¹ Cf. Bxvi and Bxviii. Following A73/B98, the hypothesis may be formulated as follows: ‘if objects as appearances conform to human cognition or what is known about objects as appearances is only what is put into them by the knower, then synthetic a priori cognition is possible.’

The frst main part of the Critique, namely the Transcendental Doctrine of Elements, contains two parts: the Transcendental Aesthetic and the Transcendental Logic. The Transcendental Logic contains the Transcendental Analytic and the Transcendental Dialectic. The second main part of the Critique, namely the Transcendental Doctrine of Elements, contains four chapters, each with its own subdivisions: The Discipline of Pure Reason; The Canon of Pure Reason; The Architectonic of Pure Reason; The History of Pure Reason. References to Kant's works other than the frst Critique are given by volume and page number to the Akademie edition (Berlin: Walter de Gruyter 1902–).

² I am especially grateful to Michael Davis, Christopher DiTeresi, Warren Schmaus, John Snapper and the anonymous reviewer for helpful comments on this section.

³ If this is the correct interpretation of Kant's distinction, then it is possible that an hypothesis, formulated as a judgement, is true, although such can never be proved, let alone apodictically. It is also possible that the same hypothesis may serve as an explanation of something in general. As Kant insists, the latter may be proved apodictically.

Although he is not explicit on this point, Kant seems to allow that a judgement may serve as an hypothesis in either natural science, as an explanation of something given in nature or appearance, or metaphysics, as an explanation of something given in reason. Moreover, it seems to be Kant's position that the use of an hypothesis in either metaphysics or natural science is for the more general purpose of making progress. In this he follows Christian Wolff's Commentary on the Institution of the Rules for the Study of Mathematics – cf. Hofmannus, J. E., ed., Gesammelte Werke, vol. 33 (Hildesheim: Georg Olms Verlagsbuchhandlung, 1971), 165–526Google Scholar. Kant would have been familiar with this work, as it is appended to Wolff's Elements of Mechanics, the textbook used for at least one of the two courses on mechanics that Kant taught. Cf. Adickes, Erich, Kant als Naturforscher, vol. 1 (Berlin: W. De Gruyter, 1942), p. 11Google Scholar.

Wolff discusses hypotheses as an important means to progress in science in §309, noting the contribution of Copernicus' hypothesis in the progress of science beyond Ptolemy and through Johannes Kepler, who discovered the three fundamental laws of planetary motion that bear his name, to Newton, who in 1687 described universal gravitation and the three fundamental laws of motion that bear his name. Kant's Preface to the second edition of the Critique is similar, noting explicitly Copernicus' use of an hypothesis to make progress in the science of astronomy (cf. Bxvi and Bxxii); it is therefore plausible that Kant had Wolff's discussion in mind when he penned the new Preface in which he announces his imitation of Copernicus in order to make progress in the science of metaphysics. The same thrust is also evident in Kant's discussion of the legitimate use of hypotheses in natural science in the Critique (cf. A769/B797–A782/B810). A good discussion of the latter is found in Buchdahl, Gerd, Metaphysics and the Philosophy of Science (Cambridge: MIT Press, 1969), esp. pp. 510–16Google Scholar. See also Butts, Robert, ‘Hypothesis and explanation in Kant's philosophy of science’, Archiv für Geschichte der Philosophie 43: 153–170 (1961)Google Scholar, which is, however, fawed in the way indicated below. For a more general discussion of Kant's philosophy of science, see Friedman, Michael, Kant and the Exact Sciences (Cambridge, MA: Harvard University Press, 1992)Google Scholar; for what is in effect a redaction of much of the latter see Friedman, Michael, ‘Philosophy of natural science,’ in The Cambridge Companion to Kant and Modern Philosophy, ed. Guyer, P. (Cambridge: Cambridge University Press, 2006), pp. 303–41Google Scholar.

⁴ The original punctuation has been preserved.

⁵ In these pages, Kant also identifes a polemical use of an hypothesis as a ‘weapon of war, not for grounding a right but only for defending it’ (A777/B805).

⁶ Butts, Robert E., ‘Kant on hypotheses in the “Doctrine of Method’ and the Logik’, Archiv für Geschichte der Philosophie, 44 (1962), p. 189CrossRefGoogle Scholar. See also Butts, ‘Hypothesis and explanation’, pp. 164–8.

⁷ Butts, ‘Kant on hypotheses’, p. 189.

⁸ Demonstration that the consequence is actual does not make up part of the apodictic proof in the Critique because such has been already proved in the Prolegomena, and so would be redundant (cf. 4: 267–73). In the Introduction to the Critique Kant adapts this discussion from the Prolegomena, proving ‘synthetic a priori judgments are contained as principles in all theoretical sciences of reason,’ including mathematics and natural science (B14; cf. B15–B24).

⁹ Even in outline, this account of the apodictic proof of Kant's hypothesis seems to undermine Hahn's, Robert account of the same in Kant's Newtonian Revolution in Philosophy (Carbondale: Southern Illinois University Press, 1988)Google Scholar, esp. chapter 9. On his view, the apodictic proof of Kant's revolutionary hypothesis, which he identifes as ‘the fundamental judgments to which any meaningful claim to knowledge must refer are synthetic a priori’, that occurs in the Metaphysical Deduction and the Transcendental Deduction of the Transcendental Analytic (op. cit., p. 101) is an adaptation of the so-called hypothetico-deductive method that Sir Isaac Newton describes and employs in Opticks: Or a Treatise of the Refections, Refractions, Infections & Colours of Light, 2nd Ediction (London: W. and J. Inny's, 1718), cf. pp. 350–82).

Granted ex hypothesi that he correctly identifes Kant's revolutionary hypothesis, Hahn's account is nevertheless fawed in at least one important respect. Hahn incorrectly locates the apodictic proof of Kant's hypothesis in the Critique. Kant clearly indicates in his new Preface that the proof occurs not only in the Transcendental Analytic, but also in the Transcendental Aesthetic. Hahn gives no consideration whatsoever to the role of the Transcendental Aesthetic in the apodictic proof of Kant's hypothesis. For this reason, Hahn's account cannot possibly be correct. Although the account of the roles of both the Transcendental Aesthetic and the Transcendental Analytic in the apodictic proof of Kant's hypothesis offered herein may require further development, it is at least preferable to Hahn's account inasmuch it is sensitive to this interpretative requirement.

¹⁰ In this place Kant notes: ‘Diese dem Naturforscher nachgeahmte Methode besteht also darin: die Elemente der reinen Vernunft in dem zu suchen, was sich durch ein Experiment bestätigen oder widerlegen läβt. Nun läβt sich zur Prüfung der Sätze der reinen Vernunft, vornehmlich wenn sie über alle Grenze möglicher Erfahrung hinaus gewagt werden, kein Experiment mit ihren Objekten machen (wie in der Naturwissenschaft): also wird es nur mit Begriffen und Grundsätzen, die wir a priori annehmen, tunlich sein, indem man sie nämlich so einrichtet, daβ dieselben Gegenstände einerseits als Gegenstände der Sinne und des Verstandes für die Erfahrung, andererseits aber doch als Gegenstände, die man bloss denkt, allenfalls für die isolierte und über Erfahrungsgrenze hinausstrebende Vernunft, mithin von zwei verschiedenen Seiten betrachtet werden können. Findet es sich nun, daβ, wenn man die Dinge aus jenem doppelten Gesichtspunkte betrachtet, Einstimmung mit dem Prinzip der reinen Vernunft stattfnde, bei einerlei Gesichtspunkte aber ein unvermeidlicher Widerstreit der Vernunft mit sich selbst entspringe, so entscheidet das Experiment für die Richtigkeit jener Unterscheidung.’

¹¹ On this, I disagree with Hans Seigfried, according to whom the dependent clause of the second sentence identifes the touchstone on which the experiment of pure reason is conducted. It is the following ‘proposition of pure reason’: ‘we must “contrive” the concepts and principles which we adopt a priori such that “they be used for viewing objects from two different points of view”, namely, as objects of experience and “as objects which are thought merely,” as appearances and as things in themselves [B XVIIIf.]’ – Hans Seigfried, ‘Transcendental experiments’, in Funke, G. and Seebohm, T. M., eds, Proceedings of the Sixth International Kant Congress (Washington, DC: University Press of America, 1989), pp. 342–3Google Scholar. On this view, then, Kant's claim in the footnote is that in order to validate this proposition an experiment of pure reason is conducted ‘to fnd out what happens if we try to conceive the possibility of the experience of objects either with it or without it’ (op. cit., p. 344).

¹² Cf. Smith, Norman Kemp, Commentary to Kant's ‘Critique of Pure Reason’ (Atlantic Highlands, NJ: Humanity Books, 1999), p. 450Google Scholar.

¹³ Tonelli, Giorgio, Kant's ‘Critique of Pure Reason’ within the Tradition of Modern Logic (Hildesheim: Georg Olms Verlag, 1994)Google Scholar, esp. Part Two, chapter III, which situates the classifcation of the sciences in the Critique within the evolution of Kant's plan for a system of philosophy from 1769.

¹⁴ Rational physiology consists of rational physics, whose object is corporeal nature, and rational psychology, whose object is thinking nature.

¹⁵ Cf. Tonelli, Modern Logic, pp. 337–8 (Table XIII).

¹⁶ In his Preface to the second edition of the Critique, Kant identifes the location of the experiment of pure reason as the Transcendental Dialectic. According to the discussion at Bxx, the experiment of pure reason demonstrates that the unconditioned, understood as the completion of the series of conditioned things, can be thought without contradiction only on the assumption that ‘our representation of things as they are given to us does not conform to these things as they are in themselves but rather that these objects as appearances conform to our way of representing’ (Bxx). The unconditioned is the object of inquiry only of the Transcendental Dialectic of the Critique (cf. A321/B377–A332/B390).

Moreover, a series of manuscripts Kant began six years after the publication of the second edition of the Critique identifes the location of the experiment of pure reason more specifcally within the Transcendental Dialectic. These manuscripts were composed by Kant in answer to the question of the prize essay competition sponsored by the Académie Royal des Sciences et des Belles-Lettres in Berlin: What real progress has metaphysics made in Germany since the time of Leibniz and Wolff? Friedrich Theodor Rink eventually published this series of manuscripts in 1804 and after Kant's death.

The manuscript consists, in part, of a discussion of what Kant identifes as the second stage of metaphysics. This stage of metaphysics is the result of the transition from ‘the conditioned in the objects of possible experience to the unconditioned, and of extending its knowledge to the completion of this series [of conditions] by means of reason’ (20: 287). Distinct from the frst stage of metaphysics, namely ontology, the second stage of metaphysics is transcendental cosmology.

It is in this context that Kant summarizes the main parts of the Critique. In particular, he notes, ‘the Antinomy of Pure Reason leads inevitably back to that limiting of our knowledge, and what was previously proved in the Analytic, in dogmatic a priori fashion, is here likewise incontestably verifed [bestätigt] in the Dialectic, by an experiment of reason [Experiment der Vernunft], which [reason] performs on its own powers’ (20: 291). This passage explicitly establishes that the experiment of pure reason occurs only in the Antinomy of Pure Reason of the Transcendental Dialectic.

¹⁷ According to Kemp Smith, ‘the ‘two’ parts of metaphysics’ are ‘immanent metaphysics’ and transcendent metaphysics (Kemp Smith, Commentary, p. 22; see also pp. liv, 33, 56 and 66). Kemp Smith is clearly incorrect in this, as ‘immanent metaphysics’ is no part of metaphysics at all. Nor is ‘transcendent metaphysics’ a kind of metaphysics, as he eventually recognizes: ‘it is never possible’ (op. cit., p. 33).