Friday, August 31, 2007

Dianniversary

At the time of her engagement to Prince Charles in 1981 she was just another dim, round-faced Sloaney girl of the kind you could see on almost every street in Pimlico, Kensington or Earl’s Court, clad in the unprepossessing uniform that prompted some observers to liken her, cruelly but accurately, to a stewardess from Air Bulgaria. By the time of her funeral sixteen years later she was routinely if ludicrously described as one of the most beautiful women in the world, and the most saintly. […] The Chancellor of the Exchequer, Gordon Brown, wondered if the anniversary of her death should henceforth be a public holiday, Diana Day.

Thus Francis Wheen, on pages 199-201 of his fab book, How Mumbo-Jumbo conquered the World. Today is, of course, Di’s tenth deathday (and the fiftieth anniversary of Malayan independence from Britain), so what shall I say about Di’s death? Not much (but I want to practice blockquoting, so:) many people believe it remains mysterious, but it seems like an ordinary accident to me—relatively ordinary anyway. Whatever made Di useful to the royal Family also seems to have made her dangerous, when their scorn inclined her towards telling tales; but then, what then made the media Circus useful to her may also have made it more dangerous, via the resulting reduction in her immunity from accidents—maybe, although I’m sure I wouldn’t know (although to see the popular story of her personal survival turn out so suddenly (and naturally tragically) to have been from such a different genre was certainly surprising). What such things mostly remind me of are a couple of relatively ordinary paradoxes (mentioned in Michael Clark’s nice Paradoxes from A to Z).
......Firstly placebos are a bit paradoxical, because if we believe that something acts only as a placebo (e.g. homeopathic medicine) then it won’t so act for us, not if we know the meaning of ‘placebo’ (which only half-explains homeopathy (which does after all do the medically important job of curing some people), although the placebo effect may well be easier to explain (e.g. as like social grooming))... so this paradox resembles Moore’s; and furthermore philosophers naturally find it paradoxical when knowledge tends to keep one unhealthy, if only personally (despite history showing that to be quite common). Anyway, I’m reminded of this paradox because Diana was (so I learn from Wheen) a fan of reflexology who lunched with Deepak Chopra shortly before her death, and also because of the following premonition of that (Wheen 2004: 154-5).

Nine months after the accident, the Mail serialised a book by Rita Rogers, the Derbyshire psychic whose ‘extraordinary powers’ had so impressed Diana and Dodi. She disclosed that at her first meeting with Dodi Fayed the previous summer she immediately had ‘a feeling of danger’: she saw a black Mercedes and a tunnel, and ‘felt there was a connection with France’. Extraordinary indeed: only the most mean-spirited sceptic could have wished for some sort of corroborative evidence, such as a letter from Fayed thanking Rogers for the warning about driving through French tunnels.

Secondly there is the paradox of deterrence, or mutually assured destruction (MAD), where the enemy is deterred from completely destroying you because your inevitable (if posthumous) retaliation, whilst being completely ineffective defensively had things got to that point, would destroy them and hence (Clark 2002: 42) “where it is rational to make yourself less rational.” Perhaps we will be safest voting for leaders who can be relied upon to behave irrationally, to act when the justification for acting (in such an extreme fashion) is absent (which shines an interesting light on their relatively proportionate reaction to 9/11). I’m reminded of this paradox because thinking of Di and Family makes me realise how remote from our world such powerful people must be; I mean, they can’t just go for a walk in the park, can they? They have to live in palaces (nice as that must be) and walk in their expensive grounds; and it seems to be difficult for them to meet up with their peers by using the usual systems of roads etc.
......In short, our ruling classes would clearly have relatively few problems adapting to life in palatial bunkers (perhaps with Eden-project-style grounds, with tulips) connected by tunnels (social and aggressive) and surrounded by dead land, surrounded as they are now by such dangerous (and increasingly useless) people—which helps to keep us safe (paradoxically) if there are such bunkers, but are there? Now, I’m sure I wouldn’t know (although maybe we should hope that it looks like there are), but intriguingly Wheen (2004: 174-5) also mentioned the billions spent by the US on procurement (without seeming to have procured much:)

Sunday, August 26, 2007

Blockquoting

Blogging will be even lighter than usual over the next few days... but incidentally I've been avoiding using the Blockquote button, because the text after the quote gets squished up, but there are apparently two sorts of solutions. One is to insert (under Edit Html) span style="line-height:1.6" (within the usual pointy brackets) after the quote (adding the usual /span at the end); and another, more permanent solution is given here.

Saturday, August 25, 2007

An Argument for Atheism

I shall, in this post, take atheism to be the belief that there is (probably) no God, where God will be defined to be an omniscient and omnipotent being that is also totally good (much as Richard defines Him), and I shall argue (as I did briefly in a comment on this post of Richard's) that such a God is (probably) impossible. There are of course other definitions, e.g. atheism is sometimes regarded as the absence of a belief in God, so that it would include both atheism (as defined above) and agnosticism (the absence of a belief either way, which includes the belief that knowledge either way is impossible, which is another definition of agnosticism), and God is sometimes defined to be the Creator of this Universe.
......Such a Creator would know (more or less) all that could be known about this Universe, just as an author would know all about her story, or a painter all about his painting; and similarly, such a Creator would have (more or less) complete power over this Universe. So, it may have been that God was originally defined to be the Creator, and that it was then deduced that such a God would be all knowing and all powerful in that sense (which is, after all, the sense that concerns us, as beings within this Universe), and that such properties only then became definitive, e.g. through their apparent utility—certainly many arguments (as in that linked post) do begin by defining God to be infinitely perfect (rather than the Creator). So, I’ll now argue that such a God, which I’ll refer to as ‘He,’ is (probably) impossible.
......My argument is primarily concerned with omniscience, with God knowing absolutely everything. Not only does He know everything about His Creation (as any Creator would), He also knows whether or not there are, for example, other Gods. If there are any, He knows everything that they know, including precisely what it is like to be them (which might imply that there is only one God), and if not then He knows how he knows that there are not. But it is quite inconceivable how he could know that there are not any other Gods (either at all, or beyond those that He does know all about). The problem is not so much with the “omni,” but with the “science.” It would of course not follow, from some conjectured infinitude having inconceivable properties, that it did not exist; but the concept of knowledge is the concept of true beliefs that are in some way tied down to (or that in some reliable way arise from) the things known about, and we are here considering one being’s knowledge of the non-existence of other similar beings, where there might well be absolutely no connection between them.
......Ironically this problem (for this fairly common kind of theism) resembles a fairly common reply to atheists, who are told that while they might obtain a justified belief that there was a God by His revealing Himself to them, they could hardly obtain scientific knowledge that there was not a God (not even in Heaven) just by failing to have had such a revelation. Imagine (for an analogy) completely separate spacetimes with absolutely no causal connections between them—how could any being, in one of them, know anything about what was going on in the others, or even whether or not there were any others? Similarly, even were there only one spacetime, and a being within it had that true belief, how could that belief be justified?
......By hypothesis God would know that He knew everything, and He would also know how he knew that there were no other Gods (beyond any He might know about more directly, via informative connections), but how could that be? Could He have deduced that fact from His knowledge of His own omniscience? But how could He not then know that such circular justification would not make His belief (that there were no other Gods) knowledge? It is all very well for us to define God to be omniscient, because we can then ask whether or not God exists, but God could hardly do that! In short, the concept of omniscience (in this strict, absolute sense) seems to be self-contradictory. It seems to be, but it may not be, but as there seems to be little logical room for manoeuvre, I regard that conclusion as at least very likely (and not necessarily inconvenient for the theist, as I mentioned here).
......Regarding omnipotence, if God has the power to do absolutely anything, then could He make 2 plus 2 equal 5? If not then it again seems that we cannot interpret His definition in such a strict way after all. And of course, God would not get any less implausible were combinations considered, such as omniscience and (via free will) responsibility, together with omnipotence and (via this Universe existing, whether or not God created it) evil. After all, if God knows what we are going to do, and if He could have stopped us but did not, then, given that He is good, it seems that whatever we do must also be good, or at least (since we are only human) good enough (in what might have to be the best of all possible worlds), which seems unlikely.

Thursday, August 23, 2007

Pseudorandom Facts IV-VIII

There might, after all, be something to be said for putting (within this game) all the facts and tags into just one post, so I’m listing my remaining 5 here. First the facts: I prefer boots to trainers, mushrooms to cheese, wasps to spiders, Risk to Chess, and Futurama to the Simpsons. And I'm tagging (for no particular reasons) Alan, Jim, Justin, Leland and Dean.

The Great and the Good

It was the summer of 1984, and as the TVs covered (rather Orwellianly) the miners’ strike I was leaving Oxford (having arrived there 3 years earlier on a scholarship to read Physics), and during an interview for a job (that I didn’t get) in the civil service, a civil servant had asked me where I thought I’d be in 10 years time. I discovered, in the summer of 1994 (see previous post), that it was Nottingham.
......One of the few memorable things that had happened to me in the intervening 10 years was that I’d shaken the hand of the prime minister, who at the time had been John Major; which is my second pseudorandom fact: I recall that fact now because I’m looking at a page of words like ‘impale,’ having just been looking at a page of words like ‘jugular’ (and thinking of George Bush), perhaps because that made me think of Spitting Image (via vampires, and today being, as usual, rather rainy and grey).
......This is not a typical fact about me, because I generally avoid shaking hands (not to mention hugs and kisses), and nor do I tend to associate with the great and the good, but at the time I was a Postman in a fairly new sorting office in Cambridge, which is near to (what was) Major’s constituency, which may be why he was visiting; and my typing speed (converting postcodes into rows of blue dots) was relatively high, as I had only just finished my training (prior to which I used to deliver to such as Stephen Hawking, which is my third not-so-random fact), and so had not yet succumbed to the general disgruntlement (into which I was soon to settle), which may be why one of the line managers pointed me out to the PM as he toured the office.
......Of those two facts, having once been Hawking’s postman seems to me to be the most impressive. Perhaps that’s because, whilst I disagree with his physics no less than I disagree with Major’s politics, the former subject is the more philosophical. Whatever—I’ve managed to drop two names into my pseudorandom facts, which is the main thing (why blog if not to show off?)... and so to the tagging (within this game), of Albert and Anne.

Wednesday, August 22, 2007

Random Fact I

Having been tagged within this game, via this post, in this and following posts I shall be telling you 8 random facts about myself and tagging a further 8 bloggers. In the earliest play that I’ve found, the telling and tagging was done via 8 separate posts, so in this post I’ll also begin with just one of each, but I’m unsure that that’s playing the game (and if it proves too slow then I’ll lump the remainder together). My first problem, then, was to obtain just one fact about myself at “random,” and since I’m not even sure what that means I’ve settled for the following, pseudorandom system.
......To begin with, the “RAN#” button on my calculator gave me a 3-digit ‘random’ number, and doubling that told me where to open my 2,000-page dictionary. I then tried to pick words without looking at them, in various hopeless ways, before deciding that whatever fact occurred to me as I read those words would be random enough. So, I got 435 on the calculator, and the words on pages 870 and 871 were such as Judaic and July. And the first fact that occurred to me was that once, in the summer of 1994, I saw the word ‘RAN’ written (in capitals) in clouds in the sky.
......An odd sort of message from God, I thought to myself, why not something more imperative? But of course, the clouds had just formed that way at random, quasi-ironically... which makes me think of monkeys on typewriters. Suppose that a monkey called ‘George’ typed, “This was typed by George.” Anyone reading that might suppose that George had accidentally typed something that was true. But why would that typed ‘George’ refer to that monkey?
......If someone who did not know that monkey’s name, but who did know the President’s name, saw what that monkey had typed, she might suppose that the monkey had typed something funny but false. The reference, along with the meanings of all the words (since the monkey does not know English, of course), seems to come from the reader. So we might suppose that that ‘George’ refers to no one in particular, e.g. that names are indexical (that their reference is determined by speakers’ intentions and/or readers’ presumptions).
......We might instead suppose that that ‘George’ does not refer at all, but what if the monkey had typed, on its English typewriter, “This was typed by a monkey called ‘George’ ”? If it is sentences, and not propositions, that might be true or false, then that seems to be an accidental truth; but then why not the earlier one? I don’t know (and explications of the direct view of reference (which I think I disagree with) would be welcome). Anyway, I’m tagging Laïyna. And incidentally, something else that I was thinking about, in that summer of 1994, was that I finally knew the answer to a question that someone in authority had once asked me, 10 years earlier (to be continued).

Thursday, August 16, 2007

An Argument for Agnosticism

Either the world was deliberately created, so that some sort of theism is true, or else atheism is true, but both options involve us in such mysteries (as the two below) that to choose either, given only such evidence as is publicly available (and so worthy of being called ‘evidence’), would be to favour irrationally one mystery over another, whence agnosticism (i.e. the absence of a belief either way) is to be preferred.
......The obvious problem with theism is that, when we look at the world we see only mundane things, no gods and not even angels or fairies. We don’t even see any clear evidence that the world was deliberately created, or is being guided from above, or even watched over. But more importantly our language is so orientated towards the world that we are unable even to form a clear idea of what its creator might be like.
......Conversely we know a lot about the world. We even know that our brains are composed of many brain cells, each of which is composed of a lot of organic molecules, many of them highly complicated but all of them composed of atoms. Atoms themselves have a very tidy structure (as shown, for example, by the Periodic table of the elements), and they are the building blocks of, not just brain cells but rodents and radishes, rocks and raindrops, robots and radios.
......But it is precisely because we know so much about how atoms behave that it is so troubling that (although we can see how information-processing mechanisms can be composed of them) we are unable to make much sense of the idea of their giving rise to such conscious individuals as we know ourselves to be. We might deduce that there must be more to them than we know at present, but it is quite mysterious even what sort of stuff there would need to be (or even its whereabouts, given how much we already know about atoms).
......Perhaps the way that organisms have atoms is akin to how they have skeletons—if the X-ray photograph of an organism shows only its skeleton (which could account for all its scientific properties, had few enough of its properties been observed and measured) that does not mean that there is not more to the organism. But again it is difficult (and not so much because of the complexity as the conceptual obscurity) to make much sense of that idea, not without introducing some sort of non-physical substance (akin to the flesh on the skeleton).
......Still, prima facie we are non-physical individuals, and the mysteries of how and why such mental beings interact with physical structures would seem less of a problem (less of an unlikely coincidence) were the world created because then both the mental and the physical would have had a common origin in a deliberate creation (cf. inventing trains and tracks together). So were we to reject the obscure possibility of atoms giving rise (via natural processes) to conscious beings like ourselves, then we might conclude that the physical world is (probably) a deliberate creation.
......But of course, were we to reject the possibility of a creator for its obscurity, we could instead conclude that there must be some way in which atoms do give rise to us. After all, the considerable evidence that the world is Newtonian turned out to only be evidence that it is approximately Newtonian, and so it is not unreasonable to suppose that atoms might also be only approximately how we think of them, deviating from our simplest picture of them in some similarly unforeseeable way.
......But similarly, neither would it be unreasonable to suppose that we might have been created (e.g. as below). So, it being completely obscure (at present) how either theism or atheism could be consistent with what we know of the world, it is surely impossible to tell, from the publicly available evidence, which one is most likely. And so although (for various reasons) each of us is actually quite likely to presume one of them, the more objectively rational option is surely agnosticism.
......I shall end with an example of one such reason (evolution) for preferring one of those two options (atheism) that seems to be fairly common amongst philosophers (for fairly obvious reasons, e.g. see ScienceBlogs). (This example was suggested by Aaron's comment on the recent post that inspired this post.) Suppose that modern accounts of the evolution of life are (at least approximately) true (as a lot of quite varied evidence indicates). Even so, only such ideas of creation as a too-literal reading of Genesis would consequently be false (and even then, only correspondingly approximately). (In this post I considered one possible motive for creating a world via evolutionary processes, but of course any actual motive is likely to lie well beyond our imaginations.)
......Similarly a simplistic, billiard-ball style of materialism is rendered improbable by our self-awareness, but I’m here considering theism vs. atheism, not literalism vs. materialism. It was once said (fallaciously) that incremental evolution could never explain our eyes, but we now have mathematical models of how eyes might arise incrementally. Nonetheless the likelihood of our being unable to provide any such explanation would surely (had it existed) have undermined this reason for preferring atheism. And so we return to the lack of any indication whatsoever of how an evolutionary explanation of consciousnesses such as ours might go.

Monday, August 13, 2007

PW Semantics

I keep bumping into possible worlds semantics, for subjunctive conditionals, in the course of trying to find out about (the metaphysics of) various other things, and so I need to work out what they are doing, what they bring to such analyses. I’ve not studied them properly, so what follows is just my thoughts on what I take to be a typical example (so if it’s atypical, or my thoughts about it are poor, please let me know). Anne bumps into a table, which she’d previously asked Bob to move, and says, “If you’d moved that table I wouldn’t have bumped into it.
......Clearly Anne is, with her utterance, doing something like blaming her accident on Bob, but what was actually said, literally? Anne said that, had Bob moved the table, she would not have bumped into it, so my first thought is that if the table had been moved, Anne might actually have been more likely to bump into it, especially if the table had been moved by only a small amount. (Indeed, it is quite consistent with the story thus far that Bob did disturb it slightly.) Would that alone be enough to make Anne’s claim literally false? Maybe, but then maybe bumps in general, and the intended ones in particular, are not defined well enough for Anne’s claim to have a definite truth-value.
......Still, I’ll presume that we can include, in the literal meaning, all sorts of information that was implicit in the context of the utterance (otherwise much of what we said might have no literal meaning at all). The literal meaning might still be some vague range of more precise meanings; but what are they? E.g. what if the world was deterministic, so that the actual table could not actually have been moved? Are we then considering similar tables, in some hypothetical Universe? But Anne was explicitly talking about “that table,” not some similar tables (and about Bob, not someone similar). Is it that her subjunctive talk changes those references?
......But why does it not instead mean that we are not assuming that the world is so deterministic? In the conversation there was a presumption of free will (of responsibility for moving the table) and reference to the actual world (via “you” and “that table”). Maybe the world isn’t deterministic (and if it is then maybe Anne’s utterance did not literally have its intended meaning), so why not build some presumption of indeterminism (whose kind might in general depend upon the context) into our interpretation of that utterance (rather than changing its subjects)?

Saturday, August 11, 2007

What am I like?

Philosopher know thyself, they say, whence I wonder what I'm like. For starters, what kind of thinker am I? Existential, it seems, which means I'd make a good philosopher. And which science-fiction writer am I? Philip K Dick. So far, so coherent, but that only gives me a 20% chance of surviving a Zombie Apolcalypse. Were I a superhero, I'd be Spiderman, which might help. More plausibly, were I an ancient language I'd be Linear B, although again that would make me the strong silent type.

Thursday, August 09, 2007

Not seeing the Oasis for the Mirage

Consider the next girl to be named Oasis. She might be an American, and clearly by “she” I mean Oasis, but if that “Oasis” refers to her directly (i.e. not via that name’s sense but via some appropriate causal connection, between that use of her name and her baptism) then is there some sort of backwards causation, acting from her future baptism to that reference? Maybe it’s indeterminate who I’m referring to (unless that aspect of the Universe is already determined) until the time of her baptism (or until that aspect is determined), but would there then be some instantaneous causation-at-a-distance? Or is my feeling that I’ve just been referring to Oasis just a mirage?
......I’ve no idea, so consider a more traditional kind of scenario. Suppose you’re in a desert, looking for an oasis. You know that there’s an oasis to the North, and so you look northwards, and see what you take to be the oasis. Of course, it’s really a mirage. Still, just where you take the oasis to be does happen to be where the oasis is, hidden behind the mirage. In fact, had the oasis not been there, reflecting sunlight and evaporating, the air would’ve been so differently heated by the Sun that the mirage wouldn’t have been there either. As you move northwards, the mirage fades, and is imperceptibly replaced by an increasingly clear sight of the oasis. What you are looking at changes smoothly from mirage to oasis, but does the reference of your “that oasis” also change smoothly, from nothing (via referential failure) to that oasis?
......I’m not sure. In the traditional (epistemological) scenario, a vase is hidden behind a hologram (a picture whose image has depth) of the same vase (apparently in the same place). If you saw that hologram and said “That vase,” you might well be referring to the vase because the hologram is of the vase, but would you know that the vase was there, just by seeing its image? Is it that you would not, because anything might have been behind the hologram? But then, even were the hologram switched on by placing the vase there, and even were only that vase ever put there (in what might be a fairly deterministic bit of the Universe), still, would it not seem that you wouldn’t know, just by seeing its image, that it was there?
......Perhaps the relevant personnel would only ever put that vase there. So suppose instead that the hologram was built up from live feed, from cameras trained upon the plinth. That might give you the same picture, of the same vase, and again only when the vase is there. And again maybe only that vase is ever put there, but now it seems that you might know that the vase was there (even if again, you don’t know about the mechanism). After all, that situation is like having night-sight cameras in front of a vehicle, showing the driver what’s in front of it, which is itself not unlike wearing goggles, or spectacles (or indeed, simply having eyes).

Wednesday, August 08, 2007

Twice as interesting as Sex

Bloggers can now browse Profiles. As of today there are over 30,000 interested in Philosophy (whereas only 15,000 have expressed an interest in Sex) so I'm now included instead amongst the 24 interested in Philosophy of Mathematics. So far I've discovered Chicory Root Mugwort Tea and, rather shockingly, that I'm the only blogger who counts Martian Time-Slip amongst their favourite books.

Tuesday, August 07, 2007

God's messenger

He believed he was God's messenger and was eventually driven insane trying to prove his theories of infinity.” Cantor did and was, according to the blurb (a word that celebrates its centenary this year, incidentally) for Dangerous Knowledge, a documentary on BBC FOUR tomorrow night and, according to the blurb, “the story of the mathematicians who have seen facets of the universe as it really is and driven themselves mad in the process.

Monday, August 06, 2007

What is logical possibility?

It is said that 1 + 1 = 2 is true in all possible worlds, that it is logically impossible for it to be false. And yet aliens might, for all we know, have made us believe that equation despite it being false. Although we might now believe that it is true by definition, and so could not possibly be false, perhaps we are wrong about that. Perhaps those terms really get their meaning in some other way, which the aliens have made us forget about. Perhaps they are preventing us from imagining how the world really is—is that not conceivable? And yet the falsity of that equation is said to be logically impossible.
......At another extreme, it is sometimes said of beings—zombies—that are physically identical to us but which do not have subjective experiences, by definition, that they are both logically possible and physically (or nomologically) impossible. It is said that they are conceivable, and hence logically possible, but that the matter of which we are composed happens to be such that our minds arise from (or supervene upon) our brains. But it seems to me that a being that was, by definition, physically identical to a being that was necessarily, by the laws of physics (of nature), conscious, would be conscious by definition, so that a zombie would be both conscious by definition, and lacking in consciousness by definition.
......That is, zombies seem to me to be logically impossible. Consider why round squares are logically impossible. If something is square then it is, by definition, geometrical, and so it must obey the laws of (Euclidean) geometry, and it is geometrically impossible for the same (Euclidean) shape to be both square and round. A round square is geometrically impossible and so, because it would be by definition geometrical if it existed, it is therefore logically impossible.
......I might imagine something that was topologically identical both to a circle and to a square, but it could not be a round square because roundness and being a square are not topological properties. And when I try to imagine a zombie I presume that just as tables are clouds of molecules so are we, and then I imagine such a cloud of molecules obeying the physical laws of nature (a bit like planets, stars and galaxies moving through the darkness), whence I am not imagining any consciousness there (in that darkness).
......But if zombies are physically (or nomologically) impossible then, insofar as what I’m imagining might be my body, there would have to be consciousness there. It is like trying to imagine both (i) that a table is a cloud of molecules and (ii) that we can have that same cloud of molecules without the table. Similarly, I have no trouble imagining a talking donkey, but were I to imagine it becoming more and more like an actual donkey, it should eventually become impossible for me to imagine it talking (assuming that actual donkeys cannot talk).

Post Script


Soft-as-moths moggy
on moth-eaten sofa curled
to mothball her world.
.

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.

Saturday, August 04, 2007

Puzzling Puss


Quizzical moggy
ponders upon a fishpond:
Frigid frog, or frond?
.

Thursday, August 02, 2007

Stuff and Nonsense

The following paragraph is from Vann McGee’s “There’s a Rule for Everything” (in Absolute Generality, which I mentioned in my post on the next Carnival):

......Vagueness is omnipresent in human language. Our most rigorous efforts at
......scientific exactitude reduce, but do not eliminate imprecision. Unrestricted
......quantification offers us something quite extraordinary: a sharp boundary.
......Vagueness appears when there are actual or potential borderline cases, and
......something that’s alleged to be on the border between being and nonbeing is
......still something, and hence not on the border. A painting that’s sketched by
......Valázquez and completed by his pupil may occupy an intermediate position
......between ‘Valázquez’ and ‘counterfeit Valázquez’, but whoever its author is,
......the painting unmistakably exists. The idea of a thing occupying a position
......intermediate between being and nonbeing is nonsensical.” (McGee 2006: pp 183-4)

I’ve already assumed that such a “sharp boundary” is prima facie unlikely, in my recent glance at Russell’s paradox, but McGee’s paper is so well written (unlike most philosophical writing; and furthermore I agree with so much of it) that I’m now wondering if I should’ve. Essentially my thought was that the stuff around us is just that, stuff—real stuff as opposed to fictional stuff, or false theoretical stuff, but still—not necessarily things.
......Consider a photograph of a fluffy white cloud floating all alone in an otherwise perfectly blue sky. Generally there is a continuum of cloudiness, from indistinct patchiness to such clouds, and while an intermediate position will be occupied by something (some possibly fuzzy stuff) it would not necessarily be occupied by a cloud, whence we would seem to have problems quantifying over all clouds. We might say that no cloud is really a thing, but what then becomes of the fact that someone once saw that white cloud (and even took its photograph)? The problem is that the everyday objects around us are not so dissimilar to that cloud—tables and chairs, cats and dogs, for example, all shade indeterminately into other stuff (in their totalities, of all actual or possible ones, and also individually, both spatially and temporally) and so, is it nonsense to think of that other stuff not being things?
......Physics tells us that the real world actually consists of clearly delineated things such as electrons, but not only might that just be a good model of reality, do we really want to say, for example, that the chair that we are sitting on (or the word you are looking at now) is not one thing? That we do not really quantify over such things? But then the connection between quantification and communication (with which McGee began his excellent essay) would become quite mysterious. And what if physical particles are not actually so perfectly defined as the practice of physics (like the practice of logic) requires us to assume that they are? Would we then really be quantifying over nothing? It seems more likely that, whatever sort of stuff the world is actually made of, we individuate it as precisely as we need to, in order to communicate truths about the world, and that we quantify over those things. But then the idea of something occupying a position intermediate between such things and the bare stuff of the world is hardly nonsense (more like the idea of a linguistic possibility, perhaps).
......Now, two people might agree that there was that white cloud, but perhaps they would (were all the data available) disagree over what counts as being that cloud (as it formed and vanished). Surely there was just the one cloud there, and yet there might have been two distinct individuations of the actual stuff of the world. We could count the distinct individuations as giving us different things, but then what of the one cloud that we began with? The problem appears to be that were we to quantify over all things, we would inevitably be drawn into considering intermediate positions, where there might well be no objective fact of the matter about what are two things, and what are two views of the same thing.
......Consider McGee’s example, of the painting: By how much could it be restored before it was a different painting? And by how much could its author (whoever that was) have painted it differently (a brushstroke? a molecule of paint?) before it would have been a different painting? In order to quantify over every thing, we might need there to be objective answers to many such questions, about all kinds of things; and the plausibility of that is surely not obvious.