Notre Dame Journal of Formal Logic 49 (3):245-260 (2008)

John Cantwell
Royal Institute of Technology, Stockholm
It is argued that the "inner" negation $\mathord{\sim}$ familiar from 3-valued logic can be interpreted as a form of "conditional" negation: $\mathord{\sim}$ is read '$A$ is false if it has a truth value'. It is argued that this reading squares well with a particular 3-valued interpretation of a conditional that in the literature has been seen as a serious candidate for capturing the truth conditions of the natural language indicative conditional (e.g., "If Jim went to the party he had a good time"). It is shown that the logic induced by the semantics shares many familiar properties with classical negation, but is orthogonal to both intuitionistic and classical negation: it differs from both in validating the inference from $A \rightarrow \nega B$ to $\nega(A\rightarrow B)$ to
Keywords three-valued logic   inner negation   outer negation   conditionals
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DOI 10.1215/00294527-2008-010
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References found in this work BETA

On Conditionals.Dorothy Edgington - 1995 - Mind 104 (414):235-329.
Conditional Probabilities and Compounds of Conditionals.Vann McGee - 1989 - Philosophical Review 98 (4):485-541.

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Citations of this work BETA

Connexive Logic.Heinrich Wansing - 2008 - Stanford Encyclopedia of Philosophy.
Weak Negation in Inquisitive Semantics.Vít Punčochář - 2015 - Journal of Logic, Language and Information 24 (3):323-355.

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