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Translated by means of Clarence Smith Howe . octavo pp. XX + 218 Brossura (wrappers) Molto Buono (Very reliable)
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The atomic M,-sentences, thus obtained, are the M,-constituents of the original M,-sentence. 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.
Thereupon we transform every one of the molecular complexes of atomic M,-sentences into its perfect disjunctive normal form in terms of all atomic M,-sentences in the list. We distribute the operators M which stand in front of the normal forms. Thereupon we transform every one of the Mlsentences, thus obtained, into i t s absolutely perfect disjunctive normal form. We distribute the operators M which stand in front of t h e s e normal forms. The atomic M,-sentences, thus obtained, are the M,-constituents of the original M,-sentence.
It will be seen from the following considerations : If A is the sole atomic predicate which occurs in a E V-sentence, there are not more than two V-constituents. viz. FA and F -A, - - 47 THE SYSTEN EV and not more than four (= 27 E V-constituents, viz. E(F A & F A ) andE(PA&NF-A)andE(-FA&F-A) andE(NFA& F A ) . Of the four EV-constituents, however, the first expresses a proposition which is always false in virtue of the Principle of Non-Falsification. For, E ( P A & F - A ) means that there exists a thing - in the appropriate Universe of Discourse which is known to be neither A nor not-A, and this is an impossiN N N bility.