On the Formal Validity of Proof by Contradiction in Kant’s Logic
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Abstract
The paper provides a reconstruction of proof by contradiction in Kant’s pure general logic. A seemingly less-explored point of view on this topic is how apagogical proof can account for the formal truth of a judgement. Integrating the argument held by Kjosavik (2019), I intend to highlight how one can use proof by contradiction, conceived as a modus tollens, to establish the logical actuality (logical or formal truth) of a cognition. Although one might agree on the capacity of the proof to prove formal falsity, the logical actuality of a judgement is assessable based on a logically grounded judgement and, as for transcendental logic, this cognitive operation has to presuppose the real possibility of an object.
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Kant, I. Gesammelte Schriften. Abteilung III: Handschriftlicher Nachlass. Band XVI: Logik. Adickes, E. & Königlich Preußische Akademie der Wissenschaften (eds.). 1924 (2nd ed.). Berlin – Leipzig: De Gruyter. (= Refl.)
-
Kant, I. Gesammelte Schriften. Abteilung IV: Vorlesungen. Band XVIII: Metaphysik. Adickes, E. & Königlich Preußische Akademie der Wissenschaften (eds.). 1924 (2nd ed.). Berlin – Leipzig: De Gruyter. (= AA: 28)
-
Kant, I. Gesammelte Schriften. Abteilung IV: Vorlesungen. Band XXIX: Kleinere Vorlesungen (Enziklopädie, Mathematik und Physik) und Ergänzungen. Adickes, E. & Königlich Preußische Akademie der Wissenschaften (eds.). 1924 (2nd ed.). Berlin – Leipzig: De Gruyter. (= AA: 29)
-
Kant, I. Logic. Hartman, R.S. & Schwarz, W. (trs., intr.). 1974. New York: Dover Publications. (= JL)
-
Kant, I. Lectures on Logic. Young, J. M. (tr., ed.), 1992. Cambridge: Cambridge University Press.
-
Kant, I. (1997). Lectures on Metaphysics. K. Ameriks and S. Naragon. (trs., ed.), 1997. Cambridge and New York: Cambridge University Press.
-
Kant, I. Critique of Pure Reason. Guyer, P. & Wood, A. W. (trs., eds.), 1998. New York / Cambridge: Cambridge University Press. (= KrV)
-
Achourioti, T. & Van Lambalgen, M. 2011. A Formalization of Kant’s Transcendental Logic. Review of Symbolic Logic 4(2), 254–289.
-
Achourioti, T. & Van Lambalgen, M. 2017. Kant’s Logic Revisited. The IfCoLog Journal of Logics and their Applications 4, 845–865.
-
Bader, R. (manuscript). Kant’s Theory of Modality.
-
Capozzi, M. 1980. Osservazioni sulla riduzione delle figure sillogistiche in Kant. Annali della Facoltà di Lettere e Filosofia dell’Università di Siena 1, 79–98.
-
Chignell, A. 2007. Kant’s Concepts of Justification. Nôus, 41(1), 33–63.
-
Dutilh-Novaes, C. 2016. Reductio ad absurdum from a Dialogical Perspective. Philosophical Studies 173, 2605–2628.
-
Heis, J. 2014. Kant (vs. Leibniz, Wolff and Lambert) on Real Definitions in Geometry. Canadian Journal of Philosophy 44, 605–630.
-
Hintikka, J. 1974. Kant on Mathematical Method. The Monist 51, 352–375.
-
Kannisto, T. 2018. Transcendental Paralogisms as Formal Fallacies – Kant’s Refutation of Pure Rational Psychology. Kant Studien 109(2), 195–227.
-
Kjosavik, F. 2019. Kant on the Possibilities of the Mathematics and the Scope and the Limits of Logic. Inquiry. DOI: 10.1080/0020174X.2019.1651087.
-
Kovac, S. 2008. In what Sense Is Kantian Principle of Non-Contradiction Non-Classical? Logic and Logical Philosophy 17(3), 251–274.
-
Kovac, S. 2020. Logical Foundations and Kant’s Principles of Formal Logic. History and Philosophy of Logic 41(1), 48–70.
-
Lanier Anderson, R. 2015. The Poverty of Conceptual Truth. Oxford: Oxford University Press.
-
Leech, J. 2012. Kant’s Modalities of Judgement. European Journal of Philosophy 20(2), 260–284.
-
Lu-Adler, H. 2013. The Objects and Formal Truth of Kantian Analytic Judgements. History of Philosophy Quarterly 30(2), 177–193.
-
MacFarlane, J. 2002. Kant, Frege and the Logic in Logicism. Philosophical Review 111(1), 25–65.
-
Oberst, M. Analyticity, Logical Entailment, and the Structure of Concepts in Kant a Reply to Lanier Anderson. URL: <https://www.academia.edu/32367166/Analyticity_Logical_Entailment_and_the_Structure_of_Concepts_in_Kant_a_Reply_to_Lanier_Anderson>.
-
Pasternack, L. (2014). Kant on Opinion: Assent, Hypothesis, and the Norms of General Applied Logic. Kant-Studien 105(1), 41–82.
-
Shamoon, A. 1979. Kant’s Logic. Diss. Columbia University.
-
Stang N. 2019. A Guide to Ground in Kant’s Lectures on Metaphysics. In: Fugate, C. (ed.), Kant’s Lectures on Metaphysics. A Critical Guide. Cambridge: Cambridge University Press, 74–101.
-
Thompson, M. 1972. Singular Terms and Intuitions in Kant’s Epistemology. The Review of Metaphysics 26(2), 314–343.
-
Tolley, C. 2007. Kant’s Conception of Logic. Diss. University of Chicago.
-
Vanzo, A. 2014. Kant e la formazione dei concetti. Trento: Verifiche.
-
Watkins, E. & Willaschek, M. 2020. Kant on Cognition and Knowledge. Synthese 197, 3195–3213.
-
Wilson, K.D. 1972. Kant‘s Logical Grammar of the Twelve Forms of Judgement. Diss. University of Massachusetts Amherst.
| All Time | Past Year | Past 30 Days | |
|---|---|---|---|
| Abstract Views | 255 | 128 | 22 |
| Full Text Views | 11 | 5 | 1 |
| PDF Views & Downloads | 32 | 11 | 0 |
On the Formal Validity of Proof by Contradiction in Kant’s Logic
In: History of Philosophy & Logical AnalysisSearch for other papers by Davide Dalla Rosa in
Current site
Google Scholar
PubMed
Abstract
The paper provides a reconstruction of proof by contradiction in Kant’s pure general logic. A seemingly less-explored point of view on this topic is how apagogical proof can account for the formal truth of a judgement. Integrating the argument held by Kjosavik (2019), I intend to highlight how one can use proof by contradiction, conceived as a modus tollens, to establish the logical actuality (logical or formal truth) of a cognition. Although one might agree on the capacity of the proof to prove formal falsity, the logical actuality of a judgement is assessable based on a logically grounded judgement and, as for transcendental logic, this cognitive operation has to presuppose the real possibility of an object.
| All Time | Past Year | Past 30 Days | |
|---|---|---|---|
| Abstract Views | 255 | 128 | 22 |
| Full Text Views | 11 | 5 | 1 |
| PDF Views & Downloads | 32 | 11 | 0 |