Archive for November, 2007

Academic genealogies

November 30, 2007

Yesterday I had an interesting discussion with a friend about his academic genealogy. In an academic family tree, one’s thesis advisor is one’s “parent”, and his advisor is one’s “grandparent”, and so on. I was inspired to look up my own academic genealogy, which I was able to do through the SPIRES database. The results were fascinating, and I thought I would share them. We’ll begin with my own humble self, and work backward:

• Craig Burrell (Toronto, 2004)
• Michael Luke (Harvard, 1991)
Howard Georgi (Yale, 1971)
\hspace{1cm}Dirac Medal 2000; Sakurai Prize 1995
• Charles M. Sommerfield (Harvard, 1957)
Julian Schwinger (Columbia, 1939)
\hspace{1cm} → Nobel Prize 1965
Isidor Isaac Rabi (Columbia, 1927)
\hspace{1cm} → Nobel Prize 1944
Albert Potter Wills (Clark, 1897)
Arthur Gordon Webster (Humboldt, 1890)
Hermann Ludwig Ferdinand von Helmholtz (Humboldt, 1842)
Johannes Peter Müller (Bonn, 1819-24)
Karl Asmund Rudolphi (Greifswald, 1795)
Christian Ehrenfried von Weigel (Göttingen, 1771)
Johann Christian Polycarp Erxleben (Göttingen, 1775)
Abraham Gotthelf Kästner (Leipzig, 1739)
Christian August Hausen (Wittenberg, 1712)
Johann Christoph Wichmannshausen (Leipzig, 1685)
Otto Mencke (Leipzig, 1666/8)

That’s sixteen generations stretching back over 330 years. I am agog.

A few comments:

  • My academic roots are clearly German, the transition to the New World having come in the late nineteenth century with Arthur Gordon Webster, who acquired his doctorate at Humboldt University in Berlin, but taught at Clark University in Worcester, MA (the second oldest graduate school in the United States, I note). His name suggests he was an American by birth, and must have made the journey to Germany to study under Helmholtz. He sounds like an interesting character.
  • Hold on. If Wikipedia is to be believed, there is more to Arthur Gordon Webster than meets the eye. He was the founder of the American Physical Society! His area of research was mechanics and acoustics, he worked on the gyroscope, and he had a talent for languages, being “fluent in Latin, Greek, German, French, and Swedish, with a good knowledge of Italian and Spanish and competency in Russian and modern Greek.” Sadly, he committed suicide in 1923.
  • Webster’s advisor was Hermann von Helmholtz, one of the great scientists of the nineteenth century. He is primarily remembered today through the things that bear his name: the Helmholtz equation and the Helmholtz coil in electromagnetics, and the Helmholtz theorem in vector calculus. He did important work on the conservation of energy, and in thermodynamics. Apparently he also worked extensively on the physiology and optics of the eye, and in acoustics, publishing a book on the physiological basis of the aesthetics of music. Among his students are many illustrious names: Hertz, Michelson (of Michelson-Morley fame), Wilhelm Wundt (the “father of experimental psychology”), and even William James.
  • Helmholtz is the first “physicist”, in the modern sense, in my genealogy. His advisor, Johannes Müller, was an anatomist and physiologist, as was Müller’s advisor Karl Rudolphi, who also did work in botany and zoology. Rudolphi is remembered (happily) for arguing that plants are constituted from cells, and (unhappily) for proposing that the various human races should properly be considered different species. The Rudolphi whale is named for him. He is the founder of helminthology, which sounds great until you know what it is.
  • Rudolphi studied under Christian von Weigel, a professor of chemistry, botany, pharmacy, and mineralogy. The genus Weigela is named for him.
  • Weigel studied with Johann Christian Polycarp Erxleben. My suspicion is that Erxleben was a Catholic, for Protestants just don’t name their children “Polycarp”. He was a professor of veterinary science, and founded the first German academic veterinary school. He authored a book called Systema regni animalis (1777), which might indicate that he took an interest in the work of his contemporary Carl Linnaeus.
  • Erxleben studied with Abraham Kästner, a mathematician. Kästner wrote voluminous surveys of mathematical topics, and books of original poetry. He directed the observatory at the university in Göttingen, and the Kästner lunar crater is named for him.
  • Next in line is Christian Hausen. I am unable to find much information about him, other than to say that he did early (very early) work on electricity and electrical generation. I note with interest, however, that he worked at the University of Leipzig at the same time that J.S. Bach was living and working in the city! Is it possible that Hausen saw the great man with his own eyes and heard him with his own ears? My friends, I think it is very possible. Marvelous!
  • Curiously, Hausen’s advisor, who bore the very impressive name of Johann Wichmannshausen, was a philologist and professor of Near Eastern languages. He wrote a book on the Templars (De extinctione ordinis Templariorum) and his thesis was on an important (and still relevant) point of moral philosophy (Disputationem Moralem De Divortiis Secundum Jus Naturae).
  • With Wichmannshausen’s advisor, Otto Mencke, the trail dries up. Mencke studied at Leipzig, but I am unable to discover who his advisor was, if indeed the advisor–student relationship existed at that time in the form we have come to expect. Mencke was a distinguished man, founding Germany’s first scientific journal, Acta Eruditorum, and being a correspondent of Isaac Newton. His thesis was entitled Ex Theologia naturali – De Absoluta Dei Simplicitate, Micropolitiam, id est Rempublicam In Microcosmo Conspicuam. If I were to hazard a translation, I would say “From Natural Theology – On the Absolute Simplicity of God, the Small State, that is, the Republic as a Miniature Cosmos”. I admit that this translation makes no sense. Anyone care to help?
  • It is nice to see those two Nobel prizes in my past. Julian Schwinger’s was for his work on quantum electrodynamics, of course (awarded also to Feynman and Tomonoga). Isidor Rabi’s prize was for work on magnetic resonance properties of nuclei. It was Rabi who famously greeted the news of the discovery of the muon by asking, “Who ordered that?” Personally, I’m rather fond of the muon, but then children, even academic great-great-great-grandchildren, often seem to their elders to have peculiar tastes.

I’m quite delighted by my genealogy. There are quite a number of distinguished men in that lineage, and I am proud to be a part of it, however inconsequential. I acknowledge, however — as I bring this post back to the conversation that spawned it — that it is not half so distinguished as my friend’s, whose family tree includes, if you can believe it, Schur, Frobenius, Weierstrass, Gauss, Hilbert, Klein, Dirichlet, Poisson, Fourier, Lagrange, Euler, and Bernoulli! Well done! (Incidentally, my lineage does intersect with his, and in the following way: Abraham Kästner was advisor not only to Johann Erxleben, but also to Johann Pfaff, who was in turn the advisor of Gauss.)

UPDATE: Here is a diagram showing the lineage discussed in this post.

Spe salvi

November 30, 2007

I hate to blog and bolt, but I haven’t much time this morning. I simply note that a new encyclical, Spe salvi, which looks to be something of a “sequel” to Deus Caritas Est, has been published today by Benedict XVI. Good Advent reading!

Transcendental blues II

November 29, 2007

Groundwork for the Metaphysics of Morals (1785)
Immanuel Kant (Bobbs-Merrill, 1959)
108 p. First reading.

History of Philosophy, Vol. VI, Part II: Kant
Frederick Copleston, SJ (Image Books, 1964)
277 p. First reading.

Kant: A Very Short Introduction
Roger Scruton (Oxford University Press, 2001)
141 p. First reading.

This is the second part of my account of my first encounter with the philosophy of Immanuel Kant. As I explained in the first part, I do not really grasp the essence of his system, but in these posts I am attempting to state those aspects that I do comprehend to some degree. They are unlikely to be of much use to anyone seeking clarification, but for certain minds, such as those attracted to car wrecks, they may have a certain allure.

The Groundwork for the Metaphysics of Morals is what it claims to be: an inquiry into the metaphysical foundations of moral reasoning. Kant intends to search for and establish the supreme principle of morality. The goal is to identify the a priori element of morals, that element which is universal and necessary, being independent of all empirical facts about the world or human nature. This foundational moral principle is to be discovered within reason itself. Note that Kant is not attempting to establish the fact of moral reasoning — he is not attempting to justify the validity of moral language and concepts to a skeptic — but rather he takes for granted that moral reasoning occurs and attempts to articulate its structure.

“Nothing in the world — indeed nothing even beyond the world — can possibly be conceived which could be called good without qualification except a good will.” With this famous opening flourish Kant launches his project. He makes the startling claim that a good will is good of itself, because of its willing, and not because of what it wills. This seems to me very counter-intuitive, for surely the will is called good or evil on condition whether it wills something good or evil? But Kant is determined to examine the aspects of morality that do not depend on circumstances, and so he cannot permit any contingent or empirical considerations to enter. That being so, it raises the question of the sense in which the will is being called good.

A good will, he says, is a will that acts from duty. “The first proposition of morality is that to have moral worth an action must be done from duty.” In consequence, actions that are performed exclusively out of duty are especially admirable, and it must be admitted that this does tap into a basic moral intuition, for we do recognize the merit of fulfilling one’s duty even when doing so is difficult or dangerous. But this also seems to imply that when actions proceed from other motives, such as inclination or love, they are less praise-worthy. “I can have no respect for any inclination whatsoever,” he says. This appears to be expressly at odds with the moral theory of, for instance, Thomas Aquinas, who argued that the truly good man is the one who does the good out of love. It seems an unhappy beginning, but I must reserve my judgment, for later he seems to moderate these claims somewhat.

He makes an important distinction between actions done in accordance with duty and actions done for the sake of duty. It is only the latter which are moral in the sense he requires. I may fulfill my duty accidentally, or for ulterior motives, but this cannot be called good in an unqualified way. This too is consistent with our moral intuitions.

But what does it mean to act from duty? Kant answers that to act from duty is to act from reverence for law. “The necessity of an action is executed from respect for law”. Thus moral good exists in the conception of law as such. Since law is intrinsically rational, it follows that moral good is founded in rationality. Law is also universal, says Kant, and from this he draws important conclusions. Consider: if reverence for law is the essential characteristic of duty, which in turn sets the standard for moral goodness, then we should strive to act in accordance with law. Therefore we should invest our moral maxims with the form of law, which is universality, for by doing so we make them moral as such. Thus there is an intrinsic affinity between morals and universality, and this affinity is the justification for Kant’s famous categorical imperative: “Act only according to that maxim by which you can at the same time will that it should be a universal law”. This, he argues, is the fundamental test of an act’s being moral.

We must be careful to interpret the categorical imperative rightly. Kant has insisted throughout that the ground of morality is rational, necessary, and free of everything empirical, such as consideration of consequences. What then can be meant by the word “can” in the categorical imperative? By what criteria shall we decide whether we “can” affirm a maxim to be a universal law? I don’t know the answer to this question, but I believe that Kant has in mind a logical test: can the maxim be affirmed without logical contradiction? For example, suppose I am wondering whether it is moral to make a promise to pay for something without any intention of honouring the promise. Is it possible for me to affirm that this promising-without-keeping should be a universal law? No, for consistent promise-breaking would devalue promises. Yet — and here is the contradiction — my plan assumes that promises have value. So the maxim which I am contemplating defeats itself, and for that reason cannot consistently be affirmed.

(This raises the odd possibility that Kant considers goodness as such to consist in logical consistency. Can it really be so?)

The categorical imperative is the objective principle of morality; it is the principle that secretly underlies all our moral reasoning, and it is issued by reason itself. It happens, however, that in the real world our subjective principles are often in conflict with this objective principle. We are subject to desires and self-love, and they tempt us to courses of action other than those approved by the categorical imperative. This, says Kant, is the origin of the sense of obligation, when we want to do one thing but know we should do another. We experience obligation to the extent that our will is opposed to the objective moral law. A perfectly good will, on the other hand, is subjectively in union with the objective law and so never experiences a conflict; it wills the good without being constrained to do so. In this sense, Kant moderates his earlier statements about inclination tarnishing the lustre of duty. A holy person does good naturally, because they do their duty naturally.

Kant expressly opposes his account of morality to the Aristotelian theory based on human nature and the search for happiness. All rational creatures, says Aristotle, desire happiness. Moral acts are those which tend to advance a person toward true happiness, and prudence is the virtue by which one discerns which acts are moral and which are not. Kant rejects this theory on the grounds that it is based on a hypothetical, rather than a categorical, imperative. A hypothetical imperative says that if you want to achieve happiness then you should do such-and-such. But no-one knows in what true happiness consists. Therefore prudence can never be better than empirical and suggestive, and it can never oblige or command. But this is at odds with moral experience and with the relevance of duty. Happiness, says Kant, is an ideal of the imagination, not of reason.

You might think that, having arrived at the objective principle of morality, Kant would set down his pen and rest on his laurels, but in fact he is just warming up, for though he has shown, to his own satisfaction, what the categorical imperative is, he has not shown that it actually exists, and that is the task of the next portion of the Groundwork. His first move is a perplexing one: the ground of the objective principle of morality (the categorical imperative) is, he says, that “rational nature exists as an end in itself”. How can this be so? Does he mean that the categorical imperative is a consequence of the end-in-itselfness of a rational being? I don’t see how that is so. Unless it is this: a rational being which is an end-in-itself also legislates for itself, without being subject to anything else; it promulgates the law which it itself obeys. And this is exactly what is meant by the categorical imperative. I do not know whether this is a sound understanding of what Kant means, nor, if it is, do I understand how it demonstrates that the categorical imperative actually exists, unless it is first taken for granted that rational beings are indeed ends-in-themselves.

If we accept the idea that rational beings are ends-in-themselves, then a few consequences follow. First, we must always treat rational beings as ends, never merely as means. Second, rational nature possesses an intrinsic dignity. In addition, when we consider rational nature under the aspect of its legislating for itself by expressing universality through its will, we arrive at the concept of the “autonomous will”, the will that issues laws for itself under no constraints other than those imposed by reason. It is the autonomous will that ultimately issues the universal laws that are the foundation of moral reasoning; the autonomy of the will is the supreme principle of morality.

This principle of the autonomy of the will is only possible, however, if it draws on the idea of freedom. The freedom of a rational being, for Kant, means its being the author of its own principles. Freedom — or, at least, the idea of freedom — is a practical necessity for all morality. Ultimately it is freedom — or, at least, the idea of freedom — that makes laws. This somewhat paradoxical notion is stated forthrightly by Kant: “a free will and a will under moral laws are identical”. Freedom, like morality, is implied by rationality as such. This insight is the pinnacle toward which Kant has been struggling, and its revelation brings the Groundwork to a close.

It is a basic moral insight that morality is intrinsically dependent upon freedom. Without freedom, the “ought” of moral language is meaningless. I am pleased, therefore, to see that Kant derives a deep connection between freedom and morality, but I am not pleased by the convoluted reasoning that leads from the one to the other. Freedom, autonomy of the will, end-in-itselfness, universal legislation, duty, and finally morality: it seems such a long journey, and some of the bridges appear to be pretty rickety.

This final sense of discouragement is heightened by the manner in which Kant equivocates at the very moment of triumph: at the same time that he uncovers freedom at the root of all morality, he allows that the “idea of freedom” will serve just as well. You see, Kant has a problem: he is committed to the metaphysical proposition that the physical world is entirely governed by causal necessity. But we are part of the physical world, and so are ourselves subject to causal necessity. But this seems to imply that freedom is impossible. Kant tries to salvage the situation by claiming that, from a practical point of view, to act under the idea of freedom is to be free. Freedom, indeed, is only an idea, and according to Kant’s epistemological theory developed in the Critique of Pure Reason, no possible experience can justify its objective reality. The best we can do, therefore, is point out that it stands as a necessary presupposition of moral reasoning, and leave it at that. What a let-down.

A great many questions crowd into my field of view as I consider the arguments Kant has developed. It is not entirely clear to me, for instance, why acting in accordance with duty should be considered especially worthy of praise. Isn’t duty what one is expected to do? We don’t reward someone for doing their duty. Perhaps that is exactly his point. But where, then, does Kant’s moral theory take account of actions which are not part of one’s duty, but which are nevertheless deserving of praise for their moral excellence? I also wonder about the categorical imperative itself, which seems strangely empty. Kant has given a few examples of how it sanctions some acts and forbids others, but is the principle really sufficient to completely delineate the moral sphere? Imagine I am considering whether to go for an evening walk. Kant instructs me to ask whether I could legislate that going for a walk should be a universal practice. I see no reason to object. Does it therefore follow that evening walks are a moral obligation? Something is wrong. It may be that the categorical imperative can forbid, but not recommend, just like Socrates’ daemon. But Kant himself uses an example of the categorical imperative commanding compassion toward others, so he must have some other relevant condition in mind to prevent the categorical imperative being used to convert benign activities into moral obligations. Furthermore, the connection between freedom, autonomy, and dignity on one hand, and duty, law, and the categorical imperative on the other is very obscure, and leaves me scratching my head.

On the other hand, there is much in Kant’s theory that is admirable. In his little book, Roger Scruton praises Kant’s moral philosophy on a number of grounds. It does succeed at explicating certain basic moral tenets: respect for oneself and for others, the unacceptability of exceptions in one’s favour, as well as the proscription of basic evils like murder, suicide, theft, fraud, and dishonesty. It is very much worth noting how it accounts for the force of morality, for the difference between desire and duty, and the manner in which moral principles are known and felt even when we defy them. It places emphasis on the intent of the will, rather than strictly on the consequences of action, which accords well with the common moral instinct to limit blame for unforeseen or unintended consequences. It makes room for the concept of a moral agent who acts not just from causes, but from reasons. Indeed, his whole system is praise-worthy for the way it grounds morality in reason, not in emotion or pleasure or calculation.

My concluding thoughts are somewhat muddled. I admire Kant’s intention in attempting to ground our moral judgment in reason, but I am less than convinced about certain aspects of his system, at least in part because I fail to understand them. This is one of the exasperating things about his theory: I have strained hard, but when I turn my eyes away for a moment it seems to evaporate. The long chain of reasoning is simply so tenuous, the impression so diffuse, that his general view of morality has not condensed into a coherent picture. I’m aware that this may well be my own fault.

Cheap geek: Security

November 27, 2007

This is the fourth installment in a series on free software. Today the theme is something that is actually important: security. If you have a computer connected to the internet (and, fair reader, my guess is you do) you need to take steps to secure your system against malicious activity. Many people take a relaxed attitude toward computer security: why would anyone want to pick on little old me? The truth is that online crime is a booming business, and many attackers strike at random. They can break your system, steal information, or even take over your system and use it for their purposes without your noticing. I once left my computer insecure for a few weeks and later found that someone was using it to store their music files. I was lucky it wasn’t used for something worse.

One might argue that if security is really important, it would be more prudent to buy security software than to rely on free software. It’s not a terrible argument, but neither is it as strong as you might suppose. I purchased the security suite from McAfee, one of the leading security companies, but after a while it crapped out, I couldn’t repair it, Dell customer service was even more incompetent than me, and eventually I uninstalled it in favour of free applications. I’ve been quite happy since (except when I remember that I’m still paying for the McAfee license).

I’ll discuss a few different topics: anti-malware applications, firewalls, software updaters, and secure web browsing.


A minimum requirement is to have both anti-virus and anti-spyware protection. For an anti-virus application, I recommend the much-praised AVG Anti-Virus Free. It has a well-maintained set of virus signatures, downloads automatic updates, and can be configured to scan your computer on a regular schedule. The only significant downside is that it uses a fair amount of memory — but then so do the commercial anti-virus scanners.

AVG also produces a well-regarded anti-spyware application called, reasonably enough, AVG Anti-Spyware Free. I have tried it, but I had some problems with the auto-update feature, so I removed it from my system. Instead, I use two other applications. Spybot Search & Destroy is a good tool that performs fairly well in industry tests. It scours your system looking for tracking cookies that are used to trace your internet activity. The current version also includes a module (‘Tea-Timer’) that will raise an alert whenever changes are made to the Windows registry. Spybot’s functionality is somewhat limited – no scheduled scans or automatic updates, for instance – but I don’t consider those serious limitations. The second application I use is PC Tools Spyware Doctor, which comes bundled in the Google Pack. It offers, in addition to full system scans, a degree of real-time protection to nip problems in the bud. Regular scans can be scheduled to run in the background, and updates are automatic.


A firewall is a network traffic filter. It monitors your network connection – both ingoing and outgoing – and blocks or permits traffic in compliance with a customized set of rules. This is a tough category for anyone committed to using free software only, for while there are a number of options, I have yet to find one that is really satisfactory. Some crashed, others made previously installed software stop working. For a long while I used Jetico Personal Firewall, and if it were just a firewall I would recommend it heartily. But it also monitors your system’s processes in real time, and this component is very chatty: windows were always popping up asking whether I wanted to permit this or that. In time I grew weary of these interruptions and uninstalled it. I’m back to relying on the firewall that comes bundled with Windows XP. Since it is included in every Windows installation you could think of it as free, but only if you squint a little.

Software Updaters

Every piece of software has some bugs, and these can sometimes affect the security of your system. Certain types of software defects can be used by malicious parties to take control of the application, or even of the computer on which it is running. Software developers are constantly discovering these problems in their code, and issuing new, repaired versions of the software. For this reason, it is important to regularly update your software. I will recommend three tools that help with this task:

  • If you are running Windows, it is imperative that you regularly install the patches issued by Microsoft. On the second Tuesday of every month (‘Patch Tuesday’) they release a set of updates for Windows and other Microsoft software. Windows has an auto-update feature that will download and install these patches without your intervention; use it!
  • Secunia Personal Inspector is an application that runs in the background and monitors the software you have installed. When a new security-related bug is discovered and reported to the major agencies that track such information, the program will inform you that you are running insecure software. If a fix is available, it will help you to apply it. At the present time it monitors the security status of more than 4000 different programs. Try it out; I was very surprised to find how many insecure programs I was running.
  • The FileHippo update client doesn’t track as many programs as Secunia (indeed, it only tracks the ones that can be downloaded from the FileHippo site), but it did find several out-of-date applications on my system that Secunia missed. It doesn’t tell you why your program has been updated – was there a security problem or just a functionality change? – but even so I think it is quite useful. I run it on my system once every few weeks and update if anything new is available.

Secure web browsing

Web browsing is actually one of the more hazardous things you can do online. Your browser encounters code on web sites and executes it locally on your system. Most of the time this is benign, but it can be used for nefarious purposes. There are a few simple things you can do to protect yourself.

First, install the McAfee Site Advisor into your browser. This very helpful utility adds extra information to your Google search results, indicating whether the link you are about to click is friendly or not. If the site you are going to is known to send spam, or has malicious code embedded in it, or would otherwise be inhospitable to visitors, McAfee Site Advisor puts a big red X next to the link. If that doesn’t help, you have noone to blame but yourself.

Second, Firefox users should install the NoScript extension. NoScript prevents JavaScript and Java code from being executed by your browser, unless you grant permission. It will break the functionality of some sites – indeed, this is the whole point – but if you trust the site the functionality can be restored. It will protect you from a variety of attacks, including the increasingly common and consistently horrible (especially to those who have tried to understand them) cross-site scripting attacks.

Finally, you can try Sandboxie, an amazing tool that isolates your browser from the rest of your computer, thus preventing any nastiness you may encounter online from getting access to your files. I haven’t used this very much myself, but I sure like the idea.


That’s it for this installment. I’d be very pleased to hear if you have any recommendations or comments.

Sunday night fugue

November 25, 2007

What better way to start the new week than with one of Bach’s fugues? Here is the Emerson String Quartet playing Contrapunctus 9 from Die Kunst der Fuge (Duration: about 2 minutes).

Transcendental blues I

November 23, 2007

Prolegomena to any Future Metaphysics (1783)
Immanuel Kant (Modern Library, 1949)
76 p. First reading.

History of Philosophy, Vol. VI, Part II: Kant
Frederick Copleston, SJ (Image Books, 1964)
277 p. First reading.

Kant: A Very Short Introduction
Roger Scruton (Oxford University Press, 2001)
141 p. First reading.

Kant is difficult. Coming in, I knew that his fame rested on a two-fold reputation: his being a challenging and important figure in the history of philosophy, and his having conveyed his ideas in prose of deep and abiding opacity. I’m not sure I grasp the reasons for the former, but I can damn well vouch for the latter. For the past four months I have been slowly chiseling my way through two short, but reputedly significant, works — the Prolegomena to any Future Metaphysics and the Groundwork for the Metaphysics of Morals — supplementing them with a few haphazardly chosen secondary sources. In this post I deal with the Prolegomena, and reserve the Groundwork for a subsequent post.

In truth, my diligence has been intermittent, owing partly to discouragement and partly to the jostle of affairs, which faltering partly explains why my understanding has not come into focus. In fact, I’m sure that I don’t really understand what Kant is saying. What I propose to do here is something quite modest: to try to articulate the issues and problems that motivated his philosophical effort (insofar as they pertain to these works), and to make some gestures in the direction of the kind of solutions he proposed. This will fall far short of what he deserves, but it will be a start, and it is the best I can muster under the circumstances.

The Prolegomena was published a few years after Critique of Pure Reason, and its purpose was to serve as a precis and a pointer to the larger work. Apparently Kant’s contemporaries failed to truly grasp the significance of his great work (surprise!), and so he penned the shorter work to clarify the main points and lure his readers to their deaths — or, I should say, to the Critique itself. In that sense, it has been written for beginners. Kant takes some time to sport with those readers who find even this entry-level version of his thought too difficult, kindly reminding them to “bear in mind that it is not necessary for everyone to study metaphysics”. I didn’t permit such asides to deter me.

The subject of discussion in the Prolegomena is metaphysics, and more specifically the epistemology of metaphysics: how is metaphysical knowledge possible, if it is possible? Roger Scruton’s instructive little volume reminds us that the essential background for understanding Kant is found in Leibniz and Hume. Leibniz’s Monadology had defended the position that the mind knows certain principles (such as the Principle of Sufficient Reason and the Principle of Non-contradiction) innately, and that these principles are intuitively known to be true. They form the indispensable foundation for all knowledge of contingent and particular things. Attempting to rely only on those innately-known principles, he articulated a complex metaphysical theory of substances, causes, perception, and so forth. He considered the content of his system to be objectively true because demonstrable on the basis of principles whose truth is intuitively perceived by everyone. He had a high view of the capacity of human beings to know truths about the world.

David Hume, on the other hand, articulated a skeptical view of human knowing. He argued that there are no innate ideas. Everything in our minds was first in our senses, and we have no source for knowledge apart from sensory experience. Leibniz’s innate principles are not principles at all, says Hume, but simply inductive generalizations on the basis of experience: we assert that every effect must have a sufficient cause only because we have so frequently perceived one phenomena (the effect) conjoined to another (the cause), but in fact not only can we not assert that effects must be conjoined to causes, we cannot even assert that effects are conjoined to causes. We can say only that there are phenomena, and we impose order on the play of phenomena not because the order is objectively present, but because that is how our minds attempt to deal with the flood of sensation. It is a position that takes a dim view of the capacity of human beings to know truths about the world.

It was into this stand-off between the “rationalist” side and the “empiricist” side that Kant ventured and set up his little writing desk. But before proceeding further a third historical influence deserves mention: the scientific revolution. Kant was deeply impressed — maybe too impressed — by the success of the sciences. The agreement and cumulative progress of the sciences was in sharp contrast to the disagreement and disarray of philosophy. The careful conceptual articulation, restrained epistemological claims, and systematic method of the sciences appealed to Kant, as they did to so many of his contemporaries, as holding forth a model for the secure founding and elaboration of knowledge. As he says in the Prolegomena, the sorry state of metaphysics in comparison to the sciences convinced him that metaphysics up to his time had been founded on false principles and trafficed in invalid concepts. (He illustrated this state of affairs with his famous antinomies, apparently valid arguments that lead to the conclusions that, inter alia, a necessary being exists, a necessary being does not exist, the universe is infinite in space and time, the universe is finite in space and time, every existing thing is simple or composed of simple parts, no simple things exist, there is freedom, there is not freedom. In other words, the existing methods and concepts of metaphysics lead to contradictions and cannot be a source of truth.) The overarching motive for his own philosophical project in the Critique was to secure a sure foundation for metaphysics by examining the operation of human reason (or is it of reason pure and simple?) and delineating its limits (with, I’m convinced, emphasis on specifically human limits). This philosophy, his so-called critical philosophy, was to be to previous philosophical systems what chemistry was to alchemy and astronomy to astrology: a source of true, if circumscribed, knowledge.

If I understand the matter rightly, then, Kant stakes out a position between Leibniz and Hume. On the one hand, he argues that our capacity to know the world is limited, and many historic metaphysical claims — about our knowledge of the world, or the soul, or God — are unsound. On the other hand, he opposes the thorough skepticism of Hume, articulating by close analysis of the inner structure of reason, reason’s capacity for true knowledge. At least, I think so.

With that context in place, we can start to explore the positive content of his system. In this, we will he helped by some definitions, for Kant makes a number of distinctions at the outset intended to clarify his questions. The first distinction is between analytic and synthetic propositions. An analytic proposition is one which is known to be true simply on the basis of the meaning of the words it contains. For example, “The whole is greater than a part” or “All bachelors are unmarried”. The predicate is already implicitly contained in the subject. In synthetic propositions, on the other hand, the predicate is not contained in the concept of the subject. For example, “Canada is north of the United States” or “All bachelors are unhappy”. The truth of these statements, if they are true, cannot be determined on the basis of the propositions themselves; independent evidence must be examined. The second major distinction Kant makes is between a priori and a posteriori propositions. The a priori propositions are necessarily true; they are true independently of experience. The gold standard of such propositions is the mathematical theorem. Propositions which might or might not be true, on the other hand, and which are known only through experience, are a posteriori. For example, “Frenchmen speak exclusively while holding marbles in their mouths”. Some philosophers, such as Hume, had identified analytic propositions and a priori propositions with one another, and likewise with synthetic and a posteriori propositions. They argued that a priori propositions, which are necessarily true, must be analytic, and by the same token the contingency of a posteriori propositions meant that they must be synthetic, known only through experience.

Kant, on the other hand, insisted that these two distinctions were distinct from one another. He agreed with Hume that all analytic propositions are a priori, but he argued, and by doing so opened up the passageway by which he would proceed, that some synthetic propositions are a priori as well. Such propositions are necessarily true, and their truth, including their necessity, is known on the basis of experience. Metaphysical propositions fall into this class, so Kant’s question “How is metaphysical knowledge possible?” can be rephrased as “How is synthetic a priori knowledge possible?” This question, note, must be answered before any metaphysical conclusions can be drawn. It is interesting — and apparently controversial — that Kant claimed that certain laws of nature are synthetic and a priori:

“…among the principles of this universal physics are to be found some that really possess the universality we require, such as the proposition: substance continues and is permanent, and that, according to fixed laws: all which happens is at all times previously determined by a cause. These are really universal natural laws, existing completely a priori.” (section 15)

It is at this point, with the challenge of defending the existence of synthetic a priori truths, that Kant’s real project begins, and it is at this same point that my understanding begins to falter. I will try: in order to explain how synthetic truths can ever be a priori (and therefore known to be always and necessarily valid), he launches into an examination of how we know. How is knowledge possible at all? What is understanding, and how does it function? What are the conditions for experience of the world? This exploration is quite difficult to follow in detail, but he leavens the dough with humorous comments now and then: “Since I had found the origin of the categories in the four logical functions of all judgments of the intellect, it was only natural to seek the origin of the ideas in the three functions of the syllogisms of reason” (Section 43). But of course!

What emerges from this discussion is a general picture of human knowing. It looks something like this: experience is a combination of raw sensation and the faculties of reason. All knowledge is situated and subjective (in the sense of belonging to a particular mind) and the sphere of possible experience is determined (in part?) by the qualities of that mind. We can know things only insofar as our senses and intellect permit us to experience them. We can never know anything outside of our experience, and so we can never know things-in-themselves; we can only know things under the aspects in which they appear to us when filtered through our sensory and intellectual apparatus.

The role of the faculties of reason in this picture is crucial. The very structure of reason, says Kant, affects our knowing. Before they can cohere into experience, all perceptions must be subsumed under certain concepts. These concepts he called “categories”, and he identified them (if anyone is still reading, they are: unity, plurality, totality, reality, negation, limitation, substance, cause, reciprocity, possibility, existence, and necessity). These are “pure concepts of the understanding”. They are the concepts by which we organize our experience, and without which experience is not possible. “They are not derived from experience, but. . .experience is derived from them” (Section 30). They condition or frame our experience, revealing such aspects of the world as we are able to perceive.

At this point, it might not be clear how this theory of knowledge bears on the original motivating question: how is synthetic a priori knowledge possible? If our knowledge really is totally derived from experience, how can we ever establish an a priori truth, which is always and necessarily true? The answer lies precisely in his account of the structure of intellect, and in giving it he strikes a blow at a certain understanding of objective knowledge. Take as an example the synthetic a priori proposition Kant proposed earlier: “all which happens is at all times previously determined by a cause”. We know this to be always and necessarily true not because we have discovered that nature is governed by laws of causality, but because experience itself presupposes such laws. This general line of reasoning holds true for all synthetic a priori propositions; they are a priori not because we somehow have objective knowledge that transcends our own limited experience, but rather the opposite: our very experience of the world presupposes that such propositions are true. The truths are not, then, truths “out there”, at least not as far as we can know; they are truths “in here”, as a consequence of the way we know. Kant puts the point very directly: “The intellect does not derive its laws (a priori) from nature but prescribes them to nature.” (Section 36) This centralizing of our cognitive capacities, his making them the measure of the world as we know it, is what Kant called his “Copernican Revolution” in philosophy.

Kant’s theory secures, therefore, a certain kind of objectivity: he can claim that certain truths can be demonstrated to any rational creature. But it is at the price of locating those truths in rationality itself, rather than out in the world. At least, this is how I understand him. In so doing he cuts us off from the world in a very real sense. Late in the Prolegomena, in a section entitled “Bounds of Pure Reason”, he agrees with this conclusion: we cannot, he says, know things-in-themselves, for they are not objects of possible experience for us. This does not mean that they do not exist, or that some other kind of intellect may not know them, or know them under different aspects, but it does mean that we may not know them in themselves. There is no pre-established harmony between our minds and the world as it is in itself. The things-in-themselves he called noumena, and our experience of them he called phenomena. This is an important distinction that I believe will come up again in the discussion of his moral philosophy, but for now I will not pursue it.

Perhaps at that I will draw my discussion of the Prolegomena to an end. There is much that I have left unsaid, and that because I couldn’t piece together anything coherent. I have not mentioned at all his “transcendental idealism”, nor his “transcendental psychology”, nor his “transcendetal method”. I simply don’t know what is meant by “transcendental” in this context. Perhaps I have discussed the concepts to which these terms refer, but I don’t know it. This is a matter to be resolved some other time.

I have many remaining questions. Foremost among them is whether Kant’s analysis of reason is intended to be an analysis of specifically human reason, or of reason in general. Certainly the kind of sensation which we can experience is tied to our specifically human nature — we see the visible spectrum, for instance, and not the radio spectrum — and so our sensory faculties affect the kind of knowledge of the world we can have. But this is different from Kant’s claim, which is that our reason, or reason in general, also affects in turn the kind of knowledge we can have. I am also unclear as to what aspects of metaphysics Kant believed his ideas left standing, and which parts he believed they demolished. The troubles in which metaphysics finds itself are due to our taking concepts derived from experience and extending them, invalidly, to realms beyond experience, and he certainly thought that large swaths of metaphysical argumentation consisted of this irresponsible and ultimately nonsensical extrapolation of ideas into realms where they have no validity. I believe that he argued that proofs of the existence of God were impossible, but I am unsure whether he may have moderated that conclusion somewhat (he was himself a theist, if I’m not mistaken). I also wonder whether there might be a self-contradiction lurking somewhere in his system. I don’t say that I see one, but in my experience attempts to make knowledge subjective or to situate and relativize knowledge are usually making surreptitious exemptions in their own favour.

And then there is the most important question of all: is it true? It is ironic that while Kant founded his system to drag philosophy out of the mire of clashing claims and establish it on secure, publicly accessible methods, the mire just won’t give up; it absorbs even him. There is no doubt that Kant is important, and that his ideas merit serious consideration, and I have seen philosophical histories that divide the whole history of philosophy into pre-critical and post-critical, making Kant’s thought the watershed. But it is not true that he has succeeded in his sociological goal: that of bringing unanimity and cumulative progress to philosophy. Whether this is because his system is ultimately flawed, or whether the explanation rests in other, less conclusive reasons (such as people’s inability to understand him), I don’t know. For my own part, I certainly don’t understand him. To some extent I understand what he claims, but I don’t understand the underlying reasons why he claims what he does. I am not attracted by his conclusions; I would want to defend a more robust and intuitive concept of objective knowledge, and I would want to defend the legitimacy of metaphysical inquiry. That desire doesn’t untie the tangled mess of arguments that constitutes metaphysical history, of course, but I would rather focus on making sound arguments than forsake the project altogether. Even if I did accept Kant’s general picture of knowledge being a combination of “the world” and our sensory apparatus and our intellectual faculties, it is not evident to me that this implies we do not know things-in-themselves. May not the world and our sensory apparatus and intellectual faculties be such as to function in harmony? Kant may have assumed that they did not, but I wonder if he offered any arguments to that effect.

Since this discussion is getting over-long, I will conclude here and take up Kant’s moral philosophy in another Book Note. If you read this far, you have my sincere regard and admiration.

[Rousing polemic]
Many a naturalist of pure reason (by which I mean the man who believes he can decide in matters of metaphysics without any science) may pretend, that long ago by the prophetic spirit of his sound sense, he not only suspected, but knew and comprehended, what is here propounded with so much ado, or, if he likes, with prolix and pedantic pomp: “that with all our reason we can never reach beyond the field of experience.” But when he is questioned about his rational principles individually, he must grant, that there are many of them which be has not taken from experience, and which are therefore independent of it and valid a priori. How then and on what grounds will he restrain both himself and the dogmatist, who makes use of these concepts and principles beyond all possible experience, because they are recognized to be independent of it? And even he, this adept in sound sense, in spite of all his assumed and cheaply acquired wisdom, is not exempt from wandering inadvertently beyond objects of experience into the field of chimeras. He is often deeply enough involved in them, though in announcing everything as mere probability, rational conjecture, or analogy, he gives by his popular language a color to his groundless pretensions. (Section 31)

Feast of St. Cecilia

November 22, 2007

The name Cecilia may come from coeli lilia, lily of heaven, or from caecitate carens, lacking blindness, or from caecis via, road for the blind, or from coelum and lya, a woman who works for heaven. Or the name may be derived from coelum and laos, people. For Saint Cecilia was a heavenly lily by the modesty of her virginity. She is called a lily because of her shining cleanness, her clear conscience, and the aroma of her good renown. She was a road for the blind by giving good example, a heaven through her continual contemplation, and a worker for heaven by her application to good works. Or she is called heaven because, as Isidore says, the philosophers have said that heaven is revolving, round, and fiery, and Cecilia was revolving in a constant circle of good works, round in her perseverance, and fiery with the warmth of her charity. She was free of blindness through the splendor of her wisdom. She was a heaven of the people because in her, as in a spiritual heaven — the sun, the moon, the stars — people saw how to imitate heaven, namely, by the perspicacity of her wisdom, the magnanimity of her faith, and the variety of her virtues.

– Jacobus de Voragine, Legenda Aurea
(trans. William Granger Ryan)

The talk around town

November 21, 2007

Today a quick round-up of interesting things I’ve seen or heard online in the past few weeks:

  • In the Times Literary Supplement, John Polkinghorne favourably reviews a book-length rejoinder to Richard Dawkins written by, of all people, John Cornwell.
  • Anthony Esolen continues his series of meditations on the decline of education while paging through an old collection, The Young Folks’ Shelf of Books.
  • The Hebdomadarian (ahem!) finds a very strange talking portrait.
  • A brief but incisive discussion of the meaning of “the separation of church and state” is offered by Richard John Neuhaus.
  • Dr. Jack Hyles discourses on the divine nature of short hair. (Hat-tip: Korrektiv)
  • Reports have appeared of a breakthrough in stem cell research that could produce embryonic stem-cell equivalents (that is, pluripotent cells) without destroying embryos. Some caution is in order — science journalism is generally poor — but if true it will provide yet another good reason to put the utilitarian embryo-farmers out of business. And that would be a very good thing. Joseph Bottum reflects on political angles.
  • Andy Whitman reviews Bruce Springsteen’s latest record. I don’t think the album is as strong as Andy does, but he makes a persuasive case.
  • At An Examined Life, Scott Carson defends scientific anti-realism.
  • The Telegraph reviews the Top 10 Stupidest Laws on the books, both at home and abroad.
  • Chaucer taketh a breke fro his labour as clerk of the kinges werkes to offere thoghtes on the reforme of televisioun.
  • Clear Creek Monastery in Oklahoma has produced a good video about the monastic way of life. Meanwhile, Steven Greydanus writes a very perceptive review of Into Great Silence, the recent film about life inside the Carthusian monastery at Grand Chartreuse.
  • At SecurityFocus, Mark Rasch sees dark clouds on the e-mail privacy horizon.
  • The New Criterion is marking the twentieth anniversary of Allan Bloom’s The Closing of the American Mind, and Mark Steyn contributes an excellent essay on culture and pop music.
  • Margaret Somerville breaks the cloak of silence.
  • Finally, I’ve been dipping into the archives at The Charlie Rose Show, and I highly recommend two conversations with Monsignor Lorenzo Albacete, the first (from 2000) about John Paul II’s visit to Israel, and the second (from 2005) about the election of Benedict XVI. Both are superb.

That’s rather a lot of things. Perhaps I should do this more frequently.

Pleasures of enjambment

November 20, 2007

The Storm-Wind

When the swift-rolling brook, swollen deep,
Rushes on by the alders, full speed,
And the wild-blowing winds lowly sweep
O’er the quivering leaf and the weed,
And the willow tree writhes in each limb
Over sedge-beds that reel by the brim —

The man that is staggering by
Holds his hat to his head by the brim;
And the girl as her hair-locks outfly,
Puts a foot out, to keep herself trim,
And the quivering wavelings o’erspread
The small pool where the bird dips his head.

But out at my house, in the lee
Of the nook, where the winds die away,
The light swimming airs, round the tree
And the low-swinging ivy stem, play
So soft that a mother that’s nigh
Her still cradle, may hear her babe sigh.

— William Barnes (1801-1886)

Barcelona brief

November 18, 2007

Earlier this week I returned from my trip to Barcelona. I had a wonderful time, and thought I would post a few photographs.

It was rather difficult to take photographs inside the medieval churches in the city’s core owing to the low light levels, but here is an (highly artistic) photo of a chandelier in Santa Maria del Mar:


In the cloister of the city’s cathedral I found a fountain topped by this delightful statue of St. George:


We visited Antoni Gaudi’s monumental church La Sagrada Familia, still under construction 125 years after the foundation was laid. It’s an astonishing building: rather eccentric in many ways, but fundamentally faithful to traditions of church architecture:


There is a long history of embellishing capitals with leaves and vines, so why not have them branch into trees or burst into fruit?



The north facade is enlivened by a pair of trumpeting angels:


The highlight of the trip was a journey up into the mountains to see the Monastery of Montserrat, an abbey founded in the 9th century. It is home to both the Black Virgin of Montserrat and a famous medieval musical manuscript called Llibre Vermell de Montserrat, the latter of which has inspired me to track down some recordings. They have a spectacular location high on a mountain-side, surrounded by peaks. Here is the abbey church at dusk:


When not exploring churches, we took some time to frolic in the Mediterranean Sea:


And at the end of the day, when we were hungry, there were plenty of tasty morsels to be had at the city’s market: