Authentic Science Fiction Monthly, Issue 45 — page 135: what you’re looking at

Machine-transcribed from the original scan — historical spelling and the odd misread are preserved.

AUTHENTIC SCiENCE FICTION Disjunctive propositionsare, in effect, contradictions of the conjunctive type. They assert that it is not true to say that both p and gq are true, and that they may both be false, though leaving open the question as to whether one of them is true and the other false. For ex- ample: “It is not true that Greenwich has the largest telescope in the world and that Greenwich astronomers have photographed the farthest nebule.”’ To symbolize these propositions we use the so- called glide: uw. Thus our disjunctive proposition be- comes ~ (p. q), which can be read as “‘not both p and q” or as “it is not the case that both p and g are true.” The glide can be applied to any propositional state- ment. For example, ~(p>q) means “it is not true that P implies g.”” and wp v gq means “either p is false or q is true.”” Note that when we use brackets we negate every- thing inside the bracket, but that when we do not use brackets we negate only that symbol which immediately follows the glide. Thus wp vq means “either p is false or gq is true” but w (p v @) means “‘it is not true to say either p or gq.” In the case of the categorical propositions, we place a bar over the top of the S or P to express negation, e.g. if SaP is written for “‘All_men are mortal,” then SaP means “All men are immortal” and SaP means “All non-men are mortal.”’ Also, note that if xea means “‘John is a tall man,” then w(xea) means “John is not a tall man’ and xea means “John is a short man or a medium height man,” > Now for some homework! See if you can express these propositions in one or other of the logical forms, name them and give their symbolic form:—(a) Space _ stations are artificial satellites, (b) Japetus is not a moon of Jupiter, (c) If a spaceship hull is unsealed, then air will not leak in, (d) Men who travel in space are either brave or trying to escape from some- thing, (e) Space is not a vacuum, nor is it infinite, Till give you the answers next month, when we shall pass on to inference. This is the process of arriving at new information from given propositions. To do this validly is something of which few people are capable! 134 comiclbooks.conrn