Be sure to check out Goodness Over God, the counter-apologetics podcast hosted by myself and philosopher Michael Long!

Sunday, May 15, 2011

Grim's Cantorian Argument Against Omniscience

Philosopher Patrick Grim since the early 1980s has advanced an argument against the existence of God which turns on an incoherence he sees in the concept of omniscience, an essential property of God as understood by most orthodox incarnations of the Abrahamic religions.[1] It runs as follows: There does not exist a set T of all distinct truths. For suppose towards a contradiction that T exists. Let f be a mapping from T into the set P(T) of all subsets of T, and consider the subset S of T of every truth q which is not contained in the set f(q). By definition of S, no truth q is mapped by f to S, and we conclude that f is not surjective. Since f is an arbitrary mapping from T into P(T), it follows that no such map is surjective. Now define a map g from P(T) into T. For each subset A of T (where A is a member of the set P(T)), define g(A) by the truth expressed by the sentence "A is a subset of T." Since every member of P(T) is distinct, then g maps them to distinct truths, which is to say g is injective. So there is an inverse map which induces a map g' from T into P(T), where g' is surjective. This contradicts our conclusion that no such map is surjective. It follows that our assumption must be false---that there can be no collection T of all distinct truths. However, in order to conceive the omniscience of God we must conceive that he knows all distinct truths. Since we can always conceive of known truths as sets, then conceiving the omniscience of God requires that we be able to conceive all truths as a set. Yet we have already shown that there is no such set, and so we cannot conceive all truths in this way. Therefore we cannot conceive the omniscience of God. Since omniscience is an essential property of God, this means we cannot conceive of God at all, and this prevents us from ever affirming that God exists.

Sunday, May 1, 2011

Goodness Over God counter-apologetics podcast

I'm pleased to announce that philosophy graduate Michael Long and I have successfully launched the counter-apologetics podcast Goodness Over God, where we tackle religious and philosophical issues on a weekly (more or less) basis. We would like to have guests as often as possible, including but not limited to religious believers who wish to defend their views in a civil and friendly environment. So if you would like to participate, feel free to drop us a line at the following email address:

Here is a list of the episodes so far:

Episode 05 (2011 Apr 30) - God as an Explanatory Hypothesis and Causality (with special guest Rachael Morris)

Episode 04 (2011 Apr 23) - Easter, Miracles, and History

Episode 03 (2011 Apr 09) - Hell and Justice

Episode 02 (2011 Apr 05) - Secular Ethics, Theistic Ethics, and Faith

Episode 01 (2011 Mar 31) - Plantinga's Modal Ontological Argument

(Please note that we originally started under the name "Truly Free," so we introduce ourselves that way in our first three podcasts.)

You can also check out the Goodness Over God blog, where we discuss various issues related to the podcast.

If you don't like downloading mp3s, you can stream the podcasts directly from the website, or from right here!

And remember, if you want to be a guest, go ahead and email us at: We can discuss just about anything religion- or philosophy-related. The format is also flexible---we can either have a nice informal conversation, or we can have a more structured (but still friendly) debate, and everything in between. It's up to you!

Enjoy the shows!