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:)
Wednesday, October 03, 2007
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:)
......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:)
Sunday, September 30, 2007
"Religion"?
If Dawkins et al insist with their zeal to promote evolutionary theory as an inherently atheistic doctrine - which could be construed as a matter of faith - he may well be handing a rope to the creationist brigades. The US First Amendment forbids the teaching of faith in schools and it would be at least ironical if the creationists could use that to evict Darwin from the classroom.I've only just noticed that ironic spectre, which appeared at the close of Tristan's Religion advances despite science (and thanks to Dawkins) (13/9/2007, Science), and which raises the question, what is religion? Defining religion (8/7/2007, Religious Tolerance) is surprisingly difficult (it's fortunately clearer that evolutionary theory is just applied maths:) but as Kile says:
For Schleiermacher the sine qua non of religion was experience; a vibrant, deep, and transcendent feeling of the divine which caused him to define religion as "absolute dependence". This feeling of dependence is what Schleiermacher sees in all of the world religions as the tremendous sensation invoked at the thought of standing before what is Supreme in the universe.What I especially like about that definition is that it excludes the socio-political aspects of organised religions, except insofar as they are media for numinous experiences (since that was always a good distinction to draw:)
......Ironically, the etymology of "religion" suggests that the sciences—the study of Creation if we've a Creator, and if not then the study of what is Supreme in the universe—might be counted amongst the religions (even though they aren't inherently atheistic, and atheism isn't a religion, although it is a belief that isn't empirically justified); as Jung says:
Religion appears to me to be a peculiar attitude of the mind which could be formulated in accordance with the original use of the word religio, which means a careful consideration and observation of certain dynamic factors that are conceived as "powers": spirits, demons, gods, laws, ideas, ideals, or whatever name man has given to such factors in his world as he has found powerful, dangerous, or helpful enough to be taken into careful consideration, or grand, beautiful, and meaningful enough to be devoutly worshiped and loved.
Thursday, September 27, 2007
Science is Built of Facts
Science is built up of facts, as a house is built of stones; but an accumulation of facts is no more a science than a heap of stones is a house.
Between the elements of a continuum there is a sort of intimate bond which makes a whole of them, in which the point is not prior to the line, but the line to the point.
Poincaré said so; and lines are not made of points in the way that counting numbers bigger than one are made of ones, although the number of all the points in a line will be made of ones in a similar way.
Monday, September 24, 2007
Nothing much...
Not much work done this week, too many distractions, such as a discussion About Faith (into which I managed to introduce some maths, though (incidentally, some of the deeper issues raised by that discussion are currently being examined at Truth and Purpose):)
Sunday, September 23, 2007
My God!
My conception of God got (rather appropriately, if presumably accidentally) a perfect score on a test of its plausibility, due to my ticking just 3 boxes: (i) my God is the "Creator (of all that exists)," (ii) a "Perfectly Free" agent, and (iii) "a being with whom one can have a personal relationship."
......Do-It-Yourself Deity heads this list of games at TPM, and said of my conception:
......Anyway, had I said that God was "Omnipotent (all-powerful, able to do anything)," I'd have had the problem (according to the engineers) that S/he couldn't make 2 + 2 equal 5; and of course, nor could S/he have made it so that S/he was always nothing, but so what? Surely a perfectly free person with absolute physical and spiritual power over at least this Universe would be a God... Presumably, with such a reading of "all" I shouldn't have included "Creator," since I don't think that God must be self-created (which I suspect is impossible:)
......Incidentally, the reason why I excluded "all-loving" was the possibility of including evil acts in the quantification; but the engineers missed that, and said instead that I'd have to give up the personal relationship, in that case (I can have a personal relationship with someone only if there's something that S/he doesn't love?)
......(And why were the implausibilities of omniscience overlooked, e.g.:)
......Incidentally, I'm not religious, as such (once a Methodist, I discovered that I hate singing), but if I was going to be then according to this test I should consider:
1. Reform Judaism (100%)
2. Liberal Quakers (96%)
3. Bahai (91%)
4. Unitarian Universalism (86%)
5. Mainline - Liberal Christian Protestants (80%)
6. Orthodox Judaism (78%)
7. Sikhism (78%)
8. Neo-Pagan (75%)
9. Mahayana Buddhism (73%)
10. Islam (69%)
......Do-It-Yourself Deity heads this list of games at TPM, and said of my conception:
Not traditional? The creator of this Universe, and a personal God? Whatever...The metaphysical engineers are happy to report that, to the best of their knowledge, the God you conceive is internally consistent and could exist in our universe. But they are less sure that what you have described deserves the name of God. She is not, for example, all-powerful. A God which knows everything or is totally benign may be a wonderful ideal, but is she really a God unless she has ultimate power?
We suspect that your God is not the traditional God of the Christian, Jewish or Muslim faiths.
......Anyway, had I said that God was "Omnipotent (all-powerful, able to do anything)," I'd have had the problem (according to the engineers) that S/he couldn't make 2 + 2 equal 5; and of course, nor could S/he have made it so that S/he was always nothing, but so what? Surely a perfectly free person with absolute physical and spiritual power over at least this Universe would be a God... Presumably, with such a reading of "all" I shouldn't have included "Creator," since I don't think that God must be self-created (which I suspect is impossible:)
......Incidentally, the reason why I excluded "all-loving" was the possibility of including evil acts in the quantification; but the engineers missed that, and said instead that I'd have to give up the personal relationship, in that case (I can have a personal relationship with someone only if there's something that S/he doesn't love?)
......(And why were the implausibilities of omniscience overlooked, e.g.:)
......Incidentally, I'm not religious, as such (once a Methodist, I discovered that I hate singing), but if I was going to be then according to this test I should consider:
1. Reform Judaism (100%)
2. Liberal Quakers (96%)
3. Bahai (91%)
4. Unitarian Universalism (86%)
5. Mainline - Liberal Christian Protestants (80%)
6. Orthodox Judaism (78%)
7. Sikhism (78%)
8. Neo-Pagan (75%)
9. Mahayana Buddhism (73%)
10. Islam (69%)
Saturday, September 22, 2007
Is there a Point?
I've actually managed (accidentally) to do something relevant this week, as I'm currently commenting on an argument that points don't exist...
Thursday, September 20, 2007
Why Phi
In a shift of historic importance, America's colleges and universities have largely abandoned the idea that life's most important question is an appropriate subject for the classroom. In doing so, they have betrayed their students by depriving them of the chance to explore it in an organized way, before they are caught up in their careers and preoccupied with the urgent business of living itself. This abandonment has also helped create a society in which deeper questions of values are left in the hands of those motivated by religious conviction - a disturbing and dangerous development.Anthony Kronman, in Why are we here? (16/9/2007, The Boston Globe). Theology is as organized as philosophy, though. And what do philosophers actually do, anyway?
Wednesday, September 19, 2007
Science and Omniscience
When Patrick notices that he has overlooked something, he knows what it is like for him to notice that, but it seems odd that an omniscient being should know that... Unless that being was Patrick's creator (to whom he need be no less transparent than his own conceptions are to him) perhaps; but did Patrick overlook anything?
......Let SDL = God doesn't believe that SDL expresses a true proposition. On page 145 of The being that knew too much, Patrick argued that a rational person who believes that SDL is nonsense, and also that God believes only truths, would have to believe that God doesn't believe that SDL expresses a true proposition, whence (since that appears to be SDL) that rational person would believe that there was a truth (expressed by SDL, apparently) that God doesn't know... but appearances can be deceptive. Why should any rational person believe that nonsense could express a true proposition? (I argue here that sentences like SDL are nonsense, and as Michael said:) “You can’t say you are talking nonsense by talking nonsense, since to talk nonsense is not to say anything. But having talked nonsense, you can go on to say that it was nonsense, and now you are talking sense.”
......Anyway, bad arguments against omniscience (e.g. those that work only within set theory) aside, the following is an argument against it that goes (paradoxically) via a possible motive for the creation of a world not unlike that described by our best-tested science (an argument given more briefly earlier): Something that no sapient being (or telepathic beings, etc.) could possibly know is the full extent of what s/he doesn't (they don't) know. How could s/he rule out, for example, the existence of similar beings of which s/he was unaware? Maybe there are none (and if some, then there is something s/he doesn't know), and maybe s/he even believes that there are definitely none (although that would be foolish), but how could s/he know that? No one can have empirical access to places that are completely cut off from those s/he inhabits (by definition), so s/he could not know empirically that such places (which s/he knows are of a possible kind, since s/he inhabits one) are not inhabited by such beings (of which kind s/he is one), and how else could such propositions (about what would be, by definition, an external world) be known?
......So, even a relatively perfect being (which is, after all, the sort that we might expect to exist, much as we might expect a unified theory of physics to be elegant) might know that s/he could not be so absolutely omniscient. And rather than remaining ignorant, it would surely be better to be able to create ways of probing such unknowns (for which s/he would need to be able to change, and so exist in something like time, but since this would be better, that need not be a privation), whence s/he might want to explore such possibilities (as much as possible) by creating opportunities (insofar as s/he is capable) for such possible others to act (in some place to which s/he would therefore have empirical access:)
......Such a creator would therefore be perfectly compatible with all we know scientifically (and also religiously (to a less definite degree (naturally)))... A list of agreements would therefore be tedious, in a blog (here I'd rather ask, what is incompatible with that hypothesis?); but in short, if it was me I'd want first to find the limits of my natural place, insofar as I could discover such limits (and if not, I'd want to invent some), so that then I could make something like a bridge there (if I didn't discover something like that there already), something like a blank sheet of paper—something, in short, like this Universe, in which relatively simple physical laws allow a wide variety of agents, with little need for intervention (whence atheists note that if there is a God, he must be lazy). Of course, it may well be that there are no such others, that the quest would be endless; but therefore I'd make my paper (so to speak) beautiful, and recyclable (e.g. by having my creatures all return to my place for debriefing:) One day my walls might be found scribbled upon though, so I'd've built them to facilitate a wide range of responses too...
......Let SDL = God doesn't believe that SDL expresses a true proposition. On page 145 of The being that knew too much, Patrick argued that a rational person who believes that SDL is nonsense, and also that God believes only truths, would have to believe that God doesn't believe that SDL expresses a true proposition, whence (since that appears to be SDL) that rational person would believe that there was a truth (expressed by SDL, apparently) that God doesn't know... but appearances can be deceptive. Why should any rational person believe that nonsense could express a true proposition? (I argue here that sentences like SDL are nonsense, and as Michael said:) “You can’t say you are talking nonsense by talking nonsense, since to talk nonsense is not to say anything. But having talked nonsense, you can go on to say that it was nonsense, and now you are talking sense.”
......Anyway, bad arguments against omniscience (e.g. those that work only within set theory) aside, the following is an argument against it that goes (paradoxically) via a possible motive for the creation of a world not unlike that described by our best-tested science (an argument given more briefly earlier): Something that no sapient being (or telepathic beings, etc.) could possibly know is the full extent of what s/he doesn't (they don't) know. How could s/he rule out, for example, the existence of similar beings of which s/he was unaware? Maybe there are none (and if some, then there is something s/he doesn't know), and maybe s/he even believes that there are definitely none (although that would be foolish), but how could s/he know that? No one can have empirical access to places that are completely cut off from those s/he inhabits (by definition), so s/he could not know empirically that such places (which s/he knows are of a possible kind, since s/he inhabits one) are not inhabited by such beings (of which kind s/he is one), and how else could such propositions (about what would be, by definition, an external world) be known?
......So, even a relatively perfect being (which is, after all, the sort that we might expect to exist, much as we might expect a unified theory of physics to be elegant) might know that s/he could not be so absolutely omniscient. And rather than remaining ignorant, it would surely be better to be able to create ways of probing such unknowns (for which s/he would need to be able to change, and so exist in something like time, but since this would be better, that need not be a privation), whence s/he might want to explore such possibilities (as much as possible) by creating opportunities (insofar as s/he is capable) for such possible others to act (in some place to which s/he would therefore have empirical access:)
......Such a creator would therefore be perfectly compatible with all we know scientifically (and also religiously (to a less definite degree (naturally)))... A list of agreements would therefore be tedious, in a blog (here I'd rather ask, what is incompatible with that hypothesis?); but in short, if it was me I'd want first to find the limits of my natural place, insofar as I could discover such limits (and if not, I'd want to invent some), so that then I could make something like a bridge there (if I didn't discover something like that there already), something like a blank sheet of paper—something, in short, like this Universe, in which relatively simple physical laws allow a wide variety of agents, with little need for intervention (whence atheists note that if there is a God, he must be lazy). Of course, it may well be that there are no such others, that the quest would be endless; but therefore I'd make my paper (so to speak) beautiful, and recyclable (e.g. by having my creatures all return to my place for debriefing:) One day my walls might be found scribbled upon though, so I'd've built them to facilitate a wide range of responses too...
Sunday, September 16, 2007
Arguments for atheism
Religions are crazy.
So are scientific worldviews: are you a robot,I cannot see God.
a biochemical robot whose future already exists
in the future part of spacetime?
Can you see ten dimensions in the universe?Clever people are atheists.
I only see three in the space around us.
Clever people are bankers and lawyers.And so forth.
For more, see the carnival of the godless.
A Bad Argument (for atheism)
A famous sceptical scenario, BIV, asks you to imagine a disembodied brain (otherwise just like yours) in an alien scientist’s laboratory, being stimulated in such a way that that person (who’s brain it is), say X, seems to be in a world just like the one around you... and then asks, how do you know that you are not that person, X? The scenario is regarded as a sceptical one because it seems (the brain being disembodied) that X would not have real hands. But I think that X would have real hands if X was you; what would not be so real (as the things around us, by reference to which we all correctly interpret the word “real,” within our language) would be your brain (the one in the alien’s laboratory)—and so your brain might rightly, were you X, be thought of more or less as you now think of your soul (about which we know little). To ask, are you in such a BIV world? is to ask, do you have a soul? And to ask, does this Universe have a Creator? is to ask, is there such an alien scientist? But not even Dawkins would argue that since our hands do exist, therefore God doesn't!
Saturday, September 15, 2007
Continuity, Unity and Infinity
I’m back in Glasgow wondering, what are continua? Things that extend smoothly, is the obvious answer, but what is extension? And while things presumably extend smoothly if they contain no gaps that contain something else (whence they are unities), what if the space through which they extend is discrete? So what makes intuited space a continuum (so to speak)? Whilst we think of it as extended because it contains many things like our own body (e.g. many users of our own language), so might something more discrete (e.g. a finite matrix). So presumably another criterion is that those parts of a continuum that are not points must all be endlessly subdivisible (whence continua have infinitely many parts). But that is insufficient, as the rational number line is not thereby excluded, from being the shape of space itself (even though it does not contain the diagonal of the unit square)... (To be continued:)
Tuesday, September 11, 2007
Science is built of facts
and so is skepticism ...
It is cloudy. Trillions of droplets float in the shade of other droplets,
getting heavier and heavier until eventually they rain down. The sun
breaks through the shrinking clouds, and the sky frowns in a rainbow
(sunlight enters the drops, refracting as it does so, and when it reaches
the other sides of the drops it is reflected back; when it leaves the drops
it refracts again, and heads down to my eyes: I see a rainbow up there).
Under that grey sky, the green of the sunlit trees stands out, seeming
to be where the green trees are. But I know that that greenness is in
my mind, where the green of the rainbow is. Where are the trees?
There they are; but I put that greenness out there, so I wonder
did I put the trees there too? I take this world seriously but
I take my nightmares seriously when I am having one.
Saturday, September 08, 2007
What Katy Did
Once upon a time, Andy found a caterpillar, called it Katy, and showed it to his friend Bobby. Eventually Katy turned into a butterfly. “That’s Betty,” said Bobby. “No,” said Andy, “that’s Katy.”
......Now, is there a fact of that matter, about whether or not a caterpillar, and the butterfly that it changes into, are the same individual? I don’t see how there could be. On the one hand they have the same genetics, but on the other hand they have very different brains. And consider how, whereas a zygote divides into two cells of the same individual, an amoeba divides into two different amoebas, although maybe it would not be too unreasonable (if a little unnatural, from our human perspective) to regard that division as the original amoeba getting itself a disconnected multicellular body. Et cetera...
......But we’re rushing ahead of ourselves; so let’s return to Andy showing Katy the caterpillar to his friend Bobby. If names refer directly to the named objects, there must have been some definite object there, to be called by that definite name, ‘Katy’. Both Andy and Bobby knew (we may suppose) what caterpillars are (and what butterflies are), so that object was presumably the caterpillar in question—there was, of course, only one caterpillar there, Katy (and only one language being spoken, English), but then, for example, either that individual, Katy, had the property of sometimes having wings, or it did not. In short, either Bobby was wrong about the butterfly, or Andy was (? Although it’s probably just my failure to grasp the concept of direct reference, my intuitions being descriptivistic:)
......Now, is there a fact of that matter, about whether or not a caterpillar, and the butterfly that it changes into, are the same individual? I don’t see how there could be. On the one hand they have the same genetics, but on the other hand they have very different brains. And consider how, whereas a zygote divides into two cells of the same individual, an amoeba divides into two different amoebas, although maybe it would not be too unreasonable (if a little unnatural, from our human perspective) to regard that division as the original amoeba getting itself a disconnected multicellular body. Et cetera...
......But we’re rushing ahead of ourselves; so let’s return to Andy showing Katy the caterpillar to his friend Bobby. If names refer directly to the named objects, there must have been some definite object there, to be called by that definite name, ‘Katy’. Both Andy and Bobby knew (we may suppose) what caterpillars are (and what butterflies are), so that object was presumably the caterpillar in question—there was, of course, only one caterpillar there, Katy (and only one language being spoken, English), but then, for example, either that individual, Katy, had the property of sometimes having wings, or it did not. In short, either Bobby was wrong about the butterfly, or Andy was (? Although it’s probably just my failure to grasp the concept of direct reference, my intuitions being descriptivistic:)
Friday, September 07, 2007
Philosophy is Boring
“A detective novel written by a good philosophy student would begin: "In this novel I shall show that the butler did it." The rest will be just filling in the details.” (Jonathan Wolff:)
Thursday, September 06, 2007
Brown is the Brightest Colour
Most mathematicians and philosophers writing in English think that the counting numbers are not properties of ordinary things like pairs of shoes, even though the view that they are not originates with a Nazi sympathizer, Gottlob Frege (1848–1925).
Frege was trying to prove that 1 + 1 = 2. He did not think that he could simply define 2 to be 1 + 1, because he did not think that numbers could be composed of ones. He thought that either those ones would be the same ones, so that one and one would just be one (much as you and yourself are just you), or else they would be different, a first one and a second different one, in which case the signs for them, 1 and 1, should also be different (much as David and David, when they are the names of two different kings of Scotland, are written David I and David II).
Could the signs for those ones be given subscripts, such as i and ii? But then we would have had to have defined ii already. As a nineteenth-century German professor of mathematics with very conservative views, Frege thought that he was well placed to devise new definitions of the counting numbers (and of the infinite numbers that had recently been discovered, by another German professor of mathematics, Georg Cantor), so he did just that. And then he attempted to prove that 1 + 1 = 2 with those definitions, impressing the far more influential Bertrand Russell, who went on to make his own infamously long mathematical proof that 1 + 1 = 2 with his own definitions.
As a matter of fact, 1 + 1 = 2 because one thing and another thing make two things. Those two things are different, but each of them is one thing, and much as the red of a rose and the red of an apple might be the same red colour, those ones are the same.
Much as red is a property of physical things like roses, apples, shoes and so forth, the number one is a very simple property of things: each and every thing is one thing. And numbers bigger than one certainly seem to be properties of collections of things (a pair of shoes is two shoes). And of course, the properties of physical things are described, not defined, so Frege had to find some good reasons why numbers bigger than one are not properties of physical things.
Frege observed that how many things a collection contains depends upon what kind of thing we are talking about. Two shoes are also a lot of molecules, for example. According to Frege, colours are not like that. A red shoe is not also some other colour, for example. Except in a different light, maybe. Or to a different pair of eyes. Or against a different background. And so forth; but in any case, he also observed that while we can say "the men are white" because each is white, we cannot say "the men are many" because each man is many (although each man is a lot of molecules).
We can say it because the men are many, though. Frege explained his argument in more detail (the following is a cheap and cheerful version of Frege's argument):
If you have a blue tooth, you could mentally remove the property of being blue to leave a colourless tooth. You could then remove the property of being a tooth, in order to see in your mind's eye what was left. You can, in short, mentally remove various properties, in order to isolate the other characteristics. But if you have, say, three teeth, and you remove all of the sensory properties of the teeth (their colours, their shapes, their hardness and so forth), would you be left with a one for each apple? Would you be left with the number three?
According to a very important German, Gottfried Leibniz, you cannot have three identical things. So, because you cannot strip away all of the sensory properties and be left with the number three, the number three is not a property of collections of physical things. What is mentally removing colours, though? Is it like looking at a black-and-white photograph? That makes sense, but would mentally removing their being teeth from some teeth be like having a hologram of some teeth? Or is it like having a description of some teeth, in some language? Or a mathematical model of some teeth? Or the logical possibility of some teeth? Or the idea of some teeth? Or the memory of some teeth? I find myself mentally picturing some teeth and then imagining that I am imagining them! Still, the argument above is a simplified version of Frege's argument. Let us stick with simple properties like colours and shapes.
Suppose that I remove the shapes and sizes of the three teeth, and their positions in space, but nothing else. Presumably there would still be something real. Would it be three teeth without shapes, sizes, or positions in space? But without shapes, sizes or positions in space, how could what was left be three of anything?
Perhaps it could be three overlapping wavefunctions. But prima facie, those teeth being three in number has a lot to do with their shapes, sizes and positions in space, all of which are properties. So, that version of this argument seems to show that numbers are properties of physical things (although by mentally removing all of the sensory properties of the three teeth, you might be left with three teeth in a space containing no sensory organs, in which case there would still be those three teeth). Frege's argument may well have been better (although Idealism was popular in his day), but it is certainly a simple matter to imagine any number of identical objects:
Imagine a space containing nothing but three identical spheres at the corners of an equilateral triangle, or four at the corners of a square, and so on. It is easy enough to imagine that all of the properties of those spheres, including their external relations with each other, are identical.
Perhaps there are better arguments that numbers are not properties nowadays (there must be some reason why the view that numbers are not properties is so popular with our experts, who do not usually agree about much beyond the bare facts, such as arithmetic). However, as I wade through the rather large literature that defends this rather unnatural view of that Nazi sympathizer, I am not expecting much. At first glance, a lot of the literature assumes that there are not really any collections of physical things in the world, just individual physical things. That is a bit like saying that there are not really any colours in the world, only photons, neurons and the like. Could there be an argument that there are not really any colours? What about an argument that colours do not make sense? What about this:
One photon hits your eye and you might see one of the primary colours. If two photons hit your eye at the same time, then you might see a secondary colour. But only if three arrive together could you see brown. Brown should therefore be the brightest colour. But in fact, it isn't (yellow is). Does that mean that colours do not make sense? Does it mean that there are not really any such things as colours?
Obviously not. Indeed, how could any argument mean that there are no colours, when we can see that there are colours?
And how could any argument mean that there are no collections, when there clearly are things being referred to collectively?
There are, for example, ten words in this final sentence.
Wednesday, September 05, 2007
Is this Irrational?
Radio 4’s Beyond Belief last Monday was a discussion about embryos (and as far as I can recall it was) between a Scientist (a gradualist, defending the current 14 day rule), a Muslim (who thought that using embryos up to at 40 days, at least, was OK) and an Anglican, say A, who argued that human embryos acquire human rights at the moment of their conception, on the grounds that their humanity (in the relevant sense) is an all or nothing affair (which they certainly have after they’re born, and lack before they exist), whereas embryonic development is indeed gradual (or so I recall—there’s a listen-again feature at the above link, but I’m using my local library’s computers, and being quiet:)
......Towards the end of that 30-minute-programme, A was asked how he would respond to this scenario (more or less:) There’s a fire in a hospital, and A can choose to save either a baby, or else 5,000 embryos (which may have been created for implantation, rather than experimentation), but not both. Naturally A said that he would save the baby, and although my recollection is fuzzy, he began by saying that we don’t always do the right thing, which sounded fudgey. But after posting yesterday’s post, it occurred to me that such a scenario might have yielded a better example of a proposition that was (rationally) regarded as implausible and yet (rationally) believed.
......Incidentally Christopher’s original question explicitly concerned propositions of an ethical nature, as well as the attribution of more physical properties to objects (as in yesterday’s post); and incidentally my first suggestion (in a deleted comment on Christopher’s post) was that we might find it implausible that a certain picture was not beautiful (e.g. because of believing art experts, who say that it is beautiful) whilst simultaneously (and not irrationally) believing that it was not beautiful.
......Anyway, whereas A might know how to save a baby, he might be less sure of what he would be doing with a collection of frozen embryos—e.g. moving them might damage them more than a fire could, for all A knows. And although the scenario might be tweaked to eliminate such uncertainties, note that A had deduced that embryos probably have rights, from what was essentially a lack of information about their (apparently continuous) development as human beings; so there would naturally be more uncertainty in A’s belief that embryos have human rights than in his belief that babies have them. And since the effect of such uncertainty upon a decision naturally increases with the value of what rides upon that decision, hence it would not necessarily be immoral (or irrational) for A to save the baby’s life.
......A could believe quite rationally that saving the baby would be best, because it is only implausible (not obviously false) that saving the baby would (ethically) be better than saving the embryos, hence saving the baby would (ethically) be better than saving the embryos—that is so even if 5,000 people should, all else being equal (tweaking the scenario if necessary), take precedence over one person (this is quite standard, e.g. see the opening paragraph of Hawthone and Stanley's forthcoming Knowledge and Action), but as A pointed out, such Utilitarian assumptions might not be valid (e.g. if each life had infinite worth) and were certainly inappropriate to that radio programme, whose issue was medical scientists using (or killing) embryos, not failing to save them (cf. a doctor choosing to save six people rather than one, which might be reasonable, compared with a doctor killing one person in order to get organs to save the lives of the six, which would be insane:)
......Towards the end of that 30-minute-programme, A was asked how he would respond to this scenario (more or less:) There’s a fire in a hospital, and A can choose to save either a baby, or else 5,000 embryos (which may have been created for implantation, rather than experimentation), but not both. Naturally A said that he would save the baby, and although my recollection is fuzzy, he began by saying that we don’t always do the right thing, which sounded fudgey. But after posting yesterday’s post, it occurred to me that such a scenario might have yielded a better example of a proposition that was (rationally) regarded as implausible and yet (rationally) believed.
......Incidentally Christopher’s original question explicitly concerned propositions of an ethical nature, as well as the attribution of more physical properties to objects (as in yesterday’s post); and incidentally my first suggestion (in a deleted comment on Christopher’s post) was that we might find it implausible that a certain picture was not beautiful (e.g. because of believing art experts, who say that it is beautiful) whilst simultaneously (and not irrationally) believing that it was not beautiful.
......Anyway, whereas A might know how to save a baby, he might be less sure of what he would be doing with a collection of frozen embryos—e.g. moving them might damage them more than a fire could, for all A knows. And although the scenario might be tweaked to eliminate such uncertainties, note that A had deduced that embryos probably have rights, from what was essentially a lack of information about their (apparently continuous) development as human beings; so there would naturally be more uncertainty in A’s belief that embryos have human rights than in his belief that babies have them. And since the effect of such uncertainty upon a decision naturally increases with the value of what rides upon that decision, hence it would not necessarily be immoral (or irrational) for A to save the baby’s life.
......A could believe quite rationally that saving the baby would be best, because it is only implausible (not obviously false) that saving the baby would (ethically) be better than saving the embryos, hence saving the baby would (ethically) be better than saving the embryos—that is so even if 5,000 people should, all else being equal (tweaking the scenario if necessary), take precedence over one person (this is quite standard, e.g. see the opening paragraph of Hawthone and Stanley's forthcoming Knowledge and Action), but as A pointed out, such Utilitarian assumptions might not be valid (e.g. if each life had infinite worth) and were certainly inappropriate to that radio programme, whose issue was medical scientists using (or killing) embryos, not failing to save them (cf. a doctor choosing to save six people rather than one, which might be reasonable, compared with a doctor killing one person in order to get organs to save the lives of the six, which would be insane:)
Tuesday, September 04, 2007
What is rational?
The so-called “scientific atheists” claim that while science is rational, religious thinking is irrational (seemingly oblivious to the cogency of, for example, McGrath’s reasoning), but what do they mean by “rational”? Do they mean that our beliefs must cohere with each other and be proportioned according to the evidence? But empirical data has to be interpreted according to an existing system of beliefs, and that system can be modified catastrophically (in the mathematical sense) in the light of new evidence.
......Even within science, scientific paradigms change. And catastrophic modifications must be occurring in the minds of individual scientists as they grow up; presumably they do not fixate irrationally upon the first system of beliefs that they acquired. Indeed, similar modifications are probably occurring for all of us, a lot of the time, and so the coherence of our beliefs would seem to be more of an ideal than an actual possibility.
......Furthermore, in order for our beliefs to be realistic, they should depend upon how the world is, but we judge the importance and likelihood of possible evidence in the light of our existing beliefs, so we are rather at the world's mercy when it comes to being rational. Although I’m not quite sure what “rational” means.
......Even within science, scientific paradigms change. And catastrophic modifications must be occurring in the minds of individual scientists as they grow up; presumably they do not fixate irrationally upon the first system of beliefs that they acquired. Indeed, similar modifications are probably occurring for all of us, a lot of the time, and so the coherence of our beliefs would seem to be more of an ideal than an actual possibility.
......Furthermore, in order for our beliefs to be realistic, they should depend upon how the world is, but we judge the importance and likelihood of possible evidence in the light of our existing beliefs, so we are rather at the world's mercy when it comes to being rational. Although I’m not quite sure what “rational” means.
Imagine, for example, that Dawkins is abducted by aliens. Given such quantities of first-hand experiences, Dawkins would probably change his beliefs about UFOs. Had another man come to him earlier with such a story, Dawkins would surely have told him to take seriously the probability that he had imagined the abduction. And when Dawkins returns to Earth, and that empirical data turns into memories of a very strange character, he might naturally and not unreasonably revert to his original skeptical beliefs about UFOs (and regard the abduction as a dream). His friends would no doubt be pleased by his return to sanity.
Now, suppose that McGrath is shown all of the primary data and all of the reasoning that atheists find so important (suppose that he does not already know it), and suppose that that evidence is so good that he loses his faith, temporarily, but that he similarly reverts to his earlier beliefs eventually (and regards his loss of faith to have been the work of the devil). Scientific atheists would hardly say that that reversion was rational.We can suppose that Dawkins and McGrath were both attempting, at key moments within those fictions, to choose between one set of beliefs (with their explanation of the data) and another set (with their explanation). Making such choices rationally is clearly consistent with being in two minds about things, from time to time. It is consistent with holding inconsistent beliefs, from time to time. And whilst those two examples are naturally rather odd, that was just to keep them simple. People who try to think things through will often find themselves in analogous but much more complicated situations, often with little rational expectation of making their minds up in any reasonable time. But in various situations, one set of beliefs might be more appropriate than another. Is such appropriateness more important than coherence, when it comes to being rational? And could such appropriateness be a big part of what “scientific atheists” mean by science being rational and religious thinking irrational?
Saturday, September 01, 2007
What's in a Name?
There is a famous fictional character called Sherlock Holmes. If you discovered that there was a real Victorian detective called Sherlock Holmes who lived in London, then that might be the same person (perhaps the stories were not fictional), but if you met a detective called Sherlock Holmes who lived in London then he would definitely not be the same person, because he would not be fictional. Would it matter whether he was made of 10-dimensional string or not? No. Would it matter if he was made by God, out of whatever God would have made him out of? No, how could it matter what he was made of? Now, if you saw a movie about Sherlock Holmes, then that character could well be the same fictional character, even if the character in the movie was not exactly the same as the character in the books. But what about a character in a video game based on the Sherlock Holmes books? I ask because it is conceivable that we are now living in a Matrix-style world, and it seems to me that it would not matter what the detective that you might meet in the real world would be made of. What if he was like a character in a video game, though?
Friday, August 31, 2007
Dianniversary
Today is the tenth anniversary of Diana’s death (her tenth deathday if you like). According to Gordon Brown, this should be a public holiday (Diana Day). And Francis Wheen, on pages 154-5 of How Mumbo-Jumbo conquered the World, recounts how:
Nine months after the accident, the Mail serialised a book by Rita Rogers, the Derbyshire psychic whose ‘extraordinary powers’ had so impressed Diana and Dodi. She disclosed that at her first meeting with Dodi Fayed the previous summer she immediately had ‘a feeling of danger’: she saw a black Mercedes and a tunnel, and ‘felt there was a connection with France’. Extraordinary indeed: only the most mean-spirited sceptic could have wished for some sort of corroborative evidence, such as a letter from Fayed thanking Rogers for the warning about driving through French tunnels.Ten years ago I was working nights, so I got the early edition of the Sunday Mirror on the way home, in which Carole Malone wrote that she was sick of hearing about Diana (providing some balance to the supplement, which had lots of pictures of Diana in a bikini on a boat in the tropics). Paradoxically, she must have been very upset by Diana’s death (and not just because it meant that she heard a lot more about her).
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