# Download Delta: A Paradox Logic by Nathaniel Hellerstein PDF

By Nathaniel Hellerstein

This article is anxious with Delta, a paradox good judgment. Delta involves elements: internal delta good judgment, which resolves the classical paradoxes of mathematical common sense; and outer delta common sense, which relates delta to Z mod three, conjugate logics, cyclic distribution and the voter paradox.

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**Example text**

A tmn(xn) ) where each t;;(x) is one of these functions: {F,I,T,x,-jx,dx} Conjunctive Normal Form: F(x) = (tu (x1) V t12 (x2) V ... V tln(xn) ) A ( t21 (x1) V t22 (x2) V ... V t2n(xn) ) A ... A ( tml (xl) V tm2 (x2) V ... ) ) where each t;,(x) is one of these functions: ( F,I,T,x,- x,Dx) These normal forms are just like their counterparts in boolean logic, except that they allow differential terms. 52 Delta, A Paradox Logic Primary Normal Form: For any bracket expression F(x); F(x) _ [Ax] [B[x]] [Cx[x]] D where A, B, C and D have no occurrences of variable x.

2D. Brownian Forms 33 Thus we get the "arithmetic initials" for G. Spencer Brown's famous Laws of Form. In his book, Laws of Form, G. Brown demonstrated that these suffice to evaluate all formal expressions in Brown's calculus; and that these forms obey two "algebraic initials": A I B I I C = A C I B C I I ; "Transposition" I Al A I . "Position" He proved that these axioms are consistent, independent, and complete; that is, they prove all arithmetic identities. This "primary algebra" can be identified with Boolean logic.

Xy] [x] = [x] Proof. [xy] [x] _ [ [[x]] y ] [x] ref. [x] occ. Echelon . [[[x]y]z] _ [xz] [[y]z] Proof. [[[x]y]z] _ [[[x][[y]]]z] ref. [[[xz][[y]z]]] trans. [xz] 1[y]z] ref. Modified Generation. [[xy]y] = [[x]y] [y[y]] Proof. [[xy]y] [ [ [[x]] [[y]] ] y ] [[ I[x]y] [[y]y] ] ] [[x]y] I[yly] ref. trans. ref. Modified Extension. [[x]y] [[x][y]] = [ [x] [y[y]] ] Proof. [1x]y1 [[x][y]] _ [ I [[x]y] [[x][y]] ] ] ref [ [ [y] [[y]] ] [x] ] trans. [ [x] [y[y]] ] ref. 42 Delta , A Paradox Logic Inverse Transposition .