Reasoning As A Universal Being
We will introduce a "universal being" (i.e. as if the Holy Spirit) which we will call "U" and will assume that U may reason so perfectly that anything true on the consistency of existence of another being may be reasoned to another. I.e. if P(cog_{G}(¬x)) then we immediately find P(cog_{U}(¬x)) => P(cog_{x}(¬x)).
Likewise ¬P(cog_{G}(¬x)) => ¬P(cog_{U}(¬x)) => ¬P(cog_{x}(¬x)) and x considers itself 'necessary'. We assume that U not only reasons perfectly but in a manner common to both perfection (God) and those beings that are able to conceive of a necessary being.
We have already had a brush with "U" in the treatment of the trinity transforming perfectly. We said that:
(H~G&p) & (G&p~H) >= super(H~G & G~H) using our prior equivalence relation '~'.
Whereas we can now state (cog_{H}(G&p) & cog_{G&p}(H)) >= (cog_{G}(H) & (cog_{H}(G))
Or we may state that if it is *positive* (i.e. Pos(...)) that cog_{H}(G&p) then Pos(cog_{U}(G&p)) which results in Pos(cog_{G}(G&p)) => G&p
Likewise Pos(cog_{H}(G&¬p)) then Pos(cog_{U}(G&¬p)) which results in Pos(cog_{G}(G&¬p)) => G&¬p
We should note that the "cog" operator has two distinct parts: There is the suffix 'x' in cog_{x}(y) as well as the operand 'y'. "x" is considered a concrete being, whereas "y" is an abstraction.
Alternatively consider the suffix as an "earthly" individual and the operand as "heavenly".
We will state that from the existence of U that 'x' in cog_{x}(G) may conceive of God (G) consistently if and only if U may do so also. Thus (cog_{x}(G)<=> cog_{U}(G)) => cog_{G}(G) => N(G) (i.e. we infer from Hartshorne's assumption that "perfection is possible".) So that a consistently conceived perfect being must exist necessarily if at all: Or that it is universally correct for "G~x", which entails or requires that cog_{G}(x) is consistent in that the "image" of God reciprocated by 'x' in the definition of "being" i.e. cog_{G}(x) is consistent with the reciprocated belief of the nature of 'G' Himself.
"x~G" => "U~G" if G is consistent. Thus G=>N(G) from Hartshorne's assumption with Anselm's principle.
Then by reflexivity from the definition of '~', we have "G~U" and "U~x" => G~x (transitivity) Which requires symmetry also from the definition of '~' leading to "G~x" <=> "x~G" or "G~y" universally for all 'y' including U.
What objections may we make?
U~G is consistent is part and parcel with G~U, for "U is a being" to God that engenders perfect knowledge of the consistency of 'G'.
U~x is consistent in that U may conceive of any "being" 'x' ('x' likewise able to reason) that with reason may in itself be consistent as with itself (whether x~x or x~U). We make no assumption as to whether U is necessary or contingent. Likewise it follows from U~x that both G~x and x~x (and y~x) for any G, x and y. There is no assumption that "U" is "impossible", neither is U's existence able to be contradicted.
The result then that G~G is completely consistent carries from the result that G~x implies in itself that x~G may be done so just as consistently, and if it is possible for U~G to show reflexivity then it is true that G is consistent for all 'x' that hold true to that "one correct God held by U". We would expect the transitivity of G~U and U~x to imply that G~x is consistent with G Himself. We may substitute G or 'x' for U and have a valid result from our definition of '~'. There is no contradiction in the definition of "being" whilst using our relation '~'.
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