David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Philo 6 (1):49-58 (2003)
John Post criticized Richard Gale’s work for neglecting to consider Patrick Grim style arguments against quantification over all propositions. Such arguments would throw into question the possibility of an omniscient being and destroy the Weak Principle of Sufficient reason that Gale and I have defended, the principle that each true or at least contingently true proposition is possibly explained. Post mounts a Grim-style argument against quantification over all propositions. However, I show that, despite assurances to the contrary, Post’s argument depends on the assumption that if one can quantify over all propositions, then there is a set-like collection of all propositions. I show this by demonstrating that Post’s argument implicitly uses the Schroeder-Bernstein theorem from set theory. On the other hand, a linguistic version of Post’s argument, while not directly relevant to the theological cases, gives rise to an independently interesting paradox resembling Berry’s
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