Hostname: page-component-848d4c4894-hfldf Total loading time: 0 Render date: 2024-05-28T22:20:59.869Z Has data issue: false hasContentIssue false
  • English
  • Français

Kant on the Conceptual Possibility of Actually Infinite Tota Synthetica

Published online by Cambridge University Press:  19 April 2024

Rosalind Chaplin
Rosalind Chaplin*
Affiliation:
University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
*
Email: rchaplin@unc.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Most interpreters hold that Kant rejects actually infinite tota synthetica as conceptually impossible. This view is attributed to Kant to relieve him of the charge that the first antinomy’s thesis argument presupposes transcendental idealism. I argue that important textual evidence speaks against this view, and Kant in fact affirms the conceptual possibility of actually infinite tota synthetica. While this means the first antinomy may not be decisive as an indirect argument for idealism, it gives us a better account of how our ideas of the unconditioned generate the antinomies, and it allows us to see important and often overlooked elements in Kant’s account of the infinite.

Keywords

infinityactual infinitytotalityworld-conceptsunconditionedconceptual possibilityantinomy
Type
Article
Information
Kantian Review , First View , pp. 1 - 20
Check for updates
Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Kantian Review

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Al-Azm, Sadik (1972) The Origins of Kant’s Arguments in the Antinomies. Oxford: Oxford University Press.Google Scholar
Allison, Henry (1983) Kant’s Transcendental Idealism: An Interpretation and Defense. New Haven: Yale University Press.Google Scholar
Anderson, Lanier (2015) The Poverty of Conceptual Truth: Kant’s Analytic/Synthetic Distinction and the Limits of Metaphysics. Oxford: Oxford University Press.CrossRefGoogle Scholar
Bennett, Jonathan (2016) Kant’s Dialectic. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Boehm, Omri (2011) ‘The First Antinomy and Spinoza’. British Journal for the History of Philosophy, 19(4), 683–710.CrossRefGoogle Scholar
Chaplin, Rosalind (n.d.) ‘Compositional indeterminacy and potential infinity: Kant’s solution to the Second Antinomy’.Google Scholar
Chignell, Andrew (2012) ‘Kant, real possibility, and the threat of Spinoza’. Mind, 121(483), 635–75.CrossRefGoogle Scholar
Friedman, Michael (2015) ‘Kant on geometry and experience’. In De Risi, Vincenzo (ed.), Mathematizing Space: The Objects of Geometry from Antiquity to the Early Modern Age (Basel: Birkhäuser), 275–309.CrossRefGoogle Scholar
Grier, Michelle (2004) Kant’s Doctrine of Transcendental Illusion. Cambridge: Cambridge University Press.Google Scholar
Guyer, Paul (1987) Kant and the Claims of Knowledge. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Guyer, Paul (2018) ‘The infinite given magnitude and other myths about space and time’. In Nachtomy, Ohad and Winegar, Reed (eds), Infinity in Early Modern Philosophy (New York: Springer International Publishing Group), 181–204.CrossRefGoogle Scholar
Holden, Thomas (2004) The Architecture of Matter: Galileo to Kant. New York: Oxford University Press.CrossRefGoogle Scholar
Kant, Immanuel (1900-) Gesammelte Schriften. Ed. Preussische Akademie der Wissenschaften (volumes 1–22), Deutsche Akademie der Wissenschaften zu Berlin (vol. 23), subsequently Akademie der Wissenschaften zu Göttingen. Berlin: Walter de Gruyter and Predecessors.Google Scholar
Kant, Immanuel (1997) Lectures on Metaphysics. Trans. and ed. Ameriks, Karl and Naragon, Steven. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Kant, Immanuel (1998 [1781/1787]) The Critique of Pure Reason. Trans. and ed. Guyer, Paul and Wood, Allen. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Kant, Immanuel (2001 [1790]) Critique of the Power of Judgment. Trans. and ed. Guyer, Paul and Matthews, Eric. Cambridge: Cambridge University Press.Google Scholar
Kant, Immanuel (2002 [1770]) ‘On the form and principles of the sensible and intelligible world [Inaugural Dissertation]’. In Walford, David and Meerbote, Ralf (trans. and eds), Theoretical Philosophy 1755-1770 (Cambridge: Cambridge University Press), 373–416.Google Scholar
Kant, Immanuel (2004 [1786]) Metaphysical Foundations of Natural Science. Trans. and ed. Friedman, Michael. Cambridge: Cambridge University Press.Google Scholar
Kant, Immanuel (2005) Notes and Fragments. Ed. Paul Guyer, trans. Curtis Bowman, Paul Guyer, and Frederick Rauscher. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Kant, Immanuel (2014 [1790]) ‘On Kästner’s treatises’. In Kantian Review, 19(2), 305–13. Trans. Christian Onof and Dennis Schulting.CrossRefGoogle Scholar
Kemp Smith, Norman (1918) A Commentary to Kant’s ‘Critique of Pure Reason. London: Palgrave-Macmillan.Google Scholar
Leech, Jessica (2017) ‘Kant’s material condition of real possibility’. In Sinclair, Mark (ed.), The Actual and the Possible: Modality and Metaphysics in Modern Philosophy (Oxford: Oxford University Press), 94–116.Google Scholar
Leibniz, Gottfried Wilhelm (2000) The Labyrinth of the Continuum: Writings on the Continuum Problem, 1672-1686. Trans. Richard T. W. Arthur. New Haven: Yale University Press.Google Scholar
Leibniz, Gottfried Wilhelm (2003 [1672-1676]) Sämtliche Schriften und Briefe. Siebente Reihe: Mathematische Schriften, vol III, Berlin: Akademie Verlag. https://doi.org/10.26015/adwdocs-151 CrossRefGoogle Scholar
Melamedoff-Vosters, Damian (2023) ‘Representation and reality in Kant’s Antinomy of Pure Reason’. Kantian Review, 28(4), 615–34.CrossRefGoogle Scholar
Proops, Ian (2021) The Fiery Test of Critique: A Reading of Kant’s Dialectic. Oxford: Oxford University Press.CrossRefGoogle Scholar
Rosefeldt, Tobias (2022) ‘Kant on decomposing synthesis and the intuition of infinite space’. Philosophers’ Imprint, 22(1), 1–23.Google Scholar
Smyth, Daniel (2023) ‘Kant’s mereological account of greater and lesser actual infinities’. Archiv für Geschichte der Philosophie, 105(2), 315–48.Google Scholar
Stang, Nicholas (2016) Kant’s Modal Metaphysics. Oxford: Oxford University Press.CrossRefGoogle Scholar
Strawson, Peter F. (1966) The Bounds of Sense: An Essay on Kant’s Critique of Pure Reason. London: Routledge.Google Scholar
Sutherland, Daniel (2021) Kant’s Mathematical World: Mathematics, Cognition, and Experience. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Tolley, Clinton (2016) ‘The difference between original, metaphysical, and geometrical representations of space’. In Schulting, Dennis (ed.), Kantian Nonconceptualism (London: Palgrave-Macmillan), 257–85.CrossRefGoogle Scholar
Winegar, Reed (2016) ‘To suspend finitude itself: Hegel’s reaction to Kant’s First Antinomy’. Hegel Bulletin, 37(1), 81–103.Google Scholar
Winegar, Reed (2022) ‘Kant’s three conceptions of infinite space’. Journal of the History of Philosophy, 60(4), 635–59.Google Scholar