ALTERNATIVE AXIOMATIZATIONS OF THE CONDITIONAL SYSTEM VC

• Authors: Pizzi Claudio E. A.
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

CONDITIONAL LOGIC; CONDITION; TRIVIALIZATION; MODAL COLLAPSE

• Publisher: Institute of Philosophy of the Slovak Academy of Sciences and Institute of Philosophy of Academy of Sciences of Czech Republic
• Journal: Organon F. medzinárodný časopis pre analytickú filozofiu
• Year: 2019
• Volume: 26
• Issue: 3
• Pages: 427 – 445

Contributors

author

Pizzi Claudio E. A.

• Dipartimento di Scienze Sociali, Politiche e Cognitive, University of Siena, via Roma 56, 53100 Siena, Italy

Identifiers

DOI

https://doi.org/10.31577/orgf.2019.26305