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Deontic Modalities

Thomas Müller

Pages 179 - 182

Modalities, or modal operators, modify propositions to form new propositions, thus constituting a formal-language analogue of adverbial modification in natural language. In many instances there is a pair of dual one-place modalities, such as the alethic modalities of ‘it is possible that’ and ‘it is necessary that’. Such is also the case for the deontic modalities ‘it is permitted that’ (often symbolised as ‘P’) and ‘it is obligatory that’ (often symbolised as ‘O’). These modalities are dual in the sense that ‘non-P-non’ corresponds to ‘O’: if it is obligatory that p, then it is not permitted that non-p. (Consequently, ‘non-O-non’ corresponds to ‘P’). In formal contexts it is customary to take the strong ‘O’ modality as basic and to treat the weak ‘P’ as an abbreviation; sometimes ‘F’ (‘it is forbidden that’) is used as an abbreviation for ‘Onon’ (equivalently, for ‘non-P’).

1Department of Philosophy, University of Konstanz

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