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Saturday, February 20, 2010

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A thoughtful argument, but it is deficient because of the possible ambiguity of the word "depends."

When we say that y "depends" on x, we imply that x is a necessary cause of y (although, of course, not necessarily a sufficient cause). For the past 200-300 years, most Westerners have assumed that "cause" has a single meaning. From the time of Aristotle to the 17th or 18th centuries, however, the common practice was to distinguish between several kinds of causality: formal, material, efficient, final, and, in some cases, exemplary.

The idea that "cause" does not have a uniform meaning, and that there are four or five types of causality, is still the norm among Catholic and Shia Muslim philosophers and theologians, so it cannot be easily dismissed. Furthermore, "classical" formulations of Christian doctrine were made assuming this manifold sense of "cause." Any discussion of them needs to take this position into account.

Your example, taken from set theory, is an instance of formal causality. For philosophers and theologians in the "classical" tradition (Catholics, Shias, certain kinds of Protestants, etc) this isn't a big revelation.

"Classical" arguments for the existence of God, however, consider "cause" as efficient, final or exemplary (Duns Scotus' "On the First Principle" argues explicitly for all three). It is in those senses of "cause" that a necessary being cannot depend on another. In fact, when Ibn Sina (Avicenna) makes the distinction between "contingent" and "necessary" existence prominent in philosophy, it is this kind of causal dependence he has in mind. In fact, he defines "existing necessarily" vs "existing contingently" as existing through one's self vs through another ("per se" vs. "per aliud", in the Western phrasing).

Thomas Aquinas would reply to your argument that "a necessary being cannot depend on another" is true in the cases of efficient, final and exemplary causality, not so in the case of formal causality.

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