Garrett Gray makes a strange and ultimately unconvincing ontological argument for the existence of God that may perhaps validate that existence exists, but not that God exists.
Gray draws primarily from three theological sources–namely Rashi’s commentary on the Torah; the Catechism of the Catholic Church; and Exodus 3:14–to reach the following position:
God is That Which Is. When a Christian or a Philonian refers to God, they’re referring to “Being-In-Itself”. If we’re going to prove that God exists, then, this Being is the entity we’ll be dealing with.
God being understood as “That Which Is,” or “Being-In-Itself,” or existence, Gray then points to an argument from Parmenides for, basically, why existence exists. Gray summarizes the argument by Parmenides as follows:
P1: Being either is or is not.
P2: We can only make statements like “Being either is or is not” if Being is.
C1: Being is.
This would perhaps be a stronger argument if it included the lemma that, in accordance with P2, if a statement like “Being either is or is not” is made, then Being is. It is unclear whether there is something inherent in this mode of communication that uniquely justifies Being being, or existence existing, or whether there is any difference between this and any other praxeological argument for why existence exists.
Immediately following Gray’s propositional translation of Parmenides’s argument for why Being is, or why existence exists, he then “combine[s] this simple syllogism [the Parmenides argument] with the definition of God we discussed above [to] get an addendum”:
C1: Being is.
P3: God is Being-In-Itself.
C2: God exists.
Gray concludes his article with the next paragraph:
Quod erat demonstrandum. God, defined in the manner advocated by a number of the world’s religions and philosophers, exists. Of course, we’ve demonstrated exactly no characteristics beyond the basic point of existence, so it remains to be seen what else we can know (if anything) about HOW God exists. Most of that seeing will take place over the next few posts, in which I intend to evaluate a variety of other philosophical arguments for or against God’s existence or some part of God’s nature, and in the few posts to follow that, in which I intend to elaborate on whatever the fruit of that earlier work might be.
Fortunately for the point I seek to make, Gray concedes he has “demonstrated exactly no characteristics beyond the basic point of existence.” He has indeed not demonstrated any characteristics of God beyond the basic point of existence, but he has not even demonstrated that God exists for the following reason: One can make basically the same exact argument for sheer existence existing, and there will be nothing qualitatively different in the account.
Consider the following argument:
P1: It is either the case that there is Being, or existence, or that there is not Being, or existence.
P2: To even cognize or discuss this issue presupposes Being, or existence.
P3: If an action presupposes Being, or existence, and the action is successfully completed, then it is true that there is Being, or existence.
P4: The truth-makers of P3 obtain.
P5: Because of P4, P2 is true.
P6: Because of P5, the second disjunct of P1 does not obtain, whereas the first disjunct does obtain, and thus there is Being, or existence.
C: Ergo, there is Being, or existence.
Whether Being, or existence, is called X, or God, does not change the substance of the argument aside from the assignment of that name. If this argument, perhaps a strengthened form of that of Gray, succeeds, then it is unclear how he has demonstrated anything other than that existence exists. It is an interesting argument perhaps in light of the philosophic developments of Ludwig von Mises and Ayn Rand, but to call existence by the name “God” begs the question from the start. Nothing he has included will substantiate the claim that God is Being-in-Itself. I am doubtful that trying to “demonstrate” further characteristics of “God” will in any way strengthen his case, if his starting point is anything akin to the above examined form of an ontological argument. Furthermore, it may eventually become clear that this “God” Gray is discussing is the subject of an arbitrary assertion. We shall see.
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A Referent, or Semantic Object, is a Set Necessitated by the Inextricably Linked Axioms of Existence and Identity
The concept of a referent, or something that can be referred to, is an entailment of the metaphysical axiom of identity, itself inextricably linked to the axiom of existence. Existence exists; such is the axiom of existence, the irreducible primary of metaphysics. The universe is the set of all that exists. A set is a grouping of zero, one, or several members or elements which, when they themselves are encompassed by the set as opposed to being outside of it, meet or satisfy the criteria of the set, which is for each respective member or element to have certain distinguishing criteria: in short, some particular identity vis a vis the dialectic of potentiality/actuality; this may be called its nature, which everything necessarily has, since for something to exist is for it to be delimited, whether this is recognized or not. In thought-independent existence everything in particular is respectively delimited. Nonsense is when the contents of that which is being regarded as nonsense cannot be sussed out, or delimited. The negation of nonsense is what is sensical. Sensical thought is in accordance with the axiom of identity at least in respect to the contents of sensical thought necessarily being some type of delimited mental representations about some semantic object. Indeed, we may regard the phrase ‘semantic object’ to be synonymous with ‘referent,’ since for something to be referred to is for the object of reference (with reference being a part of semantics, the study of meaning-making) to be itself an implicit or explicit set. Why is this the case? Because when something is being referred to, it is necessarily so that there exists (when it is delimited as such) something which alone is not that which is being referred to. Even when one refers to ‘the constitutive elements of everything’ alone, one is not referring to ‘some particular constitutive element of everything’ alone. And when one is referring to bananas alone, one is not referring to music alone. As such, with any semantic set A, there is another set, namely that of not-semantic set A, consting of all sets of all semantic sets not identical to semantic set A. In accordance with the axiom of identity then, when the contents of the following variable is properly delimited, A is A and as such, A is not not-A. Notice that I earlier said there can be sets with zero elements. If one has never engaged in a certain activity, then the set of instances in which one has engaged in said certain activity that they have not engaged in would be an empty set. There can also be sets of non-existent things, or things that do not (yet?) have thought-indepdent existence, such as Thor’s Hammer, supposing that Thor’s Hammer has never had thought-independent existence. All conceivable sets can each be referred to if one exercises the mental effort to do so. Indeed, even the mental representation of something is a form of reference, though communication is the particular type of reference in which one’s thoughts are made known to others by some semantic medium. It being known that what can be referred to can necessarily be the part of a set, and it being known that what can be referred to can either be a modal conveyant (particular form of reference, communication, etc.), existent (something that exists, be it an attribute, action, material thing, etc.), or state of affairs, and these being either real or hypothetical/mental/not-thought independent, the formulation of a set does not entail the thought-independent existence of the content(s) of the set.
Against a “Set theory proof for the existence of God”
I am totally against the project of a set theory proof for the existence of God, especially one of the following line of reasoning:
Proposition: If a set is unique, then it exists.
Proof: If a set is unique, i.e. is properly specified so that a set having the properties is equal to the set, then even if the set has no members, it exists as the empty set.
Example x^2 + 1 = 0. Let A be the integer solutions. This set A is unique, but it is empty.
God is unique.
God contains other things and thus is a set.
Thus God is a unique set.
Therefore God exists.
The above alone demonstrates there being a thought-dependent modal conveyant of God, not the thought-independent existence of God. Just because I can refer to something doesn’t mean it exists; I would apply the same standard to that absurd Platonic school of thought called mathematical realism. I would go so far as to say that any supposedly coherent conception of God exchanges the primacy of existence for the primacy of consciousness, and violates the axiom of identity and law of causality, but that thread of thought will have to be pursued in writing another time.