Two False Arguments for God’s Existence


Two false arguments for God’s existence are an old one, the a priori argument of St. Anselm, and a current one, the argument from probability. Both arguments are false because both arguments are logical. That is, they are purely logical because they are initiated by definitions and yield conclusions from an analysis of those definitions. It is not possible to draw a conclusion about existence by proposing and then analyzing a definition.

A Valid Argument from St. Anselm

St. Anselm of Canterbury was greatly impressed with God’s goodness. He argued for God’s existence, apart from revelation, on the basis of the limited, but graded goodness of the things within our experience.

Due to their limitations in goodness, the material entities whose existence we experience fail to explain their own goodness (and by implication their own existence). There must exist a fully good Being who explains His own goodness and the limited goodness of the entities that we experience. There must exist a Being Who of His nature is goodness itself and concomitantly existence itself. This is the God of revelation, the I Am. This argument is essentially the Fourth Way of Aquinas.

The five ways of Aquinas reach the same conclusion, that of the existence and identity of an immaterial being based on our experience of the existence of material entities, from five different ways of argument or perspective.

False Argument One: St. Anselm’s A Priori Argument

The a priori argument begins with the definition of God as a Being greater than which it is impossible to conceive. It concludes from an analysis of the definition: Such a Being must exist because if it did not, one could conceive of a greater by explicitly, rather than implicitly, including existence in the definition.

Besides being a purely logical argument, the argument fails because God is not the greatest simply by comparison to others. He is infinite in his own nature, which is identical to his existence.

A contemporary of St. Anselm noted that the a priori argument fails in every category of greatness, when it is formulated in terms of the things, whose existence and greatness we know through our experience; e.g., the concept of a perfectly beautiful island does not require its existence. Therefore, the premise is not true. (Ref: A Short History of Philosophy, by F.J. Thonnard, A.A. p. 310-320)

A Critique of the A Priori Argument from an Aristotelian Perspective

The contemporary criticism just mentioned suffers from the fact that an island is not an entity, but rather a conglomerate of entities. Thus, the concept of an island is not that to which existence would bear an immediate relationship. A better example, from an Aristotelian perspective, would be a substantial form, which when it informs particular matter, results in a singular entity, such as a tiger. Tiger does not exist in itself as a principle or as a concept. Tiger exists as the intelligible principle, as the substantial form, of a particular tiger as it informs particular matter thereby forming a living entity, a composite of form and matter. Tiger also exists as a concept in the human mind, which has the power to abstract the mental concept of tiger from the human sensual experience of an existing tiger.

The remarkable fact in the context of the a priori argument is that the greatness of tiger is not realized through the existence of a tiger. Quite the opposite is true. The greatness of tiger is fundamentally limited due to the tiger’s existence. Existence is the result of the union of the substantial form of tiger with particular matter. This tiger, this existing tiger, is a limited expression of the fullness, the greatness of tiger as a substantial form, as an intelligible principle.

St. Anselm’s Rebuttal

St. Anselm’s rebuttal to his contemporary was that the a priori argument does not apply to created beings, but to God alone. The problem, however, is not solved by this rebuttal for two reasons. God is not that Being one greater than which cannot be thought to exist. God is that Being whose nature and act of existence are identical. He is the I Am. (There could be no greater, but that is not His identity, His essence.)

The second reason is that the intelligible principle of an entity is known by the human mind after the fact of one’s sensual experience, such as the experience of a tiger. Nothing that exists within our experience is God. Therefore, we cannot start a process of philosophical inquiry with a definition of God. Philosophically, both the nature of God as well as His existence are first known simultaneously in the conclusion of an argument, which seeks the explanation of the existence of material entities, which are within the scope of our experience.

Lest we think that a priori arguments are medieval, a cosmologist at Cal Tech has proposed an a priori argument for the non-existence of God.

Argument Two: A Preliminary Consideration of the Two Disparate Meanings of Probability

There are two disparate meanings of the word probability. One is the acknowledgment of the lack of certitude of one’s personal subjective judgment. The other is a ratio, defined in the mathematics of sets, namely, the ratio of a subset to a set.

Because it is often dressed in the garb of mathematical lingo, the lack of subjective certitude is often mistaken for the purely logical concept of mathematical probability. This lack of personal human certitude is also often presented as relevant to material events or outcomes. It is then taken to be a characteristic of material events, rather than what it is: one’s personal subjective opinion and one’s certitude about material events, which opinion and certitude are irrelevant to material events.

The other meaning of probability is solely within the confines of the logic of mathematics. Probability is the ratio of a subset to a set. A simple demonstration that this is confined to logic is the fact that the ID’s of elements in sets vis-a-vis mathematical probability are solely nominal. The mathematical probability relationships of a set consisting of two red beans and three green peas are identical to the mathematical probability relationships of a set of two bay horses and three pink elephants. In contrast, material relationships among material things depend upon their material properties.

There is a fascinating instance in which an NFL referee demonstrated a greater insight into a wave as a mathematical probability function than did a university physicist, who, rather than citing a mathematical wave, cited personal opinion as a mathematical probability function.

False Argument Two: The Argument from Probability

The argument from probability proposes an inverse relationship between intelligibility and probability. The simpler a material event or structure, i.e. the lower its intelligibility, the more readily it can be explained by probability. In other words, the lower the intelligibility, the higher the probability and vice versa.

This would be simply confounding human judgment and mathematical probability, except for the argument itself. The argument requires an explanation other than probability for instances of very low probability.

The argument itself identifies simple material events and structures of high probability as explicable in themselves as coincidences. However, the argument identifies complex material events and structures of low probability as inexplicable in themselves. They require an explanation other than coincidence, other than probability, namely an intelligent agent external to the material events or structures.

One advocate of the argument from probability stated:

The odds against all five of the anthropic coincidences happening randomly is [sic] exceedingly and almost unimaginably improbable. Most reasonable and responsible individuals would not attribute this to random occurrence (because the odds are so overwhelmingly against it), and so, they look for another explanation which is more reasonable and responsible. (How Contemporary Physics Points to God)

Critique of the Argument from Probability

The most incisive and direct critique of the argument from probability was presented by Richard Dawkins. He pointed out that any two values of a variable that is continuous over its range of definitions differ in degree, not kind. It is impossible to distinguish values of probability of a kind that serves as an explanation in itself from values of a kind of probability that cannot serve as an explanation in itself.

In The God Delusion, pages 120-122, Dawkins violated this principle by distinguishing two different kinds of improbability: the “prohibitive” kind and the “non-prohibitive” kind. However, Dawkins’ personal inconsistency doesn’t invalidate the principle he enunciated.

Another illustration that the validity and quality of a probability do not depend upon its numerical value is in the comparison of two probabilities. Consider 100 different elements in a linear sequence. The probability of any specific element of the 100 different elements in a given location in the linear sequence is one percent, or 1.0 × 10-2. There are 100 factorial or 9.3 × 10157 different linear sequences of 100 elements each. The probability of any specific linear sequence is 1.07 × 10-158. Both numerical values of probability are equally valid. They do not differ in kind, i.e. in quality. Both are equally explicable within the context of probability, which is that of pure logic, not the context of material reality. It matters not if we identify the 100 elements using nominal IDs, which in other contexts would identify material entities, events, or outcomes by their material natures and properties.

Sets of 9.3 × 10157 and 100 (or 1× 102) are equally valid in logic, but only the latter could be materially represented on earth, which has a mass slightly less than 6 × 1024 kilograms. At 45g per golf ball, 100 golf balls would have a mass of 4.5 kilograms. At 45g per golf ball, 9.3 × 10157 different linear sequences of 100 golf balls would have a mass of 4.1 × 10158 kilograms. Reducing the mass of 100 golf balls to a total of one nanogram would reduce the mass of the set of sequences to 9.3 × 10148 kilograms.


It is not possible to deduce the existence of anything, including God, from an argument whose premises are only logically defined. This is so in two false arguments for God’s existence.

One is an a priori argument beginning with a definition of God, which, as an initiating premise, can only be logical because nothing within the human experience is God. Humans know the definition or nature of an entity through the experience of its existence. Any definition of God as an initiating premise in proof of God’s existence is arbitrary and meaningless in such a context.

The other is the argument from probability, where probability is merely a logical definition in the mathematics of sets, in which the IDs of sets, subsets, and elements are purely nominal. Thus, even if the IDs are ostensibly material in name, they exhibit no material properties within the relationships of probability.

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5 thoughts on “Two False Arguments for God’s Existence”

  1. I believe your critique of St. Anselm’s a prior argument is weak, because revelation provides the ‘I Am’ as a starting point for a definition of God. Of course God is incomprehensible. Therefore St. Anselm was careful to phrase his argument in the Proslogion as ‘that than which a greater cannot be thought,’ not ‘the greatest being that can be thought.’ Kudos to you for supporting Aquinas’ Five Ways! IMO the Cal Tech argument is very weak, because evil or the bad includes the privative, which can hardly form a lattice or well-ordered set without attaching to an existing Good, presupposing at least the Five Ways, and IMO St. Anselm’s arguments too.

  2. Since the 1940’s, a number of scholars have taken seriously St. Anselm’s reasoning for the existence of God. I believe the first to publish on it was philosopher Charles Hartshorne and about the same time mathematician Kurt Gōdel began work on it.

  3. Actually, the biggest weakness in St. Anselm’s Ontological Argument is that God transcends human conceptions. We can use analogies for God, and we can say what He is not, and we can note some things He has done or how He relates to us, but “I AM WHO I AM” is not fully known even to those with the Beatific Vision.

    1. I suspect St. Anselm would answer that he did not mean “greater than which you or I cannot conceive”, since we are indeed limited, but greater than which any being, actual or hypothetical, could conceive. This, however, sounds a lot like “greater than which even God cannot conceive”, but that would mean his argument simply begs the question.

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