The Trinity, one God being three who relate to each other, seems paradoxical, prima facie, but perhaps it is only realistic (cf. how chemistry, as it became more realistic than alchemy, turned into a far stranger quantum mechanics). Let us presume that God created us, and the world around us, ex nihilo. Could He have incarnated as one of us? Well, He is presumably omnipotent; and perhaps we are essentially spirits, currently limited by our incarnation in human brains (with which we interact quantum mechanically), and perhaps God is also Spirit (who made us in His image).
......And an obvious way for us to think of creation ex nihilo is by analogy with the way we dream. When one dreams there is the creator of the dream (i.e. oneself), and the character in the dream whose point of view one has (i.e. oneself), and all the other stuff, which is not real but which corresponds (in God's creation) to us and the world around us. This is not supposed to be a very accurate model of divine incarnation; but if the other characters in one's dream were aware (as they obviously could not be) then they would naturally perceive one as a character with special powers and centrality, identified with and yet different to the creator of everything in the dream (including that special character's appearance), most strangely including themselves (which is where the analogy most obviously breaks down, but which may be where the Holy Ghost comes in).
......And quite generally perception (e.g. of a tree) seems to involve phenomena (e.g. green leaves) that are objectified (as what 'green leaves' refers to) in a rather paradoxical way (i.e. the problem of perception). Even when it is a perception of other people, so that we have a relatively direct knowledge of the kind of object, there is still an obvious distinction between how they seem to us and who they really are. And note that if there is a God then Idealism is not especially unrealistic. The connection between how something looks and what it is really like is made on the basis of wide experience and wise conjecture; and if the creator of everything else ex nihilo did incarnate as one of us, He might well be perceived by us as something more like a Trinity than not.
Friday, January 15, 2010
Thursday, January 14, 2010
Not-So-Free Thinking
Enlightened critics of religion like to point to a history of intolerance of criticism in religion. So it is nice to see Terry Eagleton and Karen Armstrong in fifth place in the New Humanist's 2009 Bad Faith awards, with about six-and-a-half percent of the votes. The New Humanist's article points out "that both have written books this year criticising the New Atheists and mounting what some might call a more sophisticated defence of religion." Quite generally it seems that whenever people talk about important things, there will be those who find good criticism most irritating; and the more popular the philosophy, the more politics there will be.
Wednesday, December 30, 2009
Duck-poo Soup
On a green pond smooth as glass,
mallards float and pass
the time. I stare
and look away. Splashes
make me turn to see water plumes
collapsing. A floating feather
makes me think of water's plumage
and up spring some ducklings, as
busy as bees in the water-lilies.
A lardy male waddles by
on lobstrous feet, evoking
with his draconian head
a Viking long boat.
A duckling ducks
submerges and emerges
like a broadside
at the adult's broad side
and nippily snatches a fly
from the bottom of the sky.
Flustered, the adult flaps
his wings, flinging off
oddly fluttering splodges. Weary of malarkey,
he fans out his butt like a pack of cards
and onto a flagstone flops. Wary of malady,
he gingerly stretches out
his white-collared neck
for soggy croutons floating
on this duck-poo soup. He wants
that sumptuous bread but he fears
being presumptuous. He does not want
to end up dead. But he cannot die.
He is a picture. I have immortalized
and immobilized him.
Unhinging winds fringe maroon-fingered moon,
like a waiter with a supernatural soup-spoon;
a crater of rubble like a burst bubble serving
as a seat of tranquillity for a duck quacking up
a soporific melody of sounds pacific:
Talk about a duck
floating on a lake,
looking like a wooden decoy does;
talk about a drake
ducking wooden ducks,
making all the ducklings he can make.
Friday, December 11, 2009
Two "proofs" that 2 + 2 = 5
The rationalist proof:
Starting with the concept of a bean, adding two beans and another two beans makes five beans because the concept of a bean is a bean (an ideal platonic bean).
The empiricist proof:
Add together two lines of length 2.36 (of our units of length) to make a line of length 4.72, and then round those lengths to the nearest whole number (of units).
Thursday, December 10, 2009
Deep Thought
First things first.
......And yet I find 'zeroth' in my dictionary, to refer to the one before the first one. In Wikipedia I find: The zeroth item is the initial item of a zero-based sequence (that is, a sequence which is numbered beginning from zero rather than one), and surely 'first' would have done just as well as 'initial' there. In such a sequence, the first element is also the second; that is, a certain equivocation has been introduced, a new sense of "first" added to our initial, informal sense.
......The idea of an ordinal number zero comes from the ordering of the integers on a number line, from negative to positive infinity (exclusive). But when we use ordinal numbers to include negatives, as with years, we naturally make the direction more explicit (e.g. with BC and AD) and exclude year zero (whence all the fuss about when the millenium began).
......Modern maths does not like directions. It finds it best to begin with a collection of natural numbers {0, 1, 2, 3, ...} that are most fundamentally ordinal numbers, and are usually reduced to pure sets. Mathematics does not like directions. Following Euclid's reduction of geometry to logic, geometry was naturally reduced to analysis following Descartes, and then arithmetized, with an arithmetic reduced to set theory.
......And yet mathematicians do like directions. Imaginary numbers were only taken seriously as numbers (like the negative numbers) when it was realised that the positive and negative imaginary numbers i and -i could be regarded as unit distances (like 1 and -1), specifically in the direstions perpendicular to the positive and negative directions of the "real" number line in a "complex" plain (which is how complex numbers are introduced to students).
......Given the foundation of the concept of direction in our experience of space, I would guess that if there really are extra dimensions in physics, they are more likely to correspond to the complex numbers of quantum mechanics (e.g. by representing dimensions of actual physical possibility) than the six dimensions of phase space (nor the ten or twelve of string theory, etc.).
......And yet I find 'zeroth' in my dictionary, to refer to the one before the first one. In Wikipedia I find: The zeroth item is the initial item of a zero-based sequence (that is, a sequence which is numbered beginning from zero rather than one), and surely 'first' would have done just as well as 'initial' there. In such a sequence, the first element is also the second; that is, a certain equivocation has been introduced, a new sense of "first" added to our initial, informal sense.
......The idea of an ordinal number zero comes from the ordering of the integers on a number line, from negative to positive infinity (exclusive). But when we use ordinal numbers to include negatives, as with years, we naturally make the direction more explicit (e.g. with BC and AD) and exclude year zero (whence all the fuss about when the millenium began).
......Modern maths does not like directions. It finds it best to begin with a collection of natural numbers {0, 1, 2, 3, ...} that are most fundamentally ordinal numbers, and are usually reduced to pure sets. Mathematics does not like directions. Following Euclid's reduction of geometry to logic, geometry was naturally reduced to analysis following Descartes, and then arithmetized, with an arithmetic reduced to set theory.
......And yet mathematicians do like directions. Imaginary numbers were only taken seriously as numbers (like the negative numbers) when it was realised that the positive and negative imaginary numbers i and -i could be regarded as unit distances (like 1 and -1), specifically in the direstions perpendicular to the positive and negative directions of the "real" number line in a "complex" plain (which is how complex numbers are introduced to students).
......Given the foundation of the concept of direction in our experience of space, I would guess that if there really are extra dimensions in physics, they are more likely to correspond to the complex numbers of quantum mechanics (e.g. by representing dimensions of actual physical possibility) than the six dimensions of phase space (nor the ten or twelve of string theory, etc.).
Tuesday, October 06, 2009
Eternity
Following on from a paper I've been writing for the past year (see previous posts under 'Theology'), I've been writing an MTh essay on the paucity of the reasons given for why Christians should believe that God is timeless. The essay glances at reasons given by Boethius, Helm and Mawson, and I'm wondering what (if anything) I've overlooked...
Thursday, October 01, 2009
Unretiring enigMan
Hi; tired of being retiring, I stretch my fingers with intermittent posts (on-going) and, as our droughtless summer (of many Painted Ladies) draws slowly to a close, I think its cultural highlights were: a sci-fi film of the good old 'new wave' kind, Precinct 9; and, more spook story than sci-fi, Iain Bank's Transition; and 60's nostalgiac Inherent Vice; and 90's nostalgiac Menage.
Saturday, May 02, 2009
Enigman at the Crossroads
Tiring of blogging (not so much reading others, as posting my own), it's time for Enigman to retire. There's a local conference in a couple of months, but even if that inspires me with any interesting thoughts, they'd be hopeless for blogging purposes. It seems to take me months (if not years) to make my thoughts coherent. Incidentally, a lot of my links will stop working soon, as my web-pages are on Geocities, which is closing this summer. I may move those web-pages to this site, probably after re-writing them (most were written a few years ago). The other thing I'll be doing this summer is starting to study theology properly (and catch up on my reading). My philosophical interests (which were originally in physics and freedom) were re-ignited ten years ago, via the metaphysics of mathematics, but were nearly quenched by professional analytical philosophy (with few exceptions, e.g. Iris Murdoch). Anyway, thanks for the comments, which made trying my hand at blogging worthwhile.
Thursday, January 29, 2009
Knowing what knowing is
When people say "I do not think it, I know it," they are saying that they are sure of it. Knowledge is important because we want bodies of knowledge that can be relied upon, and also because we need to distinguish between what we know and what we only think is the case, in all sorts of situations. When people say "I do not think it, I know it," they seem to be assuring us that what they think is indeed the case. Knowledge claims are a bit like promises. And promises can be a bit of a gamble:
Consider a boy sitting an exam, a boy who is not sure of an answer, but puts it down anyway. Suppose that his answer turns out to be correct. Would you say that he did not know the answer?I wonder if the following has some intuitive plausibility:
Proposition p is known by subject S when S's justification for believing p guarantees that p is true.How much of a guarantee S would need to provide would presumably depend upon the kind of uses that such knowledge might be put to, so it is conceivable that philosophers could disagree about what knowledge is without any of them being wrong!
A Linguistic Puzzle
Where, in ‘my tabletop is flat,’ is the meaning of that string of letters? Any meaning that it has must be read into it (it is not a string of magical sigils). You read those words, which are about the flatness of the table at which I am sitting, and perhaps you think of something like the tables that you know. You might think of such a thing being flat, and it being my table (whoever I really am). You get that string of letters, and you put your meanings into it. But the meaning of that phrase is, I think, the thought that I expressed with it, my thought that my tabletop is flat. And that is not the only mysterious thing about reading, of course. When we read something truly meaningful—e.g. a great novel—we do not seem to be getting out of it some rearrangement of what we already know. We seem to learn something about the world around us. Are we fooling ourselves?
Monday, January 19, 2009
Our Lewisian paradise
Modern philosophy (which began with Bacon and Descartes) looks antiquated until 1973, the year it acquired the now-standard way of analyzing counterfactuals: David Lewis’s possible worlds analysis (PW). If a one-eyed man is king in the land of the blind, Lewis seems to me to be like a blind man in the land of the one-eyed, successfully selling them a white stick:
......What if the difference is just a few neurons that you were born with, for example, but that those neurons also make it hard for you understand why it was difficult to tell you (since you then find such things so obvious)? What if lots of things; and so basically, how could all that really affect the meaning—and hence the truth—of what I’m saying? After all, we do seem to have got bogged down in an awful lot of fallacious arguments and counter-arguments since 1973; which may be ideal for professional philosophers in a stupid economy, but less so for those applying logic to the real world.
The blind man (Lewis) tells them that they can use the white stick to find out whether things are near enough to them to be a problem. I think that they should have told him that it is just a stick, and the wrong colour for their outfits.Lowe’s description of Lewis’s analysis is better than mine:
A counterfactual of the form ‘If it were the case that p, then it would be the case that q’ is said to be true if and only if, in the closest possible world in which p is the case, q is also the case – where the ‘closest’ possible world in question is the one in which p is the case but otherwise differs minimally from the actual world.Suppose that I’m trying to tell you something, and I know that you’ll find it hard to understand what I’m saying; I might say ‘If you knew what I was trying to tell you, you’d know how difficult this is.’ Now, if you did know, it would be trivially easy to tell you about it, so presumably I meant that after I’d told you, and you’ve understood me, you’d agree that it was difficult to tell you. But suppose it’s so hard to tell you that you never do get it. Does my meaning really depend upon which of the possible worlds in which I’ve told you is most like the actual world, in which you didn’t get it?
......What if the difference is just a few neurons that you were born with, for example, but that those neurons also make it hard for you understand why it was difficult to tell you (since you then find such things so obvious)? What if lots of things; and so basically, how could all that really affect the meaning—and hence the truth—of what I’m saying? After all, we do seem to have got bogged down in an awful lot of fallacious arguments and counter-arguments since 1973; which may be ideal for professional philosophers in a stupid economy, but less so for those applying logic to the real world.
Friday, January 16, 2009
Cartesian dualism, ii
I’ve yet to find a good philosophical argument against such substantial dualisms as (for the commonest) that our psychology results from the interaction of spiritual souls with the physical brains in which (so to speak) they’re incarnated. The two commonest arguments are (i) asserting the closure of the physical and (ii) failing to see how the spiritual could interact with the physical. Both are clearly fallacious as I’ve stated them, but I’ve yet to find a substantially fuller, non-fallacious expression of either. Now, I’ve blogged on (i) already, and have little to say about either anyway, but I’ve just been reading Lowe (Erkenntnis 65, 5–23), who put (ii) as follows (2006: 7, 11):
......As Lowe notes, people said that Newtonian action-at-a-distance was completely mysterious, and maybe it was, and is, but there was hardly any argument there against Newtonian physics (except in the minds of some philosophers). The truth turned out to be far weirder again, and it was to be had by working through Newtonian physics. There is that other problem, of how exactly the interaction works, but the way towards answering that is the relatively hard way of science, and why should it not go through Cartesian dualism?
......My analogy only worked because of the causal link between your fingers moving on the keyboard and the consequent virtual motion (as expressed in actual space on the screen), which goes via continuous paths in space (if we include force-fields in our ontology), but still, it did work. It suggests that a possible Cartesian response is to give the body, not only a spatial location, but also another, non-spatial location, at which the soul acts. How plausible is that? In the natural theistic context of Cartesian dualism, it’s very plausible, since God created space, and is himself located elsewhere.
......And suppose that Cartesian dualism is false. Then there’s some other true theory of mind. Somehow the physical brain, which changes its form and its atomic constituents continually, is associated with a subjective unit (the mind, which we know directly), which is continuously the same person. So if there could be a non-Cartesian theory, then there’s some way of associating with the physical brain a unique continuant of some sort. It is only to that that the Cartesian theory has to associate a soul. And a very simple and natural (in the Cartesian context) way to do that would be by divine stipulation, God associating each such brain-correlate with a unique soul.
......In many ways that’s far simpler and more natural than the sort of Humean regularity approach to scientific laws that philosophers are often led to by considering how mysterious are nomological necessities (a consideration that most scientists rightly ignore). If souls are possible, then they would have individual existences, in some logical space (say heaven), and would interact in some way (say via spiritual bodies). And if so then matter would’ve been created to be such as could be used in such ways (for some reason). The details are for scientific discovery, but the mere possibility is not really so mysterious.
[...] according to Descartes, whereas the mind has beliefs, desires, and volitions, but no shape, size, or velocity, the body has shape, size, and velocity, but no beliefs, desires, or volitions. [...] it is often complained that it is completely mysterious how an unextended, non-physical substance could have any causal impact upon the body – the presumption being, perhaps, that any cause of a physical event must either be located where that event is, or at least be related to it by a chain of events connecting the location of the cause to the location of the effect.As put, the problem seems to be one of mere conceptual possibility, which is easily answered. By typing into your keyboard you can make virtual beings move about in cyberspace. Clearly you don’t have to be where they are, in cyberspace, to be able to move them about. So it isn’t so very mysterious how such things are possible. And even if it were, why presume that would be a problem for dualism, rather than a personal failing?
......As Lowe notes, people said that Newtonian action-at-a-distance was completely mysterious, and maybe it was, and is, but there was hardly any argument there against Newtonian physics (except in the minds of some philosophers). The truth turned out to be far weirder again, and it was to be had by working through Newtonian physics. There is that other problem, of how exactly the interaction works, but the way towards answering that is the relatively hard way of science, and why should it not go through Cartesian dualism?
......My analogy only worked because of the causal link between your fingers moving on the keyboard and the consequent virtual motion (as expressed in actual space on the screen), which goes via continuous paths in space (if we include force-fields in our ontology), but still, it did work. It suggests that a possible Cartesian response is to give the body, not only a spatial location, but also another, non-spatial location, at which the soul acts. How plausible is that? In the natural theistic context of Cartesian dualism, it’s very plausible, since God created space, and is himself located elsewhere.
......And suppose that Cartesian dualism is false. Then there’s some other true theory of mind. Somehow the physical brain, which changes its form and its atomic constituents continually, is associated with a subjective unit (the mind, which we know directly), which is continuously the same person. So if there could be a non-Cartesian theory, then there’s some way of associating with the physical brain a unique continuant of some sort. It is only to that that the Cartesian theory has to associate a soul. And a very simple and natural (in the Cartesian context) way to do that would be by divine stipulation, God associating each such brain-correlate with a unique soul.
......In many ways that’s far simpler and more natural than the sort of Humean regularity approach to scientific laws that philosophers are often led to by considering how mysterious are nomological necessities (a consideration that most scientists rightly ignore). If souls are possible, then they would have individual existences, in some logical space (say heaven), and would interact in some way (say via spiritual bodies). And if so then matter would’ve been created to be such as could be used in such ways (for some reason). The details are for scientific discovery, but the mere possibility is not really so mysterious.
Wednesday, January 14, 2009
What's a mathematician?
A mathematician is a device for turning coffee into theorems, according to Renyi's famous joke. But since most mathematicians don't prove theorems nowadays, I tend to think of the natural mathematicians as those finding More or Less as gripping as an Agatha Christie mystery (whether or not they like set theory).
......On the news this morning, there was a story about researchers at Durham have discovered that coffee makes us hear voices. They conceded that maybe those who hear voices tend to be more stressed, and so drink more coffee, but that seems like an odd concession to me, as people who're stressed usually turn to, if not alcoholic beverages, then chocolate or cigarettes, or cannabis.
......Scientists have also claimed that cannabis can trigger psychosis. That seems more plausible, as cannabis is the famous hippy drug, but I wonder even about that. Many of the most obvious direct tests of that hypothesis would be rather unethical, and the indirect tests (e.g. statistical correlations) would be vulnerable to selection biases. It's not just that schizophrenics might be more likely to disobey the law. There is apparently a part of the brain that is involved in religious experiences, e.g. Richard Dawkins had his stimulated and experienced nothing, apparently.
......If some people are more disposed to such things (again, whether they're born that way, or whether the brain adapts to their chosen way of life, is less obvious) then that would be a relatively obscure but effective source of such a bias. Incidentally, such studies need worry religious people surprisingly little. The traditional view of God has him timelessly creating us, and so faces similar problems, e.g. from our choices to turn to him etc. And Open-theistic views must face the facts of life anyway, e.g. that some of us are born richer, or better looking, or with better brains in other ways. If they can do that, they'll be able to live with similar facts.
......Anyway (oh how tangents attract the active mind), it occurs to me that those with such a religiously inclined brain might be more inclined (statistically, not each of them of course) to hear voices and also more inclined (similarly) to drink coffee, whether because they don't drink alcohol for religious reasons, or because they like to be awake to creation, or whatever. They may also be a little more inclined (statistically) to smoke cannabis, insofar as that's associated with the mystical side of hippies, or the religious side of Rastafarians, etc. If anything, we'd expect a greater corrolation with coffee, of course (and it does seem more plausible that coffee is not actually causing us to hear voices).
......Anyway, that's one possible explanation: a common cause leading to interlinked tendencies. Another explanation is that coffee in large quantities makes some of us irritable and tense, and perhaps over-sensitive, and so maybe more likely to hear voices insofar as we're already slightly inclined towards that (although I'm not ruling out the possibility that people take coffee because they're feeling stressed), but even in that possibility there's room for biases of the former kind—a common partial cause—e.g. a weak willed person might be more likely to over indulge in coffee, and less able to resist hallucinating. Similarly, they might drink more and get into fights, for such a reason. Or they might (also) react to the drink by getting more aggressive themselves. Note that that would be no reason for those who drink to relax and socialise to drink less (you may have guessed that I drink a lot of coffee:)
......On the news this morning, there was a story about researchers at Durham have discovered that coffee makes us hear voices. They conceded that maybe those who hear voices tend to be more stressed, and so drink more coffee, but that seems like an odd concession to me, as people who're stressed usually turn to, if not alcoholic beverages, then chocolate or cigarettes, or cannabis.
......Scientists have also claimed that cannabis can trigger psychosis. That seems more plausible, as cannabis is the famous hippy drug, but I wonder even about that. Many of the most obvious direct tests of that hypothesis would be rather unethical, and the indirect tests (e.g. statistical correlations) would be vulnerable to selection biases. It's not just that schizophrenics might be more likely to disobey the law. There is apparently a part of the brain that is involved in religious experiences, e.g. Richard Dawkins had his stimulated and experienced nothing, apparently.
......If some people are more disposed to such things (again, whether they're born that way, or whether the brain adapts to their chosen way of life, is less obvious) then that would be a relatively obscure but effective source of such a bias. Incidentally, such studies need worry religious people surprisingly little. The traditional view of God has him timelessly creating us, and so faces similar problems, e.g. from our choices to turn to him etc. And Open-theistic views must face the facts of life anyway, e.g. that some of us are born richer, or better looking, or with better brains in other ways. If they can do that, they'll be able to live with similar facts.
......Anyway (oh how tangents attract the active mind), it occurs to me that those with such a religiously inclined brain might be more inclined (statistically, not each of them of course) to hear voices and also more inclined (similarly) to drink coffee, whether because they don't drink alcohol for religious reasons, or because they like to be awake to creation, or whatever. They may also be a little more inclined (statistically) to smoke cannabis, insofar as that's associated with the mystical side of hippies, or the religious side of Rastafarians, etc. If anything, we'd expect a greater corrolation with coffee, of course (and it does seem more plausible that coffee is not actually causing us to hear voices).
......Anyway, that's one possible explanation: a common cause leading to interlinked tendencies. Another explanation is that coffee in large quantities makes some of us irritable and tense, and perhaps over-sensitive, and so maybe more likely to hear voices insofar as we're already slightly inclined towards that (although I'm not ruling out the possibility that people take coffee because they're feeling stressed), but even in that possibility there's room for biases of the former kind—a common partial cause—e.g. a weak willed person might be more likely to over indulge in coffee, and less able to resist hallucinating. Similarly, they might drink more and get into fights, for such a reason. Or they might (also) react to the drink by getting more aggressive themselves. Note that that would be no reason for those who drink to relax and socialise to drink less (you may have guessed that I drink a lot of coffee:)
Tuesday, January 13, 2009
Faith, a definition
Personal faith is not assent to evidence which is so strong as to be beyond reasonable doubt. It is assent to a discernment of God which is personally overwhelming but not objectively testable. This is not discernment of a historical God, timeless and unchanging. It is discernment of an active, loving God, making himself known in personal lives at specific points which become the matrix of a communal response to his will.Keith Ward, Divine Action (London: Flame, 1990), 238.
Thursday, January 08, 2009
How mysterious is Platonism?
Arithmetical Platonism is supposed to be prima facie suspect because how, it’s asked, could we have arithmetical knowledge if the objects of that knowledge are in a world apart from us, a timeless world of Platonic objects, with which we cannot interact causally? I reply by wondering, how strange are abstract objects? You have just been reading this, for the obvious example. What have you been reading? You have been reading sentences. You look at the physical instances of these words, but you see the words, you read the words, and as you do so you are (hopefully) thinking about the thoughts expressed by means of them. So, there are, in the physical world around you, those physical instances of the shapes of (written modern English) words, and there are in your mind those thoughts; so, where are the sentences? What are the sentences? Sentences are made of words, and words are parts of a language (i.e. modern British English). They can be spoken or written, and can sometimes be spelt in different ways. Furthermore they have a meaning, a sense, and they have it essentially. The mere shape of a word is not a word, no more than meaningless strings of letters are words. Words, it seems, are abstract objects (I’m not entirely sure about that, or about what abstract objects are, so I’d welcome corrections) and you’ve just been reading some words of mine (and I’ll add that words can be true, insofar as they describe the world sufficiently accurately, or not, in case anyone wants to argue that thoughts and not words are truth-bearers:)
Saturday, January 03, 2009
Who's the Philosopher?
If good mathematics tells us that there are sets of some size, or functions of some type, or if good science tells us that there are waves or particles or forces or fields, then who is the philosopher to pipe up otherwise? As David Lewis forcefully argued, the philosopher taking any such line is apt only to make himself look foolish. Considering the case of sets in mathematics, Lewis wrote:That was Blackburn on Lewis on Philosophy, in Moore and Scott (eds.) Realism and Religion: Philosophical and Theological Perspectives (2007: 49, where he was trying to draw a line between the expertise of scientists and that of theologians).Mathematics is an established, going concern. Philosophy is as shaky as can be. To reject mathematics for philosophical reasons would be absurd [...] I’m moved to laughter at the thought of how presumptuous it would be to reject mathematics for philosophical reasons. How would you like the job of telling the mathematicians that they must change their ways, and abjure countless errors now that philosophy has discovered that there are no classes?Philosophy simply has not got the track record of certainty, or utility, or progress, or unanimity, to mount any such high horse. If it is a question of philosophy versus physics, or philosophy versus maths, everyone knows which side to back.
Mathematical classes necessarily go beyond standard set theory, as a result of the famous set-theoretic paradoxes of a hundred years ago. For the most part, their proper study is regarded by mathematicians and philosophers as the province of logicians and metaphysicians. And even the sets that mathematicians study are formal, axiomatic entities entirely suited to the algebraic ways of the mathematicians. Some mathematicians even work on constructive maths or category theory, for example, and insofar as they do so formally they are regarded as doing maths. In short, the pure mathematicians have passed the metaphysical buck to those applying the formal structures studied by them, while few applied mathematicians regard themselves as doing set theory.
Lewis doesn’t accept that there are waves or particles or forces or fields, but only spaciotemporal points with arbitrary properties that either happen to fit a pattern or don’t. He’d let us keep whatever physicists say about such things, but would change their meanings (such being his idea of what philosophers can do). But those spaciotemporal points have, he presumes, a structure isomorphic to some set-theoretical structure. He might even allow that they could have any structure, but he needs some such points, and what if such structures happen to be metaphysically impossible? Standard mathematicians actually pass the buck on such applications.
Lewis was talking about standard set theory, not mathematics (the two are often confused by American academics and those—most of the world’s leading academics—who’d like to become one), and sets have never got over the set-theoretical paradoxes. Or rather, the mathematicians—for the most part (Lewis conveniently ignores those mathematicians who’re constructivists or category theorists)—got round the problem by doing axiomatic set theory in an algebraic way, and thereby left the problem of interpretation up to those applying their maths. If there turn out to be no infinite sets really—no such metaphysically possible spatiotemporal points as Lewis presumes—then there would need to be some applicable mathematics done by someone, and whoever did it would be a mathematician. Lewis ought to be as sceptical about set theory as he is about particles and natural laws.
Lewis may be moved to laughter at the very idea—a common response to his own hopelessly unrealistic work on metaphysics—but what was he thinking of? Brouwer and Heyting were professional mathematicians, and those philosophers (e.g. Wittgenstein and Dummett) who agreed with them were agreeing with mathematicians. So what was he thinking of, the maths that he was taught at school in America? If philosophers have something to contribute then they should contribute it, and if not then they’re philosophers in name only. Was Descartes a philosopher or a mathematician? He was clearly both, and we surely need more people like Descartes, not fewer. Scientists tend to say that to say nothing of God isn’t to say that God is nothing, and those who think otherwise do so for philosophical reasons.
Mathematicians have as much right as anyone to think philosophically, and perhaps more right when it’s the philosophy of maths (e.g. Hamming and Fletcher). And what’s especially interesting nowadays is the increasing popularity of category theory, within maths. For the most part, that increasing popularity is not due to metaphysical concerns, but to concerns more internal to maths. But the underlying logic of category theory is intuitionistic. One can even envision a day when the professional mathematicians choose category theory as their standard foundation (one need only think of how popular Lewis is amongst professional philosophers) just because it provides the most interesting line of immediate research (cf. the dominance of string theory in physics) et cetera ad nauseum.
Note that there’s some difference between philosophy the professional job (cf. Lewis’s concern with having the job of saying what some of his colleagues have said), which does seem shaky, and philosophy the pursuit of truth.
Friday, January 02, 2009
Divine Liars: the devil's in the details
Hartley Slater, on page 4 of his ‘Supposed Liars, Divine Liars and Semantics’ (The Reasoner 3(1), 3–4), said, about my (4*) = ‘God doesn’t believe that (4*) ever expresses a true proposition’ (in my ‘Liars, Divine Liars and Semantics,’ The Reasoner 2(12), 4–5), that:
Cooke says, with regard to ‘Liar sentences’, that ‘they do seem to be saying, not only that they are not true, but also, if less obviously, that they are (therefore) true’. So sentences, he allows, may express more than one proposition, even if they may express one proposition more obviously than another. But if so then one cannot immediately derive, with respect to the previous case that the (one and only) proposition that (4*) expresses is (the obvious one) that God doesn’t believe that (4*) ever expresses a true proposition.The Liar sentence ‘this sentence is not true,’ where the phrase ‘this sentence’ is referring to that very sentence, seems to be saying that what it is saying is not true, in which case it would also be saying that it is not true that what it is saying is not true, so it would also be saying that what it is saying is true. Does that mean that that sentence expresses two propositions?
Well, the proposition expressed by the self-referential ‘this sentence is not true’ seems to be that that sentence is not expressing a true proposition, and that certainly seems to be a different proposition to the proposition that that sentence is expressing a true proposition, because were it the case that that sentence expressed a true proposition, the first of those two propositions would seem to be false, and the second true.That self-referential sentence seems to be saying, of itself, that it is not true. But if that sentence is saying of itself that it is not true, then it is not standing outside itself when it says that it is not true. It is not like when I say that it is not true. And when it says that what it is saying is not true, so that it is also saying that it is not true that what it is saying is not true, the latter is just part of what that sentence says when it says that it is not true. Because the former includes the latter, there is a sense in which there is only one proposition here, albeit one with a very strange part. There is also a sense in which we are talking about two propositions here, because the latter is only part of the former, and it is a part that seems to contradict the former. But the latter is part of the former, and this self-referential sentence is a very simple sentence, so we can see that it is not equivocating, and so I think that the former proposition with that very strange part is all that that self-referential sentence would be expressing, were it expressing a proposition. Perhaps that strangeness is so extreme that no proposition is being expressed. But the main thing here is that:
When we think of the proposition that that sentence is not expressing a true proposition, we might be thinking of the proposition that would be true were that sentence not expressing a true proposition, or we might be thinking of the very strange proposition that that sentence would be expressing were it expressing something propositional.Because those are two propositions, not one, talk of propositions seems to have brought with it an increased risk of equivocation, not increased clarity. With other kinds of sentences, talk of propositions may well introduce clarity, but for these self-referential sentences, we might be better off sticking with talk of sentences and their meanings, logical and other. After all, formal languages are usually designed to avoid self-referential sentences.
Tuesday, December 23, 2008
The Pope and the Archbishop
On the TV, the Pope is talking about homosexuality; and a few days ago, the Archbishop of Canterbury was talking about our borrowing our way out of a mess that we got into via greedy borrowing. That mess was more about who the City employed and why, imho; but still, why did we let them get away with it, and why will we continue to? Now, I'm sure that the Pope isn't unaware that he's pandering to homophobia, even if he talks about the sin and not the sinner. After all, a similar sin is thinking lustful thoughts about a woman other than one's wife, e.g. when watching a movie (which a lot will be doing this xmas). Marriages tend to break up because they are felt to be falling short of the dream, not because gays come out of closets. And a worse sin is pride, of course; especially pride in such trivia as being straight... or white. Homophobia is obviously like racism, and antisemitism etc. People, even straight people, often feel insecure about their sexuality (as the Church has traditionally encouraged them to), and a way to feel better about it with very little subjectively obvious psychic cost (if one is straight) is to think to yourself that at least you're not one of those disgusting gays. The similarities with racism and poor people's views of their own social positions are obvious (not to mention the Church's traditional role in antisemitism). A man can know that he's sexist and letcherous, but comfort himself with the thought that at least he fancies women. And a woman can know that she's fat and lazy, but comfort herself with the thought that at least she's a woman. The irony is that the Church traditionally regarded marriage as second-best to the monastic life (and another irony is that the latter attracted homosexuals, of course... I could go on, but I'll just wish you a merry xmas :)
A Jump Theodicy
Another name-change for my theodicy, to something less irritatingly alliterative and more evocative of its content (by comparison with Fall theodicies), which is now here (Alanyzer's thoughts on it are here). Last January my theodicy was a sketchy talk entitled ‘The Theodolite Theodicy’ at Glasgow (where I was supposed to be continuing with the metaphysics of continuity for my PhD), at which it matured slightly under the questions of Fiona and Akiko.
......In the Spring I happened upon Tim Mawson’s recent paper in Int. J. Philos. Relig. (which was essentially the second chapter of his 2005 introduction to the philosophy of religion), and the theodicy—renamed the Odyssey theodicy—became the final part of my refutation of his arguments for the timelessness of God. I’d finished writing a response to Mawson’s paper (which was essentially this version) by the time of my talk in Aberdeen in July; and its rejection arrived in November, along with three reasons for its rejection, which were so weak as to be interesting.
......The first objection was to my use of the term ‘theodicy’ (as opposed to ‘defence’) on the grounds that, while the reviewer conceded that my speculations might be possible, she (or he) didn’t find them at all plausible. But when atheists find no (so-called) theodicy plausible, are all theodicies thereby misnamed? Hardly, and so (similarly) that she found my theodicy implausible hardly stops it being a theodicy. It should’ve been obvious that I’m not trying to demonstrate the logical compatibility of God’s existence and evil’s occurrence (which is surely trivial) but to maximise the explanatory power of Open theism, by trying to give a good account of why a perfect being would make an imperfect world.
......So her first objection amounted—at best (it may just have been incompetent, in view of the quality of the other two)—to no more than the claim that I’d failed to give a good account of that. As for why I had so failed, there were only the following two objections. Since philosophy ought to be more like amateur science than a professional game, I’d rather add that had she been able to ask me, I could’ve easily cleared up her confusions. Such is blind reviewing.
......Her second objection was that, while one of the aims of Open theism is to bring the philosophical picture of God closer to the Biblical picture, my theodicy would forfeit that aim. However, she said nothing about why it would. And having read the Bible inclusivistically (e.g. with metaphysical humility) and found no incompatibility with my theodicy, I don’t know which verses she was thinking of (or how). If the readers of this post have any ideas of what they might be, I’d be very interested in any possibilities. My theodicy could hardly take us further from the Biblical picture(s) than the doctrine of God’s timelessness has traditionally taken us.
......But what’s most apposite, from the point of view of reviewing a submission, is that even were this objection sound the first half of my submission would still have shown that a perfect person might be everlasting (contra Mawson) and indeed, would be (according to Mawson’s own methodology), while the final half would still have further increased the likelihood of Open theism.
......The final objection was basically a Straw Man fallacy, and was (in full) as follows.
......In the Spring I happened upon Tim Mawson’s recent paper in Int. J. Philos. Relig. (which was essentially the second chapter of his 2005 introduction to the philosophy of religion), and the theodicy—renamed the Odyssey theodicy—became the final part of my refutation of his arguments for the timelessness of God. I’d finished writing a response to Mawson’s paper (which was essentially this version) by the time of my talk in Aberdeen in July; and its rejection arrived in November, along with three reasons for its rejection, which were so weak as to be interesting.
......The first objection was to my use of the term ‘theodicy’ (as opposed to ‘defence’) on the grounds that, while the reviewer conceded that my speculations might be possible, she (or he) didn’t find them at all plausible. But when atheists find no (so-called) theodicy plausible, are all theodicies thereby misnamed? Hardly, and so (similarly) that she found my theodicy implausible hardly stops it being a theodicy. It should’ve been obvious that I’m not trying to demonstrate the logical compatibility of God’s existence and evil’s occurrence (which is surely trivial) but to maximise the explanatory power of Open theism, by trying to give a good account of why a perfect being would make an imperfect world.
......So her first objection amounted—at best (it may just have been incompetent, in view of the quality of the other two)—to no more than the claim that I’d failed to give a good account of that. As for why I had so failed, there were only the following two objections. Since philosophy ought to be more like amateur science than a professional game, I’d rather add that had she been able to ask me, I could’ve easily cleared up her confusions. Such is blind reviewing.
......Her second objection was that, while one of the aims of Open theism is to bring the philosophical picture of God closer to the Biblical picture, my theodicy would forfeit that aim. However, she said nothing about why it would. And having read the Bible inclusivistically (e.g. with metaphysical humility) and found no incompatibility with my theodicy, I don’t know which verses she was thinking of (or how). If the readers of this post have any ideas of what they might be, I’d be very interested in any possibilities. My theodicy could hardly take us further from the Biblical picture(s) than the doctrine of God’s timelessness has traditionally taken us.
......But what’s most apposite, from the point of view of reviewing a submission, is that even were this objection sound the first half of my submission would still have shown that a perfect person might be everlasting (contra Mawson) and indeed, would be (according to Mawson’s own methodology), while the final half would still have further increased the likelihood of Open theism.
......The final objection was basically a Straw Man fallacy, and was (in full) as follows.
There are several arguments in the literature that it is not possible that there be two omnipotent beings. The relevance of these arguments to the author’s project is obvious. But the soundness of these arguments is no where contested in the paper. If these arguments are sound, then God, as omnipotent, can be quite confident that there are no other unknown deities about.God presumably is omnipotent but, as I’d argued, it hardly follows that he could be fully justified in being completely sure that he is. And clearly, if God is only fairly confident (and fully justified in being so) then there is, for him, the epistemic possibility that grounds my theodicy. None of those arguments of mine were criticised by her, as though she was unaware of them (despite their obvious relevance). But a trivial consequence of them is that the arguments she mentioned are none of them relevant (not even the one published alongside Mawson).
Wednesday, December 17, 2008
What Next? Turkey
For Turkey to become an EU member would change the Union, a point that we should not seek to hide from our citizens. The European demos has to be party to the deal, and it should not be impossible to convince the public of the Turkish case if we try. A Turkey with a population of rising 90 million with a vibrant economy and young workforce would help to vitalize Europe’s economy as the west-European population ages and declines. A democratic Turkey, secular and Muslim, would assist in preventing the cultural divisions and clashes that we sometimes appear intent on provoking around the world. A militarily professional Turkey would give the EU more credibility as a civilian power able to act occasionally with an effective military smack. Reject Turkey and the EU will have chosen to write a much smaller part for itself in the history of the twenty-first century, and having been so successful in promoting stability around our borders we may find ourselves doing the reverse.That’s from Lord Patten’s ‘What Next? Surviving the Twenty-first Century’ (2008: Allen Lane, p. 419), which everyone should read, if only to get clear on what’s been happening recently.
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