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It boils down to 'a priori knowledge'. The agnostic restricts themselves to the material plane and therefore requires empirical evidence. The deist is neutral to the material plane and therefore does not restrict themselves to the material plane to empirics.
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Since we both agree that this is the difference in between the method of an agnostic and a deist, I think it is interesting to note that this is also the difference between the alchemists and chemists from the seventeenth and eighteenth centuries. The alchemists derived axioms (a priori truths) about the nature of the world using Aristotelian reasoning, and then they tried to fit their observations within their understanding of the world. The chemists on the other hand used induction, where by they would derive axioms directly from their observations and then test these axioms to gain a further understand the world. Not sure I really have a specific point with this but there are obviously a lot of parallels, and I find it interesting.
Anyway, while we seem to have found a difference in their methods we haven't really addressed the differences in their motives. Looking at the above discussion of alchemist, there seems to be a definite difference in the kind of truth that the alchemist sought versus what the chemists sought. For instance, the alchemists wanted a more certain understanding of the world, while the chemists were willing to accept a contingent understanding of the world. I think it goes without saying that an agnostic satisfies himself with a contingent understanding. As for a deist wanting certain truth I can't say but I wouldn't be surprised.
Another interesting thing I learned about a priori knowledge comes from Kant's idea of a categorical imperative. The categorical imperative, if your not familiar with it, is basically a version of the golden rule. Kant, while not a deist, used deductive logic quite heavily in his proof of the categorical imperative. In his proof he makes use of an additional rule of inference, not accepted by most people, which basically says: anything people universally accept is equivalent to an objective fact. On the surface this seems absurd or at least highly questionable. However, I've been thinking about this and it seems to me, if you break up the world into a social and material realm it kind of makes sense. If you were reasoning about a social issue, perhaps morals, then if any particular desire was held by everybody concerned it logically would be indistinguishable from an objective fact. Speaking in terms of how you would treat this statement in a deductive logic system, of course. In this way, Kant seems to prove that synthetic a priori knowledge is achievable in the social realm.
At least this is how I saw it.
All this makes me wonder if deists might not be more inclined think about social issues, while an agnostic is more concerned with natural issues. Perhaps, these motivational differences are what prompt the difference in their methods.