TY - JOUR
AU - Pizzi, Claudio E. A.
PY - 2021/03/24
Y2 - 2022/11/27
TI - A Syntactical Analysis of Lewis’s Triviality Result
JF - Logic and Logical Philosophy
JA - LLP
VL - 30
IS - 3
SE - Articles
DO - 10.12775/LLP.2021.006
UR - https://apcz.umk.pl/LLP/article/view/LLP.2021.006
SP - 417-434
AB - <p>The first part of the paper contains a probabilistic axiomatic extension of the conditional system WV, here named WVPr. This system is extended with the axiom (Pr4): PrA = 1 ⊃ □A. The resulting system, named WVPr∗, is proved to be consistent and non-trivial, in the sense that it does not contain the wff (Triv): A ≡□A. Extending WVPr∗ with the so-called Generalized Stalnaker’s Thesis (GST) yields the (first) Lewis’s Triviality Result (LTriv) in the form (◊(A ∧ B) ∧◊(A ∧ ¬B)) ⊃ PrB|A = PrB. In §4 it is shown that a consequence of this theorem is the thesis (CT1): ¬A ⊃ (A > B ⊃ A ⥽ B). It is then proven that (CT1) subjoined to the conditional system WVPr∗ yields the collapse formula (Triv). The final result is that WVPr∗+(GST) is equivalent to WVPr∗+(Triv). In the last section a discussion is opened about the intuitive and philosophical plausibility of axiom (Pr4) and its role in the derivation of (Triv).</p>
ER -