Which I distinguish from Hume's philosophy of the mathematics studied by mathematicians. Hume does, in fact, say some interesting things about what mathematicians study. I've briefly discussed some of them -- for instance, Hume insists that geometry is necessarily imprecise, approximate, and inexact, and that geometers are fooling themselves if they think they work with any sort of precision. But perhaps more interesting than this is what Hume says about mathematical practice.
To discover what Hume says on this subject, we have to look at the subject of curiosity, which Hume sometimes glosses, a bit misleadingly, as love of truth. Curiosity is actually an extremely important concept for Hume. As a skeptic, he tends to think that there are no (stable) speculative or theoretical justifications for particular fields of enquiry, and, what is more, he is quite frank and straightforward about the horrors of 'philosophical melancholy' that this can induce if nothing compensates for it. So Hume's justification for intellectual endeavors is always rooted in what he considers to be stable driving passions -- most generally curiosity and vanity. This is the justification for philosophical investigation Hume gives in Treatise 1.4.7, a justification even skepticism cannot defeat (one which he calls "the first source" of his inquiries in Treatise 2.3.10. I've dramatized it a bit in a doggerel mnemonic or 'dogmonic' called The Shipwreck of David Hume. It makes for quite an adventure; but, as you can see if you compare it to the relevant section of the Treatise, I didn't have to take much poetic license to make it one.
But my interest here is to discuss what Hume's justification of mathematics by curiosity commits him to saying about mathematical practice. The relevant section of the Treatise is 2.3.10. His primary interest in this section is to argue that truth is not desired as such; rather, it is desired only insofar as it is "endow'd with certain qualities". I won't go through the arguments, although I have also discussed some of them elsewhere. Rather, I want to sum up what I think these 'qualities' are that make mathematics an object for curiosity.
(1) An occasion for exercising ingenuity. Hume calls this the "first and most considerable circumstance to render truth agreeable." It is enjoyable to exercise one's mind in a way that reflects well on one's skill. The point here is not merely that mathematics is difficult; even difficulty doesn't always exercise our "genius and capacity," as Hume calls it. What curiosity requires is not merely a difficulty but an intriguing challenge, something that requires us to "fix our attention or exert our genius."
(2) An occasion of importance. Even the potential for stimulating thought is not really adequate. It might be sufficient for a mild recreation, but it just doesn't capture the passion of an intellectual endeavor. What is necessary is that the problem or puzzle challenging us is in some way important. Hume has an interesting idea about how to understand this importance; he appeals to his account of sympathy. Imagine, he says, an engineer surveying a properly fortified city. He gets satisfaction and pleasure from seeing how well done the fortifications are. This is not, however, because he gets any immediate use from them. Rather, he gets the satisfaction because, being human, he sympathizes with those who benefit from them (and presumably with the satisfaction of the engineers who built the fortifications in order to benefit them). So by sympathy we can have a very broad sense of the utility of something indeed -- even things that don't immediately benefit us or anyone we know can still give us a sense of this broader utility, if we can have some notion that it might be of real value to someone somewhere.
(3) An occasion that admits of success. The project, after all, must not be completely futile. But Hume is very concerned to reject the claim that avoiding futility requires finding truth; which is not at all surprising, since curiosity is the primary justification of his philosophical work in the face of skepticism about whether the truth can be found in many important areas of research. To argue this, he treats study and research as analogous to pursuits like gambling and hunting. In such recreations, we actually have a dual sort of success. There's the immediate success -- in the case of gambling, winning, and in the case of hunting, catching the prey. But a person's passion for gambling simply can't be explained in terms of his desire to win; this desire may spark the passion, but the passion is for gambling itself. And so with hunting. The pursuit itself becomes its own form of success. For this to be possible we need the precondition of importance -- someone who loves hunting partridges is not going to get the same enjoyment out of hunting magpies, because he's not going to be able to value magpies at the same level; the first are fit for the table (and note that by Hume's understanding of importance, this can be operative even if the hunter himself doesn't eat partridge), whereas magpies are largely useless for things like that.
Thus the object of curiosity, the prospect that really enlivens our interest and justifies mathematical endeavors, is, according to Hume: the discovery of possibly viable solutions to puzzles that are, from the perspective of the community, important, and that are, from the perspective of the individual mind, stimulating. To the extent that a field like mathematics provides this, Hume thinks, it justifies the pursuit of truth in that field. And, of course, as a matter of empirical fact we find that mathematics can provide it in spades.
Curiosity, then, is the governing motive of mathematics, the one that shapes it into a pursuit and a passion. It is not, of course, the only motive; nor is it in every particular case the strongest motive. There is, for instance, vanity, the desire to make a name for oneself. And we should not pretend that academics are above such sordid desires; anyone who has ever had dealings with academics knows that they are often almost obsessed with the possibility of being well respected, and that this motivation in at least many cases overtops even curiosity as a driving force in their work. Academia is filled to the brim with vanity; on a Humean view, this is one of the reasons it works in the first place. But vanity, unlike curiosity, doesn't shape the endeavor itself, considered as a community effort; the goal of the community of mathematicians is, at least in principle, determined by curiosity. What vanity adds to this is merely a powerful incentive for meeting the curiosity-proposed standards of that community; it cannot shape the community because it presupposes it. Curiosity, however, really does shape the community, especially when joined with sympathy.
So that, more or less, is Hume's account of mathematical practice. It's rather general, of course, since Hume was not a mathematician and does not seem to have had much notion of mathematics itself; it's really an account of intellectual inquiry in general, in which he continually appeals to mathematics as a paradigm example. But it's interesting in its own right, I think. I started thinking about this topic again on reading one of David Corfield's posts at "The n-Category Café"; some of what he says there is similar to what Hume is trying to get at, although at least part of what Hume is saying is shaped by his attempt to build an apraxia objection to certain forms of skepticism. One of the things Hume is missing that would greatly strengthen his account is the notion mentioned in that post of a 'mathematical story'; a problem with his analysis is that if it's taken as sufficient, we just get a string of interesting puzzles. But, of course, part of what really drives our curiosity in any field is the sense of taking part in what is (so to speak) an epic adventure of the mind. Even if the 'adventure' is only minor, it still needs a bit of sweep to it, a background against which the individual problems can be placed. Hume's sympathy account of intellectual importance is interesting and carries, I think, a serious grain of truth; but on its own it is clearly not adequate. Hume is right that importance is a major necessary condition for serious, sustained intellectual inquiry; he is right that sympathy plays a role; but an adequate account has to appeal to more than this. It needs a telos, a goal or end, and this telos needs to be that not merely of the individual problem but of the field as a whole. Corfield has argued (PDF) that this is a matter of tradition-constituted inquiry. Hume, of course, doesn't think in such terms. He goes far enough that he thinks in terms of community -- an immensely important achievement to which most people discussing mathematical, scientific, and philosophical practice don't attain -- but never develops a sense of the history or narrative of the community as a community that is (so to speak) united together in common cause, of the discipline not merely as a recreation but as an adventure of progress in a form of civilization. Something like that is needed to give an adequate account of any major field of intellectual inquiry.
Saturday, February 17, 2007
A Mixed Tape for My Readers
As quirky as you'd expect, given that it's from me to you.
Ben Folds Five, Philosophy
Alphaville, Forever Young
Sufjan Stevens, Chicago
Metallica, Nothing Else Matters
Capercaillie, Miracle of Being
Ellis Paul, God's Promise (by Woody Guthrie)
Duke Ellington and John Coltrane, In a Sentimental Mood
Raymond Levesque, Quand les hommes vivront d'amour
Freddie Mercury and Montserrat Caballé, Barcelona
Amy Grant, El Shaddai
Joe Strummer and the Mescaleros, Redemption Song (by Bob Marley)
Kansas, Dust in the Wind
Johnny Cash, God's Gonna Cut You Down
Leonard Cohen, First We Take Manhattan
Ben Folds Five, Philosophy
Alphaville, Forever Young
Sufjan Stevens, Chicago
Metallica, Nothing Else Matters
Capercaillie, Miracle of Being
Ellis Paul, God's Promise (by Woody Guthrie)
Duke Ellington and John Coltrane, In a Sentimental Mood
Raymond Levesque, Quand les hommes vivront d'amour
Freddie Mercury and Montserrat Caballé, Barcelona
Amy Grant, El Shaddai
Joe Strummer and the Mescaleros, Redemption Song (by Bob Marley)
Kansas, Dust in the Wind
Johnny Cash, God's Gonna Cut You Down
Leonard Cohen, First We Take Manhattan
Vincent of Lerins on Development of Doctrine
An extended passage, but it's worth quoting:
But some one will say, perhaps, Shall there, then, be no progress in Christ’s Church? Certainly; all possible progress. For what being is there, so envious of men, so full of hatred to God, who would seek to forbid it? Yet on condition that it be real progress, not alteration of the faith. For progress requires that the subject be enlarged n itself, alteration, that it be transformed into something else. The intelligence, then, the knowledge, the wisdom, as well of individuals as of all, as well of one man as of the whole Church, ought, in the course of ages and centuries, to increase and make much and vigorous progress; but yet only in its own kind; that is to say, in the same doctrine, in the same sense, and in the same meaning.
The growth of religion in the soul must be analogous to the growth of the body, which, though in process of years it is developed and attains its full size, yet remains still the same....This, then, is undoubtedly the true and legitimate rule of progress, this the established and most beautiful order of growth, that mature age ever develops in the man those parts and forms which the wisdom of the Creator had already framed beforehand in the infant. Whereas, if the human form were changed into some shape belonging to another kind, or at any rate, if the number of its limbs were increased or diminished, the result would be that the whole body would become either a wreck or a monster, or, at the least, would be impaired and enfeebled.
In like manner, it behoves Christian doctrine to follow the same laws of progress, so as to be consolidated by years, enlarged by time, refined by age, and yet, withal, to continue uncorrupt and unadulterate, complete and perfect in all the measurement of its parts, and, so to speak, in all its proper members and senses, admitting no change, no waste of its distinctive property, no variation in its limits....
Therefore, whatever has been sown by the fidelity of the Fathers in this husbandry of God’s Church, the same ought to be cultivated and taken care of by the industry of their children, the same ought to flourish and ripen, the same ought to advance and go forward to perfection. For it is right that those ancient doctrines of heavenly philosophy should, as time goes on, be cared for, smoothed, polished; but not that they should be changed, not that they should be maimed, not that they should be mutilated. They may receive proof, illustration, definiteness; but they must retain withal their completeness, their integrity, their characteristic properties.
Commonitorium Chapter XXIII. I will be discussing this at some point.
But some one will say, perhaps, Shall there, then, be no progress in Christ’s Church? Certainly; all possible progress. For what being is there, so envious of men, so full of hatred to God, who would seek to forbid it? Yet on condition that it be real progress, not alteration of the faith. For progress requires that the subject be enlarged n itself, alteration, that it be transformed into something else. The intelligence, then, the knowledge, the wisdom, as well of individuals as of all, as well of one man as of the whole Church, ought, in the course of ages and centuries, to increase and make much and vigorous progress; but yet only in its own kind; that is to say, in the same doctrine, in the same sense, and in the same meaning.
The growth of religion in the soul must be analogous to the growth of the body, which, though in process of years it is developed and attains its full size, yet remains still the same....This, then, is undoubtedly the true and legitimate rule of progress, this the established and most beautiful order of growth, that mature age ever develops in the man those parts and forms which the wisdom of the Creator had already framed beforehand in the infant. Whereas, if the human form were changed into some shape belonging to another kind, or at any rate, if the number of its limbs were increased or diminished, the result would be that the whole body would become either a wreck or a monster, or, at the least, would be impaired and enfeebled.
In like manner, it behoves Christian doctrine to follow the same laws of progress, so as to be consolidated by years, enlarged by time, refined by age, and yet, withal, to continue uncorrupt and unadulterate, complete and perfect in all the measurement of its parts, and, so to speak, in all its proper members and senses, admitting no change, no waste of its distinctive property, no variation in its limits....
Therefore, whatever has been sown by the fidelity of the Fathers in this husbandry of God’s Church, the same ought to be cultivated and taken care of by the industry of their children, the same ought to flourish and ripen, the same ought to advance and go forward to perfection. For it is right that those ancient doctrines of heavenly philosophy should, as time goes on, be cared for, smoothed, polished; but not that they should be changed, not that they should be maimed, not that they should be mutilated. They may receive proof, illustration, definiteness; but they must retain withal their completeness, their integrity, their characteristic properties.
Commonitorium Chapter XXIII. I will be discussing this at some point.
A Thought on the Filioque
It occurred to me recently that one complication in the dispute over the Filioque that is often overlooked is that the Latins think of the matter chiefly in terms of spiration. One might expound the view as follows. When you take the notion of spiration seriously, it becomes difficult to see how you can avoid saying that both the Father and the Son spirate, or that the Holy Spirit is spirated by both Father and Son alike. For we know that the Holy Spirit is not merely the Spirit of the Father, nor merely the Spirit of the Son; He is the Spirit of the Father and the Son both, and, moreover, He is the Spirit of the Son precisely because He is the Spirit of the Father. If we were to deny that the Holy Spirit is spirated by the Son, we would have effectively denied that He is really the Spirit of the Son; if we were to hold that He is spirated only by the Father, we would have effectively affirmed that He is really the Spirit only of the Father.
In this light we can make sense of virtually all Latin claims about the procession of the Spirit. First, that the Spirit proceeds from the Father and the Son: for He is spirated by Father and Son alike. Second, that the Spirit proceeds from the Father principally: for He is the Spirit of the Son because He is the Spirit of the Father, not vice versa. Third, that the Spirit proceeds from the Father and the Son as from one principle: for He is the Spirit of both wholly in virtue of the fact that He is breathed forth by the Father. Fourth, that the Spirit proceeds from the Father through the Son: for He is immediately the Spirit of the Father and also the Spirit of the Father by being the Spirit of the Son. Bonaventure, in fact, has lots of arguments very similar to these; and his sharpest criticism of the Greeks on this issue (to whom he generally tends to be sympathetic) is that they have an inadequate understanding of spiration.
So the Latin understanding of procession is dominated by this notion of spiration. And, indeed, the scholastic way of discussing the Filioque, although not common today, suggests this very strongly. For, if we might summarize it a little oversimply it is this: essentially, i.e., insofar as He subsists in the divine nature, He is God in His own right; personally, i.e., insofar as He receives the divine nature from the Father as Principle of the Godhead, He is from the Father alone; notionally, i.e., insofar as He is not the Son but the Spirit of both the Father and the Son, He is from the Father and the Son. The Father and the Son are one notional principle of the Spirit inasmuch as the Spirit must be marked by an idea that makes Him the Spirit of the Father and of the Son alike, and that not incidentally; thus He is spirated from both, but by a single spiration; which is why the Father and the Son are said to breath forth the Spirit inasmuch as they are the same God, for the Son has it from the Father that the Spirit is the Spirit of the Son.
This does not, I think, resolve the dispute; rather, it shows more clearly just how difficult the dispute is to pin down; thus, for instance, the argument never occurs in terms of spiration, although the Latin notion of spiration is clearly a significant reason why the Latins think the Filioque not only to be plausible but essential to the faith.
In this light we can make sense of virtually all Latin claims about the procession of the Spirit. First, that the Spirit proceeds from the Father and the Son: for He is spirated by Father and Son alike. Second, that the Spirit proceeds from the Father principally: for He is the Spirit of the Son because He is the Spirit of the Father, not vice versa. Third, that the Spirit proceeds from the Father and the Son as from one principle: for He is the Spirit of both wholly in virtue of the fact that He is breathed forth by the Father. Fourth, that the Spirit proceeds from the Father through the Son: for He is immediately the Spirit of the Father and also the Spirit of the Father by being the Spirit of the Son. Bonaventure, in fact, has lots of arguments very similar to these; and his sharpest criticism of the Greeks on this issue (to whom he generally tends to be sympathetic) is that they have an inadequate understanding of spiration.
So the Latin understanding of procession is dominated by this notion of spiration. And, indeed, the scholastic way of discussing the Filioque, although not common today, suggests this very strongly. For, if we might summarize it a little oversimply it is this: essentially, i.e., insofar as He subsists in the divine nature, He is God in His own right; personally, i.e., insofar as He receives the divine nature from the Father as Principle of the Godhead, He is from the Father alone; notionally, i.e., insofar as He is not the Son but the Spirit of both the Father and the Son, He is from the Father and the Son. The Father and the Son are one notional principle of the Spirit inasmuch as the Spirit must be marked by an idea that makes Him the Spirit of the Father and of the Son alike, and that not incidentally; thus He is spirated from both, but by a single spiration; which is why the Father and the Son are said to breath forth the Spirit inasmuch as they are the same God, for the Son has it from the Father that the Spirit is the Spirit of the Son.
This does not, I think, resolve the dispute; rather, it shows more clearly just how difficult the dispute is to pin down; thus, for instance, the argument never occurs in terms of spiration, although the Latin notion of spiration is clearly a significant reason why the Latins think the Filioque not only to be plausible but essential to the faith.
Friday, February 16, 2007
Three More Poem Drafts
Nightmare While Flying
All our city lights,
all our human might,
all our gardens, graces, greatness;
all our hair-thin roads,
all our troubles and our goads:
gold dust in the darkness.
All our hopes and deeds,
all our wants and needs,
all our worries, wonders, wars;
all the things we know,
blurred to a gold-green glow,
gold dust in the darkness.
All our palatial spaces,
all our care-worn faces,
all our crying, dying, rising;
all our engines and machines,
all our lanterns, wires, screens,
gold dust in the darkness.
All our goodness and our waste,
all our fashion and our taste,
all our vision, fission, fire,
our sinning hid by silence,
our safety and our violence,
gold dust in the darkness,
and despair:
all the progress of our nation
as the hope of desperation,
the collapsing of creation,
and a falling through the air.
What Great Poems Say
The sky is blue, the sun is bright,
the grass is green, the clouds are white,
the rose is red and touched with dew,
the sunrise starts the day anew,
in autumn splendor bright leaves fall,
death is sad and takes us all,
the love of friends is bright with glow,
great poems say what all hearts know.
Matutinal
In the silent distance I can hear
the tumult of the dogs a-glow
as they bound on clouds and bay;
a shaft shoots swiftly forth,
striking the fleeing beast.
It staggers, stumbles, falls.
The sun leaps up and in smooth stroke
slits the throat of darkness.
All our city lights,
all our human might,
all our gardens, graces, greatness;
all our hair-thin roads,
all our troubles and our goads:
gold dust in the darkness.
All our hopes and deeds,
all our wants and needs,
all our worries, wonders, wars;
all the things we know,
blurred to a gold-green glow,
gold dust in the darkness.
All our palatial spaces,
all our care-worn faces,
all our crying, dying, rising;
all our engines and machines,
all our lanterns, wires, screens,
gold dust in the darkness.
All our goodness and our waste,
all our fashion and our taste,
all our vision, fission, fire,
our sinning hid by silence,
our safety and our violence,
gold dust in the darkness,
and despair:
all the progress of our nation
as the hope of desperation,
the collapsing of creation,
and a falling through the air.
What Great Poems Say
The sky is blue, the sun is bright,
the grass is green, the clouds are white,
the rose is red and touched with dew,
the sunrise starts the day anew,
in autumn splendor bright leaves fall,
death is sad and takes us all,
the love of friends is bright with glow,
great poems say what all hearts know.
Matutinal
In the silent distance I can hear
the tumult of the dogs a-glow
as they bound on clouds and bay;
a shaft shoots swiftly forth,
striking the fleeing beast.
It staggers, stumbles, falls.
The sun leaps up and in smooth stroke
slits the throat of darkness.
Popularization
As I've pointed out before, one of the issues in philosophy of science that I think important that apparently no one else does is popularization as a form of general scientific pedagogy; and I've complained before that people seem to have a dangerously confused view of what popularization in general is and requires. H. Allen Orr, thankfully, gets it right (about a different sort of popularization):
This is exactly right. Good popularization requires more rigor and careful reasoning than writing for those in the know -- precisely because it is writing for those who aren't in the know. When you popularize you need to work even harder to get it right than when you are writing in more scholarly mode because (1) you have to convey the ideas to people who aren't used to them; (2) you have to avoid shortcuts (metaphors, analogies, etc.) that are useful for experts who can distinguish the relevant from the irrelevant, or else use them much more critically and carefully than the experts themselves do; (3) you have to make it easy for people to distinguish understanding the subject from understanding (say) the point of the subject; and many, many more. There are so many constraints to good popularization that it's inevitably going to be harder than scholarly writing, where you can trust that your already informed audience will be able to take away the point without becoming confused by incidentals. This is true for all forms of popularization in any subject. The worst forms of popularization are those that 'dumb down' or oversimplify or give themselves a free pass for bad reasoning and sloppy thinking because it's for the consumption of the masses. The ideal forms are those that revolutionize common sense by finding a way for ordinary people to see immediately the point, value, and content of an important discovery or theory. It's too much to expect that every (or perhaps any) popularization will succeed in the latter way; but as there is an entire spectrum between the two extremes, it's not too much to demand that they succeed better than popularizations in the former group.
Daniel Dennett's main complaint about my review is that I held Dawkins's book to too high a standard. The God Delusion was, he says, a popular work and, as such, one can't expect it to grapple seriously with religious thought. There are two things wrong with this objection. The first is that the mere fact that a book is intended for a broad audience doesn't mean its author can ignore the best thinking on a subject. Indeed it's precisely the task of the popularizer to take this best thinking and present it in a form that can be understood by intelligent laymen.
This is exactly right. Good popularization requires more rigor and careful reasoning than writing for those in the know -- precisely because it is writing for those who aren't in the know. When you popularize you need to work even harder to get it right than when you are writing in more scholarly mode because (1) you have to convey the ideas to people who aren't used to them; (2) you have to avoid shortcuts (metaphors, analogies, etc.) that are useful for experts who can distinguish the relevant from the irrelevant, or else use them much more critically and carefully than the experts themselves do; (3) you have to make it easy for people to distinguish understanding the subject from understanding (say) the point of the subject; and many, many more. There are so many constraints to good popularization that it's inevitably going to be harder than scholarly writing, where you can trust that your already informed audience will be able to take away the point without becoming confused by incidentals. This is true for all forms of popularization in any subject. The worst forms of popularization are those that 'dumb down' or oversimplify or give themselves a free pass for bad reasoning and sloppy thinking because it's for the consumption of the masses. The ideal forms are those that revolutionize common sense by finding a way for ordinary people to see immediately the point, value, and content of an important discovery or theory. It's too much to expect that every (or perhaps any) popularization will succeed in the latter way; but as there is an entire spectrum between the two extremes, it's not too much to demand that they succeed better than popularizations in the former group.
Vincentian Canon
Michael Liccione criticizes, rightly, a misuse of the Vincentian Canon. I left a comment, but as the topic fits very well with what I often talk about here (being a misinterpretation of an important theological text), I thought I'd also post it here:
What always strikes me about this sort of use of the VC is that St. Vincent didn't put it forward as a definition of the Church; he put it forward as a guideline for how we individuals can interpret Scripture in conformity with the Church -- namely, by taking into account the confession of the whole Church (everywhere), respecting the interpretations of our holy predecessors in the Church (always), and sticking as much as possible to those truths that have achieved a consensus among bishops and teachers of the Church (by all). So it's a very odd thing to use as an ecclesiological criterion a guideline for interpreting Scripture that already presupposes the Church as its reference point.
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