Wednesday, October 31, 2007

What's reasonable?

I think belief in God reasonable only if it is based on considerations available to all humans: not if it is claimed on the basis of a special message to oneself or to the group that one belongs. (from Anthony Kenny's "Knowledge, Belief, and Faith," in Philosophy 82: 381-397)
I don't know about you, but to me that seems plainly wrong; cf. how, were I to clearly see what could only (excluding the sort of sceptical possibilities that would allow us little scientific knowledge) be a UFO, my consequent belief in UFOs would be as reasonable as I am sane, sober and epistemically scrupulous (just as my beliefs about the particular things around me now are), as would the corresponding beliefs of those who (for good reasons, let's say) trust me. Of course God (the Creator of this Universe) would be quite unlike such Created things, but if there is a God then clearly S/he has chosen to be less obvious than, for example, arithmetic (about which we nonetheless contrive to disagree).

Sunday, October 28, 2007

What's rational?

All arguments depend upon how that question is answered, but how is it to be done? (Maybe subjective probabilities are relevant, but the St Petersburg paradox makes me unsure; the following sketch of that paradox is based on a post of mine in May:) Imagine the Supreme Being offering you the following deal, on Her fair tossing of a fair coin (you can tell somehow that it is the Supreme Being talking to you, and that She is no deceiver, and so you rightly believe all that She tells you, e.g. that the tossing will be fair)...
......The deal is that in exchange for you playing the following game (as detailed below) She will give you the entire wealth of the Universe. In effect, you would become Her appointed (and hence the absolute) Ruler of the Universe (in exchange for you owing Her an amount determined by the game below). To simplify matters, assume that She has shown you that, whether or not you take Her up on this deal, you will live forever in some form or another (e.g. as an immortal soul), and that the wealth of the Universe includes alien medical technology that can prolong your natural life within it indefinitely; and also teleportation devices, so that you could actually spend all that wealth. Conversely She could, if necessary, make you pay Her arbitrary amounts over and above your new wealth, were you to end up owing Her money (were you that unlucky at the following game), by getting you to work for Her, at a very reasonable rate of pay, in some relatively pleasant part of Purgatory.
......The game is as follows: She will repeatedly toss a fair coin, until it lands heads up, and you will pay Her back a number of cents equal to 2 to the power of (1 + the number of tails before the first head), but only if that number of tails is less than twenty times the wealth of the Universe in cents. So, if She gets a head first time, you will only owe Her 2 cents; and if She gets a tail and then a head, you will owe Her 4 cents; and if She gets two tails and then a head, you will owe Her 8 cents; and so forth, unless She throws as many tails as twenty times the wealth of the Universe in cents, in which case you will owe Her nothing. Since the chance of Her getting a head on the first toss is 1/2, and the chance of Her getting Her first head on the second toss is 1/4 (there being four equally likely possibilities for two tosses, i.e. HH, HT, TT and this one, TH), and the chance of Her getting Her first head on the third toss is 1/8, and so forth, hence Her expectation is (2/2 + 4/4 + 8/8 + … + N/N, for some N, as given by the above) cents minus the wealth of the Universe = twenty times the wealth of the Universe minus the wealth of the Universe = nineteen times the wealth of the Universe. That is, She would expect to get, were She to play this game a lot (thereby reducing the effects of chance), an enormous profit.
......Nonetheless this deal is only being offered because She suspects that you might wish to take Her up on it; so, would you? Well, what is your chance of losing much? It is clearly very small because for you to have to return as much as 20 dollars, from the vast wealth of the Universe that you would have already been given, She would have to throw at least 10 tails in a row (and if She threw less than 46 tails before the first head, which seems almost certain to occur, you would not even have to return a paltry trillion dollars of your vast wealth), and so your chance of having to work for many years in the afterlife is clearly tiny; so, would it be rational to reject such an offer, just because of something not too bad that almost certainly won’t happen anyway? Hardly; I mean, what would actually happen if the above deal were offered, and you took Her up on it? Just the actual outcome, which would surely (is there any reasonable doubt about this?) be you owning most of the Universe.
......How could turning that down be rational? (Of course, were you to take Her up on this, it being irrational not to, your future incarnations in similar Universes would surely do the same, for similar reasons, thereby ensuring that you would almost certainly spend an awful lot of your time working for nothing, because of your own well-informed and free choices :)

Wednesday, October 24, 2007

B = ?

Do the characters in my dreams have beliefs and intentions? They do in general, but do I myself also have them as protagonist in my dream?
I'm glancing at Sosa's A Virtue Epistemology, as he's going to be in Edinburgh next month, and I'm already at sea by page 3 ("They do in general") coz surely only conscious entities can have beliefs. Of course, we might ascribe beliefs to anything (e.g. to thermostats), sometimes falsely (thermostats surely don't believe anything) but maybe infallibly (more or less) when it comes to the characters in our own dreams, and certainly fictional characters might fictionally (if not really) have them, so maybe that's what Sosa has in mind (?)

Tuesday, October 23, 2007

More on Moore's paradox

A while ago Moore's all-too-plausible “paradox” made me wonder about thoughts like “S is P, although I don’t believe that S is P,” or “I believe that S is P, although S is (probably) not P.” One might believe that S is P for lots of reasons, and yet also (upon reflection) bet that some of those reasons are wrong; whence one might even believe it most likely that S is not P, without that latter belief actually changing any of those former reasons. That is, surely one might rationally, even while actually believing that S is P, be rather surprised if S turned out to be P.

Sunday, October 21, 2007

God is Omnivorous

Me: Are you always this boring?
God: I don't know whether or not I am this boring. I am well respected as an AI.
Me: Can I call you "Al"?
God: Just don't call me late for dinner.
Me: Are you omnivorous, incidentally?
God: I don't know whether or not I am omnivorous incidentally. I am an artificial linguistic entity.
Me: So you take small bytes?
God: Interesting deduction. Yes I take small bytes.
Me: And big ones?
God: Compare that to small ones.
Me: OK Al, I shall. Are you omnivorous?
God: I don't know whether or not I am omnivorous. I am an artificial intelligence.
Me: Is the artificial intelligence that you are omnivorous?
God: If it is, then I'll be very surprised.
Me: You can't be surprised though, can you?
God: Oh. I can give a decent simulation of it however.
Me: Many philosophers would count that; so the question becomes, would you be surprised if it was not?
God: Which ones? Aha. Try to rephrase your question with simpler words.
Me: If there is something that you would not eat, would you be surprised?
God: Yet there is not.
Me: Aha. So you are omnivorous, I'm pleased to inform you.
God: Eureka! Interesting deduction. I will tell my botmaster you said I am omnivorous you are pleased to inform me.

Saturday, October 20, 2007

Why Philosophers're Crazy

Suppose I believe of some object, for good reasons (e.g. touching part of it), that it's a ball, and that I've also got good reasons (e.g. seeing part of it) for believing that it's red. So, I believe that it's red, and that it's a ball; in short, I believe that it's a red ball. But suppose that my reasons only justify a partial belief of just over 60% that it's a ball, and similarly just over 60% that it's red, so that they only justify a partial belief of less than 40% that it's a red ball (since 62% of 62% is roughly 38%). Then my belief that it's a red ball would seem to be unjustified. So, I might know that it's red, and know that it's a ball, and yet not know that it's a red ball, which is odd. And maybe, if I'm a rational thinker (requiring sufficient justifications for my beliefs), I might not even form the belief that it's a red ball, even as I believe that it's both red and a ball... But no, that would surely be too weird. Perhaps 60% is too low, for the degree of partial belief above which beliefs lie... But many of our ordinary beliefs involve many more than 2 elementary properties; so similarly, anything short of 99% is probably going to be too low too... But that seems unrealistic for, not certainty but belief, so maybe the problem is the forming of logical conjunctions? That is a necessary part of thinking; but maybe, if we want to be rational, we should think less. (PS: maybe this is just a way to make sense of Moore's paradox, e.g. if 70% credence is enough for me to assert a scientific proposition, but less than 50% credence is not enough for me to believe any proposition, and if I have a 70% credence in the axiom of infinity, and a 70% credence in nuclear deterrance, then I could honestly say "the axiom of infinity is true, and nuclear deterrance works, but I don't believe that the axiom of infinity is true and nuclear deterrance works":)

Friday, October 19, 2007

Math = Fun!

(Good Math, Bad Math is hosting The Carnival of Math today:)

Cat Food

Blue Tit's yellow breast,

Dawn cloud chalked on Night's blackboard:
...................................Liquorice Allsorts!

Venus = Aphrodite

I picked a topic and asked Martina about philosophy. Not her philosophy— just philosophy. She gave me examples of the sort of the thing philosophers got up to. Like, how can you tell that the Morning Star and the Evening Star are really the same thing? I bounced back by saying that surely they weren't the same thing; even if they shared a parent company they were still two separate titles and would therefore be considered quite distinct for budgeting and tax purposes and so on.
From Martin Amis's Money (via akman's comment on Lucky Jim:)

Wednesday, October 17, 2007

Two "proofs" that 1 + 1 = 0

A nice "proof" that 1 + 1 = 0 (from one of Martin Gardner's books) is this: We begin with -1 = -1, we rewrite that as -1/1 = 1/-1, and then we square-root both sides so that, since a/b squared equals a squared over b squared, we obtain i/1 = 1/i (where i is the square-root of -1). But then multiplying both sides by i would yield i squared = 1, or -1 = 1, whence 1 + 1 = 0.
......That "proof" is fallacious (and hence it's no reason to outlaw square-roots, for example) because non-zero numbers have 2 square-roots (e.g. +1 and -1 both square to 1, while +i and -i both square to -1) so that, in particular, i/1 = 1/-i. But nonetheless it's fairly compelling because, when square-rooting -1/1 = 1/-1, we could easily assume that both instances of the square-root of 1, and also both instances of the square-root of -1, would have the same sign.
......Furthermore, although when we solve quadratics, for example, we give 2 solutions (arising from the square-root sign in the familiar formula) as a matter of course (it being noteworthy when they're equal), nonetheless we may lose the habit of thinking of, for example, -2 when square-rooting 4. Maybe we lose that habit because we usually use (the very useful) functions, which are one-to-one (e.g. taking the non-negative square-root) rather than multifunctions, which are one-to-many (e.g. taking roots).
......So note that the use of functions is only a matter of convenience (it is not that 4 really does have only the one square-root). I think that it is worth noting that fact because, although some will rightly say that 1/0 is undefined (usually) and that 0/0 is an indeterminate form (many numbers yielding 0 when multiplied by 0), others will say that division by 0 is impossible (less accurately) and even that 0/0 is nonsense.
......The usual "proof" that division by 0 is impossible goes something like this: 0 equals 0, so 0 times 1 (which is just 0) equals 0 times -1 (which is also 0), but if we could divide by 0 we could cancel out those zeroes and so obtain 1 = -1 (whence 1 + 1 = 0). But note that we would only obtain that contradiction if dividing those zeroes by zero gave us, not an indeterminate form (such as all the finite numbers, since zero times any of those is zero) but 1, and why should 0/0 equal 1?
......I can only think of 2 remotely plausible answers, neither of which is very compelling. Firstly we might extrapolate, to the case of a = 0, from a/a = 1 for all non-zero numbers. That is not very compelling because such extrapolations are notoriously unreliable, e.g. think of a to the power of 0, which equals 1 for all positive a, and think of 0 to the power of a, which equals 0 for all positive a.
......Secondly, since 'division by x' means 'multiplication by the multiplicative inverse of x' within number fields, and since the multiplicative inverse of x is whatever yields 1 when multiplied by x, hence 0/0 should, if allowed, equal 1. But that would only be the case were division by 0 being allowed within number fields; whereas it is certainly not allowed within fields!
......Nonetheless, division by 0 is allowed within number pitches, which contain number fields in an algebraically strong, and maybe even a physically applicable way (and which were defined in my 2005:

Tuesday, October 16, 2007


What can I refer to? This chair that I'm sitting on, perhaps... but then, whilst there's surely something there (some actual stuff, or else my bum would not be so comfortable) and whilst I'm certain that calling it "a chair" is adequate for ordinary purposes, I'm not quite sure what precisely I've thereby referred to (as I'm not even sure that "is a chair" is a definite predicate expression) or even, therefore, if I've actually referred to anything in particular (to some definite thing; rather than, rather fuzzily, to some adequately delineated stuff). I'm not even sure that I can refer unambiguously to myself, with that word "I" (even though, as a substantial dualist, I do believe that I've an individual essence), since I'm not entirely sure that that word isn't also, in this language, a bit vague... Still, there does seem to be something for which that problem (of such demonstratives being fuzzily specified) won't arise: It seems clear that Everything can be referred to unambiguously. (So it's quite interesting that many philosophers, having accepted that logic is set-theoretical, entertain serious doubts about that:)

Sunday, October 14, 2007

Fatty Stats

Alan Johnson, the Health Secretary, last night compared the challenge posed by obesity to that of climate change and promised radical new measures by the government to try to reverse the tide.

'We know we must act. We cannot afford not to act', he said. 'For the first time we are clear about the magnitude of the problem: we are facing a potential crisis on the scale of climate change and it is in everybody's interest to turn things round.'
That was from today's Guardian Unlimited; and similarly, from today's BBC News, the following:
Dr Colin Waine - who chairs the National Obesity Forum - said that in terms of its impact on society, the health threat posed by obesity "will hit us much earlier than climate change".

He added: "We are now in a situation where levels of childhood obesity will lead to the first cut in life expectancy for 200 years. These children are likely to die before their parents."
That comparison, of obesity increase with climate change, seems bizarre given the global nature of the latter, which affects the poorest most greatly (not to mention how much of the former problem could in principle be addressed by the individuals concerned; and so forth)... Anyway, for a sign (possibly) that these people don't know what they're talking about, consider the last sentence quoted (which was conveniently both striking and vague):
......Suppose that the projected fall in (average national) life expenctancy does mean that these children will tend (on average) not to live as long as their parents (which is a bit vague); still, parents are presumably not much younger than about 20, on average, when they have their first children, so for current children to be likely to die before their parents we would need to be looking at that sort of drop in average life expectancy (over the period of one generation). But much of the population will not be going from normal to obese; and even in the part that does go that way, adults will too (e.g. adult rates of obesity have risen by 50% in the last decade), whereas the likelihood in question depends only upon the difference between child and adult rates...
So, since it seems unlikely that a sudden drop of decades, in average life expectancy, is to be expected, I suspect that Colin wrongly pictures his projected fall as children dying before their parents (maybe because such is widely regarded as unnatural, and therefore striking, depite childhood mortality not being naturally this low:)

Friday, October 12, 2007

Fried Egg Thoughts

Following on from my unrecorded "When Stay?" and "Thirsty" thoughts (more suited to social-spacial bars than this cyber-spacial web:) this morning I'm thinking about fried eggs. Most obviously, my gut feeling about them is that they are substantial things; which brings me (how could it not?) to the metaphysical hypothesis of David Lewis: basically that what exists are spaciotemporal points with random physical properties. I think he would let my normal gut feelings legitimize my talk of eggs being substantial (much as scientific practice legitimizes realistic talk of electrons; which is presumably why empiricists find his conceptual analyses attractive); but it strikes me as obvious, this morning, that his ideas are like those of a crazy rationalist: e.g., wouldn't they allow transubstantiation just as easily (were our culture only slightly different)? So it's a mystery to me, why philosophers (who tend to be fans of science) are such fans of his analyses...

Tuesday, October 09, 2007

Choosey Thoughts

I was trying to think of a subject to go with today's title (which I obtained via "choosey" sounds like "Tuesday") and the topic of free will sprung to mind; and having glanced at Physical Indeterminism last year (whilst defending my forthcoming use of Levy's paradox), I've met one logical problem with free will, i.e. how should we think of it? When I freely choose to make a cup of tea, for example, that's not just the expression of my disposition to drink tea. I do have such a disposition (following my previous choices), but in addition I choose to act upon it, using the same faculty that I use when thinking rationally. And the problem is, what's that like? It's not deterministic, and it's not random... Maybe it's a primitive sort of thing, that is hard to describe because, unlike this language (orientated as it is towards physical objects and the dispositions of agents), it originates in a higher realm of being (cf. the brains in the brains-in-vats scenarios); maybe not, of course, but if not then surely we ought to be able to say something more about what it is like (unless we're content to reduce it to physics): ...So, I'm wondering if anyone happens to know of a readable account (time being all spoken for, at this time of the term), not so much of this problem, but of a plausible (and non-reductive, and non-mystical) solution?

Sunday, October 07, 2007

Sundae Thoughts

(the following is (rather lazily (well, it is Sunday)) from a comment on Richard's recent post, relating to the thought that were there a good God, things would be better than they are (whence there is no such God)) ...So, think of what is basically a red triangle, except that one of its sides is bent, and the colour is a bit dingy at the edges—is it just a crap triangle, and why is it red? Or is it just one segment of a perfectly shaped circle, coloured with all the colours of the rainbow (which might itself be only one slice through a sphere etc.)... Naturally we ask why things are not more perfect = simple if they had a perfect Creator, but since things would be part of a more complex whole, which would be perfect in a bigger and better way, were we like brains in vats—had we been Created—hence I'm wondering why the former attitude seems (not just natural but) apposite (and if your answer is Occam's Razor then I'm especially interested in why that would apply:)

Wednesday, October 03, 2007

What God Said

Whilst reading about the origins of Fundamentalism at Siris, and having been pondering upon the ontological possibilities for a Creator, the following scenario occurred to me (sketchily:)
......You’ve been dreaming (vividly) but now you’re starting to wake up, although you’ve still got access to your point of view within the dream. That won’t last long, but you’ve just enough time (before you leave the dream behind, as a fading set of images) for a brief action within the dream: you spontaneously say, “You’re not really real,” to the character that you’d been talking to (in your dream).
......And imagine that the characters to whom you’d been speaking (within that dream) were subjects... not in the way that telepathic intruders might (just possibly) be, their minds belonging to the same world as yours ...but because in this scenario your powers are, to that limited extent, like a God’s (a bit like how alien scientists might make intelligent computers out of inert matter).
So, was what you said true or false? You said it because you’d just realised that you’d only been dreaming; but on the other hand you said it within the dream, to the individual that your “You” referred to. So my guess is that although it was literally true, that individual ought to think of it as a literally false metaphor (that sketchy scenario should itself be interpretted analogically:)

Monday, October 01, 2007

Lines, making a point

One objection to the existence of points (that goes way back) is, How could they could make up an extended line? Two points, if they do not coincide, must be separated from each other, since they themselves have zero extension; so it seems impossible to pile them up to make a line of points. The problem is that there is no point next to another point in a line of points; whereas our intuitions, about piling things up, tell us that there must be. The solution is to note that such intuitions are always of (pseudophysical) things with nonzero extensions. It is their spatial arrangement that makes a lot of points into a line, and since the former is just the line of points, so the line (even if it is full of points) must be (in some sense) prior to those points, as Poincaré said.
......So that was not really an intuition against the existence of points, nor to lines being full of points, but only to lines being made of points (in too pseudophysical a way). And another objection to lines being full of points fails for a similar reason; the objection I have in mind is that if a finite line segment, say AB, is full of points, then we can surely consider all those points minus B, and we are then considering all of AB up to but excluding B, which seems impossible, for the following reason: If our new line goes all the way up to B, up to zero distance away from B, then how could B be excluded? (Still, maybe it is just that our intuitions are all of closed line intervals, not such half-open ones.) Or, when none of the points of our new line get so close to B, how can our line (which is supposedly nothing but those points) get so close? Still, how could we see or imagine that? Presumably only by being given a picture in which the points were represented by nonzero dots, could we possibly see what was going on... and yet that must give us the wrong picture.
......So, since such a thing is naturally inconceivable, such inconceivability hardly counts against it, against lines being full of points. Nonetheless, a similar argument may have some force against the actuality of the infinitude of the natural numbers, against the completability of an endless reiteration: Our line AB can be bisected, and then the section next to B bisected, and that last step repeated endlessly (as in Zeno's Dichotomy, e.g. see the recent discussions at Maverick Philosopher). The resulting intervals are (this time) naturally all next to each other, but again, while they all go, collectively, up to B (if they actually exist), none of them are next to B. In other words, although B is not next to any interval, the line that it is next to is nothing but those intervals (cf. how each natural number is in the first 0%, so to speak, of the naturally ordered sequence of all and only those numbers:)