Chesterton claims in Orthodoxy that reason itself is a matter of faith since one needs to have faith that ones reason actually knows anything true. But what does this mean? True, discursive reasoning has to start somewhere, and one can’t have a starting point that isn’t seen as capable of showing us something true (even when we’re making a reductio ad absurdum) but where does faith come in to any of this?
Here’s an etymological argument: We need to have confidence that our starting points will work, but this confidence is a kind of fides. All confidence, or at least all confidence prior to reasoning, thus counts as faith (the same argument could be made from the fact that the first axioms must be credible, or even from our modern word “belief”). But then who or what are we having the faith in? The proposition? It certainly inspires no confidence as a proposition – since if it did we would have confidence in any proposition whatsoever. To say we have confidence in its credibility says no more than that we have confidence in it in virtue of its power to inspire confidence. Roars from the gallery, but nothing’s been said.
To solve this problem both Plato and Aristotle posited a power distinct from discursive reasoning (nous) that generated starting points. Both thought that one could develop this power though dialectic – and one of Aristotle’s longest books deals with precisely this. But both are also clear that there is always a gap between dialectic and the finding of the starting point. If, by way of comparison, you learn formal logic, then there’s no gap between what you know and the power to make a valid syllogism; but if you learn dialectic perfectly there will still be a gap between your arguments and the definition or credible starting point they are trying to reach. Dialectic closes the gap but it can never cross it. This is one thing Plato is driving at in the famous “catching fire” passage in the Second Letter, and it explains why Aristotle has to end the Posterior Analytics with nothing more than an image of soldiers coming to a stand. No one in the intervening centuries has proposed anything better. We can give tips and tricks that might get us closer to the definition, and we come up with definitions and starting points that were really worthy to be developed all the time, but we’ve never come up with a process for generating them.
In light of this, we can take it as a worthy starting point that starting points are reached by non-algorithmic processes. There are perfectly solid and well established algorithms for syllogistic validity, mathematical processes, syntactical and grammatical relations, and even for processes that close the gap of discovery, but as far as anyone can tell, there is not and cannot be any program we could write that could terminate in something that was a worthy starting point for reasoning. The total absence of such an algorithm – and even of a plausible method by which such a thing could be found, or modest advance toward finding it – certainly counts as a problem for any theory of mind that would involve seeing it as some process or form capable of instantiation.
But if there is no good account for how to pick out axioms then any subsequent algorithms cannot count as reasoning since reasoning is not just the execution of valid inferences but the execution of valid inferences from staring points deemed worthy of discourse. Go ahead and try to give an example of one – in giving the example you belie the attempt.
But then what about Chesterton’s point? In light of the above, reasoning is based on faith in the sense that the axiomatic, though it clearly seems to come from a process, nevertheless does not come from a process that we can lay out in front of ourselves and dominate over. We can be confident in a starting point, we can confirm or strengthen confidence in a starting point, but we can’t account for the confidence by laying out any algorithm terminating in it. The confidence is thus encountered as a confidence in something other than our selves, that is, in something other than what we can account for, dominate, reproduce, etc. We suffer inspirations, axioms, definitions, and even hypotheses.
But then we have to account for how in the world such things can be rational. We can base them in nature only if nature, beyond as it is in the human self, is also rational or something transcending reason. Absent this, we have not accounted for reasoning. It’s doubtful that we’ve even accounted for prejudice (since even prejudice is motivated by some desire to be right).