David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Mind 97 (387):501-s-501 (1988)
The wrong version of my article ‘Aspects of the Infinite in Kant’ was printed in the last issue of Mind (pp. 205–23). I should like to correct an error that thereby appeared on page 207. In A430–2/B458–60 of the Critique of Pure Reason Kant does not deny that what is (mathematically) infinite should be what I called an actual measurable totality—if, by its measure, we mean ‘the multiplicity of given units which it contains’. His point is simply that what makes it infinite cannot be the fact that its measure is the greatest possible; for there is no such thing. What he has in mind here can be illustrated as follows. Take the infinite multiplicity of hours that have elapsed up to a given moment; then the multiplicity of minutes that have elapsed, and indeed the multiplicity of hours that will have elapsed an hour later, are both greater. No multiplicity is so great that it cannot be increased in this way. (Of course, standard contemporary formal work on the infinite has superseded Kant here. A modern mathematician would want either to quarrel with this or at least to refine it.) He also refuses to allow that an infinite multiplicity is a number (cf. BIII and A526–7/B554–5). In the end, he thinks, there is no saying what it is for something to be (mathematically) infinite without falling back on ‘the true transcendental concept of infinitude,’ namely ‘that the successive synthesis of units required for the enumeration of a quantum can never be completed’
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