Psychology Dictionary of ArgumentsHome
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| Barcan formula: claims that from the fact that it is possible that an object has a certain property it follows that this object exists. The formula is valid only in a few systems. See also modal logic._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. | |||
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Robert Stalnaker on Barcan-Formula - Dictionary 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_____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Stalnaker I R. Stalnaker Ways a World may be Oxford New York 2003 |
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> Counter arguments against Stalnaker
> Counter arguments in relation to Barcan-Formula
