Disappearing Diamonds: Fitch-Like Results in Bimodal Logic
| Autor: | Weng Kin San |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Journal of Philosophical Logic. 48:1003-1016 |
| ISSN: | 1573-0433 0022-3611 |
| DOI: | 10.1007/s10992-019-09504-0 |
| Popis: | Augment the propositional language with two modal operators: □ and ■. Define \(\blacklozenge \) to be the dual of ■, i.e. \(\blacklozenge \equiv \neg \blacksquare \neg \). Whenever (X) is of the form φ → ψ, let (X\(^{\blacklozenge } \) ) be \(\varphi \rightarrow \blacklozenge \psi \). (X\(^{\blacklozenge } \) ) can be thought of as the modally qualified counterpart of (X)—for instance, under the metaphysical interpretation of \(\blacklozenge \), where (X) says φ implies ψ, (X\(^{\blacklozenge } \) ) says φ implies possiblyψ. This paper shows that for various interesting instances of (X), fairly weak assumptions suffice for (X\(^{\blacklozenge } \)) to imply (X)—so, the modally qualified principle is as strong as its unqualified counterpart. These results have surprising and interesting implications for issues spanning many areas of philosophy. |
| Databáze: | OpenAIRE |
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