By Samuel Safran
Probably the most laudable features of Safran's presentation is the methodical approach he proceeds from basic to complicated structures.
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Sample text
An ad writer for a chemical trade journal fouled this up into: \Power is Knowledge", an absurd { indeed, obscene { falsity. These examples remind us that the verb \is" has, like any other verb, a subject and a predicate; but it is seldom noted that this verb has two entirely dierent meanings. " But in Turkish these meanings are rendered by dierent words, which makes the distinction so clear that a visitor who uses the wrong word will not be understood. The latter statement is ontological, asserting the physical existence of something, while the former is epistemological, expressing only the speaker's personal perception.
2{22) becomes jC ) : (2{24) w(AB jC ) = w(AjC ) S [w(BjAC )] = w(AjC ) S ww(AB (AjC ) Again, we invoke commutativity: w(AB jC ) is symmetric in A, B , and so consistency requires that jC ) = w(BjC ) S w(BAjC ) : w(AjC ) S ww((AB AjC ) w(BjC ) This must hold for all propositions A; B; C ; in particular, (2{25) must hold when (2{25) 207 Chap. 2: THE QUANTITATIVE RULES B = AD 207 (2{26) where D is any new proposition. But then we have the truth{values noted before in (1{8): and in (2{25) we may write AB = B ; BA = A ; w(AB jC ) = w(BjC ) = S [w(BjC )] w(BAjC ) = w(AjC ) = S [w(AjC )] : (2{27) (2{28) Therefore, using now the abbreviations x w(AjC ) ; y w(B jC ) (2{29) Eq.
The domain of validity given in (2{30) is found as follows. The proposition D is arbitrary, and so by various choices of D we can achieve all values of w(DjAC ) in 0 w(DjAC ) 1 : (2{32) But S (y ) = w(ADjC ) = w(AjC )w(DjAC ), and so (2{32) is just (0 S (y ) x), as stated in (2{30). This domain is symmetric in x; y ; it can be written equally well with them interchanged. Geometrically, it consists of all points in the x y plane lying in the unit square (0 x; y 1) and on or above the curve y = S (x).