[Calculus Class Epistemology]

Now, proving it for s linear factors in the numerator and t>s linear factors in the denominator might be trickier; certainly it's more tedious.

Actually, it's easy enough to extend to the case of 1 linear factor in the numerator and t distinct linear factors in the denominator. First, assume you have one linear factor in the numerator and three in the denominator. Group any two of the factors in the denominator in a fraction with the numerator and express it as a partial fraction using the rule being discussed. The original factor is then written as a sum of two actors of the form m/(x-A)(x-B ). You can then expand each of these as a partial fraction, and after working out each of the coefficients you find they're given by the same rule. No doubt if I'd thought about the symmetry of the problem it would have fallen even more quickly into my lap. The general result with a linear numerator should follow easily from induction. But for s distinct linear factors in the numerator, that same result doesn't follow in the same way.

[Calculus Class Epistemology]

There are caveats on this method:

1) the factors of the denominator must all be different (this method won't work with (x+5)(x+5) in the denominator, for example)

2) all the factors of the denominator must be in the first degree (won't work with (x^2 + 1) in the denominator, for example)

3) The power of the denominator must be greater than that of the numerator

AND, of course

4) It's not proven.

I don't know why it's considered not proven; it took me about ten minutes to prove it for a linear numerator and two linear factors in the denominator--and only that long because I made a mistake in assigning coefficients at one point. There's no loss of generality to factor out all the coefficients of x, so take it in the form (x+A)/{(x+B )(x+C)}. For partial fractions, you express this in the form m/(x+B ) + n/(x+C). Multiply through both sides by the denominator and collect like terms to give the pair of equations m+n=1 and A=mC+nB. Eliminate n from the second using the first to get m=(A-B )/(C-B ), then substitute for m to get n=(C-A)/(C-B ). Now if you take the original fraction without (x+C) in the denominator at x=-C, you get (A-C)/(B-C), which is n, and similarly for m. Now, proving it for s linear factors in the numerator and t>s linear factors in the denominator might be trickier; certainly it's more tedious. In any case, it's a damned handy little rule. I'll have to keep it in mind in the future.

[The Only Two Things The Majority of Women Want.]

When people say "cmon let's just have some fun" or "have some fun" isn't the operative term 'fun' used in such a way that's so vague, or could mean anything and therefore nothing that it really is a stupid, nonsensical floating abstraction?

Where in the world did you get that from her post? I'd have thought it was obvious from the context that she meant "enjoy yourself in your date's company." As it is, that's like saying that since concrete values like types of music, food, and activities vary so widely from person to person, the concept of value is therefore so vague that it's really a stupid, nonsensical floating abstraction. Different people might well find they have nothing in common as fun (one woman might find the relaxed company of self-secure men fun, while someone else might well find logic-chopping in the service of alpha-male doggy-macho one-upmanship the height of fun), but that doesn't mean the concept's vague or a floating abstraction, it means it depends crucially upon individual values. Yeesh.

[Objectivism's Theory of History]

Thanks Adrian, I like your way of viewing it as "layers" of endeavor. A lower layer of historical sciences, providing the data to the higher layer of history. Viewed this way, history is the integrative portion that weaves together the findings of historical sciences and the knowledge of human behavior into a full fabric.

Though I'd make it a bit more complex to capture more of what historians actually do, in that there are different varieties of history, and what I've taken as the model here is, properly speaking, narrative history. There's also social history, economic history, military history, and intellectual history and its branches: history of philosophy, of science and technology, of art, and so on. (Political and diplomatic history are two specialized branches that are almost exclusively narrative, and intellectual history is also largely narrative--it's not narrative to the extent it focuses on the ideas in common currency at a time.) You might call these, oh, arts of social interpretation. These are distinct from social sciences like economics and sociology/anthropology in that while the latter do deal with areas of life in which people exercise conscious thought, there are still broad generalizations one can draw for various societies and eras--thus, economics deals with scarcity and value, and sociology and anthropology deal with customary acts and suchlike in various kinds of societies. (The usual dividing line is that sociology treats of industrialized societies, anthropology with non-industrial ones, or else highly literate and largely illiterate ones.) [*] On the other hand, economic history deals with the nuts and bolts of the economy in a given society in a given period, for example, and social history with its social relations and customs. The purpose of such fields is essentially to offer the best generalizations about how most people acted in a given society and period so as to allow one to understand why people might ordinarily act in one way in various circumstances, especially if it's peculiar to that time and place; its value mentally for general history is to show in stronger relief the special features of the less common actions important people took. If everyone is expected to follow a particular time-hallowed judicial process, for example, making its details clear and explaining its consequences is essential to understanding judicial change in that period.

There's a complex interplay between these sciences and their corresponding arts of social interpretation, and between the latter and general history (that is, the body of what the "generalized we" know and think about the past), of the usual sort of spiral growth in knowledge in which generalizations from the sciences are tested against the historical record and in turn broaden historians' interpretations of the past. This, incidentally, is why many historians are distrustful of grand theories of human history and nature that certain philosopher types are fond of erecting; such grand theories have to be made concrete for time and place to be testable, and frequently adding in the details shows so many basic human factors or pertinent historical facts to have been ignored that the generalizations are worthless. (Toynbee's a perfect example of this.) As a result historians tend to be highly empiricist to the extent of distrusting all but the most limited generalizations. This is not so good for contributing to the social sciences, but at least it makes them pretty rigorous judges of what social scientists do say (except for the ones who in turn go hog-wild for some grand explanatory schema like Freudianism or Marxism).

And I should add that narrative history is not just the summation of what all the important figures of the past did; it's not a collective biography, however selectively distilled, since its purpose is a selected exposition of the events of the past to the degree of detail necessary for a given person's understanding (whether of the present or of human behavior in general). The most important parts of a person's life for biography (which is devoted to getting some grasp on the lives and psychologies of important figures), however earth-shattering he may have been, are usually utterly unimportant for understanding his day and age, which instead depends on understanding his interaction (usually as a fully-formed adult, not someone learning and receiving influences and so on, all important in biography) with other important people, his effect on his day and age, and the interplay of action, consequences (intended and unintended both), and responses. This is the task of history, not of the social sciences, and it explains how history interacts with them.

It's also useful for understanding the Objectivist approach to history to think about the relation between intellectual history and general history. As I mentioned above, much intellectual history is necessarily narrative since the development of ideas is a peculiarly individual, particular process for which it's quite hard to see even how one might generalize usefully about it. (You can spin hegelian tales about it, but that's just woolly-headedness and hot air.) But which aspects of intellectual history are not narrative of this sort? The spread of ideas, their interactions (a tricky metaphor), and their influences on the temper of their time; in some societies, also the influence these ideas had on science, technology, and economy. The Objectivist view of history emphasizes the role the most basic ideas (philosophy) play in human action, and thus in human history.

[*] An interesting light on this comes from considering the case of Margaret Mead in Samoa. Usually Objectivists know only of Derek Freeman's first book about her, which called Coming of Age in Samoa entirely into question and implied she simply lied, but his later book The Fateful Hoaxing of Margaret Mead makes it much more likely she fell for a crude hoax or practical joke common in Samoan society, partly because she was very pressed for time, but to a great extent (not nearly enough emphasized by Freeman, in fact) because she fully bought into an anthropological approach common in American anthropology of the time, that of "culture areas." Regions with many different societies but similar environments and basic ways of life were claimed to have striking basic similarities in all institutions. Pacific societies with free love of the sort Mead described for Samoa were attested already; she and her advisor Boas appar simply to have assumed such would also be true of Samoa. However, Samoa was a highly stratified society with a warrior aristocracy, well-developed lineage systems, and a concomitant expectation of female virginity before marriage so's to keep lineages pure. This makes perfect sense to us now because it's the sort of thing you'd expect from human societies of that kind (warrior aristocracies with strong lineages)--and there you have the sort of generalization common in anthropology. However, it goes against the idea of culture areas, and in Mead's time (and especially among American anthropologists) that was a basic tenet of anthropology, so her results were greeted uncritically--almost criminally so.

[Objectivism's Theory of History]

Off the top of my head, I'd say that history is a recounting of the past, but not a simple listing of past events; rather, it is an integration of them, understanding why they happened the way they did. The "why" is an integral part of "what happened". Besides, without the "why" history would be pretty useless.

I've thought about this for a while, and my rough and ready suggestion is: History is the rational reconstruction of (chains of) past events. Basically, we have evidence of various sorts of what people thought and did (past events, where event is narrower than occurrence; I mean roughly considered actions; the distinction is from R.G. Collingwood's The Art of History) that the historian fits into an interpretive chronological order (reconstruction) using what knowledge we've attained of regularities in human behavior and the world people lived in at the time (hence rational). Any historian has to deal with the fundamental fact that people have free will at the very least in the sense of being able to choose freely among possible means to attain whatever ends they have (and the variability of ends and the knowledge they might have had of the means open to them is another wrinkle); the inference from actions in a given situation to motivation is what makes history an essentially interpretive field--though of course not all interpretations are equal and they can improve over time. And it is this central fact of free will that means history is not strictly speaking a science (in the sense that it doesn't itself strive for universally true statements about human nature), though good history often requires scientific knowledge (not to mention philosophical knowledge as well).

Archeology.. yes, I'd definitely put it within History, in the same way as I'd put surveying and other such activities under "Geography", or "conducting experiments" under (say) "Chemistry".

I don't consider archeology to be history proper; rather, it's a historical science. That is, roughly speaking, experimental sciences aim to go from the particular to the general through the testing of hypotheses about particular events; historical sciences use general knowledge (in the form of universal statements) to reconstruct what happened in the past (particular statements). Much of geology is a historical science, in this view, as is cosmology and a good deal of evolutionary biology. Historical linguistics is another. I consider them historical sciences rather than history because their primary focus is to use universal scientific statements to order past occurrences and do not have to deal with the interpretation of human events that free will entails. (Though you do get some of that latter in archeology; when it's questions of purely material culture, there is such a limited set of means and ends that it's barely a branch of history, but when you try to reconstruct something of the more social aspects of a culture fom its material remains then it's closer to history, though closer still to anthropology.)

By a "theory of history", I mean the broader abstractions that are made from the separate cases of "whys".

It's usually called philosophy of history, or perhaps history of philosophy in the narrow sense (in the broad sense you have the bloviated, bloated maunderings of Hegel, Toynbee & Co. that do strive for a theory of everything human; most historians don't like those). I think philosophy of historical methodology is a more exact term, but not very pretty.

[Contemporary Classical/Romantic Music?]

Two interesting composers who sound surprisingly alike in places are Peter Sculthorpe (Australian) and Minoru Miki (Japanese);

Actually, I don't think this recommendation matches what you're looking for, now that I think about it.

[Contemporary Classical/Romantic Music?]

Briefly asked: Does anyone know of any good contemporary romantic/classical composers? There's gotta be some good composers out there!

Also, you might make a point of checking out music for winds and symphonic band music. It was a refuge for more traditional American composers during the 50s-70s. A number of fine Italian-American composers, for example, wrote solid, interesting, often beautiful music for symphonic band during those days (Norman Dello Joio, Vincent Persichetti, Vittorio Giannini, and Paul Creston). Among contemporaries, David Gillingham, Frank Ticheli, and David Maslanka have all written extensively and well for symphonic bands. (Eric Ewazen, whom I mentioned before, has also.)

Ronald Perera has written some very fine choral and vocal works (The Outermost House, Crossing the Line, Visions). Two contemporary (though not young) composers who have written deliciously for voice are Ned Rorem (of course) and Dominick Argento; they've also written fine instrumental music, and both are considered neo-romantics. Gerald Cohen and Osvaldo Golijov have written beautiful vocal and instrumental music based in Jewish traditional music, and somewhat along those lines Thomas Pasatieri's Letter to Warsaw is very good.

All this is, of course, in addition to the standard famous American neo-romantics like Barber, Hanson, and (before 1950) Diamond, the neo-classicals like Piston, and the nationalist composers like Harris and Schuman (when Copland was being tonal, he fit into the first and the third categories); I assume you're already familiar with them.

[Contemporary Classical/Romantic Music?]

Movie soundtracks seem to be the only source of good orchestral contemporary music, as far as I've experienced. When at the symphony, and a modern composer's music is played, it's typically atonal and random, and certainly not enjoyable. I'd love to find some modern composers who write good classical.

Briefly asked: Does anyone know of any good contemporary romantic/classical composers? There's gotta be some good composers out there!

There are quite a few, many of them fairly obscure. First, Americans. A contemporary you must check out is Eric Ewazen. His style is influenced partly by English folksong; he specializes in music for brass and winds.

http://ericewazen.com/

From an older generation and somewhat famous is Robert Ward; another one whose reputation suffered during his lifetime was Alec Wilder, because he straddled the boundary between classical, jazz, and popular song. Lowell Liebermann is extremely good.

Also, British classical muic of the 20th century was generally tonal and tuneful. Keeping those requirements in mind, I'd suggest William Alwyn (quite romantic), Malcolm Arnold (romantic in places, neoclassical in others, and often cheeky and fun--though his symphonies are generally quite a bit darker; look for his chamber music [besides the string quartets] and his concertos--both of his clarinet concertos were written for Benny Goodman, for example, and are quite interesting), and Alan Rawsthorne (more of a modernist in the neoclassical strain of Hindemith and Stravinsky, but if I remember correctly he was also committed to a Laborite program of writing music accessible to regular modern listeners). What I've heard of Lennox Berkeley's music is very good, but you'd want to avoid his son Michael's music. Similarly, many Swedish composers up to about 1960 wrote quite traditional music--Hugo Alfven, Kurt Atterberg, Ture Rangstrom, and Vilhelm Peterson-Berger are good lesser-known lights from that period, though they don't count as contemporary, fer sure fer sure. Edward Tubin (Estonian) wrote a series of modern romantic symphonies you might want to sample to see if he's to your taste, and if you do like him (he's tough as granite in places and not always pretty but certainly dramatic and tough-minded) then give Vagn Holmboe (Danish) a try; I consider him one of the finest composers of his century, but he's not light and easy but rather Ibsenesque, if you know what I mean--no compromise in his search for musical truth but broadly tonal. Again, they're both from an older generation and not strictly speaking contemporary, but they might interest you and are not so commonly heard in the States.

Let's see...Alla Pavlova has written four very fine symphonies, quite romantic and Russian in sound. Samuel Zyman (Mexican) has written some very fine works as well. Two interesting composers who sound surprisingly alike in places are Peter Sculthorpe (Australian) and Minoru Miki (Japanese); they write music with strains of what I believe is sometimes called a "Pacific" school of composing; both draw on elements of non-western music in essentially western forms (traditional Japanese music for Miki and Indonesian and aboriginal music for Sculthorpe), and in my experience Miki is more consistent than Sculthorpe. If this interests you, Miki's Eurasian Trilogy is the work to look for; it's in three parts taken from Japanese poetic thought, jo-ha-kyu (slow introduction, complex middle section, and a fast conclusion), for which the first is a prelude for Japanese instruments and strings, the second a concerto for koto and orchestra, and the last his Symphony for Two Worlds, which I like very much indeed. There's a CD of Sculthorpe's music on Naxos tht's good too; it includes his didgeridoo concerto "Earth Song." He also has some good string quartets. Reza Vali (born Iranian, now I think an American citizen) is also worth looking for; he writes music in western styles that are quite listenable, but many of them are based on Persian modal music rather than tonal music; again, Naxos has a CD of his music, including a flute concerto, that's quite good, and he's written some fine string quartets as well as a large number of quite listenable settings of Persian folksongs. And finally, if you don't know it, you must find the music of Jean Francaix; he lived through most of the 20th century and composed up until the end (1997); he was the epitome of the witty, urbane, deliciously tuneful French musical craftman with the perfect light touch. He'd be classified as neo-classical rather than romantic. His chamber music is very fine and his concertos are delightful; I especially recommend his Concerto for Two Guitars and his Piano Concerto.

[The American Civil War]

This posting of mine is quite unsatisfactory, for while I stand behind the points I made, I should have been much clearer about when I was responding to something Drew1776 wrote versus similar arguments I have heard from others that fit in with his claim that the Civil War was not about slavery.

I mean, this is precisely the range-of-the-moment focus on immediate instances and minutiae to the exclusion of underlying causes, political ideals, and philosophical ideas that sickens me in Southern propagandists. (I hasten to add I'm not accusing Drew1776 of this, but he follows in the tracks and retails the pet arguments of some quite odious Unreconstructed Southrons, as some of them like to call themselves.)

In particular, here. A much fairer way of stating it is that to the extent Drew1776 states the Civil War was not about slavery (and it's worth asking what he and I mean by the Civil War "being about" something) he makes the same error of focusing on some of the details at the expense of the fundamental issues. And more generally, I should have made much clearer that you have to distinguish rigorously between the general question of secession under the Constitution and the specifics of Southern secession. The right to secession from a republic is an interesting issue; but it is largely discussed in the context of the American Civil War, in which secession was inescapably tied up with pro-slavery.

Saying the Civil War was "not about" slavery is precisely and as obscenely beside the point as saying that World War II was principally about the need for the Germans to acquire enough Lebensraum (fresh new slave states in the West or subjugated Slav slaves in the East, call it what you will, it's the same thing at root) to live comfortably in a hostile world.

This is true, but it's not the best example for my purposes, since the immediate cause of World War II was not a search for Lebensraum; that was one of the subsidiary issues, and in that respect it is comparable to, say, the struggle over tariffs before 1860. A much better example (and of course one more amenable to temperate conversation) would be the cause of World War I--the immediate cause was an assassination, but saying that the war was about the assassination of the Archduke Ferdinand is an error on somewhat the same scale as saying that the Civil War was about preserving the Union, not slavery. You need only ask the same sorts of questions to see this: Why did the various European states stand by their treaty obligations, brooking no compromise, that time and not earlier, when the prospect of a world war was staring them in the face?

[The American Civil War]

The North did back down at least once to placate slave states.

In 1793 the Fugitive Slave Act was passed by the federal government mandating that runaway slaves be returned to their masters. Over the years free states passed laws which made it more difficult for slaves to be returned such as allowing trial by jury for slaves. Many juries would refuse to convict so many slaves were allowed to go free despite the law. In 1842 the Supreme Court ruled that states did not have to help hunting or capturing runaway slaves. So the movement up to that point had been the gradual weakening of the Fugitive Slave Act.

Then to 1850. The US has acquired large tracts of land during the Spanish-American War. The current Missouri Compromise would have opened much of that land up to slave states. The Compromise of 1850 was drawn up so that the land would not automatically fall into the hands of slave states. Part of the compromise was a bolstering of the Fugitive Slave Act. Officials were now required to arrest an alleged runaway slave or face a stiff fine. So the North did capitulate to placate the South.

What was important to the North and the South was power. Freeing slaves in the South would have destroyed the South's economic and political power base.

Who in the North and who in the South? They certainly didn't have identical minds or act from identical motives, and public opinion changed drastically between 1850 and 1860. And more basically, power for what purpose? Power to keep the Union together at all costs? Then all those Northerners wouldn't have voted for Lincoln. Power to rule the roost? Then why not bid the Southern states farewell and run the remainder of the country in accordance with northern wishes? Power to prevent the spread of slavery? Why? Why in the world would that have mattered in the least to Northerners for so many more slave states to be carved out of western territories if there weren't something wrong with slavery? (Besides the three-fifths rule, of course--and why was that there in the first place...oh, that's right, to help safe-guard slavery, so it wouldn't have been a later issue if it hadn't been necessary to defend slavery in the South...) Why not allow the Southern slave powers to send slave hunters and slave traders throughout the northern states if that was what was necessary for the South to prosper? (Oh, wait, the North didn't want the South to prosper, because that would have given them more power. Power for what? Blank-out and please, please, whatever you do, forget the three-fifths clause.) The North too was racist, historians and Southern propagandists point out (the latter ad nauseam), so why should they have objected in the least to helping escaped blacks stay free? (Oh, wait, now remember the three-fifths clause.)

I mean, this is precisely the range-of-the-moment focus on immediate instances and minutiae to the exclusion of underlying causes, political ideals, and philosophical ideas that sickens me in Southern propagandists. (I hasten to add I'm not accusing Drew1776 of this, but he follows in the tracks and retails the pet arguments of some quite odious Unreconstructed Southrons, as some of them like to call themselves.) Yes, slavery was constitutional while secession was arguable, so the Republicans followed their Democratic predecessors (it certainly wasn't Lincoln who first officially opposed secession in 1860, but Democrats under the leadership, such as it was, of the Buchanan administration) in defending the Union against rebellion by a pugnacious bunch of sectionalists-cum-separatists who made it clear that if the Union weren't four-square behind their ownership of slaves, then the North could screw itself--and it's certainly true that many Northerners didn't care about the fates of Southern slaves but were willing to die to preserve the Union, and it was necessary to secure their support. (Keep in mind that an honest Southern effort to parting ways would have consisted of honest efforts to settle the disposition of federal property in the South and offering to compensate the northern states for the money and man-years they'd contributed to defense throughout the Southern states, not bombing the hell out of Fort Sumter to prevent Union soldiers from eating.) But why in the world did it ever come to Secession versus Union in the first place? It most certainly was not an abstract discussion of Calhoun's Disquisition carried out for the sheer hell of advancing the state of republican political theory, but the fact, as I've mentioned several times before, that the South not only wanted to own slaves but wanted the North to be their willing, unjudging accomplices in this obscene trade, and being the pugnacious touchy aristocrat wannabes that they were, they kicked aside the game board when a reasonably uncompromising opponent came on the scene.

And note more basically still that the Compromise of 1850 antedated the Civil War by a decade, and in times of crisis a decade is a lifetime that in this case saw a sea change. The Compromise and the accompanying renewed enforcement of the Fugitive Slave Act galvanized northern opinion and polarized the political scene by making it quite clear that the earlier compromises could not be continued (especially after the Dred Scott decision of 1857 stripped all blacks of national citizenship for the simple fact of their skin color, and thus declared free black citizens of northern states not citizens of the United States), and made the way for great advances in abolitionist sentiment. Note the most basic fact Drew1776 omits to mention, that the Republicans didn't even form and start running candidates until 1854, and more generally that after the Compromise of 1850 many Northerners realized and far more dreaded that the South would not be placated by letting each section mind its own affairs--the South insisted that the North would have to bow to Southern custom and law and give in on the most basic principles of Northern political thought and the Northern way of life. The 1850s were a time of boiling ferment in which both sides drew the lines much more sharply and uncompromisingly, and it is the necessary background to understanding just why the Civil War started as it did and became so bitter and based on such basic issues so quickly. In short, this is basic Antebellum history. And most basically, this was still a period in which political ideas of basic philosophical importance still ruled the political scene. It was clear to the actors precisely what the basic issue was, and they descirbed it forthrightly in their political tracts, never mind the constitutional limitations and conventions they abided by. It does a profound injustice to the Southern secessionists, in fact, to couch the issue in terms of Union versus Secession--they themselves saw these as only part of the issues and stood forthrightly for slavery against political developments that threatened the health of the Slave System and against the Union they vowed to uphold (despite their oaths when they were federal officers) only to the extent it upheld Southern ownership of slaves. That was what defined states' rights, that was what defined the Southern section (for an object lesson in the power of essential ideas in the historical context, try to define the Western states versus the Northern states nearly so easily), and that was what Southern secessionists seceded for.

Saying the Civil War was "not about" slavery is precisely and as obscenely beside the point as saying that World War II was principally about the need for the Germans to acquire enough Lebensraum (fresh new slave states in the West or subjugated Slav slaves in the East, call it what you will, it's the same thing at root) to live comfortably in a hostile world. Yes, in a short-enough range-of-the-moment view, that is an arguable thesis, but there's more to real history than looking only at what was directly staring in the faces of people in the past.

[The American Civil War]

The Confederacy was created in a political act to eliminate federal political control over the South, and to allow Southerners to live under a system of law that they believed was morally just. It might be the case that slavery was the primary motive for wanting freedom from federal control, but that doesn't change the nature of the political act of creating the Confederacy, as a political act. Hence, the use of the Confederate flag by those who wish to demonstrate that they don't give their moral sanction to federal governmental controls.

But political acts have to be judged ultimately by the explicit ideas driving them. I agree that a great part of the motivation for the southern states seceding and especially for its citizens to fight and die for what they proudly saw as their own new nation was a devotion to the "Southern way of life." But intellectually that's no better than the Russian peasants who marched for bread and land or the Germans who supported the Reich (2nd or 3rd, take yer pick) because of their devotion to the German Heimat, etc. And this is what irritates me no end about the Southern propagandists who compare the secession of the Southern states to the American Revolution. Secession was by and large in the service of pro-slavery political thought, and when its philosophical roots were made explicit (rather than cozy fantasies of happy, well-tended slaves living under better conditions than Northern factory workers, as if the liberty of the workers was nothing compared to the supposed well-being of the slaves), they were tied in with such things as Aristotle's pronouncements on natural slavery and essentially aristocratic virtues like a touchy sense of honor; and if you look at the political thought of Jefferson, say, then of Calhoun, then of Calhoun's successors among the secessionists like Brown or James Henry Hammond (governor of South Carolina, 1842-44; U.S. Senator, 1857-60), you see a continual (and in my view repulsive) degradation of political argument in which the insistence on the equality of all men is sacrificed to the insistence on the superiority of white skin. By the 1850s, slavery had long since gone from being a shameful problem the new leaders had inherited from the dark past to an institution in the service of which the leading Southern political and legal thinkers twisted, distorted, and bastardized the ideas of liberty and a constitutional republic. And as I pointed to briefly before, in the service of slavery the Southern political leadership was perfectly happy to muzzle free speech, ride roughshod over the "states rights" of Northern states, and insist on running the country their way, even though they themselves proudly admitted they were only one section of a larger nation whose sole interests were paramount; when Lincoln was elected, they knew they couldn't get their way any more, so they precipitously went to war like a band of aggrieved feudal nobles. This bundle of political ideas is what the Southern nation was founded on and it is those ideas by which it and its flag should be judged, not unfocused love of one's native county and folkways, which you can find on the cheap in every corner of the globe--and at the root of those ideas was the overriding need to defend, protect, and expand slavery.

And, hence, my statement that the Civil War cannot be reduced to "a war over slavery." I was taught in school that it is as simple as, "The Civil War was fought because the South wanted to preserve slavery, and the North wanted to end it." There is much more that is worth thinking about here, such as, should States have more or less autonomy, with respect to the federal government? And, can secession from an established country ever be morally justified?

What rights of Southerners (as opposed to the perceived political interests of the Southern sectionalists), and especially of Southerners in particular as opposed to people from other sections of the country, was the federal government infringing on before 1860? Forget the haggling over the tariff; this was couched in sectional terms by the 1840s and no one was arguing for its repeal, only for tilting it to the interests of one section or another. If you look dispassionately at the record, the most striking fact is that the federal government bent over backwards to support the slave system in the face of massive opposition by Americans outside the South (abolitionists within the South were gagged by law, of course, which tells us just how devoted to liberty the Southern slave-owners really were), and it was when this was threatened that Southerners rebelled. The fact is that it was an ideological battle, and both sides saw themselves as defending the principles of liberty and right and the good society, and thus no compromise was possible. But the good society that the Southern secessionists fought for was indissolubly linked to slave-owning, and the sectional interests that latter-day Southern propagandists play up, such as the tariff, were skirmishes over secondary issues, mere consequences of the fundamental ideas of the political systems of the North and the South.

My comments about the Tariff of Abominations and the North's primary motive being to preserve the Union were intended to support my thesis that there were other important issues besides slavery...

There were other important subsidiary issues, granted, some simply due to historical accident but most stemming from the fact that the Southern way of life was based on slavery.

- not to argue that slavery wasn't a very important influence upon the South's decision that political separation from the Union was the right way to go.

More than a "very important influence"--it was the fundamental cause. Don't glom all the different historical factors together in one mish-mash. Historical trends and forces are not all equal--some are basic and active over a longer time scale, others are their consequences and shift or fade away as circumstances change, and all are driven by the basic ideas of the historical actors.

Furthermore, that these issues are present cements the fact that there is a link between resistance to political injustice and the Civil War.

Political injustice--or disappointed sectional interest?

I tried (and failed, in a pinch) to find figures for the % of population enslaved before the formation of the CSA. But the fact that some states with a significant proportion of slaves remained in the Union (i.e. the border states), and that some states with relatively fewer slaves (I believe North Carolina and Tennessee, but again, could not find figures) joined the Confederacy, shows that the decision to join the Confederacy was not tied directly to the number of slaves in a state.

That's a very crude statement of the argument, verging in fact on a strawman. If you want to dabble in statistics, start with (1) the distribution of slaves within each state at the very least at the county level (or at the very very least find a map of the Slave Belt or Black Belt, or whatever it's called in a given state), and (2) the closeness of trade ties with the North. (For example, don't be misled by the importance of King Cotton in the Deep South--further north, where there were far fewer slaves, there was an extensive, long-standing trade in such products as pork and hemp. Pig drovers would drive caravans of pigs and other animals north from Tennessee and Kentucky into Indiana, for example, being joined along the way by hemp and other growers, to train depots for carriage to the East.) And then consider the secession of West Virginia from Virginia, the proposed secession of half of Tennessee from the other (Lincoln dissuaded its proponents from this plan), and the secession of Jones County (a.k.a. "The Free State of Jones") from the rest of Mississippi. And more basically, look at, for example, the failure of a generous plan of compensated emancipation that Lincoln worked hard on in Delaware, in which the 1800-odd slaves still owned there would have been bought by the federal government for $400 or so each. Despite the fact that Delaware was loyal and had by far the smallest slave population of any state, that didn't change the fact that many in Delaware saw themselves as a slave state and voted down the measure--only after which Lincoln turned to the Emancipation Proclamation. And don't forget that while the Emancipation Proclamation ended slavery eventually throughout the Deep South and most of the border states ended it by state act, it took the 13th Amendment to end slavery in Kentucky. The question was not whether they owned slaves and how many, the question was whether they felt they would continue to own slaves under a Republican administration and whether the federal government had the right to enforce its decisions by arms. Yes, there were subsidiary issues that criss-crossed the scene, but the fundamental question facing all Southerners was whether, how, and how much to defend slavery. (And the fundamental question facing Unionists was, if they won the war that had blown up in their faces, whether its fundamental causes would be solved if the seceded states were allowed back in the Union without renouncing slavery. The growing realization that they would not be was likely the major reason for the development of Lincoln's policies regarding slavery.)

"Being Southern" was a big part of the decision to rebel, and a big part of being southern was not being politically manipulated from a distance farther than the state capitol.

This is true. It was also a major factor in being manipulated to go to war against one's fellow Americans by the slave-owning powers in the state capitol, because it was a diffuse, often hardly intellectual sentiment that coexisted, however contradictorily, with the belief that it was right to own other human beings.

[My Room + My Car]

"Forcing"? Would you care to explain which measures you mean by that word?

Ah, wait, never mind. I thought you might be referring to such things as martial law and stationing federal troops in Maryland, which long predated any justification by the need to eliminate slavery, but I guess you were talking about the entire Civil War.

[My Room + My Car]

At face value, at issue in the Civil War was an increasingly tax-hungry and tyrannical federal government, and the fight for states rights. The fathers of Southern independence were certainly right about growing federal tyranny - look where we are now - and they were right about it then, too. The North had a history of imposing economic controls upon the South that put a damper on economic progress - see Tariff of Abominations. To me, and to many others, the Confederate flag is a symbol of resistance to unjust federal laws.

Regardless of what many of the soldiers in the field might have been fighting for, the leaders of the rebellion (i.e., the politicians who actually declared secession) actually saw the Republican victory as leading to the destruction of slavery through not upholding the slave system. A Republican administration could have appointed federal judges who would eventually have overturned the Dred Scott decision, refused to enforce the Fugitive Slave Act, eliminated the "gag rule" that prevented slavery from being discussed in Congress, allowed abolitionist tracts to be sent through the federal mail, and worked to prevent the further spread of slavery. (In other words, their rebellion was in reality resistance to the nonenforcement and eventual overturning of unjust federal laws.) The federal tyranny they saw looming before them was the "tyranny" of Northerners abolishing slavery against the will of Southerners (which was somehow very much more unjust than the federal government under Southern control enforcing the Fugitive Slave Act in the northern states and against what surely was the rights of the northern states to nullify the operation of a law they saw as unjust and an insult to the dignity of man, but "states rights" really just meant the right to own slaves, and "nullification" really just meant the right of Southern states to flout federal law):

"The rights of the South, and the institution of slavery, are not endangered by the triumph of Mr. Lincoln, as a man; but they are in imminent danger from the triumph of the powerful party which he represents, and of the fanatical abolition sentiment which brought him into power, as the candidate of the Northern section of the Union, over the united opposition of the Southern section against him. The party embracing that sentiment, has constantly enied, and still denies, our equality in the Union, and our right to hold our slaves as property; and avows its purpose to take form us our property, so soon as it has the power. Its ability to elect Mr. Lincoln as its candidate, shows it now has the power to control the Executive branch of the Government. As the President, with the advice and consent of the Senate, appoints the Judges of the Supreme Court of the United States, when vaancies occur, its control of the Executive power will, in a few years, give it control of the Judicial Department; while the constant increase of abolition sentiment, in the Northern States, now largely in the majority in Congress, together with the admission of other free States, will very soon, give it the power in the Legislative Department. The whole government will then be in the hands of our enemies....

"Second, What will be the result to the institution of slavery, which will follow submission to the inauguration and administration of Mr. Lincoln as the President of one section of the Union? My candid opinion is, that it will be the total abolition of slavery, and the utter ruin of the South, in less than twenty-five years. If we submit now, we satisfy the Northern people that, come what may, we will never resist. If Mr. Lincoln places among us his Judges, District Attorneys, Marshals, Post Masters, Custom House officers, etc., etc., by the end of his administration, with the control of these men, and the distribution of public patronage, he will have succeeded in dividing us to an extent that will destroy all our moral powers, and prepare us to tolerate the running of a Republican ticket, in most of th States of the South, in 1864...This would soon give it the control of our elections. We would then be powerless, and the aboltionists would press forward, with a steady step, to the accomplishment of their object. They would refuse to admit any more slave States to the Union. They would abolish slavery in the District of Columbia, and at the Forts, Arsenals and Dock Yards, within the Southern States, which belong to the United States. They would then abolish the internal slave trade between the States...These steps would be taken one at a time, cautiously, and our people would submit. Finally, when we wee sufficiently humiliated, and sufficiently in their power, they would abolish slavery in the States. It will not be many years before enough of free States may be formed out of the present territories of the United States, and admitted into the Union, to give them sufficient strength to change the Constitution, and remove all Constitutional barriers which now deny to Congress this power." (Public letter of Joseph E. Brown, 7 December 1860, who on the strength of it was elected Georgia's governor during the Civil War; the text can be found in William W. Freeling and Craig M. Simpson, eds., Secesson Debated: Georgia's Showdown in 1860, pp. 146-59; the passage quoted is pp. 147-9. The whole book is well worth reading.) Brown continued, by the way, to argue that the destruction of slavery would result in the impoverishment of all white Southerners, not only the large landowning class, for an attack on the property of some is an attack on the property of all. In other words, like many Southerners, Brown saw slavery as an essential, fundamental part of Southern society whose destruction would immediately entail the destruction of all the rest of the Southern way of life.

I think the issue that's really at hand, here, is whether the Civil War can be reduced to "a war over slavery." I don't think so. Southern slavery wasn't abolished by the North until well into the war, as part of the "total war" doctrine, and even then, border states kept their slaves.

In fact, this was because of the same constitutional barriers that Brown mentioned in the last sentence above, which Lincoln studiously observed in the Emancipation Proclamation by freeing only the slaves in lands in revolt once they had been reconquered; the border states were not in revolt and thus Lincoln had no constitutional authority for taking what was still constitutionally protected property.

Abraham Lincoln stated at the beginning that he was willing to endure slavery if the Union could be preserved;

Probably in part because of Fremont's failure in the 1856 election, widely thought to be due to his perceived willingness to court civil war in the name of free soil.

only later was slavery used, by him and others, as a justification for forcing certain states to remain in the Union.

"Forcing"? Would you care to explain which measures you mean by that word?

[Privacy and Sex]

Oh, I could well imagine something else being the reason. For example, you might not want other people to find out you have sex with a particular person--because they might tell your wife.

Or another conceivable reason, maybe the potential audience isn't willing to pay to watch and you won't put on a free show.

[Relativity question]

Suppose that I am moving at 25% the speed of light, and a spaceship that is 1 light year away is moving towards me at 75% the speed of light.

The basic question is: 25% and 75% of the speed of light relative to what? Velocities aren't simply additive, and to get the velocity of the other spaceship as measured in your reference frame you have to change frames. The frame you're saying measures you as having a velocity of .25c in turn has a velocity of -0.25c in your frame; in that frame the other spaceship is measured as having a velocity -0.75c, which would be measured as -(16/19)c (more generally, [v1+v2]/{1+v1*v2}, with v measured in units of c) in your reference frame. By the same token, you are measured as having a velocity (16/19)c in the other ship's frame.

By my point of view, that spaceship reaches me, and I conclude that it has moved 1 light year. By the spaceship's point of view, I have moved 1 light year.

After 19/16 years, yes.

But, due to time dilation, much less time has passed for the spaceship than it has for me.

Only when the elapsed time is measured in the third reference frame. You might want to work through a space-time diagram with all three observers taken explicitly into account and, as always, be very careful about simultaneity, which is frame-dependent.

Not only that, but the time that it took for that distance to close was less than one year...meaning that a distance of 1 light year had been covered in less than a year, from either point of view, due to time dilation.

No, from either point of view 19/16 years have passed.

How does this make sense, in the context of relativity? We both measured the speed of light to be more than it really is.

You're confusing yourself by bringing in a third observer without taking that into account in the math and then mingling measurements in his frame, your frame, and the other spaceship's.

[Why pursue pure science]

At the time of my post, I briefly forgot that Quatum Mechanics essentially entails all of physics at the atomic and subatomic level. Such study is obviously very important. I suppose I really wanted to know if particle/wave duality theory has led to any advancements in modern technology.

Electron microscopes. Neutron diffraction. The Compton effect (due to the particle aspects of photons) also has some uses in radiation therapy (and astronomy).

[Is there a "puritanical streak" among Objectivists?]

I am relatively new to the philosophy of Objectivism, but I have already observed what Leonard Peikoff calls a "...puritanical streak in many Objectivists." While he was not referring to this website when he made this statement (the context of which will be presented below), I have seen it in these message boards--specifically dealing with the issues of alcohol use and sexuality.

Since the copyright of Leonard Peikoff explicitly requests that none of his material be reproduced without permission, I will simply post the user-submitted questions from www.Peikoff.com that address these issues. Please navigate to the website and read his interesting responses.

For ease of searching, I'll just add that the first quote is the second question posted on November 1, 2006, and the second is the first question posted on March 12, 2007.

[The Art of Fiction and The art f Non-Fiction.]

I haven't read the non-Fiction book yet; but I agree that the Fiction one would be really helpful to a budding fiction writer.

I haven't read the one on fiction, but I have read The Art of Non-Fiction, which is, as you would expect, superb. It's good for improving your ability to read critically, too.

[Who Was The Greatest Military Leader Of All Time?]

Ghengis Kahn also brought good governments (he had a code of individual rights), but they were not well philosophically grounded.

Nonsense. He brought rapacious governments to settled areas in which the conquered peoples were usually divided up as the personal property of great Mongol lords in exactly the same way as they divided up conquered goods and livestock. In China, for example, there was a ruling elite of Mongols, a second class of Mongol administrators from outside of China (and thus loyal only to the Mongol overlord) called the semu ("colored eyes" in Chinese, usually Uyghurs or Iranians), a third class of subjects of North China (the regions of the former Jin dynasty, which having been conquered 40 years before South China were considered therefore to be more loyal), and then subjects of South China, who were excluded from most influence; below them were the slaves. Throughout the Yuan dynasty (the Mongol state that ruled China, 1279-1368, and the Mongol heartland until around 1400) in China there was a constant tension between the high Mongol aristocrats enslaving what remained of the Chinese population subject directly to the Khan, and the central government trying to maintain a stable tax base; in both cases the Chinese population was seen as little more than property to be squabbled over and to be milked for all they could yield. As for his law code (not "code of individual rights"), the Yasa, it does not survive even in part, but from what is known of it it was hardly a charter for individual rights but rather a draconian code governing relations among the Mongols to ensure swift obedience, certainly not something recognizing any rights of the conquered.

[Who Was The Greatest Military Leader Of All Time?]

Ghengis Kahn, for example, invaded the Ilkhanate empire when his ambassadors (who he sent to establish trade) were brutally murdered.

No. He invaded Khwarezm in 1220 after one of the Khwarezm Shah's governors killed Mongol ambassadors on the grounds they were spies (which Mongol ambassadors frequently were), and when Genghis Khan sent emissaries to demand the governor be put to death, he had the emissaries killed. While the state was quickly overthrown and the Shah forced to retreat until his death, the conquest of all of Persia took another thirty years or so. The Il-Khanate was not the state the Mongols invaded but the subordinate khanate set up by Hulegu, grandson of Genghis Khan, in 1255 to run the conquest of the Islamic world.

In the case of Persia, Alexander probably attacked Darius because he had arranged the assassination of his father.

The Macedonians under Philip had already set in motion the invasion of Anatolia to free the cities of Ionia from Persian rule; this Philip had proclaimed a campaign of all the Greeks to avenge the Persian invasion of Greece a century and more before, and it was as a symbol of attaining this goal that Alexander burned Persepolis. His later campaigns of conquest in Persia were undertaken, at least notionally, to avenge the murder of Darius by one of his lieutenants and restore the Persian empire (because the Greeks had been avenged, Alexander used this as a pretext for dismissing the Greek contingents and going on from there with Macedonian troops and various native auxiliaries), which he intended to rule through a fusion of Macedonian and Iranian culture and peoples, hence his adoption of Iranian court customs that the Greeks and Macedonians considered barbaric and repellent (such as the custom of proskynesis, some form of kneeling to the ruler, which was associated in Greek culture only with the worship of the gods).

[Who Was The Greatest Military Leader Of All Time?]

To me Ghenghis Kahn was clearly the most dominant military leader in history. Unlike Alexander who started with a well-prepared army handed to him, Ghenghis Kahn started with absolutely nothing, being born as an exile from his tribe and without a father.

Um, no, his father was poisoned when he was out searching for a bride for him. After that, yes, he, his siblings and half-brothers, and his mother (and one of his father's other wives, though she's almost entirely missing from the Secret History) were exiles.

Then he single handedly united a formerly nomadic people, then went on to conquer the largest land empire the world has EVER known, stretching across three continents, including the largest (and arguably the most powerful) and the second largest empires at that time - China and Russia.

No, he most certainly did not. He started the conquest of the non-Chinese state that ruled the North China Plain, the Jin dynasty (ruled by the Jurchens, ancestors of the Manchus who later ruled China under the Qing dynasty, 1644-1911), but this war was still going on at the time of his death. (He died in 1227, the Jin were finally conquered in 1234.) The conquest of most of China, ruled by the Later Song dynasty, did not occur until 1279 under his grandson Khubilai Khan. As for Russia (more precisely, Kievan Rus'), it was not really an empire at the time but a kingdom consisting of a congeries of cities and their surrounding territories, though I grant its territory was pretty large. The armies of Rus' were defeated by a small army under Subetei in 1223 that had been sent to scout out the area for future invasions, but the area was not conquered by the Mongols during Genghis' lifetime; that only came ten years after his death, 1237-40.

There really isn't any doubt in my mind that he could have also conquered Europe if not for the vast geographic distance from Europe to Mongolia, as well as Ghenghis Kahn's age and failing health.

The Mongols did conquer parts of Europe during the campaign of 1237-40, and they probably would have conquered much more if the Great Khan at the time, Genghis's son Ogedei, had not died, forcing the leader of the campaign, Batu, to return to Mongolia to ensure his candidate for Ogedei's successor was elected.

Actually Sun Zhu advocated all of that nearly 400 years prior to Caesar.

Who is Sun Zhu? I assume you mean Sunzi (Master Sun), whose personal name was Wu, not Zhu.

[Legal foundation for public decency, lewdness, nudity]

So you agree, that if someone projects a stimuli onto your property which objectively harms you, that this is an initiation of force? That it is not proper to expect you to plug up your senses, on your own property, to avoid being harmed by a stimulus that another is causing?

"A stimuli"!?! Oh, my eyes! My head! That hurt! And I couldn't just turn my eyes away from my own computer screen either. I think you owe me some damages.

[Should we have family names?]

If you want an ever expanding last name to appease the feminists, like Williams-Smythe (just wait until he maries Ms. Greenlough-Gunderson, and they name their kid Tiffany Williams-Smythe-Greenlough-Gunderson).

And then you get the sad case of Ivana Long marrying Pete Johnson and deciding to hyphenate the two surnames.

[Spartans: Two – Iran (née Persia): Zero]

This statement is just incredibly ignorant.

Did the author even bother pop open a book here?

C'mon; Ferdowsi, Rumi, Hafiz. Those are three of the world's greatest poets right there and they all wrote in some variety of Persian after the Muslim context.

Quite a bit of what is called "Islamic culture" is of Iranian origin.

Re-read the first sentence of the passage you quoted and then consider the second: "Second, Persian cultural accomplishments in literature, the decorative arts and architecture – great portions of them cadged or adapted from other cultures – were more or less nullified with the Arab/Islamic conquest of Persia in the mid-7th century A.D. Under the Muslims, much Persian literature simply vanished." Almost all pre-Islamic Persian literature was lost under Islamic rule, so his second sentence is in fact precisely correct.

[Grammatical error?]

In this case, the normative question on the table was whether the noun itself should have been "minds" rather than "mind" (thus the proffered rule was in sensu stricto irrelevant, as the issue is not at all about the pattern of agreement). In my view, the best way to understand this problem is in terms of the proposition that Rand intended to communicate (which doesn't seem to be at all in doubt), and then secondarily the best means of doing so. I can find no fault on the latter score, given my knowledge of the rules of English which govern how other people should be expected to understand her meaning. But naturally, even though I am a native speaker of English and Rand was, in fact, not, I am open to argumentation that we both misunderstand the nature of English grammar. That's why I'm waiting for a superior and more authoritative opinion on this matter of fact.

That would be mine.

Now, on to the serious stuff. First off, I agree with you wholeheartedly. However, I think there's more to say. As you pointed out, the grammatical point is whether (or perhaps which) English speakers distinguish the distributive and collective senses of the plural--that is, whether the plural is used to refer to each member of the group individually or to all of them as a group. Many do, including any number of great native-speaker English writers. Dismissing the distributive sense of the plural (which allows you to distinguish singlar and plural possessions of plural possessors) as ungrammatical does injustice to the many writers who have employed the distinction effectively--and if a dictum from on high prevents the reader from appreciating its use, then it's not a good rule for describing English grammar. It's a subtle distinction, however, and often people don't notice it, much less learn about it, when it's encountered while reading, but it can be used to very sharp effect. Here are some good examples from the Wikiquote page for William Hazlitt, a master of conversational prose, to get an idea of the stylistic issues involved.

First: "The slaves of power mind the cause they have to serve, because their own interest is concerned; but the friends of liberty always sacrifice their cause, which is only the cause of humanity, to their own spleen, vanity, and self-opinion." A nice parallelism there, with two sentences joined with a semicolon. You could say that each group has one cause shared by all its members (collective), or possibly that just as power or freedom is various, each member has his own idea of what his cause is (distributive), but I'd say the first reading is more natural. Going to the second half of each sentence, it would be a stretch to say he's implying that all slaves of power have the same interest (collective), though it's possible; and it's not at all sensical to say that all friends of liberty have the same self-opinion, so a distributive reading is required. So there is a contrast between the sense of the plural in each half of either sentence, collective in the first half and distributive in the second. Rather malaprop, no? Indeed no, quite the contrary. Consider the second sentence. Why do the friends of liberty sacrifice their (collective) cause? Because of their individual respective spleens, vanities, and self-opinions (distributive sense). The tension between the cause of the group and the motivation of each individual is brought home more forcefully by the contrast between the plural and singular.

Consider the effect if a singular were used in the second sentence: "The friend of liberty always sacrifices his cause...to his own spleen, vanity, and self-opinion." What is lost is the implication that this is a collective sacrifice, or better a mutual one, made as each individual friend of liberty plumps for his own spleen, vanity, and self-opinion. And notice that the spleen, vanity, and self-opinion only come into play because the friends of liberty form the same party and step on each other's toes; just as the sacrifice is mutual, so the grievances that trump the cause are with reference to each other as a group. And since this is contrasted with the cohesion of the slaves of power, who glom onto each other because their individual interests are served by the same cause, the use of the plural for parallelism all the better serves to point up the contrast between the two groups. (There's a secondary issue that the use of the singular in the second sentence allows spleen and vanity to be taken either as mass or count nouns.) You can see this especially when compared with this: "Anyone must be mainly ignorant or thoughtless, who is surprised at everything he sees; or wonderfully conceited who expects everything to conform to his standard of propriety." The singular is effective because it focuses attention on any individual who meets this condition; nothing is gained by speaking of them as a group because they don't act as a group; their mutual relations have nothing to do with their ignorance or thoughtlessness.

Second: "Those who make their dress a principal part of themselves, will, in general, become of no more value than their dress." In fact, this sentence is ambiguous--either dress is a mass noun throughout (meaning garb) or the second dress can be taken as singular (a particular woman's dress). Each reading has slightly different connotations--the former implies that they will have no value but their outer appearance, the second that their value reduces to their outfit, and by extension to their success in the futile battle of fashions and social striving. I suspect Hazlitt used the plural precisely to get both shades of meaning.

Contrast that with a third: "We all wear some disguise -- make some professions -- use some artifice to set ourselves off as being better than we are..." Surely we don't all wear the same disguise or use the same artifice, so a distributive sense is required here. This allows Hazlitt to contrast the disguise and artifice, which are singular for each of us, with the several various professions we might make, but he could have done the same by making it a singular sentence about "each of us." (I take "each of us" as sufficiently emphatic a parallel with "we all"; "everyone" would be too weak a fit parallel, though it would suit a simple "we.") The use of the plural "we" allows all the possessive pronouns to be first person rather than third person to drive his claim home--as it stands it is much more immediate than "Each of us wears some disguise -- makes some professions -- uses some artifice to set himself off as being better than he is..."

Now, against that background consider the sentence from Atlas Shrugged: "The only value men can offer me is the work of their mind." In the first part, "the only value men can offer me," it's still unclear whether men is a collective or distributive plural; are men a unitary group who can offer a collective value or are they a group of distinct individuals who each produces values separately? "The work of their minds" calls to mind a collective project whose value derives from its being cooperative, while "the works of their minds" could either be the individual works of each man separately or the various collective works of several men's minds (or all of the above). "The work of their mind" forces the distributive reading to excellent effect--the only value that all and any men can offer me is the work of their individual minds. Far from being ungrammatical, this sentence uses the resources of English masterfully and subtly.