Monday, August 06, 2007

51st Philosophers' Carnival

This, the 51st Philosophers' Carnival, is a round-up of recent stuff from philosophically inclined blogs, with a bias towards maths, science, logic etc. In the interests of making life easy for myself (an essential part of any rational philosophy) I first chose the total number of posts to be 37 (as I was listening to Femme Fatale) and then, as posts arrived, I simply added them below in descending order of my credence (a real measure of subjective probability) that they would eventually be included.
......To begin with the basics, why does 1 + 1 = 2? asks Philosophy Sucks! Although that equation is so obviously true, it is obscure what is the right proof that it is true; and regarding different types of proofs the question what is involved in arguments for the existence of God? was raised at Prosblogion; and for another view of proofs of God's existence see A brood comb. At another extreme, for a clear and stimulating account of infinity hear A W Moore on Infinity at philosophy bites. And for some more maths that philosophers may find interesting, why not take a look at Peano's Space-filling Curve at Good Math, Bad Math? And for a nice example of how maths enters into the basics, even of the philosophy of mind, read this post on formal logic and free will, at Elliptica. Not to mention how useful maths is if we want to get to the truth behind the headlines, as in this about Cannabis at Bad Science.
......Less mathematically this report on a Meta-ethics conference at Philosophy Blog was enjoyable to read; and on the topics of meta-stuff and conferences, this call for papers at bLOGOS began: "Do numbers, sets, and other abstract entities, exist?" (which seems apposite. Meta-metaphysics appears to me to be about the status of the metaphysical debates about such things, but for better views on what it is see this post about that call at Theories 'n Things, and also this post about the same thing at Metaphysical Values). The relation between virtues and flourishing is treated logically at Philosophy Journal. And there is a formal model in support of the possibility of parity at Philosophy, et cetera. And if you want to know more about the relation between religion and science, take a look at Galactic Interactions.

......More entertaining may be the claim that modal logic can solve all problems, at Thad Guy. There's a nice introduction to possible worlds at Big Ideas. Classically progressing from possible to probable goes via the principle of indifference, reconsidered at Bloggin The Question, while an important principle relating credence and chance was mentioned at Antimeta.
For those who prefer examples to principles, the ever-interesting image of tossing a coin forever was pondered upon at Probably Possible. A less tidy but more important application of probabilities, Dawkins' improbability argument against ID has been examined by Stephen Law. Probabilities also crop up in the Klein problem, at Think Tonk. And speaking of measures, the best way to measure happiness is considered at Splintered Mind.
......Experimental philosophy (applied maths if you like) yields fascinating results, e.g. those well described in this brief introduction to the Knobe effect and similar phenomena, at Natural Rationality. Poles apart, and the origin of the neologism "Pancomputationalism" was examined by Gualtiero, at Brains, while there was an example of a difficult definition in Poker at Nothing but the Truth-in-L. And very different again is this rethinking of Shell on Kant on Properties, at Rethink. More mathematically, What is the role of intuition? is the question inspired by an example from the history of geometry, at Words and Other Things. For something deeper, how about Duhem on Mathematical Generalization, at Siris? And if you don't know who the founder of modern structural proof theory is, you might want to read about Gentzen at Logic Matters.
......Inevitably some dubious oddities, e.g. this defense of Deleuze at Sportive Thoughts seems to be about maths, but as it's Continental I'm not sure. And this post about quantity at Tetrast2 seems to be more analytic, but again, who's to say? By contrast with those two, this treating of paradoxes as Mobius strips at Heart, Mind, Soul and Strength is relatively neat,
and so I leave it as an exercise for the reader to say why it's not proper philosophy (after all, picture proofs are arguably good mathematics, and philosophers do take even dialethicism seriously, as a unifying principle). But for a reminder of why it's not even worth arguing with one half of the American culture war, see some Fundamentalist Math at Ooblog. And to show we're not prejudiced, let's also laugh at academia, with Jean Kazez. For more mathematical humour read about Nowak on the Loom.
......All good things must end, and why not with the contradictions inherent in our social structures? E.g. with
when business is incontinent, at Trust Matters: "The paradox of trust is that the greatest economic success is a byproduct of putting customers' success first." Or with Hegelian families, at The Brooks Blog, which was #37... half the submissions were excluded, but posts can now be submitted to the next Philosophers' Carnival via the submission form.


The Tetrast said...

Thank you to for including me in the Philosophers' Carnival. In answer to your implied question: Well, I don't take the analytic linguistic turn, and I went through Merleau-Ponty phase, but I like C.S. Peirce more and don't regard science as sinister to some great extent that would distinguish science from the humanities. Indeed, as the as you say my stuff "seems to be more analytic" than Continental, "but who can say?" That and the general dubiousness of my stuff is also partly because I'm an insufficiently disciplined amateur, not a professional philosopher. If wishes were horses, and so forth. To date, I've engaged in discussion mainly with Peirceans (at peirce-l), which has been good for me and, I hope, not bad for them. I've read some of the important early papers in analytic philosophy and some books by Quine, but I haven't engaged in discussions with analytic philosophers, so I've lacked the benefit of criticism from them. I don't know how to rectify that but, if I'm lucky, the Philosophers' Carnival will help.

Thanks again for including me in this.

Weekend Fisher said...

Actually, paradoxes in general cannot necessarily be considered as Mobius conundrums. My point about dialetheism is that LNC falls for circular arguments while still holding for linear arguments; the carnival entry gives objective ways to test and classify these things. For example, the classic "This sentence is false" is circular and has a fluctuating truth value; LNC fails here only because the argument is circular / non-linear.

So the post shows why demonstrated cases of dialetheism don't actually overthrow LNC, in that there are boundaries for when LNC fails and therefore safe grounds for trusting LNC despite demonstrated cases of dialetheism.

I'll leave it as an exercise for the reader whether that actually counts as philosophy. :)

Anne / WF

Enigman said...

Personally I think that "This sentence is false" is non-circular nonsense, but anyway... sorry for listing you two as "dubious oddities" (I'm better at finding the right number than the right word, e.g. I've now changed "cute" to "neat" in my description of weekend fisher's post)... "dubious" was to indicate that I was not sure that, by comparison with mainstream analytic philosophy, they really were that odd, which is why I included them, whilst suspecting that a philosopher of the mainstream would have exluded them, although being "an insufficiently disciplined amateur" myself, at least for another month, I really have no idea about that bigger picture. Anyway, thanks for your clarifications (when I saw that I had 2 comments I was expecting 2 professionalistic criticisms of including your relatively interesting posts :)

Enigman said...

Incidentally I've just noticed that Logic Matters' post on Sunday was about the crucially important distinction between formal and metaphysical naturalness, in mathematics... I would have included that (high on my list, instead of his Gentzen post), but submissions later than Friday turned out to be too late (so apologies if I missed any other interesting stuff :)

The Tetrast said...

Actually I myself thought that my post would seem odd and dubious and, in the two weeks since I submitted, I did the tweakings which I mentioned in my submissions comment, removed a few things, and added an opening summary. Yet, whether a professionalistic philosopher would include or exclude such a post would depend first of all on his/her attitude toward tables -- I'm told that about half of philosophers can't stand 'em. From what I've seen, sometimes with good reason, but, I hope, not always!

I remember reading in Quine somewhere that questions of reference shift in the liar paradox can be avoided by using three sentences in a knot of inter-reference, which sort of thing seems part of why the fellow at your link says that the problem is semantic, not syntactic. (I suspect it's some combo of both.) I also read somewhere on the 'Net, some comment by a computer guy, about occasionally observing a liar paradox actually causing a switch to flicker between "true" and "false" states. So I'm not so sure that you've escaped the circularity view of the liar paradox. Anyway, it might be fun to align vacuously self-referential sentences to various shapes. If "This statement is true" (for which I see no establishable truth value, but merely a kind of self-consistency) correlates to a circular strip, and if "This statement is false" correlates to a Moebius strip, then to what sort of things do "This statement is true or false" and "This statement is true and false" correlate?

Peirce said somewhere that the problem with the liar paradox is that it does not refer to something whose character is real, which he spells out as meaning, independent of that which you or I or any finite community of minds think of it (i.e., that which you or I or etc. think of it through the symbol), and hence the symbol in question cannot truly correspond to its object.

Lynet said...

Hey, thanks for the link!

Enigman said...

Tetrast: Personally I love tables, e.g. I saw getting this nice table as evidence that 1/0 might be an actual number, e.g. the actual number of points in a line. Incidentally Peirce's view of the line was a bit like mine.

The Tetrast said...

I understood more of the linked paper than I expected to, and recognized the Peircean idea of continuity in C-I. (I don't have a horse in that race, so far as I know, and am only semi-Peircean.) I doodled tables like that years ago, some with just the same patterns, but of course they were worth little without formal mathematical reasoning to support them, and my uneducated intuition petered out as I wondered (please don't laugh) whether I had too many cells containing the stand-in for 0/0 (your "Ξ" (uppercase Greek Ksi)), which I also regarded as "the number which wishes that it were a variable." That formulation triggers in my case a heuristic constraint to extend the idea by lockstep analogy involving suitable transformations of the idea for the other three numbers. Anyway, I think through tables, so I very much like balance, comprehensiveness, accordance, and ordering. Unfortunately, as far as I can tell, not only do many philosophers really dislike tables (possibly such dislike is an understandable legacy of Lullius's tables), but also hardly any philosophers regard balance and order as "evidence" that there might be something to a given way of arranging logical quantities, philosophical categories, etc. Ah, well.

Enigman said...

A philosophical bias against tables seems perverse, given such as the Periodic Table, which says so much about the nature of Nature.

The Tetrast said...

Well, tables of ideas, anyway. The antipathy toward tables is something that I've been told about, not experienced, since I've never tried to get a paper published in a philosophical journal. The lack of interest in balance, order, etc., among ideas is something which I see in philosophers' writings. It's analogously as if statisticians didn't clearly know of Pascal's Triangle and tried to do statistical theory using only eclectic parts of the normal curve of distribution.

Mendeleev getting away from it all to his distant cabin, and laboring over various arrangements of pieces of a chart, in search of the structure which became his periodic table. I wish there were a good picture of that, I'd frame a copy and hang it up.

Perezoso said...

The central issue of mathematical and logical "foundationalism" concerns Realism vs. nominalism. Indeed, one might say that is the central philosophical issue (most others flowing from one's decision on the problem--thus in a sense Hobbes proves more important that Descartes) And, alas, once Plato Jr. up at Sappho State realizes, perhaps with a certain degree of tragedy, there are no real convincing arguments contra-nominalism (and no convincing arguments for ANY a priori truths), he begins to wonder if there really is some discipline called "philosophy" proper, and generally regrets not following Vati's advice to enter engineering or chemistry ....... (Quine realized that early on (see his essay with Goodman on Constructive Nominalism), but continually ducked the issue). And the school of Peano really faces many of the same issues (B. Russell also ducks the nominalist issue, tho' in a witty fashion).

Enigman said...

I'm commenting now (nearly a year on) because it finally struck me, what would be a good analogy for why the analogy between the Liar paradox and a Moebius strip fails: Waves move in some horizontal direction because the water particles at the surface are moving up and down, perpendicular to the wave's motion, which is a bit like how pushing a gyroscope in one direction causes it to move in another; so I would now say that the Liar paradox is to a Moebius strip as a gyroscope is to wave motion, i.e. superficially similar but not really very. The really interesting question, it seems to me (which relates to perezoso's remarks), is why analogies are so informative...