Talk:Stephenson:Neal:Quicksilver:6:Cartesian number-line (Neal Stephenson)

From the Quicksilver Metaweb.

Descartes' equivalence between ordinal number and cardinal number, the continuum hypothesis, is not accepted as a necessity in all theories of philosophy of mathematics. It is for instance possible to treat geometry and algebra as having no connection to each other. A particularly good example of how tenuous is their connection is the field of combinatorics and optimization, which emerged only in the 20th century, and which still relies on graph theory projections into polynomial forms that are, to say the least, non-obvious to the layman.

Cogito ergo sum is possibly the root of this problem, and those of the Enlightenment in general. A subject-object problem emerges when one tries to say that any aggressive being that sees and thinks, therefore is, and therefore has a point of view or perspective that must be taken into account. It's assuming God's eye view to simply assume self as subject, and some "objective" and passive concept as pliant object...

It was Martin Heidegger and Michel Foucault who challenged this in philosophy and history, and Thomas Tymoczko and Imre Lakatos and to a degree Hilary Putnam who challenged it in mathematics itself. It's an extremely important question. It deserves much more than just Neal's note.