is the same person seen hours earlier? Must an eagle make some sort of mental judgment that the hare it sees today is similar to the hare it preyed on earlier. My question was provocative. Perceiving greenness or smoothness, like similarity, does require selective focus.