Religion and evil, again

So he killed his daughter ... 'Death was the least she deserved,' said Abdel-Qader. 'I don't regret it. I had the support of all my friends who are fathers, like me, and know what she did was unacceptable to any Muslim that honours his religion,' he said. Again, comment is superfluous.

Galois connections

In his classic paper "Adjointness in foundations" (1969), F. William Lawvere writes of 'the familiar Galois connection between sets of axioms and classes of models, for a fixed [signature]'. The idea might be familiar to category theorists, but it isn't easy to find a clear account of what it involves. So, inspired by a talk by Nathan Bowler last term, I've put together a piece on Galois connections to explain. All comments, corrections, suggestions for improvements/additions very welcome. It's part of a planned longer piece about order and ordinals.

[Later] Thanks to Luca Incurvati for catching a daft thinko and a few typos too!

[Later again] I've replaced the previous version with a notationally slightly prettier version.

Folklore

I was sitting at tea at CMS yesterday listening to Martin Hyland and Thomas Forster talking about set theories, and it struck me -- not for the first time -- how important a certain kind of informal discussion is to the mathematical enterprise.

You'd miss some fun ("fun" in a rather stretched sense, but you know what I mean) if you didn't ever have face-to-face philosophical discussions. But you wouldn't necessarily miss out on a lot of philosophy. Because in written philosophy, you do still get the to and fro of ideas, the false starts, the dead ends, the conjectures, the refutations -- often in the writing of a single author as she wrestles with objections and counter-objections. The dynamic is there on the pages (not in its untidiest and rawest form, to be sure, but still very evident). With mathematics published in the approved conventional styles, on the other hand, you get the end-product, some results and their proofs. But the dynamic that led to them, the whys and the wherefores, can be very hidden, and informal commentary can often be very laconic (or altogether missing). So a few arm-waving remarks over tea that might never get into a written paper can make all the difference to your understanding of how some bits of maths fit together. Conversely, missing out on picking up the folklore of maths is arguably a much bigger loss than missing out on "live" philosophical discussions.

Three cheers for Alan Sokal

Alan Sokal's Beyond the Hoax has been out a few weeks, but I've at last got a copy. It reprints his wonderful "Transgressing the boundaries" parody with a running commentary of annotations on the opposite pages (or at least, the commentary would have been on opposite pages if he'd got the LaTeXing right!). And it has a selection of other papers, all written with his characteristic verve, directness and good sense. There is better philosophy of science here than is purveyed by some philosophers of science.

And incidentally, I was amused by Sokal's cheerful abuse of the intellectual pretensions of religion -- witness e.g. his description of the Pope as "the leader of a major pseudoscientific cult". Agree or disagree, you are at least very clear where Sokal stands (which is more that can be said for some writers on religion ...).

Believing in

Provoked by some remarks of Tim Crane's at the last meeting (where he was drawing on a paper by Zoltan Szabo), I gave a talk on Wednesday at the local Serious Metaphysics Group on whether a distinction between "believing in Fs"/"believing that there are Fs" can do any serious work for us. My answer was "no". This was dashed off the previous Saturday afternoon, and I'm outside my comfort zone here. But the talk survived the discussion: so for what it is worth, here it is.

The hollow halls of academe

A Canadian reader of this blog kindly send a link to this depressing article on the effects of the drive to push ever more and more students through some kind of university education. It has the ring of truth.

Though the effects, I hasten to add, don't really apply so much here in Cambridge where we can be exceedingly picky about those we admit, and a decent number of our undergraduates are still very clever, very committed, and very hard working. Though my sense is that at least some serious departments here, like mathematics, keep up the old standards by taking increasing numbers of undergraduates from abroad, casting the net ever wider. (Hardly a surprise that they can't get enough suitably qualified homegrown students when maths teaching in the English state education system is in a terrible state. For more depressing reading, see this report about UK maths here.)

Good news re IFL?

The annual royalty statement implied that my Introduction to Formal Logic sold pretty modestly last year (I was of course an idiot to write it, given all the competition, but there you go: I wouldn't be told!). But an e-mail from CUP today said that it had in fact sold many more than I was told, the initial big print run is almost exhausted, and there might shortly be a reprint. I won't find out till next week now which is right, the royalty department or the editorial department: but fingers crossed (as it seems rather less likely that their central computer stock system is wrong).

That would be terrific if I do get the chance of a corrected reprint, because the first printing has some horrible typos/thinkos. Getting things sorted would make me feel a lot happier about the book.

I typeset the book myself -- so yes, the printing errors were my fault entirely -- in my pre-LaTeX days, using FrameMaker which only runs under OS9. Fortunately, I've still got a working Mac with OS9 installed, and I've just checked that it all seems to be running smoothly (phew). So it shouldn't be a pain to update the files if I do get the go ahead. So here's hoping.

Write a book and get rich ...

Well, the annual Statement of Royalties for my Cambridge University Press books arrived this morning. I'm off to buy a Tuscan villa on the proceeds ...

... or rather a meal or two. Sigh. My income per paperback copy sold of the Gödel book works out at less then 81p. One euro. So sell a hundred books and we can buy a moderately decent meal out in Italy. Brilliant.

Philosophy of Religion 15: Enough already!

Suppose a first year student wrote this (about mind-body substance dualism):

There are no very persuasive arguments against dualism ... Dualism is commonly mocked rather than argued against.

Then we'd berate this exhibition of sheer ignorance. We'd send the student away with a long reading list. Start, say, with the second chapter of Armstrong's classic Materialist Theory of the Mind. Or perhaps chapters II to V (over fifty pages of careful unpicking and assessment of various arguments, pro and con) of Smith and Jones's Introduction to the Philosophy of Mind (yes, folks, it is still in print after 22 years: buy, buy while stocks last!). And we can, of course, add a lot more. The reason the vast majority of contemporary philosophers of mind reject naive substance dualism has nothing to do with mockery, and everything to do with the fact that that there are so many weighty problems with it that it has long since become, at the very least, a badly degenerating research program.

But that quotation doesn't come from a first year student but from Murray and Rea's book, at p. 266. I boggled when I read it, and despair. It really is pretty difficult to take authors who can write something like that seriously any more. My patience is at an end, so I'm going to stop. I'll not say anything then about their feeble discussion of "evolutionary models of religious beliefs", where they don't even mention Dan Dennett. And I'll not say anything about their equally feeble discussions of the status of morality.

This is not a good book. In fact, as readers of this blog will have come to suspect, I think it really is overall a rather bad, too often weakly argued, one. It is published in a prestigious series, and -- especially since student texts don't tend to get widely reviewed -- it could end up being widely read (no doubt a lot more widely read than my Gödel book which rubs shoulders with it in the series!), corrupting the minds of the youth. What was CUP thinking of?

Philosophy of Religion 14: Miracles?

Those who are getting fed up with me banging on and on about the Murray/Rea Introduction to the Philosophy of Religion and are waiting for some serious stuff can rest easy. This will be the penultimate post on that book. And then it's back to Absolute Generality (as I must finish that and write a review in the next few days). Maybe I'll also post something elementary and expository here on Galois connections if I can sort an annoying bug in my thinking. And -- if the discussion goes well enough tomorrow -- I'll post the informal talk on Szabo on "Believing in things" here too. And there's more in the pipeline. I will return to logic matters, promise!

But in the meantime, back to Murray and Rea's Ch. 7, "Religion and science". There's a central section on miracles, which makes some sound points against arguments which purport to show too quickly that the very idea of a miracle is incoherent. I won't discuss those. They then offer the following suggestion: a miracle is "an event (ultimately) caused by God that cannot be accounted for by the natural powers of natural substances alone". OK, let's work with that.

Could we have evidence of the occurrence of such events? Murray and Rea imagine being present at the parting of the Red Sea (assuming it happened for the sake of argument). "If we were present for the occurrence of the event, none of us would think it more plausible that this event is to be explained by no-cause rather than a supernatural cause. ... In this context it seems very plausible that the event was caused by a supernatural agent looking to rescue the Israelites." Not so. Don't Murray and Rea ever read any science fiction? Sure, in the described context it seems very plausible that the event was caused by some non-human agency of super-human powers. But -- to borrow from the immortal Hitchhiker's Guide to the Galaxy -- a Vogon constructor fleet is just as good as a hypothesis as something supernatural, if that means divine (which it does in the context). In fact it's a better type of hypothesis, because we have some inkling how something like a Vogon constructor fleet might pull off the trick of parting the Red Sea (big engineering works being its forte) and have no clue at all about how a disembodied being gets to do major physical interventions.

Of course, if you already believe in God and don't already believe in Vogon constructor fleets, then of course you'll be inclined to put down the parting of the Red Sea to the first, not the second. But overlooking the possibility of rival hypotheses (not about Vogons in particular, of course, but of super-human but non-divine agency) is not exactly an intellectual virtue! The point remains that being present at the parting of the Red Sea at most gives you evidence of super-human agency, and no more. It is no evidence per se of the supernatural or divine. And hence no evidence per se of a miracle defined as an event caused by divine agency (unless you already have an argument that the only super-human agency is divine -- which of course we haven't).

But of course, most of us aren't present at such events anyway. Beliefs in miracles usual rely on testimony. And discussions of miracles usually consider how to weigh up the likelihood of reliability of testimony when what is testified is in itself highly unlikely (and, perhaps, we also know we are in area where fraud, wishful thinking, and foolish credulity abound). Weirdly, Murray and Rea opt not to discuss this at all. For arguments of this sort "involve an examination of the integrity of historical evidence for the occurrence of particular miracles that is more appropriate for the domain of history than philosophy". Eh? Really? So much for the philosophical discussions of testimony, then.

Philosophy of Religion 13: Big Bang vs Steady State

In the 1950s and earlier 1960s, there was quite wide support for the Hoyle/Gold/Bondi "steady state" cosmology as a rival to what we now think of as a Big Bang model. The basic idea is that the universe, on the big scale, "looks the same" at every time, as well as in every direction. And this temporal isotropy is reconciled with the observed recession of the galaxies by postulating the continuous creation of matter, to keep the matter density of the universe constant over time. (The creation rate needed is surprisingly low: about one hydrogen atom in the volume of a skyscraper per hundred years.) This is one of those beautiful ideas in physics which ought to have been true. But the discovery in the later 1960s of the cosmic microwave background radiation -- not easy to reconcile with steady state theory, but predicted as the "echo" of the Big Bang on the standard cosmology -- led to the abandonment of the theory by all except a few diehards. (Qn: has anyone written a Lakatosian history of this episode?)

I don't at all see that the steady state theory is incompatible with ideas about divine creation, if you buy a view of an eternal God who is "outside" our universe's time frame. But I suppose that the Big Bang theory fits more immediately with a biblical view of creation (taking the Genesis story about "days" of creation with a huge pinch of salt!).

Suppose a religious apologist noted that the Big Bang theory (compatible with the bible) was eventually preferred to the steady state theory, and wrote:

Here is a case in which a conflict between science and religion was resolved by science retreating and adopting a position more congenial to a religious persective.

That would, of course, be an utterly absurd way of describing the situation, pathetically clutching at straws. "Science" in no way "retreated" (and certainly didn't retreat "in a conflict between science and religion", as if religion won the day). The steady state theory was never the only scientific game in town, and it was of course more scientific work that settled the battle of conjectures in favour of an inflationary cosmology. No retreat at all, but a resounding triumph for the theoretical cosmologists to be able to develop their hugely general theories to the point where esoteric empirical findings could get traction.

That claim above, however, is actually a quotation from Murray and Rea (p. 196, in case you think I'm making this up). To find that in a philosophy book is really quite extraordinary, and beggars belief.

Well, they do qualify their claim:

Of course, scientists did not retreat from the steady state model because it was incompatible with religion. ... Nonetheless, this case shows us just one somewhat recent instance in which conflict between science and religion was resolved and in which religion did not simply back down and revise its claims.

But that's still a bizarre way of describing the situation. A scientific theory that was inconsistent (let's suppose) with biblical stories about creation was proposed and then pretty quickly refuted -- all without reference to religious concerns. That's not a case of "resolving a conflict", which suggests give and take between battling factions. Rather a scientific theory came and went, and it turned out that one particular potential locus of conflict wasn't there after all. To talk here of science "retreating" remains an outrageous misdescription.

[P]

You can download mp3s of the whole Portishead set at the Coachella Festival yesterday in California from here

And, of course, YouTube has videos of various quality from concerts on the ongoing tour. What I find bizarre is the typical amount of crowd noise -- talking, talking, utterly misplaced whoops and cheers, talking, talking, during songs. What, I ask grumpily, is the point of going and not listening? It would drive me mad being there. It puzzles the band too: "It's hard sometimes playing your music when you can hear people chatting away." I bet.

Anyway, here are two particularly good studio videos, unadulterated with audience noise: We carry on (from BBC, Later) and Magic Doors (from their current.tv show). And the CD is out tomorrow ...

Philosophy of Religion 12: Evil and the ad hoc

Chapter 6 of the Murray/Rea book concentrates on the familiar argument that the existence of a "Perfect Being" God can't be squared with the amount of apparently utterly superfluous evil to be found in this sublunary world.

Half way through the chapter, Murray and Rea make a distinction between what they call a defence (''a possible reason, without concern for its believability, why God might permit evil" -- "a defence aims just at demonstrating the possibility of God's coexisting with evil"), and a theodicy ("a believable and reasonably comprehensive theory about why God might have permitted evil of the amount and variety we find in our world.").

That's an excellent distinction to make. But they miss the opportunity to add that a "defence", so called, is of course typically no defence at all; it's just an ad hoc patch with no virtue other that saving the appearances. A classic version of this sort of "defence" is found, of course, in Plantinga's daft ruminations about transworld depravity and so forth. This game-playing is of no more value to the struggling Perfect Being theist than any other bout of ad hockery used to save theories from potentially fatal anomalies. And students should be told so. The philosophy of science in particular has, post Lakatos, a rich literature on what makes for an ad hoc move, and why such moves are intellectually disreputable and to be roundly criticized. It would have been good to see Murray and Rea engage with this literature and similarly lambast ad hoc "defences" in the debate on the problem of evil. But they don't.

Anyway, we needn't take mere "defences" seriously -- once the Perfect Being theist is reduced to relying on those, he's as lost as anyone else in a badly degenerating research programme who has to rely on ad hockery to fend off final refutation.

So what about the theodicies that Murray and Rea consider?

1. The punishment theodicy Evil is a result of divine punishment for human wrong-doing. Murray and Rea don't like this, but they are almost offensively gentle about this horrible idea. Visiting the sins of the fathers upon the children just makes out God to be vilely vindictive.
   
2. Natural consequence theodicy Some evils are just the natural consequences of wrong doing. But as Murray and Rea note, that doesn't even get into the right ball-park for explaining the vast amount of suffering produced in the world without the intervention of moral agents.
3. Free will theodicy It is a good that there are free agents, and some free agents will (regretably) go wrong. But as Murray and Rea note again this doesn't get into the right ball-park for explaining natural evil. And of course, it doesn't get God off the hook even with respect to the actions produced by free agents. A powerful enough ominiscient being could snuff out a few conspicuously evil agents, a Hitler here, a Stalin there, and nudge down the amount of evil.
4. Natural law theodicy. Evil arises out of preconditions that must be in place for creatures to exercise their freedom. But this smacks of ad hockery again. We haven't the foggiest reason to suppose that a world with free agents has to be a world with particularly nasty terminal cancers. Why shouldn't God have created a world with a patchwork of laws of relatively local extent (actually some like Nancy Cartwright think that is what he created!) which allows rather less suffering? And if that means intervening a bit more to keep the show on the road, well an omnipotent being who cared could do and would do that. As, in effect, Murray and Rea note.
5. Soul-making theodicies We need some evil around to build a bit of moral character. But again, that's a quite ghastly idea, that a baby's terrible suffering should be there to help me make my soul better. And of course, there isn't the foggiest reason to suppose that all the evil there is in the world is needed for those supposed good purposes. Again, Murray and Rea are rather offensively silent on this singularly nasty idea.

So where have we got to? We've five theodicies mentioned, and even by Murray and Rea's own count, four of them are hopeless, and the fifth is equally bad.

Very oddly, however, they sum up the situation at the end of the chapter like this: "Are the arguments against the existence of God ... powerful? Some think so. However, as we have seen, these arguments rely on assumptions that are open to some serious challenges. How serious those challenges are is a matter for each of us to decide." Which is inept, twice over. Firstly, it misrepresents how their arguments have actually gone. But worse, beginning students -- as Murray and Rea must know -- don't need invitations to "decide" for themselves. They need precisely the opposite, injunctions to follow arguments carefully, and apportion their credences to the weight of arguments. Especially in this sort of area, students are only too willing to avail themselves of any get-outs.

Religion and evil

"Women should live under religious laws". Comments are superfluous.

Philosophy of Religion 11: Which problem of evil?

So where have we got up to, reading through Michael Murray and Michael Rea's Introduction to the Philosophy of Religion? Ah, the problem of evil. But which problem of evil?

To start with, there's the particular problem for those whose religion is Bible-based. Because there is the evident sheer moral nastiness of the God of the Old Testament, who is sadistically keen on the killing of those who lapse into a bit of adultery, homosexuality, or who blaspheme, or even do a bit of work on the sabbath -- and who commands the Israelites to wholesale slaughter and genocide. True, we like to think that the God of the New Testament has mellowed a bit: but even so, he still has some decidedly vicious tendencies. A violent end is still prophesied for those who haven't got round to seeing the light by the time of the second coming. The Bible is a bit undecided whether it is going to be a mass drowning (as in the time of Noah), or whether the destruction of the ungodly is to be by fire. But it is going to be very nasty either way. And let's not even visit the entirely repellent doctrine of eternal damnation in the fiery furnace. The Biblical God is an unpleasant piece of work, and Mill's attitude is the morally decent one: "I will call no being good who is not what I mean when I apply that epithet to my fellow creatures; and if such a creature can sentence me to hell for not so calling him, to hell I will go."

Of course, most modern believers -- leaving aside the more dingbat types of fundamentalist -- do sit fairly loose to the most morally offensive bits of the Bible, cherry pick the attractive episodes, and claim to believe in a deity not given to capricious rage and cruelty. Still, "by their fruits you shall know them" presumably applies to deities too. And the world as we find it is a ramshackle, mismanaged affair, full of suffering and pain for very many of God's creatures. And many find it very difficult to come to believe that we should worship God for his botched efforts, or think particularly kindly of the arrangements he has so cackhandedly put in place which involve so much pointless misery and worse. Didn't he care about making a world where things ran at least just a bit better (a bit less agony in some terminal cancers, for example)? It seems not. Moral rejection again seems to many the proper stance for decent grown ups.

However, I'm not going to pursue these two familiar strands of thinking about religion and evil here, for Murray and Rea don't pursue them either. They don't discuss the sheer unpleasantness of the Biblical God (you'd have thought this might have mattered more to them, given their focus of historically-rooted Christianity). Nor do they really explore the kind of moral rejection of God because of encounters with evil that often leads people to lose their faith. Though surely this is very often the way: someone -- perhaps witnessing the prolonged death agony of a close relative -- comes to think "this just makes no sense; if accepting God is accepting this, then I want no more part of it", and she stops praying, stops religious observance, stops thinking in terms of God's purposes, and so on. It would be procrustean to construe this as a change in her metaphysical views, a revision in her catalogue of the ontology of the world: it is more that -- so to speak -- thought and talk about God becomes an irrelevance to her. But as we've noted before, Murray and Rea aren't in general much interested in these sorts of phemomena of religious life.

No, what they do discuss is what we might call "the metaphysical problem of evil". Is the existence of the God of the Philosophers -- the Perfect Being of Murray and Rea's opening chapters -- incompatible with, or is it at least rendered probabilistically improbable by, the existence of so much evil in the world? Well, this is familiar territory. How do they cope? The story continues ...

Faculty colloquium

I do have doubts about the point of general faculty colloquia, meaning afternoons where we present papers to each other. People who share interests -- the logicians for example -- talk to each other anyway, and philosophy has got so professionalized that those who don't share the same interests are likely not to get much from a paper speaking to debates remote from home. (The old culture of amateurism in philosophy -- the idea we can all chip in to debates about anything -- is perhaps past its sell-by date.)

But yesterday's effort here was tolerably entertaining. Adam Stewart-Wallace, one of our grad students, gave a paper about contextualism in semantics, with Alex Oliver commenting. That session at least had the virtue of making me not feel in the least bit guilty that I'd not read Travis or Cappelan and Lepore (some of their arguments under discussion seemed -- as presented -- pretty poor, so I'm certainly not encouraged to find out more).

Next, Michael Potter talked off the cuff in part about the implications of Gödel's disjunctive conclusion from the first incompleteness theorem in his Gibbs lecture -- either our minds are not machines or there are absolutely unprovable-by-us arithmetical truths. Ben Colburn commented. I think Michael wants to read more into the second disjunct than I do (I give a very domesticated reading in my Gödel book, p. 262).

Finally Quassim Cassam fussed about the "basis" of self-knowledge with Jane Heal responding. But the distinction we need to sort that out is of course an old one -- self ascriptions of pain (say) are not evidentially based, but they aren't mysterious, they are causally based (the hook-up between pains and linguistic expressions being set up in linguistic training). The point was made in Smith and Jones and I'm not sure that I have any intellectual itch here that wasn't satisfactorily scratched by our treatment.