A fun read! Someday I will have to bite a bullet and discuss Kant’s claims re a priori geometry at length but for now I don’t want to contradict anything. On footnote 9 re completeness and compactification, my guess has been it’s the completion of series or sequences by their asymptotic limits he has in mind - completion as in “completed infinity” that had been a central concept in the Scholastics’ work on infinite sequences and series, as in Oresme, that thereby became central to Leibniz’s intensive quantity and calculus work, thus also crucial for Kant as a successor to Wolff. A crucial precursor for both modern compactness and modern completeness rather than a great match for either.
Oh, good! I did wonder if somebody might know more than me about the mathematical language of the time. And, please do contradict me on a priori geometry if you wish! It’s always good to hear about possibilities that I might not have seen.
Thanks, I would feel free but it’s a tarpit! I’ll suit up and go into the tar properly sometime, but the basic idea is that Kant’s a priori geometry is a truth about our own intuition of space rather than about real space, so relativity is a proof of his point that plane geometry was not some system of facts of nature but rather of the intuition of space. The fact that relativity is scientifically proven yet remains so unintuitive for us and our students today - to the point all our ways of working with relativity involve stitching lots of “locally Euclidean charts” - is arguably proof of his point on both sides (plane geometry not real/natural/empirical but plane geometry yes intuitive).
It’s a tarpit because talking rigorously about these intuitions is a mess, for reasons related to your earlier criticisms of MacIntyre’s Thomism. I would for instance want to criticize Kant’s account of perception quite sharply: my starting line there would be a combination of Whitehead’s criticisms of presentational immediacy and some early 20th C German observations (Jung, Spengler, others) on some usually-hereditary cultural variabilities of spatial intuition, and it would balloon fast.
The part about Galileo is great and the connection with Kant and metaphysics is great. I never was attracted to metaphysics. As an science major I always liked ontology better because it seemed more relevant to science. I definitely will read Kant now!
Brilliant synthesis of physics and philosophy. The observation that Kant's confidence about space and time being 'synthetic a priori' collapsed when spacetime itself became malleable is really underated. I ran into similar issues working on sensor calibration where assumed coordinate frames broke down at relativistic scales, had to rebuild alot of inference logic from scratch. The line about using heartbeats to time water ripples was genuinely moving btw.
A fun read! Someday I will have to bite a bullet and discuss Kant’s claims re a priori geometry at length but for now I don’t want to contradict anything. On footnote 9 re completeness and compactification, my guess has been it’s the completion of series or sequences by their asymptotic limits he has in mind - completion as in “completed infinity” that had been a central concept in the Scholastics’ work on infinite sequences and series, as in Oresme, that thereby became central to Leibniz’s intensive quantity and calculus work, thus also crucial for Kant as a successor to Wolff. A crucial precursor for both modern compactness and modern completeness rather than a great match for either.
Oh, good! I did wonder if somebody might know more than me about the mathematical language of the time. And, please do contradict me on a priori geometry if you wish! It’s always good to hear about possibilities that I might not have seen.
Thanks, I would feel free but it’s a tarpit! I’ll suit up and go into the tar properly sometime, but the basic idea is that Kant’s a priori geometry is a truth about our own intuition of space rather than about real space, so relativity is a proof of his point that plane geometry was not some system of facts of nature but rather of the intuition of space. The fact that relativity is scientifically proven yet remains so unintuitive for us and our students today - to the point all our ways of working with relativity involve stitching lots of “locally Euclidean charts” - is arguably proof of his point on both sides (plane geometry not real/natural/empirical but plane geometry yes intuitive).
It’s a tarpit because talking rigorously about these intuitions is a mess, for reasons related to your earlier criticisms of MacIntyre’s Thomism. I would for instance want to criticize Kant’s account of perception quite sharply: my starting line there would be a combination of Whitehead’s criticisms of presentational immediacy and some early 20th C German observations (Jung, Spengler, others) on some usually-hereditary cultural variabilities of spatial intuition, and it would balloon fast.
The part about Galileo is great and the connection with Kant and metaphysics is great. I never was attracted to metaphysics. As an science major I always liked ontology better because it seemed more relevant to science. I definitely will read Kant now!
Brilliant synthesis of physics and philosophy. The observation that Kant's confidence about space and time being 'synthetic a priori' collapsed when spacetime itself became malleable is really underated. I ran into similar issues working on sensor calibration where assumed coordinate frames broke down at relativistic scales, had to rebuild alot of inference logic from scratch. The line about using heartbeats to time water ripples was genuinely moving btw.