Patrick Grim’s Cantorian argument against the set of all Truths

We can concede that there is no set-theoretic semantic which allows us to quantify over all such propositions as are true. However, this isn’t necessarily a problem for omniscience since instead of affirming that “God knows all and only true propositions” we can say that “for as many propositions as are true God knows them, and for as many propositions as are false God does not believe them.” That articulation entirely avoids involving set-theoretic semantics because it doesn’t presuppose that there is a determinate set of all propositions which God knows.

Now, suppose that the Cantorian Atheist wishes to press that this latter articulation doesn’t make it clear how it could be logically possible that God be omniscient, since omniscience is having the property of knowing everything true (and not believing anything false). I don’t think that’s legitimate, but suppose we accepted for the sake of argument, or even just for the sake of dialectical charity, that such a criticism has some weight to it and deserves a more robust response on the part of the defender of omniscience. I think we could simply reject talk of logically possible worlds as maximally consistent sets of propositions, since no such set as the set of all true propositions exists (i.e., the actual world would not be a logically possible world, and strictly speaking no logically possible world would be logically possible in the absence of a new set-theoretic semantics which allows quantification over such a set as the set of all true propositions).

We should instead adopt the convention of speaking about logically possible worlds as maximally specific single propositions, such that a logically possible world is one maximally specific proposition from which can be derived an indeterminate number of mutually consonant propositions. This not only provides a model according to which omniscience can be understood, but it also accords well with classical Christian Theology which maintains that God’s knowledge is intuitive and grasps the truth as a simple whole, not comprised of discrete parts.


About tylerjourneaux

I am an aspiring Catholic theologian and philosopher, and I have a keen interest in apologetics. I am creating this blog both in order to practice and improve my writing and memory retention as I publish my thoughts, and in order to give evidence of my ability to understand and communicate thoughts on topics pertinent to Theology, Philosophy, philosophical theology, Catholic (Christian) Apologetics, philosophy of religion and textual criticism.
This entry was posted in Apologetics, Epistemology, Philosophical Theology, Philosophy, Philosophy of Religion, Theology. Bookmark the permalink.

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