# An Essay In Modal Logic by Georg H. Von Wright

By Georg H. Von Wright

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The distribution of truth-values over the propositions expressed by the M,-constituents of a given M,-sentence is - in the logic of the unrcduced higher order modalities - subject only to the restriction imposed by the Principle of Possibility. (Cf. the example given below on p. ) Consequently, every M,-sentence expresses a truth-function of the propositions expressed by its M,-constituents. Which truthfunction it expresses can be investigated and decided in a truthtable. This constitutes a solution of the decision problem of the System M,.

O(N A -+ A ) -+ OA. If failure to perform an act commits us to perform it, then this act is obligatory. N N N The following differences and resemblances are noteworthy : The operators M and N , when prefixed to sentences yield new sentences, and when prefixed to names of properties yield new names of properties. The same is true of the operators V and F . The operators P and 0, however, when prefixed to names of properties (acts) yield sentences. M A denotes a property, viz. the property of possibly being A .

It is logically impossible t o be perplexus simpliciter but possible t o be perplexus secundum quid. I a m indebted for this and some other observations concerning the deontic modalities to M i . P. Geach. DEONTIC MODALITIES 41 existential) unlike the alethic and the epistemic modalities are not capable of higher orders. Since M u is a sentence, M M a is also a sentence, and since M A is a predicate, M M A is also a predicate. P P A has no meaning. Similarly, E E A has no meaning. There is an interesting respect, in which the deontic modalities differ drom the alethic, the epistemic, and the existential alike.