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.
Thursday, August 23, 2007
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).
......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.
......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)?
......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).
......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).
......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).
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.
......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
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.
......“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.
Monday, July 23, 2007
Helios
Heavily LIGHT
Explodes continually
Like a scream. The sun
Is the signature
Of its maker? Under a
Sunny moon I dream.
Saturday, July 21, 2007
Of Mice and Mengen
As mentioned in my last post, the Burali-Forti paradox seems to be, from the standard perspective (see the aforementioned paper), the most fundamental and paradoxical of the set-theoretical paradoxes, although from my own perspective it is the least fundamental, which is why I’ve already looked at Russell’s and Cantor’s paradoxes.
......I’ll just briefly describe the standard paradox, which arises from the standard presupposition that the natural numbers are a standard set, that they form an actual (or finitesque) totality—in more picturesque terms, one that can, when they (or rather, their tokens) are envisaged spatially, be thought of as being all together, in the same space; or one that can, when their endless sequence is thought of more temporally (in the intuitive sense, i.e. not as part of a quasi-spatial space-time), be completely run through. (For an independent, scientific reason why that standard presumption is likely to be false, see my forthcoming paper.)
......Beginning with standard set theory and its von Neumann ordinals (0 = the empty set, 1 = {0}, 2 = {0, 1}, 3 = {0, 1, 2}, and so forth), we have that each ordinal is the set of the preceding ordinals. The first transfinite ordinal is omega = the set of all the natural numbers, and it is followed by omega + 1 = {0, 1, 2, …, omega}, and so on. There is no set of all such ordinals because if there were it would similarly be an ordinal, and it would be greater than (since arising higher in the set-theoretic hierarchy than) all its members, whereas they were presumed to be all such ordinals. Paradox arises because our intuition that there should be a set of all the natural numbers (and hence our first transfinite ordinal) seems also to tell us that there should be such a set of all those ordinals (and hence some last ordinal, usually denoted by capital-omega).
......Cantor originally needed transfinite inductions, and hence his set (Menge) theory, because he was investigating arbitrary functions of the real number line, as part of the development of Fourier analysis. Although the functions usually met with in physics are well behaved (smooth, differentiable etc.) almost everywhere, one generally expects there to be points (i.e. real numbers) where they are discontinuous etc. Analysis is simplest when there are not infinitely many such points in any finite interval, but if there are then they will have at least one accumulation point, and there might be infinitely many such accumulation points, with accumulation points of their own, etc.
......Cantor was therefore considering sequences of point-sets, each set of points obtained from the preceding one by keeping only the accumulation points. Often, for a given function, the Nth point-set in that sequence would, for some natural number N, contain only a finite number of points, with the (N + 1)th point-set being empty, but the particularly troubling (and therefore mathematically interesting) cases were the functions for which the Nth point-set contained infinitely many points for every natural number N (e.g. the function whose value is 1 at each rational point, and 0 elsewhere). So Cantor was considering what was left after all the naturally numbered stages of that process had been gone through, i.e. at the omegath stage, and (since that might also contain infinitely many points) beyond.
......And one reason why the Burali-Forti paradox remains so paradoxical (see the aforementioned paper) is that today’s mathematicians seem to find a use for inductions that range over ordinals that are (in some mysterious way) even bigger than capital-omega, e.g. in mouse theory. So, what got us using standard ordinals in the first place does seem to take us beyond them, paradoxically. And so perhaps the epistemic possibility that the natural numbers do not actually form a set (which does not presuppose a constructivistic view of numbers, but only that they are an objective structure, whose properties are to be discovered rather than stipulated) should not be too casually dismissed.
......If the natural numbers happen not to form a set, but are rather only potentially infinite, then although we could still consider ordinals insofar as they are the order-types of well-orderings (i.e. as reifications of certain structures) we would not have the same use for them. Cantor’s naturally numbered stages could not have been completely run through, to get us to an omegath stage, but that would not matter because geometrical lines would not then be isomorphic to real number lines, so there would not be such arbitrary functions to investigate in the first place.
......That is not to say that investigating them was not useful, that the standard approach has not given us a nice formal model of geometry, adequate for most applications, but only that it would then be (as it seems to be) no more than that. Note that Cantor did dismiss that possibility rather casually—remarking that a potential infinity (thought of as a variable) presupposes a logically prior actual infinity (the domain of the values that the variable could take)—perhaps too casually (or Hegelian?) given that he was aware of these paradoxes.
......I’ll just briefly describe the standard paradox, which arises from the standard presupposition that the natural numbers are a standard set, that they form an actual (or finitesque) totality—in more picturesque terms, one that can, when they (or rather, their tokens) are envisaged spatially, be thought of as being all together, in the same space; or one that can, when their endless sequence is thought of more temporally (in the intuitive sense, i.e. not as part of a quasi-spatial space-time), be completely run through. (For an independent, scientific reason why that standard presumption is likely to be false, see my forthcoming paper.)
......Beginning with standard set theory and its von Neumann ordinals (0 = the empty set, 1 = {0}, 2 = {0, 1}, 3 = {0, 1, 2}, and so forth), we have that each ordinal is the set of the preceding ordinals. The first transfinite ordinal is omega = the set of all the natural numbers, and it is followed by omega + 1 = {0, 1, 2, …, omega}, and so on. There is no set of all such ordinals because if there were it would similarly be an ordinal, and it would be greater than (since arising higher in the set-theoretic hierarchy than) all its members, whereas they were presumed to be all such ordinals. Paradox arises because our intuition that there should be a set of all the natural numbers (and hence our first transfinite ordinal) seems also to tell us that there should be such a set of all those ordinals (and hence some last ordinal, usually denoted by capital-omega).
......Cantor originally needed transfinite inductions, and hence his set (Menge) theory, because he was investigating arbitrary functions of the real number line, as part of the development of Fourier analysis. Although the functions usually met with in physics are well behaved (smooth, differentiable etc.) almost everywhere, one generally expects there to be points (i.e. real numbers) where they are discontinuous etc. Analysis is simplest when there are not infinitely many such points in any finite interval, but if there are then they will have at least one accumulation point, and there might be infinitely many such accumulation points, with accumulation points of their own, etc.
......Cantor was therefore considering sequences of point-sets, each set of points obtained from the preceding one by keeping only the accumulation points. Often, for a given function, the Nth point-set in that sequence would, for some natural number N, contain only a finite number of points, with the (N + 1)th point-set being empty, but the particularly troubling (and therefore mathematically interesting) cases were the functions for which the Nth point-set contained infinitely many points for every natural number N (e.g. the function whose value is 1 at each rational point, and 0 elsewhere). So Cantor was considering what was left after all the naturally numbered stages of that process had been gone through, i.e. at the omegath stage, and (since that might also contain infinitely many points) beyond.
......And one reason why the Burali-Forti paradox remains so paradoxical (see the aforementioned paper) is that today’s mathematicians seem to find a use for inductions that range over ordinals that are (in some mysterious way) even bigger than capital-omega, e.g. in mouse theory. So, what got us using standard ordinals in the first place does seem to take us beyond them, paradoxically. And so perhaps the epistemic possibility that the natural numbers do not actually form a set (which does not presuppose a constructivistic view of numbers, but only that they are an objective structure, whose properties are to be discovered rather than stipulated) should not be too casually dismissed.
......If the natural numbers happen not to form a set, but are rather only potentially infinite, then although we could still consider ordinals insofar as they are the order-types of well-orderings (i.e. as reifications of certain structures) we would not have the same use for them. Cantor’s naturally numbered stages could not have been completely run through, to get us to an omegath stage, but that would not matter because geometrical lines would not then be isomorphic to real number lines, so there would not be such arbitrary functions to investigate in the first place.
......That is not to say that investigating them was not useful, that the standard approach has not given us a nice formal model of geometry, adequate for most applications, but only that it would then be (as it seems to be) no more than that. Note that Cantor did dismiss that possibility rather casually—remarking that a potential infinity (thought of as a variable) presupposes a logically prior actual infinity (the domain of the values that the variable could take)—perhaps too casually (or Hegelian?) given that he was aware of these paradoxes.
Monday, July 16, 2007
More Carnivals
The day of the 50th Philosophers' Carnival, and time to use the carnival submission form to tell me of interesting posts related to the philosophy of mathematics (or the philosophies of logic and science) and mathematical philosophy, which is the use of mathematics (including formal logics, probabilities and scientific models) to tackle any philosophical topic.
......I don't want to exclude any interesting stuff, so any recent post will be considered, but the more mathematical it is the more extensively will “recent” be taken, and the less exceptionally interesting it will have to be. Your post doesn't need to be anything earth-shattering - it just needs to be something that other philosophically-minded people might enjoy reading.
......At the moment I'm thinking about the Burali-Forti paradox, as I'm reading All Things Indefinitely Extensible (from the book being reviewed over on Logic Matters). (PS, July 19 sees the 12th Philosophia Naturalis.)
......I don't want to exclude any interesting stuff, so any recent post will be considered, but the more mathematical it is the more extensively will “recent” be taken, and the less exceptionally interesting it will have to be. Your post doesn't need to be anything earth-shattering - it just needs to be something that other philosophically-minded people might enjoy reading.
......At the moment I'm thinking about the Burali-Forti paradox, as I'm reading All Things Indefinitely Extensible (from the book being reviewed over on Logic Matters). (PS, July 19 sees the 12th Philosophia Naturalis.)
Friday, July 13, 2007
Metaphysical Progress
Heraclitus: Everything is made of water, and the world is full of gods. Thousands of years later and we reach David Lewis: Everything supervenes upon the local properties of space-time points, and the worlds are full of miracles. Hmm…
Tuesday, July 10, 2007
Physics and Ethics
This post is a bit long (fourteen hundred words) because I’m asking a question that strikes even me as odd—and if I seem to be defending the popular answer, that is only to emphasise that there is a genuine question here—i.e. who are the experts on ethics? For an example of why that may not seem to be much of a question, consider Anthony Grayling’s commonplaces about Faith (as opposed to science) in his The Meaning of Things (page 122):
......“Contemporary science hypothesises an evolutionary tale of
......physical forces. I say ‘hypothesises’, note; hypothesises on
......the basis of good evidence, severely tested, with many
......aspects of the accompanying theory successfully applied to
......daily life – as exemplified by the light you read by, the
......computer you work on, the airplane you fly in. The great
......advantage of science’s careful and thorough hypotheses,
......always ready to yield if better evidence comes along, is that it
......makes use of no materials or speculations beyond what the
......world itself offers. Religions, in sharp contrast, offer us eternal
......certitudes on the basis only of ancient superstition.”
But to begin with, surely our sciences do not only utilise “what the world itself offers” us—e.g. for most people (including most scientists) the standard model of those physical forces is taken on trust from particle physicists—not, that is, unless such things as the reputations of such people are included within “the world,” as perhaps they ought to be since we are, each of us, part of, rather than apart from, the world—although incidentally, if they are included then religious beliefs, about the non-physical aspects of the world, might not be so very different in kind from our scientific beliefs, about its physical aspects (cf. Polkinghorne’s defence of the Trinity as the best explanation of our written records; with which, incidentally, I disagree). Anyway, particle physicists base their theories upon data taken (almost exclusively) from places that hardly anyone else could gain admittance to—or could understand the workings of (in order to check what was going on) if they did. I’m not suggesting that such people are not to be trusted, just observing that trusting their authoritative testimony is what we do.
......In fact, although the daily life and work of most scientists (and many others) may well provide plenty of support for our beliefs about chemistry and electromagnetism (and thence in quantum mechanics), this “evolutionary tale of physical forces” is hardly so straightforward. For starters, alternative hypotheses are not always eliminated on the basis of the evidence, but surprisingly often because they are just uninteresting, for various reasons—for a glimpse of the sheer range of unconsidered possibilities, consider the following. Particle (or high-energy) physics research has surely (for the last half-century, at least) been of great interest to the military wings of the great world powers, who of course believe that it is of the utmost importance that certain classes of potential discoveries run little risk of falling into the hands of potential enemies—so my question is, what evidence does the world itself offer that the standard model of particle physics is not a fabrication designed purely for public (and thence potential enemy) consumption?
......Now, that particular hypothesis is not to be taken seriously, of course (it is not in capital letters, on a more popular blog), but clearly there are many possibilities, of various kinds, some quite reasonable (e.g. some non-string-theoretic approaches to particle physics may have been neglected for socio-economic reasons), and my point is not that particle physicists are not (or should not be) the experts about physical forces—far from it—but rather that few sorts of knowledge do not require a considerable degree of faith. There may be some, e.g. elementary mathematics, and our everyday knowledge of the world, and of our own minds, but those are hardly examples of scientific knowledge. Now, I personally favour a hitherto unconsidered (and hence unfalsified) hypothesis about physical continua (see my web pages) over the standard set-theoretic hypothesis—and for such reasons I’m undecided about physics beyond elementary quantum mechanics—but even I recognise that it is important what the experts on mathematics and physics favour (for what are presumably good, if not overwhelming reasons). But then similarly, I’m thinking, surely it is important what the experts on ethics think—whether we like what they say, or not—about what the moral facts are (e.g. that would be important in law and politics). So the question is, who are those experts?
......Since the popular answer would be something like, our religious leaders, consider the last line of Grayling above. As a one-liner about Galileo’s troubles it is not too bad, but surely religions are actually what dragged humanity away from the primitive (not to say primate) morality that is just what a purely evolutionary tale would leave us with, but to which few of us (and certainly not most physicists) would wish to return. Over the intervening centuries, the ethical views of those religions have been widely applied, and hence severely tested, both by daily life (as social structures have risen and fallen) and by internal disputes (as obscure as those within modern physics)—in short, why should the experts about ethics not be found (for the most part) within the major religions, just as the experts about physics are (for the most part) in the better-funded departments? I hasten to add that I’m not a member of any religion—in fact, I disagree with many standard religious opinions, e.g. about abortion (where, as a substantial dualist, I don’t see why our rights should not begin with our first breath), and so a good argument that I’m wrong about this answer would not be inconvenient—but (unfortunately) such disagreements are not the issue.
......Similarly, Stephen Hawking is clearly an expert on physical matters irrespective of whatever I think about strings (unfortunately). My worry is that many Naturalists are simply supposing that, just because they believe (on the basis of relatively little evidence at present) that moral facts would, if they exist at all, be best explained by an evolutionary tale, therefore religious thinkers are not experts on ethics. Naturally we think that we know what is right, independently of those religious systems that we are not part of, and of course we do not need those systems in order to function socially (at least not in the short term)—but then, we also know about the physical world independently of the hypotheses of the physicists; and most of us are physically competent, athletes and craftsmen more so than most physicists, who are nonetheless the experts on physics (for good reasons). And since I mean ethics and not meta-ethics (much as I meant above, physics and not metaphysics), so the experts are unlikely to include many philosophers—what philosophy has shown (e.g. via the paradoxes of the trolley and of distance) is that the activity of our consciences no more eliminates our need for experts on ethics than our physical intuitions eliminate our need for physicists.
......But I’m no expert, and maybe I’ve made the question clear enough, so I’ll return to reading Grayling, who is even better than Russell... But on page 100: “The religious attitude is marked by a robust refusal to take things at face value if inconvenient.” That proposition would be even truer were ‘religious’ replaced by ‘naturalistic’ (think of your own feelings and choices, and the physicists’ 10-dimensional strings, etc.)... And on page 101: “Why can we not be prompted to the ethical life by our own charitable feelings? The existence of a god adds nothing to our moral situation,” which inspires me to suggest sarcastically that surely we know about the physical world by bumping around inside it, that surely the existence of strings adds nothing to our physical situation! That is, I could say much the same for mathematics and the existence of sets, or physics and the existence of strings—but even I recognise that if strings exist then they would explain not only how we bump into things—how we actually bump into them, irrespective of what we think we are doing—but also the finer (and more paradoxical) details of the world around us. (And of course, even if they don’t exist, they may—or may not—be a good way of modelling reality.)... Etc.
......“Contemporary science hypothesises an evolutionary tale of
......physical forces. I say ‘hypothesises’, note; hypothesises on
......the basis of good evidence, severely tested, with many
......aspects of the accompanying theory successfully applied to
......daily life – as exemplified by the light you read by, the
......computer you work on, the airplane you fly in. The great
......advantage of science’s careful and thorough hypotheses,
......always ready to yield if better evidence comes along, is that it
......makes use of no materials or speculations beyond what the
......world itself offers. Religions, in sharp contrast, offer us eternal
......certitudes on the basis only of ancient superstition.”
But to begin with, surely our sciences do not only utilise “what the world itself offers” us—e.g. for most people (including most scientists) the standard model of those physical forces is taken on trust from particle physicists—not, that is, unless such things as the reputations of such people are included within “the world,” as perhaps they ought to be since we are, each of us, part of, rather than apart from, the world—although incidentally, if they are included then religious beliefs, about the non-physical aspects of the world, might not be so very different in kind from our scientific beliefs, about its physical aspects (cf. Polkinghorne’s defence of the Trinity as the best explanation of our written records; with which, incidentally, I disagree). Anyway, particle physicists base their theories upon data taken (almost exclusively) from places that hardly anyone else could gain admittance to—or could understand the workings of (in order to check what was going on) if they did. I’m not suggesting that such people are not to be trusted, just observing that trusting their authoritative testimony is what we do.
......In fact, although the daily life and work of most scientists (and many others) may well provide plenty of support for our beliefs about chemistry and electromagnetism (and thence in quantum mechanics), this “evolutionary tale of physical forces” is hardly so straightforward. For starters, alternative hypotheses are not always eliminated on the basis of the evidence, but surprisingly often because they are just uninteresting, for various reasons—for a glimpse of the sheer range of unconsidered possibilities, consider the following. Particle (or high-energy) physics research has surely (for the last half-century, at least) been of great interest to the military wings of the great world powers, who of course believe that it is of the utmost importance that certain classes of potential discoveries run little risk of falling into the hands of potential enemies—so my question is, what evidence does the world itself offer that the standard model of particle physics is not a fabrication designed purely for public (and thence potential enemy) consumption?
......Now, that particular hypothesis is not to be taken seriously, of course (it is not in capital letters, on a more popular blog), but clearly there are many possibilities, of various kinds, some quite reasonable (e.g. some non-string-theoretic approaches to particle physics may have been neglected for socio-economic reasons), and my point is not that particle physicists are not (or should not be) the experts about physical forces—far from it—but rather that few sorts of knowledge do not require a considerable degree of faith. There may be some, e.g. elementary mathematics, and our everyday knowledge of the world, and of our own minds, but those are hardly examples of scientific knowledge. Now, I personally favour a hitherto unconsidered (and hence unfalsified) hypothesis about physical continua (see my web pages) over the standard set-theoretic hypothesis—and for such reasons I’m undecided about physics beyond elementary quantum mechanics—but even I recognise that it is important what the experts on mathematics and physics favour (for what are presumably good, if not overwhelming reasons). But then similarly, I’m thinking, surely it is important what the experts on ethics think—whether we like what they say, or not—about what the moral facts are (e.g. that would be important in law and politics). So the question is, who are those experts?
......Since the popular answer would be something like, our religious leaders, consider the last line of Grayling above. As a one-liner about Galileo’s troubles it is not too bad, but surely religions are actually what dragged humanity away from the primitive (not to say primate) morality that is just what a purely evolutionary tale would leave us with, but to which few of us (and certainly not most physicists) would wish to return. Over the intervening centuries, the ethical views of those religions have been widely applied, and hence severely tested, both by daily life (as social structures have risen and fallen) and by internal disputes (as obscure as those within modern physics)—in short, why should the experts about ethics not be found (for the most part) within the major religions, just as the experts about physics are (for the most part) in the better-funded departments? I hasten to add that I’m not a member of any religion—in fact, I disagree with many standard religious opinions, e.g. about abortion (where, as a substantial dualist, I don’t see why our rights should not begin with our first breath), and so a good argument that I’m wrong about this answer would not be inconvenient—but (unfortunately) such disagreements are not the issue.
......Similarly, Stephen Hawking is clearly an expert on physical matters irrespective of whatever I think about strings (unfortunately). My worry is that many Naturalists are simply supposing that, just because they believe (on the basis of relatively little evidence at present) that moral facts would, if they exist at all, be best explained by an evolutionary tale, therefore religious thinkers are not experts on ethics. Naturally we think that we know what is right, independently of those religious systems that we are not part of, and of course we do not need those systems in order to function socially (at least not in the short term)—but then, we also know about the physical world independently of the hypotheses of the physicists; and most of us are physically competent, athletes and craftsmen more so than most physicists, who are nonetheless the experts on physics (for good reasons). And since I mean ethics and not meta-ethics (much as I meant above, physics and not metaphysics), so the experts are unlikely to include many philosophers—what philosophy has shown (e.g. via the paradoxes of the trolley and of distance) is that the activity of our consciences no more eliminates our need for experts on ethics than our physical intuitions eliminate our need for physicists.
......But I’m no expert, and maybe I’ve made the question clear enough, so I’ll return to reading Grayling, who is even better than Russell... But on page 100: “The religious attitude is marked by a robust refusal to take things at face value if inconvenient.” That proposition would be even truer were ‘religious’ replaced by ‘naturalistic’ (think of your own feelings and choices, and the physicists’ 10-dimensional strings, etc.)... And on page 101: “Why can we not be prompted to the ethical life by our own charitable feelings? The existence of a god adds nothing to our moral situation,” which inspires me to suggest sarcastically that surely we know about the physical world by bumping around inside it, that surely the existence of strings adds nothing to our physical situation! That is, I could say much the same for mathematics and the existence of sets, or physics and the existence of strings—but even I recognise that if strings exist then they would explain not only how we bump into things—how we actually bump into them, irrespective of what we think we are doing—but also the finer (and more paradoxical) details of the world around us. (And of course, even if they don’t exist, they may—or may not—be a good way of modelling reality.)... Etc.
Saturday, July 07, 2007
An Empty Set?
My problem with singletons was (as previously mentioned) that although it is intuitively clear how a plurality (many things) could also be a unity (one plurality)—e.g. one deck of 52 cards—it is consequently obscure how a single object could similarly be a unity different from that object. Nonetheless there is a related obscurity with pluralities, e.g. how do two pairs of socks differ from those four socks?
......Although our 52 cards (think of any particular deck) are exactly the same as those 4 suits (hearts, clubs, diamonds, spades) of 13 cards each—an application of 4 times 13 being 52—those are two different pluralities (52 cards and 4 suits), two different numbers of (different sorts of) things. In one sense they are the same thing, the same deck, but in another sense they are two different things, two different ways of partitioning the cards. When we refer to a collection—e.g. to a par of socks—we are usually referring not to that partition but to those things—to those two socks—but still, two pairs of socks are one collection, while the same four socks are another.
......Perhaps that is why collections are regarded as abstract objects, because they are akin to partitions (which are clearly abstract objects). And when we compare partitions it makes sense to compare partitions of some given things, so perhaps we should be thinking of partitions of some totality of things that are not collections, some universe (of discourse). After all, it remains fairly mysterious what something being a thing (standing apart from everything else) amounts to, but presumably whatever it is will involve those other things (that other stuff) to some extent.
......Of course, such partitions are just collections of collections, so I’m presupposing collections (of many into one), but if collections are indeed akin to partitions then that might shed some light on singletons—e.g. were each collection all the parts but one of some such universal partition, with everything else (in the universe) in the remaining part, so that a singleton would be a part of a partition. Or perhaps the singleton would be the whole partition (an abstract object), containing its single member (that part of the partition) within the rest of itself (the set-theoretic lasso).
......Now, so far I’ve overlooked overlaps, e.g. the collection of pairs (two aces, two fours etc.) is not a partition of our 52 cards, but of three identical decks—or rather (that being impossible) I should not have excluded collections from the universe. Things would get pretty complicated were they all included to begin with, but something like the standard cumulative-hierarchical approach might work out; and if so then maybe the (non-formal) empty set would be the degenerate partition of (i.e. nothing but the lasso that is) some such cumulative-hierarchical universe?
......Although our 52 cards (think of any particular deck) are exactly the same as those 4 suits (hearts, clubs, diamonds, spades) of 13 cards each—an application of 4 times 13 being 52—those are two different pluralities (52 cards and 4 suits), two different numbers of (different sorts of) things. In one sense they are the same thing, the same deck, but in another sense they are two different things, two different ways of partitioning the cards. When we refer to a collection—e.g. to a par of socks—we are usually referring not to that partition but to those things—to those two socks—but still, two pairs of socks are one collection, while the same four socks are another.
......Perhaps that is why collections are regarded as abstract objects, because they are akin to partitions (which are clearly abstract objects). And when we compare partitions it makes sense to compare partitions of some given things, so perhaps we should be thinking of partitions of some totality of things that are not collections, some universe (of discourse). After all, it remains fairly mysterious what something being a thing (standing apart from everything else) amounts to, but presumably whatever it is will involve those other things (that other stuff) to some extent.
......Of course, such partitions are just collections of collections, so I’m presupposing collections (of many into one), but if collections are indeed akin to partitions then that might shed some light on singletons—e.g. were each collection all the parts but one of some such universal partition, with everything else (in the universe) in the remaining part, so that a singleton would be a part of a partition. Or perhaps the singleton would be the whole partition (an abstract object), containing its single member (that part of the partition) within the rest of itself (the set-theoretic lasso).
......Now, so far I’ve overlooked overlaps, e.g. the collection of pairs (two aces, two fours etc.) is not a partition of our 52 cards, but of three identical decks—or rather (that being impossible) I should not have excluded collections from the universe. Things would get pretty complicated were they all included to begin with, but something like the standard cumulative-hierarchical approach might work out; and if so then maybe the (non-formal) empty set would be the degenerate partition of (i.e. nothing but the lasso that is) some such cumulative-hierarchical universe?
Thursday, July 05, 2007
No Use?
I probably won't be posting much until I start my PhD in September (elsewhere I've noticed some interesting answers to the question What use are philosophers of mind?) although I'll be hosting the Philosophy Carnival on August 6 (with a logical/mathematical/scientific theme).
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