Étude critique de la notion de collectif by Ville J.

By Ville J.

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The diagrams of Figure 1 show that it is possible for P (z | xy) to have the extreme values 0 and 1, as well as any value in between. y x P (xyz) =0 P (xy) z z x y P (xyz) = 1. P (xy) Figure 1. Could the additional premises P (z | x) = p and P (z | y) = q sufficiently 15 Contained in the memoir Boole 1857, reprinted as Essay XVI in Boole 1952, of which the relevant pages are 355–367. On p. 356 of this book in the display labeled (1) there is a typographical error. The first numerator should be ‘Prob xz’.

Should one prefer to say “suppositional probability” or is it too late to change? 6. 2 III above) the basic semantic components are statements of the form P (φ) ∈ α, where P is an arbitrary probability function (becoming specific with a choice of probability model), and α is a subset of [0, 1]. Such subsets need not be explicitly given but may only be described—for example, the set {x ∈ [0, 1] | F(x, P (ψ1 ), . . 2 III. This enlargement of the probability semantic language beyond the simple V (φ) = 1 of verity logic brings in the need for sharper distinction between syntax and semantics, a distinction barely noticable in verity logic.

Functions are as follows. Each pk (k = 1, . . , m), Q’s primary functions, will have the same number of argument places as the predicate Pk and the values of each of these functions will range (respectively) over the m different residue classes of natural numbers modulo m (thus keeping the ranges of the pk from overlapping). This is achieved by setting: pk (x1 , . . , xmk ) = mN (mk ) (x1 , . . , xmk ) + k − 1, where N (n) (x1 , . . , xn ) is a primitive recursive function mapping n-tuples of natural numbers (= numerals, for us) to the natural numbers (numerals).

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