--- In FairfieldLife@yahoogroups.com, "Xenophaneros Anartaxius" <anartaxius@...> wrote:
> Logic is about form, about structure, not content. To quote one > of the men who demonstrated that mathematics and logic were the > same, Bertrand Russell: He demonstrated that? I rather think not. In fact he played a significant role in knocking the stuffing out of that reductionist project: http://plato.stanford.edu/entries/philosophy-mathematics/#Log Or, Wiki: "Russell and Alfred North Whitehead wrote their three-volume Principia Mathematica (PM) hoping to achieve what Frege had been unable to do. They sought to banish the paradoxes of naive set theory by employing a theory of types they devised for this purpose. While they succeeded in grounding arithmetic in a fashion, it is not at all evident that they did so by purely logical means. While PM avoided the known paradoxes and allows the derivation of a great deal of mathematics, its system gave rise to new problems. In any event, Kurt Gödel in 193031 proved that while the logic of much of PM, now known as first-order logic, is complete, Peano arithmetic is necessarily incomplete if it is consistent. This is very widely though not universally regarded as having shown the logicist program of Frege to be impossible to complete"
