the axiomatisation of logic, geometry, and all of mathematics
Euclid’s Elements predated Kant.
Nowadays we would say that the symmetries of the mathematical, geometric square are a theorem derivable from axioms, and that the symmetries of a wooden block are a physical property of a system that empirically satisfies such axioms.
I think the main problem with this is that it requires the wooden block rotation to be an empirical fact. It seems like with enough sense of space, it wouldn’t require empirically observing rotating blocks to predict that a square rotating in space 90 degrees about its center remains the same. This is derivable in Euclidean geometry.
The physical prediction about the rotating block depends on assumptions like “it’s possible to rotate the block, it doesn’t get stuck” and “the block doesn’t jump around as you rotate it”, which could be empirically falsified and which could be added as assumptions to the statement.
I think whether or not this example is valid, the main point here is that it is possible to get some predictions of possible experience from mathematical reasoning (otherwise math would be useless for engineering), and so logic has to be somehow linked to possible experience for logic to yield these predictions; this might be doable with a type system, but not raw first-order logic.
Newtonian mechanics and heliocentric astronomy were the only major pieces of knowledge available to him about the hidden structures of the world.
How does his thinking stack up against these developments?
Non-Euclidean geometry seems like a case where he correctly predicted his ignorance. His explanation of “analytic” would have been better with a more formal treatment of analytic truths (e.g. first-order logic), but I think his points are valid if “analytic” refers to what can be proven in raw first-order logic. Thermodynamics and atomic theory (and quantum mechanics) seem relevant in providing discrete foundations to the apparent continuity; I think Kant’s arguments that space and time are fully continuous are incorrect (this was the main part of the book where I straight-up disagreed), and could have been more easily recognized as incorrect given thermodynamics and atomic theory. Neuroscience similarly seems relevant in limiting the information processing the mind can do to a finite number of discrete operations.
As I mentioned the theory of special relativity is an important development on subjective spacetime, Kant successfully avoids assuming problematic objective clock time, but doesn’t discuss much linkage between subjective times.
Cognitive science would provide more detail on the mental operations Kant posits, e.g. synthesis, of which there are a lot. I am not sure what if any would be considered “false” by most contemporary thinkers, but they’d have specifics to add for sure.
I think the main problem with this is that it requires the wooden block rotation to be an empirical fact. It seems like with enough sense of space, it wouldn’t require empirically observing rotating blocks to predict that a square rotating in space 90 degrees about its center remains the same. This is derivable in Euclidean geometry.
The “sense of space” is empirical data. It is not derivable from Euclidean geometry, but results from the empirical fact that the space we live in is Euclidean (on human scales).
Even if it’s embedded in our nervous system at birth (I do not know if it is), it’s still empirical data. If space were not like that, we would not have (evolutionarily) developed to perceive it like that. Did Kant have the concept of knowledge that we are born with, which nonetheless is contingent on how the world happens to be?
Seems like an overstatement.
I’ll grant Coulomb’s law for electromagnetism, but geology and chemistry were mainly catalogues of observations, and philosophical aspects of steam engines had to wait for 19th century thermodynamics. Geology was producing the idea of a discoverable timeline for the Earth’s changes, and chemistry was groping towards the idea of elements, but that is small potatoes compared with their development in the 19th century for chemistry and the 20th for geology. The 19th century in geology was mainly filling in the timeline in more and more detail across more of the Earth, and some wrong estimates for its age.
Did Kant have the concept of knowledge that we are born with, which nonetheless is contingent on how the world happens to be?
I am not sure how much he has this. He grants that his philosophy applies to humans, not to other possible minds (e.g. God); it’s a contingent fact that, unlike God, we don’t produce things just by conceiving of them. And since he thinks spacetime is non-analytic, he grants that in a sense it “could” be otherwise, it’s just that that “could” counterfactual structure must branch before we get empirical observations. But he doesn’t much discuss the historical origins of why we have a human-like world representation, he just notes that we must have had one to some extent before we got sense-data. A possible materialist criticism of this model is that we can learn about these pre-empirical world structures through empirical psychology research on other minds, not just by making backwards (“transcendental”) inferences from the world representation that we presently have and can access introspectively.
Euclid’s Elements predated Kant.
I think the main problem with this is that it requires the wooden block rotation to be an empirical fact. It seems like with enough sense of space, it wouldn’t require empirically observing rotating blocks to predict that a square rotating in space 90 degrees about its center remains the same. This is derivable in Euclidean geometry.
The physical prediction about the rotating block depends on assumptions like “it’s possible to rotate the block, it doesn’t get stuck” and “the block doesn’t jump around as you rotate it”, which could be empirically falsified and which could be added as assumptions to the statement.
I think whether or not this example is valid, the main point here is that it is possible to get some predictions of possible experience from mathematical reasoning (otherwise math would be useless for engineering), and so logic has to be somehow linked to possible experience for logic to yield these predictions; this might be doable with a type system, but not raw first-order logic.
Seems like an overstatement.
Non-Euclidean geometry seems like a case where he correctly predicted his ignorance. His explanation of “analytic” would have been better with a more formal treatment of analytic truths (e.g. first-order logic), but I think his points are valid if “analytic” refers to what can be proven in raw first-order logic. Thermodynamics and atomic theory (and quantum mechanics) seem relevant in providing discrete foundations to the apparent continuity; I think Kant’s arguments that space and time are fully continuous are incorrect (this was the main part of the book where I straight-up disagreed), and could have been more easily recognized as incorrect given thermodynamics and atomic theory. Neuroscience similarly seems relevant in limiting the information processing the mind can do to a finite number of discrete operations.
As I mentioned the theory of special relativity is an important development on subjective spacetime, Kant successfully avoids assuming problematic objective clock time, but doesn’t discuss much linkage between subjective times.
Cognitive science would provide more detail on the mental operations Kant posits, e.g. synthesis, of which there are a lot. I am not sure what if any would be considered “false” by most contemporary thinkers, but they’d have specifics to add for sure.
The “sense of space” is empirical data. It is not derivable from Euclidean geometry, but results from the empirical fact that the space we live in is Euclidean (on human scales).
Even if it’s embedded in our nervous system at birth (I do not know if it is), it’s still empirical data. If space were not like that, we would not have (evolutionarily) developed to perceive it like that. Did Kant have the concept of knowledge that we are born with, which nonetheless is contingent on how the world happens to be?
I’ll grant Coulomb’s law for electromagnetism, but geology and chemistry were mainly catalogues of observations, and philosophical aspects of steam engines had to wait for 19th century thermodynamics. Geology was producing the idea of a discoverable timeline for the Earth’s changes, and chemistry was groping towards the idea of elements, but that is small potatoes compared with their development in the 19th century for chemistry and the 20th for geology. The 19th century in geology was mainly filling in the timeline in more and more detail across more of the Earth, and some wrong estimates for its age.
I am not sure how much he has this. He grants that his philosophy applies to humans, not to other possible minds (e.g. God); it’s a contingent fact that, unlike God, we don’t produce things just by conceiving of them. And since he thinks spacetime is non-analytic, he grants that in a sense it “could” be otherwise, it’s just that that “could” counterfactual structure must branch before we get empirical observations. But he doesn’t much discuss the historical origins of why we have a human-like world representation, he just notes that we must have had one to some extent before we got sense-data. A possible materialist criticism of this model is that we can learn about these pre-empirical world structures through empirical psychology research on other minds, not just by making backwards (“transcendental”) inferences from the world representation that we presently have and can access introspectively.