Saturday, August 23, 2014

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The Divine Non-Contradiction Principle and Why it Fails

by Francois Tremblay



Short version:

It has become commonly accepted in discussions of theistic arguments that a god cannot be defined as “being able to make contradictions”. However, everything that a god does in the universe must either follow the laws of nature, or be a contradiction of the laws of nature.

Therefore, either a god cannot create the universe or effect miracles, or a god can do impossible things. The latter is the only desirable solution for theists, although it opens the god-concept to even more strong-atheistic arguments.


Materialist Apologetics consists of using the idea of divine causation to demonstrate that theism contradicts features of human understanding. This argument can be expressed in the following syllogism:

Posit X is a feature of human understanding.

  1. X is necessary or has a necessary part.
  2. If theism is true, then divine creation obtains.
  3. If divine creation is true, then all in the universe is contingent to God’s act of creation, and nothing in the universe is necessary.
  4. If theism is true, then no X can be necessary or have a necessary part. (from 2 and 3)
  1. Theism is false. (from 1 and 4)

    The usual theistic strategy against specific materialist arguments, such as the Transcendental Argument for the Non-existence of God, is to try to deconstruct (3). The most common objection is that the features of human understanding are also an inherent part of a god’s nature. I address this rather weak objection in my article on Materialist Apologetics.

    However, I can see a much more serious objection to (3). It comes from the re-definitions that the term “omnipotence” has suffered over the years. Virtually all theologians now agree that the following restriction is necessary:

    (R) Omnipotence does not include actions with illogical results.

    This is used, for instance, to explain why we can say that:

    (P1) It is not within the purview of omnipotence to be able to create a square-circle.

    Since a square-circle is illogical, we must reject it as a possibility. This could also be used as a way to disprove (3), given that a god could not change necessary features of human understanding, because that would be illogical.

    However, theologians do not think that this argument refutes such propositions as:

    (P2) God created the universe.

    This seems reasonable at first glance. However, we then fall upon a problem, since the following proposition is also true from the materialist standpoint:

    (P3) The existence and nature of the universe is a logical necessity.

    And from there proceeds:

    (P4) Square-circles are a contradiction, due to the necessary laws of logic.

    But (P3) contradicts (P2). For it is no less of a contradiction to claim that “God created the universe”, than it is to say that “God created a square-circle”. Both are contradictions – the former because of the necessity of the universe, and the latter because of the nature of squares and circles. If (P3) is false, then so is (P4), due to the argument of Materialist Apologetics. So® does not affect Materialist Apologetics at all.

    The underlying problem of® is called the analytic-synthetic fallacy. This fallacy explains why theologians think that® agrees with (P1), and yet do not think that® contradicts (P2).

    The analytic-synthetic fallacy consists of classifying facts into two category: analytic, or “pure logic”, and synthetic, or empirical. In this fallacy, analytic facts are considered certain but unuseful, and synthetic facts are considered useful but uncertain. This kind of thinking is used by skeptics who try to deny the efficacy of reason by setting logic apart from all other methods.

    The fallacy reflects the discredited ideology of rationalism, that “real truth” can only come from logic detached from any empirical considerations. In reality, we know that this is a fallacy because, from the materialist viewpoint, there is only one kind of existent – material – and only one kind of fact – empirical. Logic is not a special method which gives us infallible knowledge above and beyond sense perception: rather, we find logic by sense perception, just like any other fact.

    Logic is our method of non-contradiction. Logic not informed by direct empirical facts is a method used on nothing. Direct empirical facts without logic can lead to contradictory conclusions. It is impossible for cognition to exist without both.

    As such, there is no epistemic difference between the following facts:

  2. Ice is a solid.
  1. Ice floats on water.

    While (1) is definitional, and an argument using it could be described as “pure logic” by skeptics, it is no less a result of sense perception than (2), and they both designate and are obtained by material facts and processes. Therefore, given®, a god can no more change (2) than it can change (1). Theologians would argue that (1) is analytic and (2) is synthetic, but we must reject such a distinction because it actually designates no difference that exists in reality. There is likewise no difference between (1) or (2) and “A square-circle is a contradictory assemblage that is both a square and a circle”.

    The theologian may try to escape our refutation by limiting the reach of his restriction:

    (R2) Given the existence of a universe containing logic as a property, omnipotence does not include actions with illogical results.

    But this is no help at all. For one thing, it leaves the existence of the universe qua universe unjustified. But most importantly, it still contradicts the uniformity of nature, and by virtue of this, principles and absolutes. For if a god can intervene in the universe at all, it must necessarily contradict the uniformity of nature. If a god can do the merest little thing that a human can do, such as moving an object from one place to another, then it contradicts logic. We can do so because our actions are part of the necessary nature of reality, but a god’s actions are not.

    Furthermore, it does not put a god off the hook, so to speak, because the Creation act contains all spacetime. Therefore we cannot make any distinction between a god creating the universe, and a god controlling the parts of the universe.

    Obviously, (R) is not a proper refutation of Materialist Apologetics. But the fact that® entails incoherency has much more serious consequences on atheology. Not only does it give us a more direct avenue to disprove the possibility of omniscience, and define what it means to have the capacity to act in a divine sense, but it also redeems contradiction-based arguments which we thought were lost to sophisticated atheology.

    Now granted, it does not rehabilitate the old horse “can God make a rock he cannot lift?. Atheists who think this shows a contradiction are wrong, because they confuse process and result. All that omnipotence says is that a god has infinite capacity to act, not that it can effect all results. God’s rock-making capacities are equal to those of his lifting, that is to say, infinite. So it must be that God cannot make a rock he cannot lift.

    As such, the “rock he cannot lift” argument is not justified because it tries to create an internal contradiction, and so does not include examples of hypothetical illogic in the universe. But the following argument is now justified:

  2. If a god is omnipotent, then it can create a square-circle.
  3. Square-circles are contradictory, and therefore cannot exist.
  1. A god cannot exist. (from 1 and 2)

    This argument is now justified because it uses an external example of illogic – square-circles – to disprove God. So as you can see, incoherency arguments are now vastly expanded, if you are convinced by the argument I have presented. I think that the conclusion is intuitive, justified and inevitable.

    A common objection I get back, regarding the result of the argument, is that to speak of a being that is beyond logic is to speak of something illogical by definition. That if we are to discuss the issue at all, we have to ignore this fact completely. But this is not convincing, since all the other properties of the god-concept are also illogical – Creator, omnipotent, omnibenevolent, personal, supernatural, are all contradictory terms, by themselves, in combination, and combined with facts of reality. There is no difference between these and “can effect contradiction”: either way, the god-concept is and remains meaningless. This does not, however, prevent meaningful discussions.

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