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By Georg H. Von Wright

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The self-evident character of the Principle of Permission should be apparent from the following considerations : If the principle were not true, it would be possible for an act and its negation both to be forbidden. But that the negation of an act is forbidden means that the act itself is obligatory. Thus to say that the act and its negation are both forbidden means the same as to say that the act itself is both forbidden and obligatory. This surely conflicts with ordinary use of language and our common sense intuitions concerning obligation concepts.

The fact that, for the determination of the possible and the impossible combinations of truth-values, we need 2” cases of entailment in virtue of the Principle of V-U-Commutation and 2@)-2 cases of entailment in virtue of the Principle of E-VCommutation requires an explanation. It has to do with the distributability of operators. , the implication-sentence PE(A & B v A & - B ) + W E F ( A & B v A & - B ) . It expresses a logically true proposition in virtue of the Principle of V - U-Commutation.

E(- P(A & B) & - - -- F(A & B) & - F(- A & B) & P(-A & B)). I n virtue of the Principle of Non-Falsification, the first E V 16. constituent expresses an always false proposition, the conjunction of all the VE-constituents expresses an always false proposition, and if all the E V-constituents express false propositions, then the last VE-constituent expresses a false proposition. I n virtue of the Principle of V-U-Commutation, the following four implication-sentences express logically true propositions: E N P(A & B).

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An Essay In Modal Logic by Georg H. Von Wright


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