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34 For example, the concept of the number 5 is instantiated in an image of 5 dots. Moreover, Kant says, when we think of a number (be it small or large) we are not so much thinking of such an image, as of a rule for producing images Mathematical certainty is also called evidence, as intuitive knowledge is clearer than discursive knowledge. e. evidence, however much the judgement may otherwise be apodictically certain. i. ’) [A734/B762] But it is not a term that Kant actually uses often. 32 ‘Einige wenige Grundsätze, welche die Geometer voraussetzen, sind zwar wirklich analytisch und beruhen auf del Satze des Widerspruchs; .

That general qualification is absent from his later work; in the light of the considerations in the present paper, that seems, conceptually if not historically as well, to be no coincidence. 24 That Brouwer here describes a sequence of nested intervals, and not of rationals, is not essential to the question at hand. 18 8 M. van Atten We call such an indefinitely proceedable sequence of nested . . intervals a point P or a real number P . We must stress that for us the sequence . . itself is the point P .

Hrsg. von der Königlich-Preussischen Akademie der Wissenschaften zu Berlin, 1902–. Kritik de reinen Vernunft. Second edition. Hartknoch, Riga, 1787. Edition used: W. ), Suhrkamp, Frankfurt, 1974. English translations of AA are my own; those of A and B are taken from N. Kemp Smith’s translation Immanuel Kant’s Critique of Pure Reason, St. Martin’s Press, New York, 1965. van Atten, M. 2007. Brouwer meets Husserl. On the phenomenology of choice sequences. Dordrecht: Springer. Beiser, F. 2008.