Thoughts on “God, Human Memory and the Certainty of Geometry” by Marc Champagne


The Cartesian Claim and the Reproof

It seems to me that Mr. Champagne has thoroughly buried Descartes’ claim that an atheist cannot know geometry. However, because the paper remains on a superficial level of insight into the situation, the independent existence of God, whether believed in or not, remains a necessary condition. Thus the claim that an atheist cannot know his own knowing of geometry and must doubt that knowledge in order to be consistent, that is, that the knowing can only be relative to his trust not only in his own memory, but in a more practical sense a trust in the work done by previous geometers that he has not redone himself. This places a huge limitation on learning. As Hegel says, “What was once the work of a lifetime of a man in possession of his full powers is now an exercise or even a game for children.” This learning from others requires faith, not as belief in God, but as trust, in this case trust in former and fellow geometers. Without such trust one is unable to learn from others and must inevitably start from scratch to remove doubt. The rationalism of Descartes has been demonstrated as inherently based on an irrational foundation, notably by Kant but by other thinkers as well. Not that this should be surprising to anyone with a developmental view – reason obviously cannot develop from reason. There is thus a necessary limitation on the degree to which we can assume reality to be rational, just as there is a limit on the degree to which we can view natural history as evolutionary – evolution itself had to develop. The section on origin is thus inappropriate to the matter at hand, since the true origin is always a change from something radically unlike what originated from it, and thus is never truly knowable. Hypothetically it is correct, but in a practical sense it is merely correct while missing the truth of the matter.

The Proper Question

The question, then, of whether or not we can trust those whom we learn from is complex. Both Self and World, as the totality of the knowable, are comprised not of things but of a narrative. This narrative is properly the mythos that gives meaning and thus allows interpretation of raw experience. Within metaphysics the previous mythos could only appear as mythology, while the current mythos appeared as religion and, in the extreme, as totalizing ideology. Postmetaphysics, beginning with Hegel, Holderlin and Schelling, comprises a new mythos based on the twin notions of tension or ‘energy’, and freedom. As the twin bases of the new mythos, neither is easily definable in itself. The operative religion of the west has not been the Abrahamic religions, but the Greco-Roman religion of Dionysius and Janus, not in the sense of Dionysius’ wildness, but in the sense that they are the guarantors of currency, which now has been rebased on energy, in keeping with the new mythos. In this change, physics takes the place of accounting as the base science, yet retains the form of accounting, specifically as an accounting-for what is revealed, primarily by technology. Revealing, not thinking, and certainly not re-presenting, is thus the locus of truth – what is revealed most fully is most obviously true. Physics itself undergoes a metamorphosis, from the study of motion to the study of tension, or ‘energy’. In attempting to retain the mechanistic view of earlier physics the basis in tension results in string theory being the only possible basis, despite any evidence against it whatsoever. However, we have to keep in mind that this is a truth based on a new narrative of Self and World, and not necessarily the truth. While technology reveals, it does not reveal in every possible way. The string in string theory, in any case, revisits Tartarus as the abyssal itself, the one dimensional abyss that is not even shallow.

The Root of Geometrical Certainty

The most intimate experience of Tartarus, for human beings and most likely for higher animals, lies in the crossing of experience into imagination and vice versa, the twin modes of knowing: episteme and techne. The certainty of geometry lies precisely in its not crossing the boundary. As purely imaginary geometry cannot be disproven by experiential evidence, it is self-contained within the imagination. While demonstrations can assist in learning, trust in the imagination of former and fellow geometers is the factical a priori for certainty in geometry. As the knower, known, and their respective narratives are in this case identical, the certainty can be said to be absolute, though never for that very reason total.

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