You will recall that Plato, in the Republic, invoked the image of the Divided Line. The means of knowing were assigned to each segment: noesis, or intellectual intuition, such as we have with axiomatic expressions; dianoia, or discursive reasoning, such as we employ in mathematics, involving the use of postulates and the mediation of inference; pistis, belief or opinion, which can be more or less likely; and fantasia, the imagination, through which we grasp mere images. Each coordinates with particular sorts of objects: the eide, or intelligible forms underlying the design of the universe; the mathematicals, those objects about which we have almost certain knowledge, except for the dependency on postulates; the objects in the world, about which we can have only belief or opinion (although when the opinion is sound, we can call it "right opinion") because there is too much indeterminacy, and they themselves are too changeable; and the images of things, which are wholly insubstantial as such.
One of the interesting things about this scheme is the acknowledgement that even mathematical truths depend upon assumptions that are fitting but not provable, and that nevertheless we consider mathematics to have a high degree of certainty. Also of interest is the idea that statements about things in the universe are always inherently qualified and probabilistic.
Even more interesting, of course, is that the one sort of knowledge that is certain is itself indemonstrable to others: you either see it or you don't. Dialectic is meant to get one to a point of seeing, but is not the same as proof.
Thus, for Plato, there are varying degrees of reliability of assertion, but none can be proven without challenge, although all might be established at a high level of probability.
This seems a pretty reasonable way of viewing things....... |
