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By Georg H. Von Wright

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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. As we know, a proposition is possible, if it is true (General Principle of Possibility), and a proposition is not falsified, if it is true (General Principle of Non-Falsification), and a property exists, if it is true of a thing (Principle of Existence).

These relations cannot be converted. If something has a certain property it need not necessarily have it, and from the mere fact that something possibly has a certain property does not follow that it has this property. This might suggest that N A names a property which is (normally) of smaller extension than the property named by A , and that A names a property which is (normally) of smaller extension than the property named by M A . The use of the modalities de re to name properties of different though related extensions would constitute an autonomous use of DE RE 21 them, with interesting consequences when combined with the use of existential modalities (quantification).

It is the only undefined deontic modality which we need. If an act is not permitted, it is called forbidden. We m u s t n o t do that which we are n o t allowed t o do. If the negation of an act is forbidden, the act itself is called obligatory. We ought to do that which we are n o t allowed n o t t o do. If an act and its negation are both permitted, the act is called (morally) indifferent. Two acts are (morally) incompatible, if their conjunction is forbidden (and compatible if it is permitted).

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