I’ve been reading Francis Wheen’s How Mumbo-Jumbo Conquered The World, which is one of the most profoundly annoying books that I’ve read in the last few years. There’s nothing more frustrating than to read a book by someone who shares several of your pet aversions (trickle down economics, Deepak Chopra, obscurantist literary theory), but who isn’t bright enough to say anything interesting or non-trivial about them. It’s a rambling, shallow book which aspires to, and occasionally even attains, the intellectual level of a middling Sunday-supplement broadside.
There’s one unintentionally hilarious bit, where Wheen vigorously excoriates literary theorists for having been taken in by the Sokal hoax and then goes on a few pages later to deliver an extended harrumph attacking Paul Feyerabend’s Against Method. Wheen cites a passage where Feyerabend attacks the teaching of science in schools as a form of tyranny (in Wheen’s reading, Feyerabend is saying that we shouldn’t be teaching children that the earth moves around the sun; we should be teaching them that some people believe that the earth moves around the sun). What makes this delicious is that Wheen, like the literary theorists whom he’s been fulminating against a few pages previously, has been taken in by a provocation. If he’d bothered to read the preface of Against Method properly, he’d know that Feyerabend is deliberately and consciously putting forward as outrageous a set of examples as he can in support of a serious argument. The essay was originally planned as one half of a twofer, in which Imre Lakatos would try to top Feyerabend with an equally vigorous set of arguments on behalf of a somewhat more orthodox account of the sources of scientific progress. Sadly, Lakatos died before the project could be completed. Unlike the postmodernists (Irigaray, Kristeva) whom Wheen lumps him in with, Feyerabend was a trained scientist who knew what he was talking about, and was engaged in a very serious debate about the scientific method and its merits as a process of generating new discoveries. As an aside, Feyerabend also wrote one of the most entertaining autobiographies, Killing Time that I’ve ever read.
I don’t want to get this started again, but that article was found puzzling by the editors who published it, doing so because they believed, mistakenly, that its physicist author was writing in good faith. I doubt very seriously it would gave gotten through a blind peer review anywhere.
And Irigaray and Kristeva were engaqed in much different projects than Feyerabend. They can’t be directly compared in any meaningful sense, especially in shots of such cheapness.
So, they deliberately published nonsense they suspected was nonsense because the physics being presented supported their preconceived political notions?
Yup, that definitely lets them off the hook.
Jonathan - I agree that the Sokal hoax didn’t prove everything that Sokal claimed it proved - but at the same time, I think that it’s perfectly fair to take potshots at Irigaray, Kristeva etc. If someone tries, like Kristeva, to invoke Hilbert spaces in her academic work, it’s not at all unfair to expect that she should actually understand what she purports to be talking about.
I don’t know, Jonathan. Have you ever read an issue of Social Text? The crazyness in Sokal’s phony article is pretty par for the course. The defense that the editors offered, and that you echo — namely, that they were puzzled by the argument but deferred to Sokal’s impressive credentials — is pretty lame. Surely the job of an editor is to exercise critical judgment, not to defer to authority.
Ehle, I’m sure I’ve probably read more issues of Social Text than anyone commenting on this thread. And I don’t know what you’re talking about, but if you have examples, then great.
Henry, were you reading something by Kristeva that invoked this irksome concept, or is your ire aroused from reading something that someone wrote about Kristeva? Remember how the telephone game always turns out?
“Preconceived political notions” are one thing. An unfamiliar perspective on issues of mutual interest to a scholarly community in a journal issue devoted to that topic is another.
I’ll bite. What is Paul Feyerabend’s serious argument?
On a similar note, I will observe that Feyerabend is one of the most frequently abused, yet least read, philosophers of the latter half of the 20th C.
Synopsis:
http://www.marxists.org/reference/subject/philosophy/works/ge/feyerabe.htm
A hero of mine. Example: If you’d said the word ‘aether’ to an astrophysicist in the last 80 years, they’d have laughed down their sleeve and kicked you out of the door. Funny, then, how ‘dark matter’ and ‘dark energy’ are quite acceptable terms today.
“Against Method” is a great, if sometimes tongue-in-cheek, argument that the conduct of science is anything but rational.
It’s also worth pointing out that one of the things we do know about the universe is that under general relativity, a heliocentric frame of reference and a geocentric one are both exactly as valid as each other. As WVO Quine pointed out, score one for Papal infallibility.
(An argument that Feyerabend never made, but I like to think he would have appreciated, is that Astrology is the quintessential Popperian science; it makes twelve specific falsifiable predictions every day and gives them away with the newspapers.)
I’ve rarely regretted money spent more than the money I spent on Wheen’s book. That’s a great second sentence you’ve got there on it. It’s really an awful book — thin and pompous, like a George Will article more than anything else.
Geocentric model is more valid than heliocentric because it’s empirically observable - and without any instruments; anyone with a pair of eyes knows that it is a correct model. Heliocentric model a confusing elitist perversion.
Probably the most pathetic set of comments I have ever had the misfortune to read onthis excellent site. Trite is an understatement. Only the original point about Feyerabend and Lakatos has any explanatory value. The pathetic snipe at Popper beggars belief. When the twelve falsifiable predictions are falsified most of us get the message about astrology.. most of us.
Jonathan, I also wondered about the point you raised and went for a look. I couldn’t find an exact instance of Kristeva citing Hilbert spaces, but I did find this survey article, not a hoax as far as I can see, which seems to support Henry’s general point.
Key quoteLacan has made use of topology to explain such things as the structure of the psychic apparatus by using borromean knots, Mobius bands, the torus, and projective geometry (the cross-cap) (see also Milovanovic, 1993b, 1994c; Granon-Lafont, 1985, 1990; Vappereau, 1988; for an introduction to topology theory, see Hilbert and Cohn-Vossen, 1952; Weeks, 1985; for non-Euclidean geometry, see Russell, 1956). In fact, in 4-D space the borromean knot of Lacan is no longer knotted. The cross-cap, which topologically portrays the working of schema R and how desire is embodied as a result of the effects of the Symbolic, Imaginary, and Real Orders, can also be presented in 3-D or 4-D space (Milovanovic, 1994c; Hilbert and Cohn-Vossen, 1952). It is not without effect when we move from 3-D to 4-D space (Rucker, 1984; Banchoff, 1990; for the contributions of nonEuclidean geometry and 4-D space on cubism in art, see Henderson, 1983). Much needs to be done in the analysis of the effects of these novel conceptions. Thus, for the postmodernists, several notions of space are currently being explored and incorporated in their analysis of the subject, discourse, causality, and society: multiple dimensional (Peat, 1988), fractal (Mandelbrot, 1983), holographic (Talbot, 1991; Bohm, 1980: Pribram, 1977), enfolded/implicate order (Bohm, 1980; Bohm and Peat, 1987), cyberspace (Gibson, 1984), hyperreal (Baudrillard, 1981), smooth space (Deleuze and Guattari, 1987), twister space (Penrose, 1989; see also Peat, 1988), and topological (Lacan, 1976, 1987a; Peat, 1988; Granon-Lafont, 1985, 1990; Vappereau, 1988; Milovanovic, 1993b, 1994c; Lem, 1984).
According to Kristeva, “one can situate the chora and, if necessary, lend it a topology, but one can never give it axiomatic form.I’ll admit to having used “topology” in metaphorical senses myself, but this is either a howler (if meant seriously) or a badly mixed metaphor. Giving a space a topology means defining a family of open subsets that satisfy four axioms
John, not only is that article not written by Kristeva, she is not cited therein.
What kind of “blogosphere” would we have if people confined themselves to commenting on books or articles that they’ve actually read? We couldn’t even imagine the shape of that future, that’s for sure.
Jonathan, I don’t understand, is it really not Kristeva’s quote, or are you just complaining that the article JQ cited cites a secondary source? This site cites this quote directly.
Jonathan, the Hilbert spaces example is in Sokal and Bricmont’s Fashionable Nonsense along with umpteen other demonstrations of Kristeva’s abuses of mathematics (it’s also mentioned in passing in the Wheen book that I’m giving grief to). As I say, I don’t think that the Sokal hoax proved what Sokal thought it proved - if a political science journal received a submission on physics from a well-known physicist they would have had trouble in reviewing it too - but you seem to me to be trying to defend the indefensible. Sokal demonstrates, using copious quotes, that Kristeva simply doesn’t understand what she is talking about. Frankly, you’re on a loser here - as John Q.’s quote shows, the facts emphatically contradict your thesis - Kristeva does demonstrably garble the math, your assertions to the contrary. I think that it’s possible to defend the obscure language of literary criticism in some instances (we can quarrel over which instances) - but on literary critics’ attempts to subsume mathematical terminology (and prestige), Sokal is absolutely right.
If you really want to defend Kristeva etc against Sokal, you need to do more than cover your ears and shout bias - you need to provide a convincing explanation of why Kristeva is right, and Sokal is wrong.
Brad - my two sentence interpretation of Feyerabend’s serious argument is that he’s arguing against both Popper’s falsificationism, and Lakatos’s more sophisticated attempt to justify the model of scientific inquiry. He tries to demonstrate that all the varied attempts to pull the scientific method up by its own bootstraps fail conceptually (and also fail to describe very well how actual knowledge is generated). The book is well worth reading - but should be read in conjunction with his correspondence with Lakatos. The autobiography is even more fun - he comes across as complicated, difficult, but very warm and human.
John Quiggin says: “Giving a space a topology means defining a family of open subsets that satisfy four axioms.”
Actually, the two first two axioms listed in the link are totally unnecessary. Since the empty collection of sets is a collection of sets (and it is indeed finite), then the first two axioms are consequences of the last two. But this is horribly pedantic on my part—if Wolfram’s definition annoys me, imagine what Kristeva and company can do!
On the other hand, I don’t feel inclined to dismiss the intellectual contributions of literary critics en masse, simply because some of them have only silly things to say about Hilbert spaces.
It’s also worth pointing out that one of the things we do know about the universe is that under general relativity, a heliocentric frame of reference and a geocentric one are both exactly as valid as each other.
In the geocentric model, the Earth does not rotatye. In the heliocentric model, the Earth does rotate. The distinction between a rotating and non-rotating frame still exists in general relativity, and the question of whether a frame is rotating or not can be answered by purely local measurements (such as the Foucault pendulum). These experiments show that the Earth is rotating.
There is a real, measurable difference betwen the geocentric and heliocentric systems. General relativity doesn’t make that go away. Specifically, relativity postulates that all non-accelerating, non-rotating frames are equivalent. That is very different from the assertion that all frames are equivalent - an assertion which a few minutes spent standing up in a bus will show to be wrong.
Pedro:
I’m took the relevant course some time ago, but I think you’re wrong.
Say X = (0,1) and T = {S=(.25,.75)}
a. We have S\subset X, so T is a collection of subsets.
b. S/\S = S is in T
c. S\/S = S is in T
So 3 and 4 are satisfied but 1 and 2 aren’t, and T isn’t a topology.
I’m defending Kristeva from quote-miners and their epigones. Sokal and Bricmont combed a lot of theory books looking for scientific and mathematical metaphors they could then argue were being used fuzzily, as they almost certainly were (nb: I never claimed otherwise). My point is simple: so? Do you think this sufficient evidence to dismiss whole volumes of work you haven’t read? How would you know how integral those metaphors are to the larger argument? Would you want that standard applied to your work?
I’m afraid your T doesn’t satisfy axioms 3 and 4. The empty collection of sets belonging to T is still a collection of sets (and finite, indeed). According to axiom 3 (or 4, I forget which), the union of the empty collection of elements of T should be in T. But this is clearly not the case, because the union of the empty collection is the empty set, and the empty set is not in T. (More interestingly, the condition of closure under taking finite intersections guarantees that X is in T.)
mg,
perhaps it helps if I write A={} is a finite collection of elements from T. The union of A is the empty set. The intersection of A is X.
Wait, wait.
A={} is surely a subset of T, but condition 1 requires that it be an element of T.
If A = {}, for my T to satisfy 3, for instance, with reference to A, we would need that S/\{all elements of A} be in T if A is finite(and it is). This is true since S/\{all element of A} is simply S.
Jonathan,
Well you previously seemed to argue that the quotes in question were misattributed.
How would you know how integral those metaphors are to the larger argument?Judging by the couple paragraphs surrounding the topology quote, it’s not at all integral to the larger argument, which makes one wonder what it’s doing there in the first place(the same goes for “discrete energy” which has unclear meaning, and again, no relevance, or so it would seem).
I’d argue that it makes sense to tentatively conclude that if some portions of the text evidently aren’t thought through, others aren’t either.
Would you want that standard applied to your work?Whether I liked it or not, it was every time I submitted work in, say, my undergrad Analysis course.
I realize that you didn’t ask me specifically, but I of course would like a PhD in Physics from a good university to proofread everything I write.
S/\{all element of A}
I got confused with sets of sets notation as well.
By the above I mean S(n), where A = {A(1), A(2), …, A(n)},
S(0) = S, and S(i) = S(i-1)/\A(i).
Do you think this sufficient evidence to dismiss whole volumes of work you haven’t read?
It seems to me that you’re labouring under a misapprehension (at least in part caused by my writing). When I say that “Feyerabend was a trained scientist who knew what he was talking about” and that Irigaray and Kristeva don’t, I mean that they don’t know what they talk about with respect to science - I’m not dismissing them wholesale. That said, I don’t think they can be let off the hook completely by any means - it doesn’t say much for their standards of argument that they grab and abuse concepts without understanding what they actually mean. Relates back to John Holbo’s criticisms of Zizek etc - they’re using theoretical concepts more for ornamentation and protection (hermit-crabbery of discourse) than for their actual content.
Jonathan, I didn’t say that Kristeva’s work should be dismissed in toto. I was interested in the factual question “Does Kristeva invoke mathematical concepts she doesn’t appear to understand?” or has she been misrepresented by Sokal and others on this score. For this purpose, I think the kinds of answers provided by Google are satisfactory.
mg: {} is a collection of elements of T, even if it consists of zero elements from T.
Axiom 3: The intersection of a finite number of sets in T is also in T.
Axiom 4: The union of an arbitrary number of sets in T is also in T.
The union of the empty collection {} is the union of exactly zero sets in T. By the definition of the union of a collection, it is trivially the empty set.
The intersection of the empty collection {} is the intersection of exactly zero sets in T. By the definition of the intersection of a collection, it is—not so trivially—the full set X.
To be fair, mg, it’s easy for people to get confused when thinking about the union or the intersection of an empty collection of sets. That’s why Wolfram decided to add those two redundant axioms 1 & 2 to begin with. But they are unnecessary, because 1 follows from 4 and 2 from 3. I googled “intersection of empty class” and I found a link to a forum in which a confused reader of a basic topology book asks for help understanding these points I’ve been making. The link is here.
Pedro — I think I understand what you’re saying now.
A question, though. A reasonable(I think) definition of intersection of a collection C is{x|((c is in C) => (x is in c))}
Now if C={}, the intersection of all the elements of C would be X if the definition were
{x in X|((c is in C) => (x is in c))}
That’s reasonable enough, but it’s not generally understood that that’s the definition.
I think that that’s the reason the first two axioms are included.
(Crosspost)
OK, I think this is as resolved as can be, though thisSo all x (in X, for this is your domain of discourse) fulfill the second condition, so the intersection is all of X.
Sounds too close to Kristeva for comfort.
mg—I think you got it. But your first definition needs to have a universe of discourse implicit in it. Allowing elements to vary indefinitely gives rise to troubling paradoxes in set theory. The reasonable definition for the intersection of a collection of subsets of X is indeed your second definition.
Again, how do you know how they’re using these concepts if you haven’t read the work entire? How about if the entire argument of the book involved misappropriation? How would you know? This was my original point: Kristeva and Irigaray worked within a tradition which allowed for (and expected) extended metaphor and nebulous gesture. Lacan and Deleuze went far beyond either of them in terms of stretching ill-understood science and mathematics to conceptual rupture. But the alarm that Sokal and Bricmont sound is far removed from their intent (and accomplishment).
Pedro — thanks for your time, BTW.
mg: no problem!
Dsquared: That may quite possibly be the funniest web site I’ve ever seen. Especially this quote (not by Irigary):
“The privileging of solid over fluid mechanics, and indeed the inability of science to deal with turbulent flow at all, she attributes to the association of fluidity with femininity. Whereas men have sex organs that protrude and become rigid, women have openings that leak menstrual blood and vaginal fluids… From this perspective it is no wonder that science has not been able to arrive at a successful model for turbulence.”
I’ve had nose bleeds. Does that make me more likely to solve the problem of turbulence than a man who has not? Since solving turbulence (the Navier-Stokes equations) is a Clay Millenium problem with a million dollar prize, I hope she’s right.
“Actually, the two first two axioms listed in the link are totally unnecessary. Since the empty collection of sets is a collection of sets (and it is indeed finite), then the first two axioms are consequences of the last two.”
NO NO NO!
Suppose you don’t have the first axiom. Then {X} would be a topological space.
Or suppose you don’t have the second axiom. Then {e} would be a topological space (where e is an empty set).
So the first two axioms are not redundant.
“where e is an empty set”
where e is the empty set, of course
Andrew is right.
“Since the empty collection of sets is a collection of sets (and it is indeed finite)…”
Well okay, but the most natural way to read axiom 3 is so that this reasoning does not apply. “A finite number of sets in T” excludes the empty collection of sets.
Suppose one had written, “The intersection of a finite number of sets X1, X2, …, Xn in T is also in T.” I think most mathematicians would find it pedantic if someone said, “Well n could be equal to 0.”
“There’s nothing more frustrating than to read a book by someone who shares several of your pet aversions (trickle down economics, Deepak Chopra, obscurantist literary theory), but who isn’t bright enough to say anything interesting or non-trivial about them.”
Heaven forfend that anyone try to show a broader audience than, say, academics and socialists why these ideas might be wrong.
And heaven twice forfend that anyone should put together a bunch of arguments well known to professionals in a single place, in a work of popular journalism - they might run the risk of not titillating your sensibilities.
“nothing more frustrating”?
You really are the most pretentious ass!
“Heaven forfend that anyone try to show a broader audience .. why these ideas might be wrong.”
But that’s precisely the trouble with Wheen’s book — it isn’t addressed to a ‘broader audience’. It’s not designed to change the minds of people who believe in mumbo-jumbo; it’s designed to flatter the prejudices of people who don’t.
Brad, my way of putting the same point that Henry makes above, is that Feyerabend is arguing against the implicit authoritarianism of Popper. I don’t use the expression ‘authoritarian’ as a pejorative, only as the description of a project.
Popper great self professed motivation was to seek to demarcate science from nonsense - or non-science. Examples of the former being physics of the latter Marxism and Psychoanalysis. Feyerabend argues that Popper fails and that the project to come up with rules of demarcation is doomed to failure - that one cannot successfully tie down the refined professional commonsense by which scientific consensus moves to a set of rules.
There ain’t nothing that you can say in advance isn’t scientific. It requires judgement to decide whether something is scientifically plausible or not, you won’t succeed if you try to legislate the boundary with rules. That’s what I always took to be his argument. Seems to me that he won it too.
Walt Pohl and Andrew Boucher rephrased: if you want to know anything about anything, you must either make an appointment with one of the sciences or else be content to be cheated. Outside the sciences there is no information. The poets may beguile you or exalt you but they cannot tell you anything. Theologians may bewilder you, philosophers may rack and rhetoricians may soothe you. But none of them can tell you anything.
“Suppose one had written, “The intersection of a finite number of sets X1, X2, …, Xn in T is also in T.” I think most mathematicians would find it pedantic if someone said, “Well n could be equal to 0.” “
While I like the inclusions of axioms one and two for the sake of clarity, All of my professors and most of my fellow grad students would have no problem saying n could be zero. It certainly wouldn’t be the most pedantic thing we had ever done.
Andrew Boucher is wrong, of course. Zero is indeed a finite number.
What Andrew C. said - not only is the Wheen book written to flatter the prejudices of those who already agree with him, it’s pretentious to boot, promiscuously dropping the names of Marx, Tawney, Hume etc at every opportunity. Frankly, it’s you who is being condescending here, by assuming that a book written for a popular audience can’t be intelligent and say interesting things. If anyone’s looking for a popular book that addresses some of the same topics but is well written and smart, I can’t recommend John Sladek’s The New Apocrypha enough. It’s a little outdated at this stage - but UFO cultism, homeopathy etc are hardy perennials. I only wish he’d had a chance to write about David Icke before he died.
Pedro: in my example would you correct someone and say, “n can equal 0” ?
Pedro, the Wolfram defintions are indeed slightly unparsimonious. As Wikipedia and others do you could insist only that intersections of pairs of elements in T were also in T and then deduce that finite, in the sense of one or more, intersections were also in T.
However the Wolfram definitions do not imply that X is in T, we don’t know that every element of X is contained in an element of T, nor is it necessarily usual to insist that zero is a finite number in situations like this. By your definition the statement “All finites subsets of elements of T contain only elements of T” would fail if T didn’t have the empty set as an elemnt. Basically intersection is not defined for less than two subsets. These distinctions can become important in various constructions and abstractions.
dk.au, you’ve seen someone take an inch and accused them of taking a mile. If your rephrase is what they meant I’m sure they would have said it.
Yeah, jack is right. Though zero is indeed a finite number, it often behaves exceptionally and should be treated differently. For instance, are intersections of finite sets finite? I think you should say yes, rather than a pedro flavoured “no”.
Besides, a minimal set of axioms is by no means the most desirable and clarity should trump parsimony every time.
Yeah, jack is right. Though zero is indeed a finite number, it often behaves exceptionally and should be treated differently. For instance, are intersections of finite sets finite? I think you should say yes, rather than a pedro flavoured “no”.
Besides, a minimal set of axioms is by no means the most desirable and clarity should trump parsimony every time.
Yeah, jack is right. Though zero is indeed a finite number, it often behaves exceptionally and should be treated differently. For instance, are intersections of finite sets finite? I think you should say yes, rather than a pedro flavoured “no”.
Besides, a minimal set of axioms is by no means the most desirable and clarity should trump parsimony every time.
Walt, I think you actually are being a little unfair to that quote. It seems pretty inarguable that whether a mathematical problem is solved may depend not only on its intrinsic difficulty but on how much effort is spent on it. Hayles attributes to Irigaray a sociological explanation of why more collective effort has been spent on solid than on fluid mechanics. That explanation wouldn’t entail that any individual would be more skilled at any particular problem.
Now, I doubt that Irigaray has done the research to establish the truth of this explanation, and I suspect that she’s talking through her hat somewhat. The linked author seems to think that there are also valid points to be made about whether progress could be made on the problem with cellular automata, circumventing the Navier-Stokes equations. The whole New Kind of Science thing makes me suspicious here, though.
I would submit, Andrew, that your example invokes misleading notation. The intersection of any finite number of subsets of X belonging to T can be written as A_1 int A_2 int … int A_n only if you make the provision that n can be taken to be zero, and that in such a case, you mean to be taking the intersection of the empty collection of subsets of X belonging to T. After all, the statement invokes any finite number of elements in T. You may take the position of excluding zero as the possible cardinality of a finite collection of sets, but that is rather artificial and completely unnecessary. Insisting that adding the redundant axioms is somehow wrong would be totally pedantic, but insisting that they are not redundant is rather pedantic as well—particularly so, because it contradicts the professional opinion of many logicians, set theorists, and topologists.
Jack: there are two different intersection operations involved. One is at the level of sets. The other, which is the one Wolfram refers to (since Wolfram talks about the intersection of any finite number of sets), is the intersection of a collection of sets. The intersection of a collection of subsets of X belonging to T is defined naturally as the set of all elements in X which belong to every element of the collection. By elementary logic, the intersection of the empty collection of subsets of X is X. And since the empty collection of subsets of X is indeed a finite collection of subsets of X belonging to T (it consists of exactyly zero subsets of X belonging to T), then its intersection must belong to T.
I wonder if—psychologically—my calling myself “pedro” (with a lower case p on top of the “ethnic” reference) makes people not take seriously my opinion. I wonder what would happen if I signed with a different name, like John Webster. ;)
Oh, and there’s nothing wrong with starting with intersections of pairs of sets. It’s simply not the way Wolfram’s axioms are stated.
armando: intersections of finite sets are indeed finite! It is intersections of the empty collection of subsets of a set X that behaves oddly.
Feyerabend’s basic point in all his writings was that scientists can get on perfectly well with the business of doing science, thank you, without philosopher-nannies instructing them as to how they “should” be doing it. A point of view that more conventional philosophers understandably dislike, but one with which few scientists should feel disposed to quarrel.
But pedro, what about intersections of finite subsets of the natural numbers? You can be consistent here only at the cost of having to say some pretty horribly unituitive things.
I’m pretty sure we utlimately agree here, and its not that you are incorrect - you are perfectly correct, actually - but the point you make is awful in terms of clarity. I reckon that your point about excluding zero being artificial is where I have the complaint - it seems pretty natural to me.
pedro - Please no hard feelings.
Pedro,
You’re inadvertently supporting the general thrust that one shouldn’t critique areas where one is insufficiently knowledgable. ‘Course the stands of blog are a smidge lower than academic ones so we’ll likely let it slide. :)
I’ll clear things up as best I can. Consider the set S = {x, y, z}. Here are some topologies on S:
1) the simple topology T1:
{}, {x, y, z}
2) the discrete topology T2:
{}, {x}, {y}, {z}, {x,y}, {x,y}, {y,z}, {x,y,z}
3) another topology T3:
{}, {x}, {x,y}, {x,y,z}
Note that each of them contain the empty set {} and the entire space {x,y,z}. Note further that if you intersect any finite number of them you get a set that is already listed. Finally note that if you intersect any number of then you get a set that is already listed.
The following is not a topology of S:
{x}, {x,y}, {x,y,z}
because it does not contain the empty set. Note that no combination of intersection or union operations on the above sets will yield the empty set, because x is an element of each of them.
Lastly, consider the following non-topology of S:
{}, {x}, {y}, {x,y}
This does not contain S={x,y,z} and you cannot construct S from it because none of the above sets contain z.
Cheers,
Scott
“The following is not a topology of S:
{x}, {x,y}, {x,y,z}
because it does not contain the empty set. Note that no combination of intersection or union operations on the above sets will yield the empty set, because x is an element of each of them.”
…except, of course, the union of the empty collection of the above mentioned elements, which is the empty set. One can argue, then, that the above collection is not a topology because it is not closed under taking arbitrary unions.
andrew—no problem.
armando: good catch. Intersections of nonempty collections of finite subsets are finite.
scott swank: what on earth gives you the idea that it is I who is insufficiently knowledgeable about these matters?
The more substantive point: People can be incredibly pedantic and possessive about their field of work. I was particularly disgusted by the quotes I read in Sokal’s attack on postmodernist mumbo-jumbo. But as soon as I educated myself a bit more on particular trends in literary criticism, I learned not to be quite as dismissive as others are about some of the ideas circulating in English departments. I still feel a general repulsion for Lacan, and more generally for theory, as it is articulated by its exponents: Zizek, Derrida, etc. And yet, I seriously believe that new historicist scholars of the Renaissance—for example—are very illuminating to read, and that the underlying assumptions about the dynamics of culture that operate in their work are far more sensible than one would expect from reading the quotes selected by Sokal.
Oops, I listed {x,y} twice in the discrete topology instead of listing {x,y} and {x,z}.
In any case Pedro, I missed your suggestion that the empty intersection always yields the empty set. This is in fact true, and can be used to construct a topology from a “spanning subset” for that topology. So, for example,
{x}, {y}, {z}
is a spanning subset of the discrete topology of X, T2. From these three sets you can construct all of the sets the comprise T2. That does not mean that those three sets are the sets that comprise T1 — this is the crucial distinction.
Cheers,
Scott
pedro I actually agreed with you that Wolfram’s axioms were slightly sloppy. However you still need at least three — you can’t deduce that X is in T — and actually it is undesirable to use a definition of intersection that lets the empty set in through the back door.
For preference the axioms should make it transparent that the topology is a lattice and rolling the null set axiom into the intersection/closure algorithm is not helpful. Nor does it work well with the dual definition. It is for that reason that I preferred the Wikipedia version.
Dk.au: Huh?
Matt: I think you’re giving them too much credit. They claim a fact, with no evidence, and then they invent a bullshit theory to explain the fact. People have been studying fluid mechanics intensely for a century. It turns out it really is hard.
Final verdict on the topology axiom question: if you allow for finite to include zero, then Pedro is right, you can drop the empty set requirement. If you invent a new intersection operation “intersection of subsets of a set X”, then you can drop the requirement that X is in the topology. If you use the usual meaning of intersection, then Andrew is right, and you need to require that X be a member of the topology, otherwise {e} would be a valid topology on a non-empty set.
scott: I’m afraid I didn’t say that the intersection of the empty collection of subsets of X is empty, but that it is the entire underlying set X. mg wrote down somewhere on the thread a perfectly reasonable definition for the intersection of an arbitrary collection C of subsets of a set X:
{x in X|((c is in C) => (x is in c))}
If the collection C is empty, then the implication in the definition is true for any x in X. Hence every element x in X belongs to the intersection of the collection.
pedro: you’re right on the intersection of a collection - but Wolfram didn’t mention the intersection of a collection.
Anyway, I think by the principle of self-reflection, pedro wins, in the sense that if there is this much back-and-forth over a definition, the definition is lacking.
jack: I believe it perfectly sensible to say that the infimum over the empty set of real numbers is positive infinity (which is a piece of folklore about the empty set with which many people are familiar).
I believe any peculiarity arising from the inclusion of the empty collection can be avoided by quantifying over nonempty collections. For example, it is not uncommon to say that a vector lattice X is Dedekind-complete if every nonempty subset of it has an infimum and a supremum in X.
Granted, you can make a choice. You can have aversion to quantification over empty collections, and save yourself the trouble of thinking about them. Some people, however, are extraordinarily careful about the empty set. I know of at least one outstanding mathematician who cannot stand it when he discovers that the “theorem” written on the blackboard has a trivial counterexample.
Although Feyerabend is (IMHO) correct about the failure of the Popperian project as described above, I still always found him annoying. He’s too obviously trying to be provacative whether or not he needs the flamboyance to make a point. If he posted on a blog you’d call him a troll.
Besides, I’ve always found Quine quite sufficient to handle the whole falsificationism bru-ha-ha.
Defenders of Larry Summers point out that it is likely that there are differences between the brains of men and women and logically possible that these could have a role in explaining the lack of women in science departments. So he is not, prima facie, wrong.
However in making his statement he has seemingly ignored what people who have considered this rather old notion have found out and has implicitly deprioritised tackling other factors where it seems more likely that progress could be made On balance he seems to be at odds with current knowledge and therefore unable to make his argument stand up.
From someone in his position and with his credentials we might have hoped less philistine.
I think the negative feelings his statements aroused are similar to those aroused in people sympathetic to Sokal et al. I’m sure that as with Derrida, at some level the man himself is much less idiotic than his travestied received persona. It is not clear that the travessties in this case are any less serious from a philosphicalpoint of view than is pop Popper but pop Popperians don’t pick on Physics or maths much.
I wonder if the whole difficulty actually arises because maths is much more familiar to the French and they therefore feel more able to play fast and loose with it. It is impossible to get far in the French educational system without doing quite a lot of maths. France is one of the few countries in the world where mathsis a cool subject that might get you dates. (Singapore and the former Soviet Union being the only other examples that spring to mind)
BTW the cellular automaton example is a crock. Like fractals, they were useless computationaly until the advent of the digital computer. They were invented by one of the inventors of both the atomic bomb itself and the strategy used to deploy it. The discoverers of the application of cellular automata to fluid dynamcs were men.
There might be significant gender relate issues with maths but better examples are needed. PZ Myers point that the brain is not hardwired for advanced math and the novelty of discoveries in the field mean both that any gender differences are extremely subtle and that knowing what would have been different if more mathematicians had been women is extremely difficult.
In any case while the example of men being solid while women are fluid is plausible if stereotyped, the extension of this metaphor to turbulence seems forced.
…more serious from a philosphical point of view than pop Popper.
I guess it’s appropriate that a post about Feyerabend, that great philosophical troll (not that that’s a bad thing at all) also allows Adequacy.org to continue trolling people three years after it shut down. Surely it’s obvious that that article is a joke from the moement it refers to Wolfram as a ‘noted genius’?
Oh, and BTW, if you want a French philosopher who uses maths (in particular, set theory) and knows what he’s talking about, check out Alain Badiou. His Lacanian discussion of non-constructible sets is very good indeed.
Tim F: That adequacy.org post was a joke? Fooled me, though I never heard of the website before.
Jack: What math does the average person study study in France that they don’t study elsewhere?
Jonathan quotes this news story
under the title:”Today’s Irrelevant Clause”
In Trier, Germany, birthplace of Karl Marx, the prosecutor’s office has been investigating the claim of a woman that babies were being cut up and eaten in Satanist rituals.
As I tried to remind him, it’s a story. The mention of Marx is merely a means to pull people in; It’s a rhetorical device, a little silly but as I noted, if Walt Disney had been born in Trier they might have used him.
It is in fact very hard to tell what part of any structure is irrelevent to its function. Do do so you have to decide what that function is. What is the function of a news story?
To communicated factual information? To entertain? To make money for the publisher?
I find very little difference between any of you, and your arguments, between Sokal and the idiots at Social Text. All of you are trying to find ways to turn ambiguity into something managable, something concrete, something to which you can apply simple numbers and/or rules. What is economics but a set of assumptions? At what point do those assumptions become unsupportable? You all find ways to generalize from specific cases, and you do it in ways that are either over-simple or perfectly arcane.
You might as well be race car mechanics.
None of you value the specifics of things, the tastes and smells. A cook deals in specifics, an actor deals in specifics, a lawyer deals in specifics. A poet writes in untranslatable specifics. But for the academy everything must fit within a generalization. And when the generalization defines the thing, the thing, as a specificity, no longer exists. And what’s worse, every mediocre graduate student and cow-town professor must be able to make such generalizations. Every holder of a Ph.D must be able not only to teach important problems but to solve them!. Every assistant professor must have an original mind. And they don’t.
My mother gives perhaps the worst performance of Bach on the piano that I have ever heard. She plays the notes, unable or unwilling to take the indulgence of adding any variation, any idiosyncratic gesture that might make the playing personal. She refuses to perform</> as if by performing she would become merely a specific thing in time, a part of the world, unaware, un-intellectual.
If you can’t understand specifics your generalizations will be meaningless. And if you can’t play Bach as if you wrote the music yourself you’ll never understand the music he wrote.
The value of this is what Alan Sokal disputes. And what disgusts me is that nervous professors in the humanities are worried that he’s right. Why else would they indulge in pseudoscientific bullshit except in a desperate attempt to find a way to say that they too are worthy of respect.
Jonathan quotes this news story
under the title:”Today’s Irrelevant Clause”
In Trier, Germany, birthplace of Karl Marx, the prosecutor’s office has been investigating the claim of a woman that babies were being cut up and eaten in Satanist rituals.
As I tried to remind him, it’s a story. The mention of Marx is merely a means to pull people in; It’s a rhetorical device, a little silly but as I noted, if Walt Disney had been born in Trier they might have used him.
It is in fact very hard to tell what part of any structure is irrelevent to its function. Do do so you have to decide what that function is. What is the function of a news story?
To communicated factual information? To entertain? To make money for the publisher?
I find very little difference between any of you, and your arguments, between Sokal and the idiots at Social Text. All of you are trying to find ways to turn ambiguity into something managable, something concrete, something to which you can apply simple numbers and/or rules. What is economics but a set of assumptions? At what point do those assumptions become unsupportable? You all find ways to generalize from specific cases, and you do it in ways that are either over-simple or perfectly arcane.
You might as well be race car mechanics.
None of you value the specifics of things, the tastes and smells. A cook deals in specifics, an actor deals in specifics, a lawyer deals in specifics. A poet writes in untranslatable specifics. But for the academy everything must fit within a generalization. And when the generalization defines the thing, the thing, as a specificity, no longer exists. And what’s worse, every mediocre graduate student and cow-town professor must be able to make such generalizations. Every holder of a Ph.D must be able not only to teach important problems but to solve them!. Every assistant professor must have an original mind. And they don’t.
My mother gives perhaps the worst performance of Bach on the piano that I have ever heard. She plays the notes, unable or unwilling to take the indulgence of adding any variation, any idiosyncratic gesture that might make the playing personal. She refuses to perform</> as if by performing she would become merely a specific thing in time, a part of the world, unaware, un-intellectual.
If you can’t understand specifics your generalizations will be meaningless. And if you can’t play Bach as if you wrote the music yourself you’ll never understand the music he wrote.
The value of this is what Alan Sokal disputes. And what disgusts me is that nervous professors in the humanities are worried that he’s right. Why else would they indulge in pseudoscientific bullshit except in a desperate attempt to find a way to say that they too are worthy of respect.
Jonathan Goodwin quotes this news story
under the title:”Today’s Irrelevant Clause”
In Trier, Germany, birthplace of Karl Marx, the prosecutor’s office has been investigating the claim of a woman that babies were being cut up and eaten in Satanist rituals.
As I tried to remind him, it’s a story. The mention of Marx is merely a means to pull people in; It’s a rhetorical device, a little silly but as I noted, if Walt Disney had been born in Trier they might have used him.
It is in fact very hard to tell what part of any structure is irrelevent to its function. Do do so you have to decide what that function is. What is the function of a news story,
to communicated factual information? To entertain? To make money for the publisher?
I find very little difference between any of you, and your arguments, between Sokal and the idiots at Social Text. All of you are trying to find ways to turn ambiguity into something managable, something concrete, something to which you can apply simple numbers and/or rules. What is economics but a set of assumptions? At what point do those assumptions become unsupportable? You all find ways to generalize from specific cases, and you do it in ways that are either over-simple or perfectly arcane.
You might as well be race car mechanics.
None of you value the specifics of things, the tastes and smells. A cook deals in specifics, an actor deals in specifics, a lawyer deals in specifics. A poet writes in untranslatable specifics. But for the academy everything must fit within a generalization. And when the generalization defines the thing, the thing, as a specificity, no longer exists. And what’s worse, every mediocre graduate student and cow-town professor must be able to make such generalizations. Every holder of a Ph.D must be able not only to teach important problems but to solve them!. Every assistant professor must have an original mind. And they don’t.
My mother gives perhaps the worst performance of Bach on the piano that I have ever heard. She plays the notes, unable or unwilling to take the indulgence of adding any variation, any idiosyncratic gesture that might make the playing personal. She refuses to perform as if by performing she would become merely a specific thing in time, a part of the world, unaware, un-intellectual.
If you can’t understand specifics your generalizations will be meaningless. And if you can’t play Bach as if you wrote the music yourself you’ll never understand the music he wrote.
The value of this is what Alan Sokal disputes. And what disgusts me is that nervous professors in the humanities are worried that he’s right. Why else would they indulge in pseudoscientific bullshit except in a desperate attempt to find a way to say that they too are worthy of respect.
Sorry for the triple post.
I got an ‘internal server error’
message
My honest reaction to your post, Seth, is that you just hit play on some prepared speech you had. You have no idea of how scientists feel about poetry or about art, or about all of the subtleties of humanity. You can be offended by misuses of scientific terminology without being some sort of soulless automaton; you can be in a quantitative discipline without approaching every aspect of life with the green eyeshades of the accountant.
I wonder who wrote that adequacy article, though.
I’m an athiest, I don’t know what you mean by soul.
On the other hand I’m not a ‘Bright.”
Nor am I a member of Mensa or any other cult.
I meant “soul” in a metaphoric sense. You know, like in poetry.
Walt, even the least maths focussed student willl have to take calculus in high school to the level of an English A Level. It’s often extended further for students going to preparation courses for the grand ecoles that are the source of most academics. I think the trend is continued in higher education.
This is a claim built on a large pile of anecdotes — reading French textbooks, the superior design of the French interest rate derivative market — but I think the general attitude to maths is quite different to that found in the Anglo-Saxin world where it is a mystery and necessary evil as opposed to an intellectual treasure.
My point is that philosophers play fast and loose with all sorts of subjects. My point is that greater familiarity might include maths in the field of play in France at times when Anglo-Saxon philosophers would steer well clear.
I was first introduced to Kristeva by a mathematician who was a fan.
Just in case anyone is reading this thread, the author of the adequacy article is Dsquared. Jsm (or John Saul Montoya, or streetlawyer) was a pseudonym he used while (hilariously) trolling slashdot.org and kuro5hin.org, and creating adequacy.org.
Short comment: I born, raised and educated in France, now live and work (largely in molecular biology) in Canada, and deny that there is a more respectful attitude toward mathematics in France than in the so-called anglo-saxon countries. In my view that is just nonsense — indeed, I have no idea on what people are basing this assertion. My experience/impression is that French mathematics is middle-of-the-pack. And, btw, Kristeva has no standing at all in (serious) French maths or physics (my PhD) circles, any more than she has in North America.
I described the anecdotes upon which my assertion was based. The point was more about familiarity breeding contempt. No one escapes maths in the baccalaureate whereas in the UK you can get a degree in economics without calculus. At a guess a majority of UK philosophy students will not have any maths from beyond 16. I suggest that might make a difference.
In grad school I would pretend to be an egyptologist so that people would talk to me about my subject. People quite happily say that they barely passed their GCSEs. I know a tetralingual , multiple prize winning lawyer who still feels intellectually inferior because she wasn’t in the top stream in Maths. She’s not English. I report you decide.
In any case the person who introduced me to Kristeva was indeed a mathematician. I imagine most mathematicians ignore her, some will have read Sokal for laughs. This one was interested in Rilke and thought she had good things to say.
I still don’t know what you mean.
The absurd argument between logic and ‘soul’ is what got all us here in the first place. And I’m not interested in any form of religious/metaphysical argument.
The problem is simple, and although I return to it again and again, I get better at articulating it the more I try. I have my stubbornness (and CT I suppose) to thank for this .
I do not focus on problems that can be solved. I am not interested in such things. I am interesting in aporias, in conflicts that recur, in different forms, again and again.
What is justice? What is obligation? What is the relationship of the individual to the collective? There are no right answers to these questions, but there is a certain form of intelligence that centers on them, though they’re ruled by ambiguity and contingency: the form of intelligence that fosters a respect for judgement as opposed to mechanism.
The history of organized religion is the history of formal structures, as in a book of stories and laws that foster debate and define the rules for it to follow. Is it any wonder mysticism is always represented on the fringes of society? But simple faith is not the point. The point is the system of language, of order and community. The existence of God matters no more or less than the guilt or innocence of any one man who comes before a judge. In a courtroom the lawyers perform soliloquies. Isn’t it odd that life and death decisions are made this way, by formal rite? What does ‘due process’ mean anyway?
Most scientists like to solve problems, and once they’re solved, they go to the next one. Their language is defined in terms of ‘advance’ and ‘progress’. And many in this country at least extend this logic to their view of the world at large (one of the few exceptions in print these days is Richard Lewontin) This is not a paradigm that I would want for my children to follow. I would not want to think that my children would choose to see the dilemmas of human life as problem to be solved. There’s a lot of tragedy to life. It can be cruel. I’ve seen weak people crushed and strong one’s oblivious. I’ve also seen people very aware of the results of their actions. What does it mean to fire someone for being incompetent, if it means he won’t be able to pay the rent? What does it mean to for an officer to send an enlisted man to his death?
None of this has anything to do with religion. It is about the weight that accrues to specifics; a weight about which the hard sciences, as generalization, can say nothing.
Reading Brad DeLong I’m not convinced for one minute that he understands this notion of weight. He’s a mechanic, an engineer.
Rules sing for most of you, like music. You think generalizations are the highest form of thought. They’re not. The highest form of thought is the ability to communicate specifics. But then once they’re communicated they’re no longer specific are they?
Though I said otherwise, the comment above is a bit flabby. But only a bit.
I’m done.
As one of those panicked humanities professors who browses here occasionally I’d like to interject that Julia Kristeva is fundamentally flawed as a psychoanalytic thinker, but not because of her prowess or lack thereof in math.
I am not able to follow the intricacies of your mathematical discussions here, and I can’t get into a detailed refutation of her theoretical interventions here, but I would like to say in all fair mindedness that her importance to the development of French linguistics was very important because being Bulgarian, she was able to introduce and work with many of the concepts of Greimas and integrate them with the work of Saussure. That said, her book on Chinese Women is a terribly misleading account of the emancipatory power of the Chinese Cultural Revolution for the fair sex, and her presentation of pre-linguistic experience is fairly schematic.
She is also a terrible novelist. Do not read her autobiographical roman a clef, The Samourai. It is self-congratulatory.
“necessarily usual to insist that zero is a finite number in situations like this”
“if you allow for finite to include zero”
I’m curious: are there people for whom the status of zero as a finite number is open to question or interpretation?
I think I’ve heard physicists say “finite” when they mean “nonzero”, as in, “a finite probability”. This seems strange and wrong to me (and has kept me up nights). Are they thinking that zero is infinitely small, and therefore, non-finite in its own way? Or what?
In math, like in ordinary language, the meaning of words can depend on the context (which is fine as long as the context is clear). In some contexts, “finite” may include zero, and in other contexts, it might not.
The Seth Edelbaum Experience writes:
I find very little difference between any of you, and your arguments, between Sokal and the idiots at Social Text. All of you are trying to find ways to turn ambiguity into something managable, something concrete, something to which you can apply simple numbers and/or rules.
and
Most scientists like to solve problems, and once they’re solved, they go to the next one. …
Their language is defined in terms of ‘advance’ and ‘progress’. …
And many in this country at least extend this logic to their view of the world at large …
Rules sing for most of you, like music.
and then
You think generalizations are the highest form of thought. They’re not.
Why so many generalizations from you then?
I am perfectly willing to agree with what you seem to be saying, that educated people, here and elsewhere, are caught in the grip of language(s) that they employ without fully understanding, like counters in a game that have more ritual significance than anything else. But you describe your project as emphasizing:
the form of intelligence that fosters a respect for judgement as opposed to mechanism.
It should be obvious that the generalizations you make about “you scientists” are expressions of ideas that you have about social mechanism. In other words, they are not expressions of judgment. Judgment would discriminate individuals and understand that each individual here has a very specific, idiosycratic relationship to their own misunderstood kaleidoscope of linguistic rituals.
So your basic ideas, if followed properly to their conclusion, would seem to undermine your current rhetorical position just as much as theirs. Shouldn’t you be turning into some kind of Buddhist? (I consider that to be a respectable option for any thinker holding your premises.)
For the files. And again
A Buddhist?
No. Although I’ve played at being one for purposes of argument (but not this time)
It’s an old problem, the problem of being an anti-intellectual: either shut up or admit defeat. But I’m not being so simple minded, and I’m not being anti-intellectual; I’m criticizing a tendency among a certain group of people. Let’s call that group: Those who take libertarian ideas seriously enough not to break out in laughter at the mention of the word.
I was unlucky enough to get a shard of steel in my eye twice in one year. Both times I went to NY Eye and Ear Hospital to have the splinters removed. The second time the procedure was performed by a resident under the supervision of an attending surgeon. The resident was a young and attractive woman, born in this country. The surgeon was an eastern European immigrant.
The young woman was intelligent and professional, but emotionally sort of blank. She spoke without affect. She did what she needed to and then went to her supervisor to get him to sign off. He asked her if she was sure she’d removed everything. She seemed a little surprised at the question, and he decided to reexamine me himself. “It’s his eye” he reminded her, and then explained that what she assumed to be a rust stain might still contain particles that could cause future damage. He repeated the procedure, and I went home.
I won’t fall into the trap of saying simply that to the attending surgeon I was a person and that to the resident I was merely an idea (I’m sure someone here would try to catch me on that). But I will say that when he asked her that question I know he had felt an empathetic shiver for what might happen to me if she had been wrong.
How do you measure that shiver? How do you define its worth? How can it be taught?
Johnathan Goodwin mocked something as ‘irrelevant’ without first asking why anyone might consider it otherwise. He made an assumption based on what he thought was logical. He was arrogant, but his logic was wrong.
Is that better?
“In math, like in ordinary language, the meaning of words can depend on the context (which is fine as long as the context is clear). In some contexts, “finite” may include zero, and in other contexts, it might not.”
More tersely, “Walt Pohl is one of those people” (for whom zero is sometimes not finite).
I’ll ask again at more length. What meanings do “finite” and “zero” have for you, such that sometimes zero is finite, and sometimes it isn’t? Beyond the present one, what contexts can you adduce where zero is not finite?
Seth, yes, much better. Thank you! Back to your starting point then:
(from s.e. first comment) It is in fact very hard to tell what part of any structure is irrelevent to its function.
So, when somebody automatically dismisses a sentence which introduces an article about satanism in Trier by mentioning Karl Marx was born in Trier, this is for you indicative of a general propensity among academics to treat sentences as if they are only supposed work one way.
And you connect this propensity, in one leap, with the loss of affect among young surgical residents at NY Eye and Ear.
Do you expect other than a hostile and incredulous general response? Believe it or not, I agree with you completely that there is a connection! But surely this particular rhetoric cannot be expected to convince anybody that is not yet convinced?
The question
How do you measure that shiver? [of subjective humanity] How do you define its worth? How can it be taught?
… is an essentially religious question. And one that has been attacked again and again from all over the map. Kierkegaard spent a lot of time on it, for example. Hell, the sentence from you I just quoted is just about verbatim from one of the Zen gathas.
Rightly or wrongly, Social Text et al have tried to address the question in a novel fashion, by creating their own impenetrable jargon. Rightly or wrongly, this jargon has not convinced outsiders that there is a problem with language or the use of language (let alone the possible implication that there is subjective humanity outside language that has great significance), it’s just convinced outsiders that the users and defenders of that jargon are crazy.
postscript to my last — yes, I know it’s an act of charity to confidently assert that what Social Text et al are doing is addressing the question of how to communicate subjective humanity.
However, as Kierkegaard said, we can never know the subjective intention of another. (Unless of course they display no facility with irony, which proves them to be incapable of understanding eternal matters.)
OK, Social Text is disqualified. Sorry. Well, take them as a sort of synechdoche for the whole project …
You lost me from the point of saying it’s “a religious question.”
No it isn’t.
Call it whatever you want, it’s the only question. And people have been struggling with it for a lot longer than any contemporary theory.
Follow the links.
You’ll find my comments.
Elizabeth Anderson is a woman without a mind.
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