28 Aug 2013: Home of the Whopper

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On p 613 of the Guyer/Moore translation (the Cambridge University Press paperback), there’s a sentence of about 180 words in the English translation and about 150 words in the original German tucked away in an obscure section (the Critique of All Speculative Theology) which I had to diagram to understand as above. I call it The Whopper:

“The absolute totality of the series of these conditions in the derivations of their members is an idea which of course can never come about fully in the empirical use of reason, but nevertheless serves as a rule for the way in which we ought to proceed in regard to them: namely that in the explanation of given appearances (in a regress or ascent) we ought to proceed as if the series were in itself infinite, i.e., proceed in indefinitum, but where reason itself is considered as the determining cause (in the case of freedom), hence in the case of practical principles, we should proceed as if we did not have before us an object of sense but one of pure understanding, where the conditions can no longer be posited in the series of appearances, but are posited outside it, and the series of states can be regarded as if it began absolutely (through an intelligible cause); all this proves that the cosmological ideas are nothing but regulative principles, and are far from positing, as it were constitutively, an actual totality in such series.”

The Whopper is only slightly shorter in German:

Die absolute Totalität der Reihen dieser Bedingungen, in der Ableitung ihrer Glieder, ist eine Idee, die zwar im empirischen Gebrauche der Vernunft niemals völlig zustande kommen kann, aber doch zur Regel dient, wie wir in Ansehung derselben verfahren sollen, nämlich in der Erklärung gegebener Erscheinungen (im Zurückgehen oder Aufsteigen) so, als ob die Reihe an sich unendlich wäre, d.i. in indefinitum, aber wo die Vernunft selbst als bestimmende Ursache betrachtet wird (in der Freiheit), also bei praktischen Prinzipien, als ob wir nicht ein Objekt der Sinne, sondern des reinen Verstandes vor uns hätten, wo die Bedingungen nicht mehr in der Reihe der Erscheinungen, sondern außer derselben gesetzt werden können, und die Reihe der Zustände angesehen werden kann, als ob sie schlechthin (durch eine intelligible Ursache) angefangen würde; welches alles beweist, daß die kosmologischen Ideen nichts als regulative Prinzipien, und weit davon entfernt sind, gleichsam konstitutiv, eine wirkliche Totalität solcher Reihen zu setzen.

In the Whopper, Kant in an almost anguished way, reminiscent of his near-contemporary Beethoven’s late quartets with their middle movements that oscillate between themes, tries to show the distinction between what Stephan Körner (The Philosophy of Mathematics) calls “Platonism” (logicism) and intuitionism as applied to the contemplation or construction of infinity.

Intuitionism was developed by Brouwer, Heyting et al. based on Kant so the tragedy of Kant is that he lacked a language for expressing what he knew but provided the preconditions for the development of that language! Kant is trying to tell us, like a returning spaceman who’s seen what the astronaut of 2001 sees at the end, that while we cannot contemplate a finished infinity, we can “contemplate” the recursive or otherwise rule that generates the infinity.

We cannot contemplate the last number (or the smallest real number s such that 0<s<p where p is as small as you like) or the existence of a finished infinity as opposed to a construction rule. The Intuitionists' (continental European) education stressed Kant and they constructed Intuitionist mathematical philosophy on a groundwork painfully laid by a philosopher who lacked the logic and language they, primarily Brouwer and Heyting, developed!

With what I consider to be a tragic grandeur (see the sentence diagram of The Whopper above) Kant gave Kantians their language without himself knowing that language. Like Moses, or Simon Bolivar, Kant never made it to the promised land.

One Response to “28 Aug 2013: Home of the Whopper”

  1. […] German word sentence on p 712 of the 1787 Critique and p 613 of the Guyer/Moore translation that I have covered in this blog) I realized that here was mathematical intuitionism and its distinction, between constructive and […]

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