God and entailment
In his Warranted Christian Belief, Alvin Plantinga writes (p. 332, note 4):
if God is a necessary being, as most of the Christian tradition has thought, then his existence is entailed by the existence of my experience, because entailed by the existence of anything at all.
What is at stake here is that any necessary proposition seems to be entailed by no matter what set of propositions, if one construes ‘entailment’ as follows:
- a proposition p is entailed by a set A of propositions iff it is not possible for A to be true and p false. (Where ‘a set of propositions is true’ is shorthand for ‘all propositions in that set are true’ – sets of propositions are not literally true.)
Now, Edgington 2004 argues that this is not quite right, and I concur. Why? Well, take this example, assuming Kripke is right about the necessity of identity and that this is one of those cases:
Phosphorus is bright.
Therefore, Venus is bright.
Anyone who does not know that Phosphorus is Venus fails to see that this argument is valid. And is that person wrong? Arguably, she is not. She makes no reasoning mistake; she errs not in her logic, but rather in her geography. Presumably, a mistake in geography is not eo ipso a mistake in logic.
And yet, assuming Kripke and all that, it is not metaphysically possible for the premise to be true and the conclusion false. Thus, if we do not amend the standard definition, we are forced to say that the argument is valid after all.
The proposed amendment (or my amendment of Edgington’s proposed amendment) is this:
- an argument is valid iff (a) it is not possible for its premises to be true and its conclusion false and (b) we can know that a priori.
Thus, the argument above is not valid precisely because the agent does not know a priori that it is not possible for the premise to be true and the conclusion false because to know that one has to know that Phosphorus is Venus, and this in turn is something you can know only a posteriori (in standard conditions).
Lets go back, then, to Plantinga’s thought. Assume that God exists necessarily; does it follow that for any proposition p, p entails that God exists? Not if one does not know a priori that God exists. I for one do not know that because I am not lucky enough to feel the internal instigation of the Holy Ghost and my sensus divinitatis is not working as it should, which is, according to Plantinga, the ways one can have a warranted belief that God exists.
However, assume that an agent does have her sensus divinitatis working fine, or that she can feel the internal instigation of the Holy Ghost. Does that constitute a priori knowledge that God exists?
I am not sure what Plantinga thinks about this, but I guess it is a priori knowledge only if you construe it negatively in terms of not involving empirical input, but not if you construe it more positively as a sort of rational intuition. The knowledge of God given by faith is not obviously a priori, on Plantinga’s Aquinas/Calvin model. Thus, it is not as clear as Plantinga makes it sound that God’s existence, assuming he exists necessarily, is entailed by “anything at all”.
- Edgington, D. 2004. Two Kinds of Possibility. Aristotelian Society Supplementary Volume 78:1–22.
- Plantinga, A. 2000. Warranted Christian Belief. Oxford: Oxford University Press.