They point is Euclid wasn’t trying to prove propositions with the help of undeclared assumptions and visual aids. He was trying to formalize it deductively and thought he had. The fact that he doesn’t actually do that is a flaw not a feature of the Elements. Similarly, if indeed one of Kant’s formulations of the CI fails to tell us how to act in an a priori way then one wouldn’t conclude that Kant sought to explain morality as a concern about impacts. Rather, one would conclude that Kant had failed to show morality isn’t a concern about impacts.
The fact that he doesn’t actually do that is a flaw not a feature of the Elements.
I’m sorry, this conclusion doesn’t follow. According to modern mathematicians, Euclid’s contributions to mathematics were twofold:
systematizing geometrical knowledge (much like the Bourbaki group would systematize math in the 20th century)
developing the deductive, axiomatic method with rigorous proofs.
It is true that Euclid’s axioms had a number of gaps which Euclid himself would probably have remedied if he had known about them (e.g. the assumption that a line has at least two points). But the status of his visual aids is far less clear: Euclid himself had no notion of formal proof, and his use of visual aids is in fact quite rigorous. So describing them as a flaw of the Elements seems unjustified: we do not know what Euclid would have done if he’d known about our modern notions of proof, but most likely he would have used them anyway, and he could still be credited with developing the axiomatic method.
Similarly, Kant’s contributions from the POV of modern ethicists were:
coming up with the various formulations of the CI
making a fairly convincing argument that these may be apriori justified by the principles of “pure practical reason”
The technicalities of what Kant meant exactly by “a priori” and “pure practical reason”, and whether the notion of “impact” is consistent with them are largely irrelevant to Kant’s accomplishment. Even if Kant’s CI turned out to be largely concerned with impact, it would still be widely cited as an example of moral duty, and one which may be in some sense logically justified by the principles of rationality.
They point is Euclid wasn’t trying to prove propositions with the help of undeclared assumptions and visual aids. He was trying to formalize it deductively and thought he had. The fact that he doesn’t actually do that is a flaw not a feature of the Elements. Similarly, if indeed one of Kant’s formulations of the CI fails to tell us how to act in an a priori way then one wouldn’t conclude that Kant sought to explain morality as a concern about impacts. Rather, one would conclude that Kant had failed to show morality isn’t a concern about impacts.
I’m sorry, this conclusion doesn’t follow. According to modern mathematicians, Euclid’s contributions to mathematics were twofold:
systematizing geometrical knowledge (much like the Bourbaki group would systematize math in the 20th century)
developing the deductive, axiomatic method with rigorous proofs.
It is true that Euclid’s axioms had a number of gaps which Euclid himself would probably have remedied if he had known about them (e.g. the assumption that a line has at least two points). But the status of his visual aids is far less clear: Euclid himself had no notion of formal proof, and his use of visual aids is in fact quite rigorous. So describing them as a flaw of the Elements seems unjustified: we do not know what Euclid would have done if he’d known about our modern notions of proof, but most likely he would have used them anyway, and he could still be credited with developing the axiomatic method.
Similarly, Kant’s contributions from the POV of modern ethicists were:
coming up with the various formulations of the CI
making a fairly convincing argument that these may be apriori justified by the principles of “pure practical reason”
The technicalities of what Kant meant exactly by “a priori” and “pure practical reason”, and whether the notion of “impact” is consistent with them are largely irrelevant to Kant’s accomplishment. Even if Kant’s CI turned out to be largely concerned with impact, it would still be widely cited as an example of moral duty, and one which may be in some sense logically justified by the principles of rationality.