Saturday, May 29, 2010

Coyne and the Preface Paradox

Jerry Coyne manages to bungle the Paradox of the Preface in a hilariously funny way. He's responding to this piece by Andrew Pessin.

The basic structure of a paradox of the preface is this. Take a number of claims, each of which has the following characteristic: we believe there is very good reason, of whatever relevant kind, to think that it is true. However, we still can have independent reason for thinking that almost certainly somewhere in this batch of claims there is some claim that is in fact false. So one way to gloss this is that we believe of each claim in the set that it is true but we believe of the set as a whole that it has at least one false claim. This is a paradox. The name comes from the usual scenario used to describe it, a scenario which was originally put forward by David Makinson (you can find Makinson's classic paper on his website). Suppose an author believes each sentence he writes in a book: he's very honest, and would never write a sentence he thinks is false. Moreover, he has taken great care in each case to make sure that he is right. So he has good reason to think that each one is true. But the author recognizes that he is fallible, and that with so many sentences in his book he certainly slipped somewhere. So in the preface to the book he admits that some sentences in the book are almost certainly false (perhaps hoping that someone might correct them if they find them). He has good reason to think each sentence is true, and good reason to think at least one of them is false.

Another, somewhat looser, way of putting the paradox is this. To assert contradictory things is irrational. The author believes what seem to be contradictory things. However, asserting what one thinks one has good reason to think true while at the same time recognizing one's own fallibility is rational. Makinson uses an analogy. A philosopher who says, "Every single one of my beliefs is currently correct," is exhibiting hubris, not rationality; but a philosopher who says, "It's pretty much guaranteed that some of my beliefs will turn out to be false," is being rational and honest. So either it's OK to believe contradictory things, or writing this preface seems both irrational and rational, or something weirder is going on. There are lots of different attempts to handle this; the most common of which is to deny that there is actually a contradiction by denying that beliefs (or good reasons, or certainty, or any of the other things you can run preface paradoxes with) agglomerate -- that is, that believing p is true and believing q is true doesn't logically require believing that both p and q are true. (For an example, see John Williams's discussion of the paradox (PDF).) This makes the logic governing the rationality of belief (or whatever) in a certain sense nonstandard; we can make sense of that, because there are perfectly viable logical systems that would allow this (certain kinds of modal logics), but there doesn't seem to be any general consensus about the best way to handle the preface paradox.

Pessin's argument is that religious belief has a structure similar to that which we find in the preface paradox:

[Y]ou can now say, first, that you believe, with certainty, on the basis of reason and evidence and testimony, in the truth of, say, the various individual tenets of your version of Christianity, and thus believe, with equal certainty, in all the things entailed by that belief: that, say, all other competing religions and doctrines are simply false.

But then you can say, second, something else: that you may be wrong.

Got it? You can simultaneously be certain that Christianity is true and everything conflicting with it is false, and yet acknowledge that you may be wrong without taking away your certainty. You can thus keep your certainties without having to claim that you are, in fact, and grossly implausibly, infallible.

He's surely right that the religious case can exhibit the preface paradox structure. I'm not sure it's quite such a revelation as he thinks, because one would expect preface paradoxes to arise, at least potentially, wherever we can consider beliefs both individually and as a group. Indeed, as Makinson noted in his original article, the paradox of the preface is a cousin to MacIver's paradox (e.g., "I'm fairly sure that such-and-such is the case, but I know I could be wrong"); and MacIver's paradox crops up everywhere in discussing rationality. Pessin is implicitly taking a positon on how to handle the preface paradox here, but it's not an unusual one. He's saying that, despite the apparent contradiction in the paradox, there is no actual contradiction; this is how almost everyone handles preface paradoxes. And Pessin is certainly right that insofar as the religious case exhibits the preface paradox structure, someone could reasonably be fully certain of each thing said by (say) Islam that it is true without necessarily being fully certain that there is nothing in Islam that is false. Thus, says Pessin, you can be a Humble Absolutist.

There's nothing out of the pale here; the preface paradox is an actual epistemological paradox, it is unsurprising that it or an analogous paradox can obtain in the religious case, and the solution that Pessin is assuming is a fairly common one that was formulated for purely epistemological reasons and can be given a solid logical grounding. And since Pessin is simply aiming at the "Humble Absolutist" claim, the preface paradox structure is actually the outside limit -- it's stronger than he actually needs for the conclusion he draws, but since one can draw similar conclusions for the preface paradox, one can, a fortiori, draw those conclusions in the weaker case. I'm not sure why Pessin is so excited about it; but, then, I haven't seen anyone apply it directly to the religious case before, so it was certainly worth doing.

In any case, here we enter Coyne's hilariously funny post, which makes me burst into laughter every time I read it. His summary of Pessin's argument?

How can you be dead certain that the tenets of your faith are right and still tell others that the contradictory tenets of their faiths might also be right?

Pessin’s solution: you just assert it.

This in a post titled, "Religious beliefs can be true and false at the same time." This is such a mockably bad misreading of the paradox that I still can't get over it; it's not as if we're dealing with an especially difficult point to grasp here, nor as if it takes much epistemological or logical acumen to see the point, nor does it exactly take a genius to figure out the basic structure of Pessin's argument. And it's all the funnier in the logical equivocation that Coyne's question carries, which shows that he has missed the whole point and then some: Pessin is saying you can be "dead certain" of each tenet that it is right, but still recognize, on the basis of one's fallibility, that some of those tenets (you don't know which ones) might actually be false. That is, there are two different ways of being "dead certain" about the tenets of one's faith; and there are, correspondingly, two different ways to concede that exclusive tenets might be true. But Coyne, of course, doesn't see the need to bother with trifles like logic and rational approaches to epistemology.

It wouldn't be so bad if he didn't try to smear Andrew in the process of displaying his ignorance and logical incompetence; but his doing so simply takes the cake. But we can't be too hard on him; he's Coyne -- consideration of the possibility of his own fallibility, and what might follow from it logically and epistemologically, is just plain foreign to him, so we should have some sympathy for his difficulty in grasping the elementary issues of it.

(Incidentally, my own preferred approach to resolve preface paradoxes generally is fairly similar to Dale Jacquette's (PDF), who also has a good discussion of different kinds of proposals.)

ADDED LATER: Jean Kazez provides a sharp contrast with Coyne by having a reasonable discussion of Pessin's argument.

What has actually surprised me in some of the discussion throughout the blogosphere is that there are people in the discussion with backgrounds in philosophy who seem to have no real acquaintance with the paradox. For instance, there seems a common misconception that the paradox can be dissolved simply by eliminating the issue of certainty; but this is provably untrue (and has been known for decades now), and most versions of the preface paradox that have been developed since Makinson's first identification of it do not appeal to certainty. You can run preface paradoxes for almost any concept associated with rationality, including several that do not require certainty. It is, as I note above, possible to have a preface paradox in virtually any conditions under which you can treat beliefs, claims, assertions, etc., both individually and as a group. Precisely the reason philosophers have studied it is that it cannot be easily waved away.

Friday, May 28, 2010

More on Turretin on Infinite Regresses

Richard Hennessey had some comments on the passage from Turretin recently quoted. In his post he structures the argument as follows:

1. Only series having a first member are series ordered as to prior and posterior.
Therefore, all series ordered as to prior and posterior are series having a first member.

2. So, all series ordered as to prior and posterior are series having a first member.
But all series of producing causes are series ordered as to prior and posterior.
Therefore, all series of producing causes are series having a first member.

3. But no series having a first member are infinite series.
And all series of producing causes are series having a first member.
Therefore, no series of producing causes are infinite series.

I don't think this is quite right as a statement of the formal structure of Turretin's argument. One of the problems, I think, is that the regimentation treats "Only series having a first member are series ordered as to prior and posterior" as an initial premise when it is clearly a conclusion. And I think the last half of the passage, which is omitted, is doing the bulk of the work. The beginnings of a better reconstruction would be something like:

1) A causal series must be ordered according to prior and posterior.
2) In causal series that infinitely regresses there is no first cause.
3) Therefore in such a series every cause is a middle cause, with a cause prior to it. (from 1 and 2)
4) But in causal series consisting of producing causes, any collection of serial producing causes in the series is itself a producing cause.
5) Therefore the collection of all the superior producing causes in the series is a producing cause. (from 4)
6) Therefore the collection of all the superior producing causes in the series is a middle cause, with a superior cause that is prior to it. (from 3 and 5)
7) Therefore in an infinitely regressing series of producing causes there is a cause that both has and does not have a prior cause. (from 6)
8) Therefore a causal series of producing causes that infinitely regresses both is and is not ordered according to prior and posterior (from 1 and 7)
9) Therefore no causal series of producing causes infinitely regresses. (from 8)

That's somewhat loose and on-the-fly; it could be tightened up by filling in the implied premises. The point is that it is not enough to respond to the argument by saying that we can identify order according to prior and posterior in a causal series without regard to a first cause (for which we'd need an account of how to do so, in any case); this is not an assumption of the argument but its very nerve. And the part about the collection of causes is actually important: it's an argument that a series of causes consisting only of middle causes is impossible.

The most important premise here is actually (4). Since Turretin is only summarizing a form of scholastic argument that was common in various versions, he doesn't justify (4); traditionally it would be justified by an analysis of the sort of causation involved. And, indeed, this is the major issue as to the soundness of the argument: whether there are any real causes that work in such a way that they can be called producing causes in exactly Turretin's sense. If there are, there is a first producing cause. If there aren't, then maybe there are first causes in some other sense of the term 'cause' or maybe there aren't.

The One Voice of Wave and Tree

The Sea-Limits
by Dante Gabriel Rossetti

Consider the sea’s listless chime:
Time’s self it is, made audible,—
The murmur of the earth’s own shell.
Secret continuance sublime
Is the sea’s end: our sight may pass
No furlong further. Since time was,
This sound hath told the lapse of time.

No quiet, which is death’s,—it hath
The mournfulness of ancient life,
Enduring always at dull strife.
As the world’s heart of rest and wrath,
Its painful pulse is in the sands.
Last utterly, the whole sky stands,
Grey and not known, along its path.

Listen alone beside the sea,
Listen alone among the woods;
Those voices of twin solitudes
Shall have one sound alike to thee:
Hark where the murmurs of thronged men
Surge and sink back and surge again,—
Still the one voice of wave and tree.

Gather a shell from the strown beach
And listen at its lips: they sigh
The same desire and mystery,
The echo of the whole sea’s speech.
And all mankind is thus at heart
Not anything but what thou art:
And Earth, Sea, Man, are all in each.

How Millenial Are You?

Pew Research has a little quiz gauging how similar one's activities and attitudes are to the 'Millenial' generation. I got a 45, and although that's getting close to the upper bound for me, it's low for people my age, at the tail-end of Generation X. (ht)

Thursday, May 27, 2010

Two New Poem Drafts

Discourse of St. Symeon

Who stands upon the ocean-shore
and looks out to horizon's end
may in its vastness somewhat share
but yet is bound upon the sand;
such see in truth the boundless sea
and yet the sea extends beyond;
unbounded sea they truly saw
and yet their seeing had a bound.
Yet, content not merely to see,
will others into vastness wade,
and what shall we of these folk say
who feel the waves roll strong and wet?
They too the endless ocean share
and yet are conscious and made full,
far more than any on the shore,
of fullness, depth, and overflow.
But will not those who wade out lose
their vision as the water weaves
a wall through which their eyes see less
of anything but wave on wave?
And to the one who simply swims
all but the ocean then will fade;
in such a state the world then seems
to be but currents that enfold.
Even so with glory bright!
Even thus will be the lot
of those who by God's grace are brought
into God's deep and endless light.


The false and faithless gods of yore
are haunting me this sleepless night;
their leering faces, mirror-like,
are mocking me beneath the stars.
Their tongues are long, their teeth are sharp,
their eyes are cold and fatal-fierce;
they know the ways and tricks of fear
and rob me of my chance to sleep.
But sleep remains a greater god;
his ruthless hand will rule the end,
his dark and piercing eye will win:
none escape him but the dead.

Wednesday, May 26, 2010

Viability of Theories

Richard Brown is re-reading Plantinga's Against Materialism (PDF) paper and is not impressed. I'm not especially impressed, either, but I found this argument at the end of Richard's post curious:

The very concept of an immaterial substance is unintelligible. Attempts to make them intelligible render them into ordinary physical substances at the next level up, so to speak. And it is of course out of the question to simply say that an immaterial substance is perfectly intelligible since they are just minds (as Plantinga seems to do). It is obvious that there is thinking but it is not at all obvious that an immaterial substance could think. What would that even mean? The upshot then is that substance dualism is not a viable theory.

I think this runs into problems when one considers what actually makes a theory viable rather than glossing it over with this extremely ambiguous question, "What would that even mean?" For it is an extremely ambiguous question. There are several different questions that could be asked in those words, and the answers to each of those questions do not impact on the question of the viability of a theory in the same way. The spread of possibilities when we are asking about the intelligibility of something is closely related.

Imagine someone trying to figure out what scientists mean when they talk about black holes. "What would that even mean?" or "What makes that intelligible?" (asked in good faith) may mean, "What reasons could one have for believing that this is true?" In that case, the physicist would reply by giving his or her reasons to think that there are, in fact, black holes -- certain astronomical phenomena and theoretical considerations based on general relativity, for instance. More broadly, it might mean, "What reasons could one have for believing that this is possible?" The same type of evidence would suffice for answering the question; we are just dealing with a weaker standard of proof.

However, it could be that the concern about intelligibility is not a concern about underlying reasons for thinking that a thing is but concern that we don't know what a thing is. But obviously if you have reasons to believe something exists you know what it is to the extent that you have reasons to believe it; the 'what' that contrasts with 'that' here has to do with our grounds for further inferences. In other words, "What would that even mean?" when applied to black holes would be the question, "On what basis could you say anything more about how this works?" or "What grounds does that provide for further inferences?" The reason that we associate this question with intelligibility is that the greater one's understanding of something, the more easily one can answer further questions. So, for instance, asked this question about black holes, the physicist would respond by talking about the most advanced theories about black holes currently available and the evidence about black holes that underlies them.

It's important to draw the distinction because which side of the distinction one is on at a given moment makes all the difference in the world. One of the most important distinctions to be drawn in any sort of inquiry is the distinction between problems that are problems for a theory and problems that are problems within it. The former put the theory into question; the latter are merely research problems. And making this distinction is essential to determining whether a theory is viable. The physics of black holes is certainly a viable set of theories; they are not made less viable by the fact that there are plenty of things about black holes that are not yet understood or that are purely speculative or that are based on extrapolation from other kinds of cases or that still involve a bit of guesswork. These are all points for further research, not problems for the theory. In talking about evolutionary theory, a biologist may say, "OK, but what does it mean to say that a population of reptile-like theropods eventually became a population of bird-like theropods?" If there were no immediate answer available, the biologist's response would not be, "Oh, then the theory must not be viable because the claim that one became the other is unintelligible." Rather, the biologist would respond by setting out to see what answer the question could be given, which would involve clearing up conceptual confusions, looking at evidence, etc. Such an inquiry might eventually uncover insuperable problems, i.e., problems that put the claim in question rather than simply raise questions for further research, but it might also end up justifying the theory as an excellent theory. A skeptic about evolution might ask, "What would it even mean?" in the same sense as the biologist; in which case he is simply trying to figure out where the theory leads. But he might also be trying to suggest with the question that the whole claim is just unintelligible; in which case the biologist doesn't have to respond by answering the research-problem question but simply by saying why the claim has enough evidential support and theoretical usefulness to merit provisional acceptance and further research. What the skeptic could not do is take the incompleteness of the answer to the research-problem to indicate that it is a fundamental problem for the theory itself; at least, asking "What could that even mean?" in this way would be selective obscurantism, or as we sometimes say more bluntly, playing stupid.

Viability of theories, in other words, is viability in terms of inquiry, and it makes a big difference to inquiry whether we are talking about what leads to a claim or what follows from it. Now, I think it's clear enough that Richard's argument as stated above fails to make this distinction properly. The 'attempts to make intelligible' are dealing with the research-problem question; but whether they fail or not is irrelevant to whether the theory is viable or intelligible, because they are all attempts to extend what we know about immaterial substances on the assumption that they exist. The only question that would be relevant to whether the theory is viable or intelligible would be whether its reasons for saying that thinking could not be a material activity are coherent and reasonable (even if ultimately wrong); but this is not what the argument considers. The argument then seems to founder on considerations of what constitutes viability.

Et Praevalet

Magna Est Veritas
by Coventry Patmore

Here, in this little Bay
Full of tumultuous life and great repose,
Where, twice a day,
The purposeless, glad ocean comes and goes,
Under high cliffs, and far from the huge town,
I sit me down.
For want of me the world's course will not fail;
When all its work is done, the lie shall rot;
The truth is great, and shall prevail,
When none cares whether it prevail or not.

This poem appeared in Patmore's 1877 collection, The Unknown Eros.

Tuesday, May 25, 2010

Bede's Day

Today is the Feast of St. Beda, more widely known as the Venerable Bede. Here is a bit of poetry attributed to him:

Bede's Death Song

Before the needful journey there, no one becomes
wiser of thought than him who necessarily
ponders, before his going-hence,
what good and evil within his soul
after his death-day may be judged.

I say 'attributed' because, while we know Bede recited a poem in Anglo-Saxon on his death-bed, Cuthbert only gives us a Latin paraphrase; starting from the ninth century we find Anglo-Saxon versions of the poem, but they could either be Bede's actual poem or someone's later attempt to recapture it.

The poem, in any case, shows Bede teaching even to his dying day. Bede, of course, is also the patron saint of historians. Bede's classic work, The Ecclesiastical History of England, is easily available online. Bede's historical practices are not completely consistent, but they still show an admirable grasp of the nature of historical evidence and the sort of conclusions that can be drawn from it; he really is an exemplary historian.

Turretin on Infinite Regress

Neither can an infinite series of producing causes be allowed because in causes there must necessarily be some order as to prior and posterior. But an infinite series of producing causes rejects all order, for then no cause would be first; rather all would be middle, having some preceding cause. Indeed there would be no cause which ought not to have infinite superior causes before itself which is impossible [asystaton]). If there were infinite causes before each and every cause, before the whole multitude and collection of causes there would be infinite causes and thus that collection would not be total.

Francis Turretin, Institutes of Elenctic Theology, Third Topic, Question I, Section VI (Giger, tr.).

Monday, May 24, 2010

"Doubtless There Are Other Roads"

The Wayfarer
by Stephen Crane

The wayfarer,
Perceiving the pathway to truth,
Was struck with astonishment.
It was thickly grown with weeds.
“Ha,” he said,
“I see that none has passed here
In a long time.”
Later he saw that each weed
Was a singular knife.
“Well,” he mumbled at last,
“Doubtless there are other roads.”

Sunday, May 23, 2010

Martin Gardner (1914-2010)

Martin Gardner recently died. His writing is very uneven, but he has some gems. His best book-length work is his novel of ideas, The Flight of Peter Fromm (very under-appreciated); but his strength was in smaller works, where an occasionally Chestertonian wit sparks through. He will be missed; he was that rare creature, the genuinely excellent popularizer.

I can't say I was very influenced by him, but, as I said, I liked The Flight of Peter Fromm, and Gardner happens to be where I first read about Raymond Lull.

The Brute Fact Pencil

Nicholas Smith has a really extraordinarily bad argument on the question of whether "God exists" can be a necessary truth:

If that were true than the could be no possible world (=a world that can be described without contradiction) in which God did not exist. But it seems obvious that there can be such a world. Consider this description:

World W = a world in which only a single pencil exists.

It's hard to spot the contradiction in that simple world!

But it's not at all difficult to see that a possible world containing only a pencil is contradictory. When we are talking about possible worlds we are not saying, "Imagine a universe with only a pencil in it at a given point in time." But a possible world in which only a single pencil exists is a possible world in which a pencil exists without anything -- past, present, future, material, immaterial -- to cause it. To say that a world can exist in which only a pencil exists is to say that it is possible for a pencil to exist as a brute fact with no further explanation. But pencils are composed artifacts; as such they are effects, and thus World W is a world in which an effect exists without its cause. That's a contradiction. The only way one can get around this is to argue that pencils can, in fact, be brute facts, i.e., things that are not caused by anything at all, don't necessarily exist, and yet can still happen to exist for no reason whatsoever. But this stretches the concept of a pencil beyond all recognition. Moreover (although full consideration of the question would require a longer argument than this), it is a contradiction for something to exist uncaused and not be necessary, since what exists but is uncaused is something that exists whose existence is not contingent on anything else.

And it's easy to see that the matter is not going to be as easy as Smith suggests, because if God is a necessary part of the explanation for why anything other than God could exist, God is necessary. But it's easy enough to see that this will be a common reason for saying that God is necessary; and therefore no one can be sure of the coherence of the claim that a possible world in which nothing exists but a single nondivine entity unless they are already sure that God is not necessary for the explanation of the existence of any nondivine entity. In other words, the World W argument boils down to the claim, "Well, it just seems obvious that it's possible for God not to exist; just think of what it would be like for God not to exist." But this is just question-begging from the beginning.