Lexicon of Arguments

 

I 150
Barcan formula/BF/Stalnaker: the Barcan formula involves the interaction of the universal quantifier with the necessity operator: (BF) " NF x ^ > N " x ^ F. Conversely: (CBF) N " F ^ x > " x ^ NF (Kripke 1963)⁽¹⁾: Kripke's semantics showed that semantic assumptions are also needed. He also showed a fallacy in the proofs that they supposedly deduced, in which these assumptions were missing. It is valid if wuU, Du < Dw, i.e. if the subject matter of the accessible possible world is a subset of the range of the output possible world - vice versa for the converse.
Qualified converse of Barcan-Formula/Stalnaker: a qualified converse with the Barcon-Formula is made with the existence adoption: ( QCBF ) N "x ^ F> " x ^ N ex > F).
Existence predicate e: Ey ^ (x = y ).
I 151
Barcan-Formula/qualified converse/Stalnaker: if in possible world w it is necessary that everything satisfies F, then everything that must exist in w, must satisfy F in any accessible possible world, in which this individual exists. That is valid in our semantics but it is not a theorem because it is a variant of the invalid semantics. This is what we examine here.


1. S. A. Kripke, 1963. Semantical Analysis of Modal Logic I Normal Modal Propositional Calculi. Mathematical Logic Quarterly Volume 9, Issue 5‐6