Friday, February 20, 2009

Weinandy on Swinburne

Thomas Weinandy has a scathingly critical review of Swinburne's Was Jesus God? at First Things:

In this review I have only touched on a few of the most blatantly false or misconceived presuppositions that in Was Jesus God? give rise to spurious issues and erroneous conclusions. There are many more. To write an apology for the faith, one has to know the faith—the faith as it has been traditionally proclaimed and understood through the centuries. Only then is one adequately equipped to give rational arguments for why one should believe it.

I haven't read the book in question, but if it is anything like his others, I'd probably end up agreeing with Weinandy. Swinburne is not stupid, but what I usually see in his work is a brilliant person developing very dubious arguments at very great length and in very clever ways. Clever development does not make the arguments less dubious (although it perhaps makes them more interesting). Plus he's one of the people behind this horrid Bayesian epistemology that has infected so much of analytic philosophy of religion (leading to yet more brilliant people wasting their time developing dubious arguments in clever ways). I always leave off Swinburne feeling extraordinarily depressed about the future of philosophy of religion; only reading analytic philosophers discussing the Trinity or the Incarnation leaves me more pessimistic. From Weinandy's review, it sounds like Swinburne's book will ever be useful if I ever need a double dose of melancholy.

Thursday, February 19, 2009

Three Fallacies in Conditional Arguments

Whenever we teach about fallacies involving arguments with conditional propositions, we usually tell students about two: denying the antecedent and affirming the consequent. I would suggest that it would make at least a little bit more sense to identify three, the third being the following:

If p, q
If p, r
Therefore, If q, r.

Why add this one, which (as far as I know) has no name? The reason is that it brings out more clearly an important and often overlooked parallel, namely, that every argument using conditional propositions has a corresponding categorical syllogism using A propositions. This has been something recognized off and on throughout the history of logic. But it was Jevons in the nineteenth century, as far as I am aware, who first recognized that whenever the conditional version of the argument committed the fallacy of affirming the consequent, the corresponding categorical version committed the fallacy of the undistributed middle. Similarly, whenever the conditional argument committed the fallacy of denying the antecedent, the corresponding categorical version committed the fallacy of the illicit process of the major term.

And this is where the third fallacy, above, comes in. For there is a third fallacy having to do with the distribution of terms in a categorical syllogism, namely, illicit process of the minor term. And, as you may have guessed, the above argument is the fallacious conditional argument corresponding to a categorical syllogism that commits that fallacy. As I said, I don't know of any name that goes with it; but when you think about it, it does occur quite a bit in real life. We could call it "false chaining" or something like that.

Whewell on Scientific Laws

An important passage that gives a good summary of Whewell's view of scientific laws:
Text not available
The Philosophy of the Inductive Sciences Founded Upon Their History By William Whewell

The idea, of course, is that general laws like Newton's laws of motion are simply general necessary principles insofar as they take form under certain possible conditions; thus they also need empirical support, in order to rule out other possible conditions. So, for instance, the first law is derived from the axiom that nothing can begin to exist without a cause, and therefore has a sort of derivative necessity to it, and can function as a sort of axiom on its own. But it's not necessary in itself; in order to apply the general causal principle to motion in particular, makes assumptions about motion that need to be confirmed against experience -- for instance, that time, and location, and the like don't in themselves function as causes of motion and rest. In other words, there's a sense in which the general form of the law is just a necessary causal principle, but in order to apply it to the particular field of motion we must go to experience to see what's relevant to a causal explanation of motion. This strikes a nice (and very deliberately intended) balance between granting the law a sort of fundamental and axiomatic character and allowing that it depends on hard-won empirical facts (and could potentially change if more precise accounting of those facts introduced qualifications).

Wednesday, February 18, 2009

Angelic Painter

Today is the memorial for Blessed Giovanni of Fiesole, better known to the world as Fra Angelico.

It's hard to express in words the art of Il Beato; fortunately, a picture is worth a thousand words.

(Fra Angelico, The Transfiguration, c. 1441, Museo di San Marco)

Knowing Each and Knowing All

Hence, even if one prove of each kind of triangle that its angles are equal to two right angles, whether by means of the same or different proofs; still, as long as one treats separately equilateral, scalene, and isosceles, one does not yet know, except sophistically, that triangle has its angles equal to two right angles, nor does one yet know that triangle has this property commensurately and universally, even if there is no other species of triangle but these. For one does not know that triangle as such has this property, nor even that 'all' triangles have it-unless 'all' means 'each taken singly': if 'all' means 'as a whole class', then, though there be none in which one does not recognize this property, one does not know it of 'all triangles'.

Aristotle, Posterior Analytics, I.5. Likewise, one could show that 'able to laugh' or 'tool-using' applies to every kind of human being; this does not show that human beings are defined by these characteristics, even partially. Or to stay in mathematical bounds: defining something by induction does tell you something -- for instance, you can determine in this way each thing that is a natural number. But this doesn't tell you what a natural number is; you learn what counts as a natural number, but even if you've covered them all, you aren't simply by that fact any more enlightened about what it is to be a natural number. The two are closely related, of course, and one can lead to the other, but conflating them is sophistry -- related, I think, to what Aristotle elsewhere calls the sophistical mistake of thinking that to know is to possess knowledge (we can know things, which is an act of acquaintance, without possessing knowledge of them, which is a disposition of being able to draw conclusions based on understanding of the things we know).

Tuesday, February 17, 2009

A Dream a Little Less Inconstant

I've always thought that this is one of Pascal's most lyrical passages. You have to like the touch of humor in the first paragraph, too.

386. If we dreamt the same thing every night, it would affect us as much as the objects we see every day. And if an artisan were sure to dream every night for twelve hours' duration that he was a king, I believe he would be almost as happy as a king, who should dream every night for twelve hours on end that he was an artisan.

If we were to dream every night that we were pursued by enemies and harassed by these painful phantoms, or that we passed every day in different occupations, as in making a voyage, we should suffer almost as much as if it were real, and should fear to sleep, as we fear to wake when we dread in fact to enter on such mishaps. And, indeed, it would cause pretty nearly the same discomforts as the reality.

But since dreams are all different, and each single one is diversified, what is seen in them affects us much less than what we see when awake, because of its continuity, which is not, however, so continuous and level as not to change too; but it changes less abruptly, except rarely, as when we travel, and then we say, "It seems to me I am dreaming." For life is a dream a little less inconstant.

Pascal, Pensées

Monday, February 16, 2009

Validity as a Modal Operator

Since validity is a modal notion, it makes sense for it to be described by a modal operator. Here's a gesture at one way one might do it.


The validity operator applies to arguments, of course, rather than propositions. There are two tricky things, related to each other, that you have to work out in order to have a modal logic that takes arguments rather than propositions:

(1) What is the default modality (in most modal systems 'true' or 'actual' is used as the default modality, neither of which make sense here)?
(2) What is the negation of a, ~a?

Without good answers to these, there's really no hope of an interesting modal formal description of validity. However, they can both be answered. Think through a moment what validity means. If an argument is valid, then in all the kinds of situations to which it may relevantly be applied, the conjunction of the premises and the conclusion will correctly describe the situation. By 'correct description' I don't mean, true, exactly; rather that the premises have a bearing on the conclusion so that either it is true or it would be true if the premises were true. (Or, in other words, a means that the argument 'works' in the relevant kind of situation.) So this gives us the default modality: a, read modally, tells us that the conjunction of the premises and the conclusion correctly describes a given relevant kind of situation. Given this we can easily add our validity operator, with the following interpretations:

Va: any relevant kind of situation is one in which a (a is a valid argument)

~Va: there is a relevant kind of situation in which ~a (a is an invalid argument)

Thus we have validity and invalidity. But we'd like to know what ~V~a is. To pin this down, we start with our interpretation of the default modality: the conjunction of premises and conclusion correctly describes a given relevant kind of situation. The negation of this, ~a, is then suggestive of a counterexample: a given relevant kind of situation which the conjunction of the premises and the conclusion does not correctly describe. This gives us the other operator; we can call it viability, and understand it in the following way:

*a: this is shorthand for ~V~a

*a: there is some relevant kind of situation in which a (a is a viable argument)

~*a: any relevant kind of situation is one where ~a (a is a nonviable argument)

Viability is actually as important as validity, although more often overlooked; an argument may be viable but not valid, in which case it does not guarantee its conclusion in every relevant kind of situation, but the truth of its premises is not irrelevant to the truth of the conclusion, either.


It's all well and good to have interpretations of modal operators, but you need rules in order to do things with them. It's clear enough that the standard sorts of rules of inference won't work here, since they are designed to handle propositions rather than arguments. Exactly what the best group of operators will be, I'm not sure, although I suspect a final system would have a way of conjoining and disjoining arguments that is analogous, but not identical, to propositional conjunction and disjunction. What I want to do here is simply identify two rules with which you can do a great deal. First, let |- indicate that one can infer the right from the left. Then we can have a rule:

Va |- a |- *a

This makes the modal system analogous to M, and can easily be seen to be right under our interpretation: If an argument is valid, the conjunction of its premises and conclusion correctly describes the kind of situation, in the sense above; and if this defaul modality is true, there is some relevant kind of situation that is correctly described.

In addition, we want to be able to make comparisons between arguments. Let (Va : Vb) indicate that the validity of a and b are linked, so that if a is valid, so is b, and vice versa. In other words, they have the same relevant structure. Then we want an inference rule such that

Va, (Va : Vb) |- Vb

This is a typical way we argue from scratch about validity: we identify a particular argument as valid and generalize this conclusion to all arguments with the same relevant structure; combined with the fact that ~a indicates a counterexample, and you already have a pretty useful selection of tools for arguing about validity. I'm sure that additional descriptions of other types of inference about validity, invalidity, viability, and nonviability, could be added; this is just a fragment to show that it can be done.

Sunday, February 15, 2009

Poem Re-Draft


The sun is not a ball of fire
but the sum of one desire:
to lure; and thus must it appear
to thoughtless eyes a burning sphere.
But all this rolling globe of light
is more than what appears to sight;
less like a flame, more like a word
in which the thought and deed are blurred
it rolls, and in a single thought
all the paths of light are caught
and bent around it like a sea
extending to infinity;
it speaks, commanding: Come to me.

Some have thought this world to fly
like merest droplets flung on high;
a little water, a bit of earth,
a thing of nothing as to worth.
But they who ponder on the skies
study better, grow more wise,
and know: each star in moving course
is subject to its endless force;
and all the glories near and far
are made to feel it where they are
by whispers born of ecstasy.
The whispers beckon: Come to me.

The stars are moved; each like a thought
has searched the sky and gently sought
the paths and ways by which things flow;
each is a word to those who know,
a gesture to each thing and kind
like searching queries in your mind;
each calls out to eternity,
words ripple out upon the sea,
each summons, saying: Come to me.

Frelinghuysen on Indian Removal

Since I mentioned Theodore Frelinghuysen in the previous post, I thought I would also post some quotations from his famous attack on Cherokee Removal:

God, in his providence, planted these tribes on this Western continent, so far as we know, before Great Britain herself had a political existence. I believe, sir, it is not now seriously denied that the Indians are men, endowed with kindred faculties and powers with ourselves; that they have a place in human sympathy, and are justly entitled to a share in the common bounties of a benignant Providence. And, with this conceded, I ask in what code of the law of nations, or by what process of abstract deduction, their rights have been extinguished? Where is the decree or ordinance that has stripped these early and first lords of the soil? Sir, no record of such measure can be found. And I might triumphantly rest the hopes of these feeble fragments of once great nations upon this impregnable foundation. However mere human policy, or the law of power, or the tyrant's plea of expediency, may have found it convenient at any or in all times to recede from the unchangeable principles of eternal justice, no argument can shake the political maxim, that, where the Indian always has been, he enjoys an absolute right still to be, in the free exercise of his own modes of thought, government, and conduct....

Do the obligations of justice change with the color of the skin? Is it one of the prerogatives of the white man, that he may disregard the dictates of moral principles, when an Indian shall be concerned? No, sir. In that severe and impartial scrutiny which futurity will cast over this subject, the righteous award will be, that those very causes which are now pleaded for the relaxed enforcement of the rules of equity, urged upon us not only a rigid execution of the highest justice, to the very letter, but claimed at our hands a generous and magnanimous policy.

Ranking Presidents

I just came across this list (from October) ranking the 'Greatest U.S. Presidents'; these things are always a bit subjective, but it seems to me that this list is dangerously Machiavellian. Any list in which Polk gets more points for gaining territory in the Mexican-American War than Arthur gets for civil service reform is a list that is not ranking according to good governance. It likewise makes no sense for Harding to be less severely penalized for massive corruption than Hoover for failure to reverse to a completely new level of economic crisis. Jackson ranks very high despite the horrors of Indian Removal, but Van Buren ranks very low for continuing and enforcing Jackson's policies. The article says the ranking was by a "panel of experts"; but everyone on the panel seems to have been a journalist. Nonetheless, the list bears similarities to the sorts of rankings you get when historians and political scientists are asked to do it.

My own view is that it's best not to think in terms of Presidents but in terms of notable Presidential accomplishments. Thus we would see why it makes sense for Lincoln to rank high (successful termination of the Civil War and the Emancipation Proclamation were very good) without overlooking the fact that he suspended habeas corpus (three times!) and tried civilians in military tribunals, which is bad. Franklin Roosevelt would be properly recognized as the man who put Japanese-American citizens in detention camps, Jackson as the man who took a beautiful Cherokee civilization that was beginning to flourish and ruthlessly crushed it, and people would finally have to at least take seriously the argument that these were massively shameful failures. Likewise, Garfield's and Arthur's work in the reform of civil service (the Star Route inquiry, the Pendleton Act), which actually and undeniably made the U.S. government more efficient and less corrupt, would be recognized for the victory for the public weal it was. And so forth through the list. Further, if the list tended hawkish -- as rankings of Presidents often do -- it would be much more directly noticeable. That would be an interesting and informative set of lists: the 100 best and 100 worst Presidential accomplishments.

(Also, although obviously construction of such lists is much more complicated, we should have more lists of great Senators and Representatives. We live in a Republic. Give Daniel Webster, Theodore Frelinghuysen, and Henry Clay their due.)

Thomism vs. ID

Michael Tacz discusses the distaste Thomists tend to have for 'intelligent design theory' (ht):

One day I received a phone call from a professor of philosophy at a nearby private, religiously affiliated college. He had just returned from an international conference devoted to challenges to evolutionary biology from intelligent design (ID) theory. There was a bit of urgency in the professor’s tone, so I agreed to meet him. As it turned out, he had something of a complaint to make, for he opened our meeting by showering me with a series of questions: Where are the Thomists? Where are the Catholics? How come you are not out there defending us ID advocates? After all, we are on the same side, are we not? He explained that the conference organizers had invited several Thomists to participate, and he was dismayed that, far from expressing sympathy with the ID movement and its challenge to Darwinism, they were quite critical of it. Perhaps feeling a bit betrayed, he wanted to ask me, a Thomist, just what was going on.

The article actually only touches the surface, I think; the reasons a Thomist might give for not liking ID would make up a very long list: Tkacz mentions confusion between efficient causes in the proper sense and moving causes, the inability of ID to capture the notion of creation, confusion between epistemology and metaphysics, and misunderstanding of chance and contingency, but more could be added (confusion of primary causes and secondary causes, inadequate causal theory, etc.). There's very little they're actually capable of sharing.