In What Sense is Kantian Principle of Contradiction Non-classical?
Logic and Logical Philosophy 17 (3):251-274 (2008)
| Abstract | On the ground of Kant’s reformulation of the principle of con- tradiction, a non-classical logic KC and its extension KC+ are constructed. In KC and KC+, \neg(\phi \wedge \neg\phi), \phi \rightarrow (\neg\phi \rightarrow \phi), and \phi \vee \neg\phi are not valid due to specific changes in the meaning of connectives and quantifiers, although there is the explosion of derivable consequences from {\phi, ¬\phi} (the deduc- tion theorem lacking). KC and KC+ are interpreted as fragments of an S5-based first-order modal logic M. The quantification in M is combined with a “subject abstraction” device, which excepts predicate letters from the scope of modal operators. Derivability is defined by an appropriate labelled tableau system rules. Informally, KC is mainly ontologically motivated (in contrast, for example, to Jaśkowski’s discussive logic), relativizing state of affairs with respect to conditions such as time. | |||||||||
| Keywords | Kant paracompleteness paraconsistency principle of contradiction square of oppositions subject abstraction labelled tableau | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,865 |
| External links |
|
| Through your library | Configure |
Tuomas E. Tahko (2009). The Law of Non-Contradiction as a Metaphysical Principle. Australasian Journal of Logic 7:32-47.
Dag Westerståhl (1996). Self-Commuting Quantifiers. Journal of Symbolic Logic 61 (1):212-224.
Andrew M. Pitts (1992). On an Interpretation of Second Order Quantification in First Order Intuitionistic Propositional Logic. Journal of Symbolic Logic 57 (1):33-52.
J. Duparc (2003). The Steel Hierarchy of Ordinal Valued Borel Mappings. Journal of Symbolic Logic 68 (1):187-234.
Venanzio Raspa (1999). Łukasiewicz on the Principle of Contradiction. Journal of Philosophical Research 24:57-112.
Juha Kontinen & Jouko Väänänen (2010). A Remark on Negation in Dependence Logic. Notre Dame Journal of Formal Logic 52 (1):55-65.
Giovanni Sambin (1976). An Effective Fixed-Point Theorem in Intuitionistic Diagonalizable Algebras. Studia Logica 35 (4):345 - 361.
Jaap Van Oosten (1991). Extension of Lifschitz' Realizability to Higher Order Arithmetic, and a Solution to a Problem of F. Richman. Journal of Symbolic Logic 56 (3):964 - 973.
Srećko Kovač (2009). First-Order Belief and Paraconsistency. Logic and Logical Philosophy 18 (2):127-143.
Monthly downloads |
Added to index2009-06-06Total downloads29 ( #43,119 of 556,807 )Recent downloads (6 months)3 ( #27,255 of 556,807 )How can I increase my downloads? |

