6. Consistency Proof
The aim of this chapter is to show that the axiomatic system about God’s Omniscience Omnipotence and Benevolence and about existing evil developed in chapters 4 and 5 is consistent. This will be done by defining a 10-valued matrix representing a 10-valued decidable logic which serves as a model for the axiomatic system in such a way that the axioms and theorems of the system are satisfied in this model. First, we shall define the model OBE, and secondly, we shall show that and how the axioms, definitions, and theorems are satisfied in this model (OBE for Omnipotence, Benevolence, Evil). (Cf. ASG, p. 280ff).
Definition: The model OBE is the set of all formulas (built up from propositional variables p, q, r … in the usual way) which are satisfied by the matrix M = ‹True, False, ¬, →, gK, gC, gW, gP, gCC, gCW, gCN, gL, T (g), T (LM), gCS, xCS, xAccepts, p ε T (CR), p e G, p e Goal, Op, p e E, p e ME› where True = 11111, False = 00000 and the connectives ¬, → and the above-listed operations are defined by the following matrices.
The model OBE is an extension of Classical Two-Valued Propositional Calculus (CPC) which has 5 values for true (instead of 1) and 5 values for false (instead of 1) but nothing between true and false. For the definitions of the different operations the different positions (position 1–10) are decisive.
Observe that the above operations are...
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