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Monday, July 25, 2011


Before continuing our story, I need to say a few things about the very interesting responses to yesterday's post, both in emails and as comments on the blog, concerning the logical status of Euclidean Geometry. This will be brief, because bigger things await us. I am afraid I did not make myself entirely clear, although I did try in a parenthetic aside. It is of course true that one can prove Euclid's theorems rigorously, using modern mathematical techniques, such as those suggested by Summortus [I love these web names!]. I mean, the theorems are true, after all. But the point is that they do not follow, by logic alone, from Euclid's definitions, axioms and postulates. The modern formalizations and axiomatizations of Geometry all involve adding some powerful additional algebraic or topological premises, as Marinus indicates. If one were to carry out such an axiomatization and, contrary to historical fact, present it to Kant, along with the possibility of alternative formal systems of Geometry, he would, I imagine, reply that although Geometry, thus reconceived, is analytic and hence logically rigorous, it remains the fact that we know with certainty that our space, that is the space in which material things appear to us, is Euclidean, and that proposition is both synthetic and known a priori.

Ok, enough about that. What is really important is the challenge presented to Kant by Hume's sceptical critique of the sorts of causal judgments that appear in Newtonian Physics. Hume's argument is quite simple -- deceptively so -- and easy to state. It can be summarized like this: The object or event we identify as a cause is distinct and distinguishable from the object or event we identify as its effect. Since the cause and the effect are thus distinguishable, it is possible to imagine one occurring without the other, our imagination having the power to separate distinguishable ideas from one another and call them to mind separately. But if we can imagine the one without the other, then we can have no ground for saying that one necessitates the other, which is what is meant by saying that one is the cause of the other. [By contrast, it is beyond the powers of our imagination, or of any imagination, to call to mind the idea of a bachelor who is married, or of a triangle with four interior angles.] Hence, causal judgments, involving as they do an assertion of necessity of connection between cause and effect, are never warranted by reason.

As Hume aficionados will recall, this argument appears in section iii of part three of the first book of the Treatise, "Why a cause is always necessary." Here, as they say in the blogging world, is the money quote:

"We can never demonstrate the necessity of a cause to every new existence, or new modification of existence, without shewing at the same time the impossibility there is, that any thing can ever begin to exist without some productive principle; and where the latter proposition cannot be prov'd, we must despair of ever being able to prove the former. Now that the latter proposition is utterly incapable of a demonstrative proof we may satisfy ourselves by considering, that as all distinct ideas are separable from each other, and as the ideas of cause and effect are evidently distinct, 'twill be easy for us to conceive any object to be non-existence this moment, and existent the next, without conjoining to it the distinct idea of a cause or productive principle." [page 79 in the Selby-Bigge edition of the Treatise.]

Was Kant aware of this argument? Yes. Beattie quotes the last part of this passage directly [beginning with "'twill be easy ..."] as well as several lines earlier on the same page. And those quotes were indeed included in the German translation of Beattie's work that Kant read. Thus my miniscule contribution to the ever-accumulating knowledge of the History of Ideas.

Now, Kant had forever given up hope of establishing a priori the truth of any of the familiar claims of rational metaphysics that had been the bread and butter of philosophy since Plato. He was prepared to throw Leibniz and the rest over the side, in part because he saw a way, by doing so, to carve out a space for his Ethical theory. Briefly -- we will have to return to this a good deal later on -- Kant was fully aware of the seemingly impossible conflict between the deterministic teachings of Newtonian science and the quite incompatible claims of Free Will on which moral responsibility rests. Having drawn a distinction between Appearance and Reality, between things as they are in themselves and things as they appear to us in space and time, he believed that he could successfully argue that Appearance is the realm of necessity, in which Newton's laws reign unchallenged, while Reality is the realm of freedom, in which the Moral Law rules supreme. In short, he thought he could resolve the age old conflict between Free Will and Determinism.

But if Hume was right -- and Kant, better than anyone else alive in the eighteenth century, could appreciate the full force of Hume's deceptively simply arguments -- than even when restricted to the realm of appearance, Newton's laws cannot be established with the requisite necessity and universality. This would, from Kant's point of view, be an utter disaster, leaving him with nothing but scepticism about the possibility of knowing anything other than mathematics a priori.

Kant postponed his plans for the immediate release of a Critique of Reason and launched into nine years of the most intense work. After his death in 1804, a hagiographic biography appeared in which the author, at one point, described Kant in his last years as distressed that he "could no longer bring to bear the full force of his intellectual powers" on his philosophical problems. When I read that line, I formed the image of Kant in that great nine year period, seated at his desk and bringing the full force of his intellectual powers to bear on his philosophical problems, sparks rising from his hair like a living Tesla Coil [think Gene Wilder in Young Frankenstein.]

It was in this period that he conceived the framework of the so-called Architectonic as a way of managing and keeping control over the many more or less independent lines of philosophical investigation that he was pursuing simultaneously. Before talking about that framework and the central ideas on which it was based, and also launching into a extended discussion of Kant's solution to the challenge posed by Hume's sceptical arguments, I need to step back for a bit and talk about a fundamental reorientation in Philosophy that had been under way for a century and a half, and which Kant brought to completion. This reorientation is sometimes referred to as The Epistemological Turn, and it is the most important philosophical development between the early seventeenth century and the late eighteenth century. For those of you who are professional philosophers [assuming there is such a thing], I will just add that it is this Turn that was eventually directly rejected by Saul Kripke and a number of other late twentieth century Anglo-American philosophers [wrongly, in my humble opinion, but that really is another matter entirely.]


Michael said...

Your response on Kant's part to the development of consistent non-Euclidean geometries is exactly the position Frege took on the matter. He knew all about non-Euclidean geometries (it was the topic of his doctoral dissertation), but he maintained that our actual experience of the world is Euclidean.

(He broke with Kant concerning arithmetic. In effect, Frege's entire life's work was to show that arithmetic is analytic.)

Chris said...

Another great update.

As usual I'm left with questions though ;)

1. Why do you call Hume's argument deceptive? It might be wrong - albeit I've never read a good refutation - but I can't envision Hume being a deceiver...
2. Will your ongoing discussion actually involve cracking up the critique and running through it section by section? Or is this a broader discussion? I ask because I have the Critique coming in the mail and I wonder if I should dive right in, or read it along with your updates.

Robert Paul Wolff said...

No no. I said his argument was deceptively simple -- i.e., it looks simpler than it is because he writes so simply and clearly. It was a compliment!

I won't go through the Critique section by section. I did that in my book, and it would be insane to try to reproduce that here. It is far to complex and demanding for that.

Chris said...

I quite miss authors like Hume. Between Descartes to Hume philosophy was so crisp and clear. Once Kant gets on the scene, followed by those German really wonders what the hell happened!