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This is a great statement, because it points to the fundamental problem with Descartes' legacy: "His philosophical results are now largely a historical marker

This is a great statement, because it points to the fundamental problem with Descartes' legacy: "His philosophical results are now largely a historical marker on a road to nowhere. His formalisms are still used by every human practitioner of math from elementary school students on up." As if his "formalisms" could stand on their own without the philosophical foundations of his entire system. And yes this is what modernity after Hume did -- take Descartes' project forward long after the core assumptions had been completely undermined. In many ways the history of modern philosophy since has been a quest to re-ground the Cartesian project with the kind of confidence he promised, and a succession of regressive rear-guard actions taken against the encroaching skepticism that threatened the entire enterprise at every turn. And finally we're left with a weird, cobbled-together Popperian/Kuhnian pragmatism that long ago gave up on "certainty" or "clarity" and settled for "less wrong." No wonder philosophy is held in such low regard in scientific communities. It has done science no favors whatsoever in the last century, other than to progressively undermine its naive epistemological assumptions and redirect it back to some kind of Formal Realism -- at which point the scientific community yells "remember Galileo!!" and runs the other direction. It's a sad state of affairs when we can't distinguish between the salutary philosophical insights of Aristotle and religious tyranny. It's going to take a long, long time to recast the entire narrative to where the two points of view can inform each other once again.

jasonwatkinspdx 14y ago
In what way are the notations Descartes introduced dependent upon his philosophical views? "And finally we're left with a weird, cobbled-together Popperian/Kuhnian pragmatism that long ago gave up on "certainty" or "clarity" and settled for "less wrong." What surprises me is that people are so willing to assume that such certainty is desirable. That quantified symbolic logic is both primary and desirable, and that probabilistic reasoning is at best an occasionally necessary but highly suspect tool. What a sadly limited universe of discourse that is, being forever circumscribed by Godel. It is fortunate that we don't exist trapped in it. I see no reason to intellectually place myself in the same prison.
- davesims 14y ago
  Sure -- Descartes mathematics in the abstract are surely not dependent on his foundationlism/rationalism. As such they are merely tautological. But the science that deploys that math in pursuit of practical knowledge is. Agreed that 'certainty,' at least the kind that Descartes was advocating, is an abstraction in search of a definition, and as such not desirable. Godel and incompleteness is just one species of the problem. This is where I would rather see a reformed Baconian science, tempered with (rather than utterly rejecting) an Aristotelian view which had a more sophisticated language for dealing with ambiguity and the fluid borders between substances. Our physics has advanced far beyond simplistic atomism, why can't our philosophy of science? Popper and falsification is a good rear-guard action against skepticism and making unwarranted philosophical leaps within the Cartesian taxonomy, but why can't we question the taxonomy itself? There are plenty of good starting points -- Whitehead and Bergson come to mind, as well as an open re-examination of medieval and pre-socratic philosophy, as Heidegger does in the Question Concerning Technology. On and on. It's not as if no one is asking these questions or refining philosophical language to deal with them -- it just seems that the scientific community would rather declare its own sovereignty and emancipate itself from first-order questions once and for all.

jasonwatkinspdx 14y ago

In what way are the notations Descartes introduced dependent upon his philosophical views? "And finally we're left with a weird, cobbled-together Popperian/Kuhnian pragmatism that long ago gave up on "certainty" or "clarity" and settled for "less wrong." What surprises me is that people are so willing to assume that such certainty is desirable. That quantified symbolic logic is both primary and desirable, and that probabilistic reasoning is at best an occasionally necessary but highly suspect tool. What a sadly limited universe of discourse that is, being forever circumscribed by Godel. It is fortunate that we don't exist trapped in it. I see no reason to intellectually place myself in the same prison.

davesims 14y ago
Sure -- Descartes mathematics in the abstract are surely not dependent on his foundationlism/rationalism. As such they are merely tautological. But the science that deploys that math in pursuit of practical knowledge is. Agreed that 'certainty,' at least the kind that Descartes was advocating, is an abstraction in search of a definition, and as such not desirable. Godel and incompleteness is just one species of the problem. This is where I would rather see a reformed Baconian science, tempered with (rather than utterly rejecting) an Aristotelian view which had a more sophisticated language for dealing with ambiguity and the fluid borders between substances. Our physics has advanced far beyond simplistic atomism, why can't our philosophy of science? Popper and falsification is a good rear-guard action against skepticism and making unwarranted philosophical leaps within the Cartesian taxonomy, but why can't we question the taxonomy itself? There are plenty of good starting points -- Whitehead and Bergson come to mind, as well as an open re-examination of medieval and pre-socratic philosophy, as Heidegger does in the Question Concerning Technology. On and on. It's not as if no one is asking these questions or refining philosophical language to deal with them -- it just seems that the scientific community would rather declare its own sovereignty and emancipate itself from first-order questions once and for all.