Brian Bosse
"The Brain"
Hello Eveyone,
Sometime last summer there was a discussion regarding the question: Can God create a stone too heavy to lift? Someone was good enough to provide two articles dealing with the subject. One article was written by a guy named Wade, and was critical of the other article written by Mavrodes. At the time I concluded that Wade's criticism was good, and shelved the two papers. Recently, I went back to the two papers, and reviewed my thoughts. I have now come to the contrary conclusion that Wade did not understand Mavrodes' argument and that Mavrodes was spot on. I have produced my own defense against the skeptic's question, and would like your thoughts and/or criticisms.
The Problem
Question: Can God create a stone too heavy for Him to lift?
At the heart of this question is a skeptic’s argument against the existence of an omnipotent God. The essence of the argument is as follows:
Case (1) – If God exists, then He is omnipotent. If He is omnipotent, then He can create a stone too heavy for Him to lift. If He can create a stone too heavy for Him to lift, then it is possible for there to be a stone God cannot lift. If it is possible for there to be a stone God cannot lift, then God cannot be omnipotent. If God is not omnipotent, then God does not exist.
Case (2) – If God exists, then He is omnipotent. If He is omnipotent, then He can create a stone too heavy for Him to lift. If He cannot create a stone too heavy for Him to lift, then God is not omnipotent. If God is not omnipotent, then God does not exist.
Since cases (1) and (2) exhaust all possibilities, and since both cases conclude that God does not exist, then the inevitable conclusion is that God does not exist.
The Solution
It is clear from the Scriptures that God is omnipotent and in some sense limited. For instance, the Scriptures teach that God cannot lie and that He cannot sin. In fact, God cannot do anything contrary to His character. As such, when the Bible speaks of God being omnipotent it does not understand ‘omnipotence’ to mean “able to do anything.” St. Thomas Aquinas pointed out that God’s omnipotence should only be construed to range over objects, actions, or states of affairs whose descriptions are not self-contradictory.[1] George I. Mavrodes[2] clarifies this point when he says, “My failure to draw a circle on the exam may indicate my lack of geometric skill, but my failure to draw a square circle does not indicate any such lack. Therefore, the fact that it is false (or perhaps meaningless) to say that God could draw one does no damage to the doctrine of His omnipotence.”[3] St. Thomas Aquinas and Professor Mavrodes have outlined a possible refutation of the skeptic’s argument. If it can be shown that the object – a stone too heavy for God to lift – is a self-contradictory object, then God’s not being able to create such an object “does no damage to the doctrine of His omnipotence.” In order to make this determination we need to explain what we mean when we say an object is self-contradictory.
Self-Contradictory Objects
It seems to be fairly uncontroversial that a square circle would be a self-contradictory object. As such, let’s analyze why such an object is considered self-contradictory. Assuming Euclidean Geometry, the following are definitions for a circle and a square…
Square: A regular polygon with four sides.
Circle: A set of points in a plane all equal distant from a given point.
When we say that object ‘x’ is a square circle we are in effect asserting that the object is a regular polygon with four sides and at the same time a set of points in a plane all equal distant from a given point. The can be symbolically represented as…
(1) (S(x) ∧ C(x))
From (1) we can derive the following propositions:
We have derived a contradiction. (c) contradicts (a). However, (c) is based only on the assumption that there is another point whose x coordinate is r. What happens if we assume the opposite, namely that there is not another point whose x coordinate is r? That means there is only one such point, and this contradicts (b). What we have shown is that given (1) we can derive contradictions. In short, we were able to show that…
(2) (S(x) → ¬C(x))
This gives us the key insight into what we mean when we say that an object is self-contradictory. An object is self-contradictory if and only if the object has two properties that are contradictory.
The Incoherent Stone
Consider the object that has the following two properties: (1) ‘stoniness’, and (2) “too heavy for God to lift.” In order for this object to be self-contradictory, then (1) must be inconsistent with (2) in some sense. From a Christian perspective, all things have been created by God and are sustained by Him (Col. 1:16-17). As such, any object that is a stone is an object created by God. All objects created by God are objects that can be lifted by God. Therefore, any object that has the property of ‘stoniness’ is an object that can be lifted by God. From this, it can be shown that “a stone too heavy for God to lift” is self-contradictory. The Christian argues (via Mavrodes and Aquinas) that since such self-contradictory objects cannot exist, then God cannot create such objects, and God’s not being able to create such objects in no way militates against His omnipotence.
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[1] St. Thomas Aquinas, Summa Theologica, Part I, Q. 25, Art. 3.
[2] Dr. Mavrodes, a former Professor of Philosophy at the University of Michigan, has served as President of the Society for Philosophy of Religion and the Society of Christian Philosophers, and as a member of the Executive Committee of the American Theological Society. He has held editorial positions with American Philosophical Quarterly, Faith and Philosophy, and The Reformed Journal.
[3] George I. Mavrodes, “Some Puzzles Concerning Omnipotence,” The Philosophical Review, Vol. 72, No. 2. (Apr., 1963), pp. 221
Sometime last summer there was a discussion regarding the question: Can God create a stone too heavy to lift? Someone was good enough to provide two articles dealing with the subject. One article was written by a guy named Wade, and was critical of the other article written by Mavrodes. At the time I concluded that Wade's criticism was good, and shelved the two papers. Recently, I went back to the two papers, and reviewed my thoughts. I have now come to the contrary conclusion that Wade did not understand Mavrodes' argument and that Mavrodes was spot on. I have produced my own defense against the skeptic's question, and would like your thoughts and/or criticisms.
The Problem
Question: Can God create a stone too heavy for Him to lift?
At the heart of this question is a skeptic’s argument against the existence of an omnipotent God. The essence of the argument is as follows:
Case (1) – If God exists, then He is omnipotent. If He is omnipotent, then He can create a stone too heavy for Him to lift. If He can create a stone too heavy for Him to lift, then it is possible for there to be a stone God cannot lift. If it is possible for there to be a stone God cannot lift, then God cannot be omnipotent. If God is not omnipotent, then God does not exist.
Case (2) – If God exists, then He is omnipotent. If He is omnipotent, then He can create a stone too heavy for Him to lift. If He cannot create a stone too heavy for Him to lift, then God is not omnipotent. If God is not omnipotent, then God does not exist.
Since cases (1) and (2) exhaust all possibilities, and since both cases conclude that God does not exist, then the inevitable conclusion is that God does not exist.
The Solution
It is clear from the Scriptures that God is omnipotent and in some sense limited. For instance, the Scriptures teach that God cannot lie and that He cannot sin. In fact, God cannot do anything contrary to His character. As such, when the Bible speaks of God being omnipotent it does not understand ‘omnipotence’ to mean “able to do anything.” St. Thomas Aquinas pointed out that God’s omnipotence should only be construed to range over objects, actions, or states of affairs whose descriptions are not self-contradictory.[1] George I. Mavrodes[2] clarifies this point when he says, “My failure to draw a circle on the exam may indicate my lack of geometric skill, but my failure to draw a square circle does not indicate any such lack. Therefore, the fact that it is false (or perhaps meaningless) to say that God could draw one does no damage to the doctrine of His omnipotence.”[3] St. Thomas Aquinas and Professor Mavrodes have outlined a possible refutation of the skeptic’s argument. If it can be shown that the object – a stone too heavy for God to lift – is a self-contradictory object, then God’s not being able to create such an object “does no damage to the doctrine of His omnipotence.” In order to make this determination we need to explain what we mean when we say an object is self-contradictory.
Self-Contradictory Objects
It seems to be fairly uncontroversial that a square circle would be a self-contradictory object. As such, let’s analyze why such an object is considered self-contradictory. Assuming Euclidean Geometry, the following are definitions for a circle and a square…
Square: A regular polygon with four sides.
Circle: A set of points in a plane all equal distant from a given point.
When we say that object ‘x’ is a square circle we are in effect asserting that the object is a regular polygon with four sides and at the same time a set of points in a plane all equal distant from a given point. The can be symbolically represented as…
(1) (S(x) ∧ C(x))
From (1) we can derive the following propositions:
(a) Given object M, if (r, s) is a point on M, then there is at most one more point on M whose x coordinate is r. (This follows from the property of being a circle.)
(b) Given object M, if (r, s) is a point on M, then there is at least one more point on M whose x coordinate is r. (This follows from the property of being a square.)
(c) Given object M, if (r, s) is a point on M, then if there is another point whose x coordinate is r, there are an infinite number of such points.
(b) Given object M, if (r, s) is a point on M, then there is at least one more point on M whose x coordinate is r. (This follows from the property of being a square.)
(c) Given object M, if (r, s) is a point on M, then if there is another point whose x coordinate is r, there are an infinite number of such points.
We have derived a contradiction. (c) contradicts (a). However, (c) is based only on the assumption that there is another point whose x coordinate is r. What happens if we assume the opposite, namely that there is not another point whose x coordinate is r? That means there is only one such point, and this contradicts (b). What we have shown is that given (1) we can derive contradictions. In short, we were able to show that…
(2) (S(x) → ¬C(x))
This gives us the key insight into what we mean when we say that an object is self-contradictory. An object is self-contradictory if and only if the object has two properties that are contradictory.
The Incoherent Stone
Consider the object that has the following two properties: (1) ‘stoniness’, and (2) “too heavy for God to lift.” In order for this object to be self-contradictory, then (1) must be inconsistent with (2) in some sense. From a Christian perspective, all things have been created by God and are sustained by Him (Col. 1:16-17). As such, any object that is a stone is an object created by God. All objects created by God are objects that can be lifted by God. Therefore, any object that has the property of ‘stoniness’ is an object that can be lifted by God. From this, it can be shown that “a stone too heavy for God to lift” is self-contradictory. The Christian argues (via Mavrodes and Aquinas) that since such self-contradictory objects cannot exist, then God cannot create such objects, and God’s not being able to create such objects in no way militates against His omnipotence.
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[1] St. Thomas Aquinas, Summa Theologica, Part I, Q. 25, Art. 3.
[2] Dr. Mavrodes, a former Professor of Philosophy at the University of Michigan, has served as President of the Society for Philosophy of Religion and the Society of Christian Philosophers, and as a member of the Executive Committee of the American Theological Society. He has held editorial positions with American Philosophical Quarterly, Faith and Philosophy, and The Reformed Journal.
[3] George I. Mavrodes, “Some Puzzles Concerning Omnipotence,” The Philosophical Review, Vol. 72, No. 2. (Apr., 1963), pp. 221