Logical Foundations and Kant's Principles of Formal Logic

The abstract status of Kant's account of his ‘general logic’ is explained in comparison with Gödel's general definition of a formal logical system and reflections on ‘abstract’ (‘absolute’) concepts. Thereafter, an informal reconstruction of Kant's general logic is given from the aspect of the principles of contradiction, of sufficient reason, and of excluded middle. It is shown that Kant's composition of logic consists in a gradual strengthening of logical principles, starting from a weak principle of contradiction that tolerates a sort of contradictions in predication, and then proceeding to the (constructive) principle of sufficient reason, and to a classical-like logic, which includes the principle of excluded middle. A first-order formalisation is applied to this reconstruction, which reveals implicit modalities in Kant's account of logic, and confirms the implementability of Kant's logic into a sound and complete formal system.

[1]  Immanuel Kant,et al.  Kant's gesammelte schriften , 1910 .

[2]  Kurt Gödel,et al.  On undecidable propositions of formal mathematical systems , 1934 .

[3]  Kurt Gödel,et al.  On Formally Undecidable Propositions of Principia Mathematica and Related Systems , 1966 .

[4]  R. Goodstein ON FORMALLY UNDECIDABLE PROPOSITIONS OF PRINCIPIA MATHEMATICA AND RELATED SYSTEMS , 1963 .

[5]  John Corcoran,et al.  Completeness of an ancient logic , 1972, Journal of Symbolic Logic.

[6]  Daniel Gallin,et al.  Intensional and Higher-Order Modal Logic, With Applications to Montague Semantics , 1975 .

[7]  J. Myhill,et al.  Choice Implies Excluded Middle , 1978, Math. Log. Q..

[8]  K. Dosen,et al.  Models for normal intuitionistic modal logics , 1984 .

[9]  Kosta Dosen,et al.  Models for stronger normal intuitionistic modal logics , 1985, Stud Logica.

[10]  Christopher Menzel,et al.  The true modal logic , 1991, J. Philos. Log..

[11]  M. Losonsky,et al.  The Completeness of Kant's Table of Judgments , 1992 .

[12]  W. Harper,et al.  Kant and the Exact Sciences , 1992 .

[13]  Alex K. Simpson,et al.  The proof theory and semantics of intuitionistic modal logic , 1994 .

[14]  M. Wolff Die Vollständigkeit der kantischen Urteilstafel , 1995 .

[15]  K. Westphal Kant and the Capacity to Judge , 2000 .

[16]  R. Wahsner Review of: Kant, Immanuel: Logik-Vorlesung : unveröffentlichte Nachschriften II. Logik Hechsel. Warschauer Logik. Bearbeitet von Tillmann Pinder. (Kant-Forschungen. Bd 9.) Hamburg: Meiner 1998 , 2001 .

[17]  B. Russell THE AXIOM OF CHOICE , 2003 .

[18]  Mary Tiles,et al.  Kant: From general to transcendental logic , 2004, The Rise of Modern Logic: From Leibniz to Frege.

[19]  Yuri Gureoich Intuitionistic Logic , 2008 .

[20]  In what sense is Kantian principle of contradiction non-classical? , 2008 .

[21]  Catarina Dutilh Novaes,et al.  Logic in the 14th century after Ockham , 2008, Mediaeval and Renaissance Logic.

[22]  M. V. Lambalgen,et al.  A FORMALIZATION OF KANT’S TRANSCENDENTAL LOGIC , 2011, The Review of Symbolic Logic.

[23]  Michiel van Lambalgen,et al.  A FORMALIZATION OF KANT’S TRANSCENDENTAL LOGIC , 2011, The Review of Symbolic Logic.

[24]  C. Novaes Form and Matter in Later Latin Medieval Logic: The Cases of Suppositio and Consequentia , 2012 .

[25]  M. Sgarbi Immanuel Kant, Die falsche Spitzfindigkeit der vier syllogistischen Figuren , 2012 .

[26]  S. Kovac Forms of Judgment as a Link between Mind and the Concepts of Substance and Cause (Kant, Gödel) , 2014 .

[27]  J. Kennedy Gödel’s 1946 Princeton bicentennial lecture: an appreciation , 2014 .

[28]  Paul Strauss,et al.  Kant And The Exact Sciences , 2016 .

[29]  G. Crocco Informal and Absolute Proofs: Some Remarks from a Gödelian Perspective , 2019 .

[30]  S. Kovac The Totality of Predicates and the Possibility of the Most Real Being , 2018, FLAP.

[31]  Gregor Nickel,et al.  Preisschrift über die Fortschritte der Metaphysik [Nachlaß: Erster Entwurf (Rink)] (1804) , 2018 .