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By Georg H. Von Wright
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Extra info for An Essay In Modal Logic
We thereupon replace every one of the molecular complexes of predicates which occur in the VE-sentence by its perfect disjunctive normal form in terms of all predicates in our list. After doing this, we distribute the operator E in front of every one of the normal forms. The atomic E-sentences which occur in the VE-sentence after the distribution we shall call the E-constituents of the (original) VE-sentence. N” 44 COMBINED MODALITIES We now make a complete list of all the E-constituents. We thereupon replace every one of the E-sentences which occur in the VE-sentence by its perfect disjunctive normal form in terms of all E-constituents in our list.
The quantifiers E and U resemble in this respect the deontic operators. When prefixed to predicates they yield sentences. If A names the property of being red, EA expresses the proposition that there are red things. It follows from the above that the deontic (and the existential) unlike the alethic and the epistemic modalities cannot be taken alternatively de dicto and de re. Further, it follows from the above that the deontic (and the of many examples which show that moral arguments may involve considerable logical subtleties and that, therefore, a logical study of moral concepts is philosophically relevant.
Cf. above p. ) We shall divide the treatment into two sections according to whether or not certain principles for the reduction of higher order modalities to first order modalities are accepted. A. THE UNREDUCED MODALITIES 1. The Systems M,, etc. By an atomic M2-sentence we shall understand the sentence which we get when we prefix the operator M to a Ml-sentence. (Ml-sentences, it should be remembered, are molecular complexes of atomic Ml- and/or N,-sentences. ) By a M,-sentence we shall understand a molecular complex of atomic M,-sentences.
An Essay In Modal Logic by Georg H. Von Wright