Alternative Axiomatizations of the Conditional System VC

Rok, strany: 2019, 427 - 445

The central result of the paper is an alternative axiomatization of the conditional system VC which does not make use of Conditional Modus Ponens: (A > B) (A  B) and of the axiom-schema CS: (A  B)  (A > B). Essential use is made of two schemata, i.e. X1: (A  ♢A)  (♢A >< A) and T: □A  A, which are subjoined to a basic principle named Int: (A  B)  (♢A > ♢B). A hierarchy of extensions of the basic system V called VInt, VInt1, VInt1T is then construed and submitted to a semantic analysis. In Section 3 VInt1T is shown to be deductively equivalent to VC. Section 4 shows that in VC the thesis X1 is equivalent to X1: (♢A >< A)  (♢¬A >< ¬A), so that VC is also equivalent to a variant of VInt1T here called VInt1To. In Section 6 both X1 and X1 offer the basis for a discussion on systems containing CS, in which it is argued that they cannot avoid various kinds of partial or full trivialization of some non truth-functional operators.

ISO 690:

Pizzi, C. 2019. Alternative Axiomatizations of the Conditional System VC. In Organon F, vol. 26, no.3, pp. 427-445. 1335-0668. DOI: https://doi.org/10.31577/orgf.2019.26305

APA:

Pizzi, C. (2019). Alternative Axiomatizations of the Conditional System VC. Organon F, 26(3), 427-445. 1335-0668. DOI: https://doi.org/10.31577/orgf.2019.26305

Vydavateľ: Institute of Philosophy of the Slovak Academy of Sciences, Institute of Philosophy of the Czech Academy of Sciences

Claudio E. A. Pizzi