Monday, April 30, 2007

Proof that God exists!

A: If God does not exist then Life is absurd.
C: Consequently God exists.

C follows from A by reductio ad absurdum, while for A consider, e.g., that you are camping, and that lions are about to attack your camp, so you dress up as a ballerina and dance the tango with a twig, in your remaining moments. Clearly that would be absurd.

But if God does not exist then there is nothing that we can do to avert the terrible, inevitable extinction of all that matters to us. We can have no possible saviour if we had no greater Creator than the natural selection of random mutations amongst the rocks and stones. And if we are too petrified by that terrible fact to act at all, death will only come the quicker, so we must live as best we can, and act on whatever whim takes our fancy. To live is so to act, and furthermore we must do so in a world that will soon be lit up only by alien lights, as our own are extinguished.

We will not be remembered as who we knew ourselves to be, for all that we inhabit a world that is surely as we think it is, rather than as, say, the ancients believed it to be. Were the ancients just as they thought they were? Of course not, so consider what will ultimately be known of us by the alien language-users of the future? Might not we be no more than twigs to them? Now, although that ‘proof’ was admittedly not a very convincing reductio, it does raise some interesting logical questions.

E.g. if God's nonexistence is prima facie absurd then ought not the burden of argumentation to lie with the atheist? But how could we find good physical evidence of God's nonexistence? Cf. how, from a grainy photograph, we can't tell if we're looking through a microscope at Michelangelo's David, or through a telescope at a meteor (not without the bigger picture), or how, given only a short sequence of letters, we would be unable to tell if they were produced by monkeys on typewriters or by a brilliant crytologist.

(The following paragraph was added on May 9:) After all, empirical evidence, even of quantum mechanics, need not undermine belief in the existence of this Universe—we need only say that that is more or less how this Universe appears to be (maybe pausing to do some philosophy, to reflect upon how we represent our representation of it to ourselves). Similarly nothing within any sequence of words would necessarily undermine a justified belief in the existence of its author—perhaps its author is Joyce, or a Surrealist, or an alien and so forth (that its author is not Austin might of course be strongly indicated). And I have yet to discover why saying that finding no miracles, for example, might amount to finding evidence that this Universe has no Creator is so dissimilar to saying that finding no typographical errors might indicate that our string of words had no intelligent author (which is absurd). After all, even if there were unnatural events, scientists could hardly accept any evidence for them as more probable than its deceptiveness, whence (what Dawkins consistently avoids) the absence of scientific evidence could hardly imply the non-existence of the unnatural.

Another interesting logical question is, if atheism is true, then why should we care about (what we have somehow come to think of as) truth to the extreme of challenging major political blocks within our own society? And a more metaphysical question is, what’s so wrong about absurdity anyway? Why not embrace, say, paraconsistent logic, or Humean Supervenience?

Sunday, April 29, 2007

Deep Thought

The sea cries with its meaningless voice,
Treating alike its dead and its living,
Probably bored with the appearance of heaven
After so many millions of nights without sleep,
Without purpose, without self-deception.
That's from Hughes’ Pibroch, 1967

Saturday, April 28, 2007

A Mysterious Subject

Mathematics has a mysterious subject-matter, e.g. what is 1 + 1 = 2? Presumably it is a non-empirical fact. Furthermore, what is 1? Well, paradigmatically we ourselves are ones, as everyone knows (equally incontrovertibly). So the “mysterious subject” of this post will be oneself. In particular it is mysterious to me why materialism has been so popular, in modern philosophy. So for the sake of argument, suppose that we (or if that is too implausible, that aliens in the distant future) have a materialistic theory that explains everything about the world (as observed by scientists) in terms of fundamental physics.
...... When you drink a cup of coffee, for example, all those physical movements and all of the chemical reactions involved in that action are, let us say, accommodated by our theory.
What could not be accommodated, of course, is the fact that there are such (scientific) observations, rather than merely (mechanical) interactions; that you taste the coffee, having chosen to drink it, and then feel its warmth in your guts. Even if all the functioning of the brain had been accommodated by our theory, and even if it also included a plausible story of how such structures could evolve by natural selection, nonetheless where and how, in our theory, would our awareness of the world arise?
...... Presumably if such a purely material world is possible, sensory organs could evolve within it (whatever innumerate ID people believe). And I’m sure that biochemical structures could be selected for behaving (e.g. for computing neurologically) as though they were individual subjects, with social consciences, and religious beliefs etc. But why would such structures also be subjects (i.e. individual beings with subjective experiences)? Why would they need to be individual subjects as well as (fuzzy) collections of objects? Not in order to enhance their fitness if, as our theory says, all their behaviour could be explained in terms of what their neurones do, and thence what the underlying particles do. But furthermore how could such an option be available in the first place, to be selected for?
...... Yet our minds certainly exist, as every scientist (and non-scientist) knows in an incontrovertibly direct way. Hypothetically our theory explains everything that our minds do, insofar as those things might be observed and spoken of, but our theory says nothing about the bare subjectivity that (as we know more directly) underlies them.
So the question arises, what in the world could not be associated with something of the sort of (superficial and ineffective) subjectivity that remains unexplained by our theory? Would plants have, not minds, and perhaps not even perceptions (as we have them), but something like primitive individual sensations or feelings? Would amoebae? Maybe not, but since our brains are composed of interacting neurones (which presumably also lack minds like ours) why should a forest, for example, not have something akin to a mind? Are we really sure that there is nothing that it is like to be a forest (or a plant, a cell, an electron, a fact, a language, etc.)?
...... In other words, if our feelings of choosing to drink coffee, for example, are only a superficial companion to biochemical processes in our brains, then why should some of the biochemical processes within such ecosystems as forests (or indeed, whole biospheres) not be similarly accompanied by subjective feelings of choosing to do whatever occurs?
Indeed, why would something akin to our own (directly known) subjectivity not be associated with everything and (such subjectivity being superficial and ineffective) every subset of everything? Although we naturally draw some sort of line at the brain, considering subjects to be absent beneath it, the problem is that no objective line will be indicated by our theory. That is a problem because there clearly exists one especially complex and well-defined physical individual, i.e. this Universe.
...... Now there may well be other problems with our theory saying nothing about subjectivity itself, e.g. if primitive subjectivity is associated with every subset of everything then surely telepathic communication would have been naturally selected to be a lot more common that it appears to be! But anyway, even if we were to consider subjectivity to be absent beneath the level of, say, the brain, still our theory does not make it implausible (and indeed, it actually indicates) that there would be, above that line, something that was (to put it analogically) to us much as we are to our neurones—something that may well know itself to be choosing all that occurs (much as we choose to have a cup of coffee, only more so), which would be everywhere (much as we are where our brains are), and which might even know everything (since we know so little, while our neurones know nothing), and so forth.
...... In short, materialism seems to amount to an unjustified belief about God.
It would be unjustified because we could have had no scientific reason for supposing that our hypothetical theory could even amount to our most realistic theory of subjectivity, let alone God. Quite the converse, if the questions above are any indication. And it would seem to be about God because surely a more agnostic theory (one that did not equate the immaterial with nothingness) could have accommodated no less tidily the same physical observations. The difference would therefore appear to lie entirely in what those two theories imply about the subjectivity of the Universe as a whole; and note that ‘God’ was indeed the right word to use for that, despite its other connotations (or rather because of the wide variety of them). Analogously, what you drink out of is clearly a cup even if your concept of a cup requires it to be a classical object in Euclidean space while the object being drunk from is a fuzzy set of wavefunctions in more than three relativistic dimensions.
Anyway, if the motivations of materialism and of atheism are sufficiently akin, then our materialistic theory of everything is essentially incoherent. Of course thus far I have presented only an intuition-pump, rather than an actual argument, so note that the underlying problem here is not the incompatibility of materialism and atheism, after all (the idea that this Universe has a Creator of some sort is slightly more sensible once we are dualists, with the need to explain the origin of immaterial minds, which would clearly be more than mere subjectivities if they existed). No, the basic problem for the materialist is to explain how some sort of structure, of some sort of material objects, could have such properties as would amount to the subjectivity of an individual subject. Prima facie either no such structure could, or else all of them would, whence it is quite mysterious to me, the popularity of materialism (of either the reductive or the supervenient kind) in the absence of such an explanation. After all, the human brain not being the physical origin of so much as the physical medium for the human mind means that we could, whilst retaining all our interest in the former mechanism, also retain such hopeful (and therefore helpful) probabilities as some objective meaning to life, beyond life itself, and our personal survival beyond this life.

Thursday, April 26, 2007

A Mysterious Paradox

Time to post something on the philosophy of maths I guess. As far as I can see, the mysterious thing about the Banach-Tarski paradox (which recently cropped up in an irrelevant aside here) is how elusive are the intuitions that are offended by it, as Feferman observed in his 2000 'Mathematical Intuition Vs. Mathematical Monsters' (Synthese 125, 317-32).

Very roughly, a unit sphere (within a standard 3-space) can be considered to be made up of five pieces, which can be rearranged to form two unit spheres. That appears to be particularly paradoxical in an imaginary 4-space. Think of an impenetrably rigid 3-dimensional sphere, made of some perfectly smooth material (unrealistic but classical), in a 4-dimensional space. According to the Banach-Tarski theorem, it can be broken up into 5 similarly rigid pieces (connected subsets of points) that can be moved rigidly (in the fourth dimension, since they cannot pass through each other) to form two new spheres, each identical to the original sphere (in intuitive contravention of some sort of conservation law).

The paradox seems to arise from some intuition that pieces of things should not behave like that, but I find it hard to pin that intuition down in such a way that it would still apply to classical (and therefore unrealistic) things. E.g. I recently thought that dropping one of the 5 pieces into a measuring flask would give us a more paradoxical result, whereas either the measuring fluid would be unable to fill up all the space around the piece, or the fluid would develop a weird surface (or else be useless for measuring anything). So I wonder how other people think of the paradoxicality of the Banach-Tarski...

Wednesday, April 25, 2007

The Tao of Tao

Trawling through the blogs, I find that some days ago Shawn observed that Tao's generic advice about succeeding in Academia would be good for philosophers, as well as mathematicians. So (as my PhD begins in September, whence I ought to ponder upon such matters) 'tis noted here. (June 12:) Tao's advice is now on his blog, here.

Tuesday, April 24, 2007

Do Chimps Count?

Can you count faster than a chimp?
This subitizing test is from last night's
more or less (on BBC Radio 4).

Monday, April 23, 2007

My First Post

The One remains, the many change and pass;
Heaven’s light forever shines, Earth’s shadows fly;
Life, like a dome of many-coloured glass,
Stains the white radiance of Eternity,

Until Death tramples it to fragments.

That's from Shelley’s Adonais, 1821