Wednesday, April 30, 2008

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?

Tuesday, April 29, 2008

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.

Monday, April 28, 2008

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.

Sunday, April 27, 2008


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 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.

Saturday, April 19, 2008

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.

Tuesday, April 15, 2008

Sigma_1 functions and properties

Rob Trueman, one of our undergraduates, came up with a nice question today which left me kicking myself that I'd not footnoted the point/forestalled the question in my Gödel book.

In Ch. 13, I'd proved that any function that is expressible by a Sigma_1 expression of arithmetic can be represented in e.g. PA, again by a Sigma_1 wff. (Or as I prefer to say, it can be "CAPtured", as that is memnonic for CAse-by-case Proved). In Ch. 21, I'd also proved that, while the property of Gödel-numbering a PA-theorem is expressible by a Sigma_1 expression of arithmetic, it can't be represented in PA (whether by a Sigma_1 wff or anything else).

How come, asked Rob, is there that stark lack of parallelism, given that we can move to-and-fro from property talk to function talk by the characteristic function trick?

The answer, of course(?!), is that just because a property is Sigma_1 expressible it doesn't follow that its characteristic function is Sigma_1 expressible. But it takes a moment to see this, and I should have explained.

Friday, April 11, 2008


When I lived in Sheffield, there was a record shop which had a wonderful stock of second-hand classical CDs (frequently topped up by a couple of people living in the area who reviewed for music magazines and sold off heaps of review copies). I spent a lot of time and too much money there.

It was in that shop I first heard Portishead's Dummy being played. I was bowled over, asked who it was, and have been hooked ever since.

I say this with some awkward self-consciousness, as I'm quite the wrong generation. And you can't listen to Portsihead with the amused if admiring detachment that comes with the years -- as I do, for example to The White Stripes (on the iPod down the gym), entertained by the sheer cheek of it all as the kids have fun. Portishead don't exactly do fun. Dummy is dark and tangled, Portishead more so. You either have to dismiss their music as pretentious self-indulgence, or take it seriously. Sometimes I don't listen to them for months, and I begin to wonder. But then, in the right mood, I hear Beth Gibbons singing Wandering Star or Sour Times and I'm instantly captured again.

And now, ten years on from Portishead, their Third is coming out at the end of the month. But I confess I downloaded the torrent of a pre-release version (I hereby promise to buy the CD!). I am not sure what I was expecting. But not this. Darker still. Music it seems for the end of our times. Not a comfortable listen. And nothing with the instant appeal of a Glory Box or Roads or Over.* But it gets under the skin.

Here's their video of Machine Gun. Beth Gibbons' voice never more beautiful. The background never more harsh. And there is no consolation at the end ... her voice does not return.

*Nothing here, then, that could be co-opted for consumer adverts? But walking through the Grafton Centre mall the other day, the piped music was Dylan's Desolation Row. And if that can be domesticated and defanged ...

Thursday, April 10, 2008

Gödel exercises

OK, I've at last really started what I've been promising to do ever since my Gödel book finally went to press, namely get sets of exercises up onto the book's website. There's now a slightly improved set of exercises for Chapter 2, and a brand new set for Chapter 3. And I'll try to keep going with a new set every few days for a while so that there is a decent array before the autumn term/semester starts.

In fact, constructing the exercises is always the thing that takes the thought: putting together solutions just takes a bit of time, and I hope to start doing that in spare moments fairly soon too.

Wednesday, April 09, 2008

Philosophy of Religion 10: Anti-theistic arguments

Where have we got to, then, a bit over half way through Murray and Rea's An Introduction to the Philosophy of Religion?

Religious belief has been tied (I'd say pretty misguidedly) to "perfect being" theology. Murray and Rea have a shot at making metaphysical sense of talk of a perfect being in the first couple of chapters -- which I haven't discussed enough here, and really should come back to. But the notion is (unsurprisingly) left pretty murky. Their attempts in Ch. 3 to make sense of the doctrines of the Trinity and the incarnation are based on hopeless analogies. They seem to place some weight on "religious experience" in Ch. 4 but are remarkably silent on what that might consist in -- and they give no good reasons for supposing that such experiences are a reliable guide to anything. And in Ch. 5 our authors themselves defeat most of the standard arguments they consider for theism, except for the fine-tuning argument; and if that last one is still in play, it's arguably because they don't properly examine the probabilistic reasoning on which it depends.

So where do we go from here? The story continues ...

In Chapter 6, Murray and Rea turn to "Anti-theistic arguments". But, at this stage in the game, in what sense does the atheist need anti-theistic arguments? She might well muse along the following lines:

"Burden tennis", batting the burden of proof to and fro over the net, is rarely a very profitable pastime! But still, maybe this case is an exception. After all, "perfect being" theists, when you come down to it, are making some highly exotic claims, claims that aren't that much clearer after Murray and Rea's labours, and which make the beliefs, say, of ancient Greek religion look very modest and humdrum. Not just powerful gods, but an omnipotent god. Not just gods intermittently casting an amused eye over mortal folly, but an omniscient god. And one not just occasionally taking a passing interest in some of us, for good or ill (and occasionally, understandably, running off with a particularly pretty nymph) but loving us all equally. And on it goes, wilder and wilder (e.g. the three-for-the-price-of-one Trinity). By the workaday epistemic standards we use in most of our lives, those extravagant claims look quite extraordinarily fanciful. So we can reasonably insist that someone who advances such claims literally (not, for example, as inspiring myth) and expects to be taken seriously, had better have some very, very, good arguments. Pending such arguments, which we haven't been given yet, we atheists don't have much to do.
Or at any rate, recalling Russell's teapot, we needn't do much by way of coming up with additional reasons against a perfect being to add to the lack of weighty enough reasons for believing in any such a thing. But of course -- in a spirit of human curiosity -- we might well be interested in reflecting about what it is about our minds and about human societies that make us rather prone to be gripped by such fanciful ideas. What role do they play for us? What sustains religious belief in our emotional and social life in the absence of weighty reasons? Well, there's a very long tradition of intriguing enquiry about this -- the "natural history of religion", if you like -- which seeks to explain the role of religious belief. Thus, for example, Dennett's speculations about the evolutionary advantages of a tendency to over-interpret agency in our environment are just the latest ingredient in a long and complex story. And this evolving story seems to make a pretty good stab at the beginnings of explaining the role of religious beliefs without sustaining their truth-claims

Now, you might well have expected Murray and Rea to have addressed this sort of calm "default atheism" head on and at length at this point. For in a highly secularized society like large swathes of "middle England", inchoate versions of this kind of detachment from religion are nowadays very widely shared.

But at the beginning of the "Anti-theistic arguments" chapter, they in fact say that "we will set aside arguments which claim that the absence of evidence makes belief in atheism more reasonable or obligatory since that issue was addressed in chapter 4." However, chapter 4 doesn't address default atheism. It talks about the notion of faith and about whether "religious experience" might be the result of a reliable belief-acquiring mechanism -- but we saw that the discussion of the latter was vitiated by a failure to properly discuss naturalistic stories about our proneness to such "experiences". As I noted before, Dennett (for example) is nowhere mentioned. Nor is the Hume of the Natural History mentioned. Nor are Hegel, Feuerbach, Marx in the index (to take names from just one other familiar strand of enquiry about the roots of religion). It looks as if Murray and Rea are just not interested in engaging with the naturalizing default atheist.

Glancing ahead just at the subsection titles, however, I notice the next chapter "Religion and science" does in fact say something about evolutionary psychology and religious belief. So I'd better suspend judgement for a bit here. It may be that the complaint is only going to be that key bits of missing discussion come not in Ch. 4 but later in Ch. 7 (which might be pretty ill-judged arrangement, but that's better than a disastrous lacuna). We shall have to see! For the moment, then, I just note that default atheism, seemingly the position of most of the students I've taught over the years, is not yet getting the kind of direct discussion that I'd have expected (at the point I would have expected it given what's gone before). I wonder: does this betoken the fact that North American authors are more used to dealing with students who are, as they say, coming from somewhere else? Anyway, we'll move on to consider what they do discuss in Chapter 6, which is mostly the argument from evil. (But I need to gather my strength for that, so don't hold your breath ....)

Non-Classical Logic

I've just picked up a copy of the second edition of Graham Priest's An Introduction to Non-Classical Logic from the CUP bookshop. More than twice the length of the first edition which just covered propositional logics, this covers their extensions with quantifiers and identity too.

I thought the first edition was terrific: so this is a hugely welcome expansion. And I'm delighted to report that CUP has published this as a paperback in their Cambridge Introductions to Philosophy Series at just £18.99/$34.99, which is surely an amazing bargain for a well-produced 613 page book. So three cheers to the Press, and in particular to Hilary Gaskin the philosophy editor, for that!

A must-buy, and a must-read!

Tuesday, April 08, 2008

Order and ordinals

One nice feature of Thomas Forster's quirky but fun Logic, Induction and Sets is that it brings out how the theory of ordinals can be developed before doing any serious set theory, and why doing things that way round is philosophically the right approach. Ok, other people say that too! -- but I found Thomas's take on all this particularly congenial.

Sunday, April 06, 2008

Philosophy of Religion 9: Theistic arguments

Chapter 5 of the Murray/Rea Introduction is called "Theistic arguments". They start off -- perhaps rather too predictably -- by considering at length the tricksy argument which philosophy of religion courses seem to get obsessed with, but which (at least in my experience) has the least to do with the actual reasons real-world believers give for their beliefs. That's our old friend the ontological argument, of course.

Murray and Rea have no trouble in kicking into touch a classical version of the argument (their pp. 129-130 explanation is exemplary). Though they are a bit feeble earlier when talking about the existence-isn't-a-property objection. For they just don't mention how you might try to make sense of what is going with that objection by linking existence talk to the existential quantifier, etc. (an odd omission, as the intended readers' intro logic lecturer has probably been mentioning that very point -- why not make the connection?).

But instead of leaving well alone, Murray and Rea next go on to consider a Plantinga-style modal version of the argument (which even Plantinga doesn't think is probative). But if their readers aren't supposed to know enough logic to be in a position to cope with the existential quantifier in discussing responses to the classical argument, they are surely just going to be flummoxed by this! They certainly aren't going to be in a position to discuss it properly (e.g. by evaluating the S5 principle for the needed metaphysical modality, discussing whether freedom from self-contradiction is a ground for attributing the requisite kind of metaphysical possibility, and so on -- certainly Murray and Rea don't give them the tools to do this).

Anyway, leaving the modal argument rather in the air, our authors go on to consider cosmological arguments. And again they have no great problem disposing of some classical varieties, perhaps after unnecessary palaver. (Though another odd omission is that they don't explicitly connect what they say to the quantifier shift fallacy exposed in intro logic courses, where various cosmological and design arguments are typically offered as a prime illustration.)

Finally, Murray and Rea discuss design arguments, ending up with a weak treatment of the "fine tuning" argument. I say weak, because they rightly present the argument as a probabilistic one -- but say nothing about the kind of probability involved or the probability principles being applied. Since critics have suggested that the argument confuses different kinds of probabilities, and/or argued that the principles involved about distributions of the values of physical constants in possible ranges are fallacious, this is a pretty serious omission. And worryingly so, given that of all the arguments mentioned in the chapter, this is the one that actually has some currency in half-informed thinking outside the academy. You might have thought that Murray and Rea would really want to be wrestling with it, and pushing a lot harder on its probabilistic credentials. To say the least, an opportunity badly missed here.

Saturday, April 05, 2008

The joy of The Joy of Sets

I'd not really come across Keith Devlin's book The Joy of Sets before. But I was looking for something to recommend the first few chapters of -- as a taster, so to speak, giving a sense of the structure of the set-theoretic hierarchy and some basic knowledge about the standard axioms -- and I started reading this. And I found myself actually reading quite a lot of the book. It really is terrifically well done. I love the style (and its willingness in later chapters to give illuminating proof sketches rather than dive into too much detail). OK, the pace picks up markedly as the book the progresses. But it is surely very hard to beat the first couple of chapters if you are looking for a clear and intuitive motivation for the ZFC axioms.

Thursday, April 03, 2008

Philosophy of Religion 8: Pluralism

No. I'm not giving up my day job. A new logic book project is under way and taking nearly all my attention. When I'm more confident that it is "taking off" and going places, I'll say more about it here: but not yet -- after all, I don't want to ... erm ... tempt fate! I also must finish Absolute Generality in the next week or two. So the Introduction to the Philosophy of Religion is just a bit of late-evening reading, and the comments are dashed off quickly for fun.

Anyway: I've just been looking at the section where Murray and Rea wonder whether the fact that religious experience seems to tell different people such different things might rationally rather undermine an inclination to take our own experiences at face value. To which you'd think the answer is a plain "yes". But ah no, they say, that would be a mistake.

Suppose you are a Christian who thinks that only those like you who, by special grace, have been granted a revelation of the divine have access to reliable religious experiences: then widespread disagreement among the heathens is only what you'd expect. "Far from being evidence of unreliability, her particular circumstances are precisely what she should expect" if she were among the elect.

Indeed. But beside the point.

The issue isn't whether someone can have an internally coherent set of beliefs which enables her to "explain" to herself why -- in the face of massive disagreement -- hers are the correct views and everyone else is out of step. That's only too easy (though also that way madness lies).

The issue at stake is surely this. I don't already believe I am one of the elect, because I don't yet know what to believe. Perhaps I'm seeking God, but at this point I'm unsure about the path. But here I am having certain experiences which seem to intimate some kind of divine presence, seem to have religious content or whatever. Initially, let's suppose, I'm rather inclined to accept the experiences as veridical. But in a calmer moment I start reflecting. I want to know how trustworthy these experiences are. Am I just suffering some kind of illusion? Satan's stratagems are many. I try to crosscheck with others (as I might crosscheck with others about other surprising experiences). I find -- at least if I look outside those subject to the same immediate cultural influences -- unending disagreements about their experiences. Some give quite different religious interpretations, some seem to give interpretations freighted with aesthetic concepts, or other non-religious readings. It certainly now seems that this diversity should rationally lead me to reduce my initial higher degree confidence in how to interpret what is happening to me. Why not?

Noting that such disagreements needn't reduce the confidence of someone else who already "knows" that she is one of the elect and "knows" that her experiences are reliable is neither here nor there. The question is how someone who doesn't already know their religious experiences are trustworthy should change their rational degrees of belief in the light of finding that initially compelling-seeming experiences don't readily crosscheck.

Wednesday, April 02, 2008

Philosophy of Religion (an aside)

Luca Incurvati has just drawn my attention to this metaphysical speculation on the incarnation. Of course, the question whether you should be a counterpart theorist takes us into a whole different ballgame!

Philosophy of Religion 7: Religious experience

I'm finding myself blogging about the Murray/Rea book in more detail than I ever intended: and having got into my stride, I really ought to go back to say more about the first chapter about which I have so far said very little here. Ok, I might do that in due course, especially if I get round to organizing these comments into a single document. But for the moment, let me just press on talking about Chapter 4, this time picking up on some of their remarks about "religious experience".

I'm always highly suspicious about talk of "religious experience", as if it is some special and distinctive category of experience. So what do Murray and Rea mean? Well, they talk of (i) "mystical experiences -- visions or other sorts of overwhelming experiences that present themselves as experiences of God", more mundanely (ii) "a sense of divine forgiveness, a subtle awareness of the presence of God, an internal impression that this or that sacred book is divinely inspired", (iii) experiences which people have "taken to involve some sort of direct awareness of God, or of God's communicating something to them".

Well, that's already a very mixed bag. "An internal impression that this or that sacred book is divinely inspired" sounds like a gut hunch -- a sort of thought. Thinking you are forgiven is presumably another thought (if you hold that perceptual experiences have non-conceptual content, then it would be entirely obscure how you can have a quasi-perceptual experience freighted with the concept of forgiveness!). "Visions", by contrast, are presumably visual experiences -- though it beats me how those can be experiences of an incorporeal God. And talk of "some sort of direct awareness" is just arm-waving.

But ok, let's take "religious experience" as a catch-all label, without worrying too much about the connotations of "experience". (But so understood -- as it seems to be by Murray and Rea -- we shouldn't be at all impressed by claims like Alston's that religious experiences are analogous to perceptual experiences. Many of the supposed examples covered by the catch-all usage are plainly not analogous). Anyway: what reasons are there for trusting the deliverances of "religious experiences"?

Murray and Rea write, following Alston, "it is very hard to find reasons for thinking religious experience ought not to be trusted that do not also indict perceptual experience". Really? A common-or-garden account of the origins of my perceptual experience has it that, when I see the cup of coffee on the desk right now, my having that experience is caused by the cup of coffee on the desk. It is very far from clear, by contrast, that the obvious account of someone's "sort of direct awareness of God" when she has that experience is that the experience is caused by some interaction with a deity. Dan Dennett, for example, offers a nice evolutionary account of why we might be prone to just those kinds of thought, over-interpreting the presence of agency in the world, even though they are false and not generated by the presence of deities. And whether his story is exactly right or not doesn't matter too much: the point is that it gives us a template for an inviting kind of naturalistic story about our proneness to certain kinds of illusory thoughts and experiences (intimations of the supernatural) that does not also indict ordinary perceptual experience. Given that we can, in 2008, begin to see at least the outlines of various possible naturalistic stories, and putting that together with a presumption in favour of not multiplying entities beyond necessity, it is of course -- to say the very least -- a wide open question whether religious experience has any claim at all to be trusted.

Murray and Rea are reliabilists in epistemology (I'm happy to agree), and seem to think that "there is at least prima facie reason for thinking that religious experience can justify religious belief in just the same way that perceptual experience justifies perceptual belief" because it is prima facie reasonable to presume that religious experiences are reliably generated. Well if 'prima facie' means 'on very first impression, before we think about it', so be it. But just on a moment's second thought, that first impression should entirely evaporate.

Oh, bother ...

Adil Sanaulla has emailed to point out that the Proof Sketch at the bottom of p. 178 of IGT is flawed. I cheerfully say [with an obvious slight change of notation] that "it will be easy to prove that the Sigma_1 wff NPrf(w, x) is equivalent to the Pi_1 wff (Az)(NPrf(w, z) --> z = x)", which is just false. Suppose w is such that NPrf(w, z) is false for every z because w is not a super Gödel number. Ouch. I guess I must have been bamboozled by Theorem 13.1, unthinkly applying the same argument while forgetting that NPrf(w, x) is not functional.

I wonder what the minimum mutilation repair is ...

Something like "it will be fairly easy to prove that the Sigma_1 wff NPrf(w, x) is equivalent to a Pi_1 wff of the form Sg(w) ^ (Az)(NPrf(w, z) --> z = x), where Sg(w) says that w is a super Gödel number" should work, but isn't pretty.

Tuesday, April 01, 2008

Philosophy of Religion 6: Faith

Onwards! Chapter 4 of the Murray/Rea Introduction is entitled 'Faith and Rationality'. There's quite a bit in this chapter. I don't have faith in any of it. Let's start with faith itself.

They are interested in faith in that sense in which it is, as they put it, "just a kind of belief" ("believing by faith" rather than "believing by reason"):

To say that a person S has faith in a proposition p is to say that S believes p despite the fact that (a) there are alternatives to p which are compatible with whatever evidence supports S's belief that p, and (b) there is genuine and somewhat weighty evidence in favor of one or more of those alternatives.

Murray and Rea say that, as a welcome consequence of this characterization, faith comes in degrees because the extent to which p is underdetermined by the data/the weight of counterevidence comes in degrees. But they seem to forget entirely that, more basically, belief comes in degrees. What level of credence in p is required for 'faith'? They don't say.

Take the case of the scientist who endorses theory T, although the theory is underdetermined by the evidence, and there is some evidence for a rival theory. Murray and Rea offer this as a case of rationally "believing by faith" (to support their case that faith can be rational, because scientists are surely rational!). But of course, the normal situation here is that the scientist has a certain high degree of credence in T; she is prepared to bet, perhaps quite heavily in terms of her research time and energy, on T's truth; but equally, good scientist that she is, she still aims as best she can to apportion her degree of belief to the evidence. So if the cognitive situation of our scientist here is the model, then to "believe by faith" is just to have a suitable high degree of credence apportioned to the non-conclusive evidence. Now that is indeed a cognitively virtuous state, to be sure: but the proffered label now seems an entirely unhelpful one (we are just left with the difference between credence based on conclusive reasons and credence based on non-conclusive reasons -- two modes of "believing by reason").

Perhaps, however, the idea is that having faith in a proposition is having a degree of belief that is higher than that which appropriate given the balance of evidence? It is, so to speak, to bet more heavily than the evidence warrants. This would seem to chime with Murray and Rea's talk of "believing by faith" as being compatible with having some good reasons, but as going beyond "believing by reason". But they don't give any grounds for supposing that this is ever a cognitively virtuous state to be in. You might well think that failing to apportion your credence levels to the evidence is, to the extent that you do so, exactly to fail as an ideally rational agent (and certainly isn't what the well-trained scientist does).

Now, true, some degree of irrational excess faith by individuals in their pet theories can sometimes promote the rational growth of knowledge by ensuring that initially unpromising theories don't get killed off prematurely. But we certainly shouldn't be going round encouraging excess faith, given our natural human proclivities already to love our own brain-children far too much don't need any help at all! So it surely remains the case that our scientist should do her best not to have excess faith, but should continue, as best she can, to apportion credence to the balance of evidence.

So the situation is this. If "faith in a proposition" for Murray and Rea involves having a high degree of belief that exceeds that warranted by the evidence, then they fail to give any reason at all for supposing this is ever a cognitive state to be encouraged and recommended. While if, to have "faith in a proposition" is to have a high level of credence which is rationally apportioned to the weight of non-decisive evidence, then "faith" is just a misnomer for ... believing to a degree appropriate to the weight of (non-conclusive) evidence.

What we don't end up with, then, is a concept of faith (qua kind of belief) that is both properly so called and which picks out a state appropriate to a rational agent. Which is hardly a surprise.