Gödel's Ontological Failure
In 2013 a pair of computer researchers reportedly "verified" an ontological theorem* proposed by the late mathematician Kurt Gödel. Predictably, the media irresponsibly hailed this event as science "proving" Gödel's argument for God's existence. Just as predictably, some have unquestionably accepted it as a validation of their own religious beliefs.
What is uniformly ignored is that it was a mathematical "translation" (using Henkin semantics) -- NOT Gödel's original argument -- which was supposedly "proven." What remains is to thoroughly analyze the actual original theorem to determine its logical, philosophical or factual value (and whether the mathematical syntax truly constitutes a valid translation).
The essence of every ontological argument is the attribution of some quality exclusively to God. By assuming the quality exists, and asserting that only God possesses that quality, we presumably conclude that God exists. The inherent weakness of such arguments is that the attribution is wholly arbitrary, and the quality itself is often arbitrarily defined, and is usually so generic or abstract that it can be applied to practically anything, rendering the argument useless.
In Anselm's classic argument, he urged us to imagine a being "than which no greater can be conceived." Descartes proposed a supremely perfect being. Gödel suggests a being that "possesses all positive properties" in a theorem that can be distilled into three fundamental premises:
1) A "God-like being" possesses all existing properties.
2) The property of possessing all existing properties is an "essence."
3) Essences necessarily demonstrate an individual's existence.
Since a "God-like being" has the "essence" of possessing all existing properties, and since an essence necessarily demonstrates an individual's existence, then a "God-like being" must exist.
By far the most crucial task (and greatest initial difficulty) in assessing Gödel's theorem is comprehending his particular meaning for words and phrases -- often possible only by considering the context in which they are used. For example, Gödel appears to use the term "positive" in a strictly logical (not evaluative) sense. Hence, a "positive" property means a property that actually exists, as opposed to not existing (affirmed in his very first axiom, below).
In his translation, mathematician Dana Scott assigned alpha-numeric designations to each of Gödel's axioms, definitions, corollaries and component theorems (for example, A1 is "axiom 1"), listed below in original order and quoted verbatim. To make sense of Gödel's vague, redundant and often circular phrasing, I've offered more conventional translations or clarifications (in parentheses):
A1 -- "Either a property or its negation is positive, but not both" (Either a property positively exists or doesn't positively exist, but can't do both). This is an expression of the logical principle of non-contradiction.
A2 -- "A property necessarily implied by a positive property is positive" (If a positively existing property necessarily implies another property, that second property must also positively exist).
T1 -- "Positive properties are possibly exemplified" (If a property positively exists, it is possible to demonstrate it).
D1 -- "A God-like being possesses all positive properties" (positively existing properties).
A3 -- "The property of being God-like is positive" (The property of being "God-like" positively exists).
C1 -- "Possibly, God exists" (Self-explanatory).
A4 -- "Positive properties are necessarily positive" (By definition, positively existing properties must exist).
D2 -- "An essence of an individual is a property possessed by it and necessarily implying any of its properties" (If any property of an individual necessarily implies any of that individual's properties, it is an "essence").
T2 -- "Being God-like is an essence of any God-like being" (Every "God-like being" possesses the essence known by name as "being God-like").
D3 -- "Necessary existence of an individual is the necessary exemplification of all its essences" (An individual's existence is an inevitable or unavoidable representation or demonstration of all its essences (properties that "necessarily imply" other properties). If an individual posesses these "essences," he must "necessarily exist").
A5 -- "Necessary existence is a positive property" (The necessary existence of an individual is a property that positively exists).
T3 -- "Necessarily, God exists" (Self-explanatory).
A comprehensive analysis reveals problems regarding a number of Gödel's specific concepts. For example:
"Necessarily implied" (A2, D2) -- Gödel insists that, if a positively existing property "necessarily implies" another, the implied property must also positively exist. But he offers no proof that a property can actually be "necessarily implied" (that circumstances make the implied existence of a property essential or inevitable), and he offers no guidance for determining WHICH specific properties are "necessarily implied," and which are not. Thus, it is open to interpretation which "implied" properties positively exist.
"Necessary existence" (D3, A5, T3) -- Even if we accept the concept of "necessary existence" -- that the existence of ANY individual is logically inevitable or essential -- it is a "positive property" ONLY if the individual actually exists. If the individual DOESN'T exist, such a property can ONLY be hypothetical.
"God-like beings" (D1, T2) -- Gödel declares -- without qualification -- that "a God-like being possesses all positive properties" (not "some" or "may" or "possibly"), thereby eliminating potential exceptions. Thus, to demonstrate the definition's counterfactuality, one need provide only a single, specific example of a "God-like being" who possesses only SOME (but not all) positive properties -- and mythology is FULL of them!
"Being God-like" (A3, T2) -- Gödel insists that such a property (or "essence") positively exists, yet offers no proof beyond his own assertion -- again, making it valid ONLY as a hypothetical premise.
"Essence" (D2, T2, D3) -- If one accepts that an individual has "essences" to "exemplify" its existence, one must FIRST presuppose that the individual actually exists -- which already establishes the individual's "necessary existence" BEFORE any "exemplification." The "necessary existence" of an individual ISN'T the exemplification of its essences, but an exemplification of a PRIOR PRESUMPTION of the individual's existence.
Throughout his argument, Gödel offers theorems that are highly speculative, definitions that are unsupported or outright counterfactual, and numerous examples of the logical fallacy of "begging the question" (wherein the expected conclusion is inherent in an argument's propositions). In the end, an argument is only as valid as its premises, and Gödel's are a nebulous, unsubstantiated, presuppositional mess.
*To view the pdf version of Gödel's theorem, including the mathematical "translation," visit
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