Existence Is A Predicate

The most sustained counter argument to the ontological arguments for the existence of God lies in the idea that existence is not a predicate, i.e. a "property" of the object calld "God". Rather, existence is a matter of the ordinal, becuase nothing changes in the properties of an object whether four, ten or indeed none of the object actually exist. The ontological arguments assert that God is more perfect if He is existent, and thus existence as a positive property is a predicate of "God", a perfect being.

In order to show that indeed, God's existence which we state is necessary, or a logical "a priori" existence is predicate to the concept of a perfect being, we proceed as follows. First we draw a distinction between contingent existence which we familiarly know as our own mode, which indeed falls into matters of ordinality and to the contrary, the existence of God.

First, we assume that there is a difference between the contingently existent, which may or may not be eternal, and necessary existence.

If a being "x" may conceive of a being "G" that may exist for longer (prior to and/or afterward) than x, then we may ascend a chain of the age of such beings using Zorn's lemma to reach or choose the top bound of the poset, to a being that conceivably would exist forever. (though as yet is still a contingent being).

That is, every contingent being may consider the possibility of his own non-existence (in his being and inner person), so it is possible for him to infer the existence of another being that would "out live" himself. We ascend every possible chain of such beings and we may choose an eternal being that is truly "conceived as eternal". Now, though this may be only a hyperthetical being, it is a logically possible and also most notably a logically conceivable one.

Some effort is made to qualify such existence with an equivalence relation, by only conceiving of beings G that may likewise conceive of x by reciprocation. More on this later in the site.

Now, if we now reverse the roles, if it were not possible for x to conceive of such a being G, then we logically arrive at the modus tollens, and it is then impossible for the being x to conceive of his own limited mortality. (we assume that all such x are capable. so (¬N(x)=>P(x~G)) <=> (¬P(x~G) => N(x))

In fact, we totally skirt aside the issue of necessary existence by inferring that x is unable to conceive of an end to his own contingent existence, and we state that the modus tollens logically so derived states that x may only conceive of himself as necessarily existent, (though necessary logically rather than in actuality; as x surely has no concept of his finite existence.) Or rather for all of our benefit here, that x is not able to conceive of his own non-existence. Whilst this is not in truth equivalent to necessary existence, the difference is between "logically existent", and "not conceived as logically non-existent".

Now we have an impasse, for by construction x is contingent and merely unable to come to terms with it: whereas G in reciprocating to x, were G in truth eternal, G could only conceive of one such being, namely the remaining necessary one, which by the modus tollens as above, would become by inclusion G himself.

G, unable to consider a being with longer life than His own, logically is unable to conceive of his own non-existence.

So, is G then necessarily existent?

Ascending a chain of contingently existent "G" leads us to an eternal yet contingent G that is unable to logically conceive of His own non-existence. Now, if x by virtue of predicating G with necessary existence had correctly chosen the perfect rather than the contingent, then G in reciprocating to Himself, could not conceive of His possible non-existence either.

Rather than examine every point of contingency, it is easier to write ¬N(x) => P(x~G) is equivalent to ¬P(x~G) => N(x) and then x is such a G himself.

Yet if G is eternal and yet still contingent then if G conceives of a necessary being, we state that this is a positive property of some H found so, and is therefore a predicate. (Because necessary existence was not found ascending the chain in the poset but was chosen as necessary existence in H.) So P(G~H) => N(H) else ¬N(H)=>~P(G~H)=> N(G).

So, by definition of predicate, we infer necessary existence is found as an essence in God, that if ¬P(x~G) then N(x) rather than x being simply unaware of his finite mortality. Thus, H chosen as necessary rather than eternal is more "perfect" than a "G" chosen merely as eternal from the poset. And, thus far, positive and necessary existence must be predicated to H to separate us suffering misidentification as to G.

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