William Lane Craig uses Hilbert's hotel in an attempt to illustrate the impossibility of an existing actually infinite multitude, but I find several serious gaps in his arguments which, in my judgment, prevent them from having any force. His approach takes two forms: First, he claims that certain logical contradictions follow from the existence of actual infinites; second, his intuition tells him that an existing infinite multitude is absurd. In response, I want to resolve the alleged contradictions, and argue that intuition is an unreliable guide to the possibility or impossibility of an existing actual infinite.
Saturday, January 28, 2012
Sunday, January 1, 2012
WLC suggests we characterize objective morality in terms of God's nature. In particular, he suggests a form of DCT, that "God's own nature is the standard of goodness, and his commandments to us are expressions of his nature" (On Guard, pp135-6). The obvious reply here is that we can conceive a God whose commandments are morally wrong; so for instance we can envision a God who expresses his nature by commanding, say, a father to sacrifice his son. Clearly this would be an immoral act, and since definitions are true essentially it shows that morality is not defined by God's nature. WLC anticipates this sort of objection, but complains that the envisioned scenario is "logically impossible," on par with suggesting that a square can also be a circle (p136). On his view, of course, that's true enough---but if the contradiction only manifests when we assume DCT in advance, then that just goes to show that DCT is wrongheaded. Since we know human sacrifice is wrong by our moral intuitions, and since we appear to be able to coherently conceive (apart from DCT) a God who expresses his nature by commanding human sacrifice, then clearly morality does not essentially accord with expressions of God's nature.