I. Can a computer remember something it never learned? The human mind does exactly that through intuition. This is what Plato called anamnesis and Kant called synthetic a priori knowledge. Computers will never be able to do that. Their way of learning and thinking is just a kind of “ars combinatorica” (Leibniz). Why? I will clarify this soon in a paper I will publish on my blog.
II. With his view of mathematics (13:29), Prof. Yang-Hui He reminded me that I once said (in my undergraduate thesis at the Faculty of Physics: Modeling in Physics and its Epistemological Significance, 1986) that ”mathematics can also be seen as pure rhetoric, that is, the art of talking endlessly without contradicting yourself and without saying anything in particular.” Later I discovered that, in a way, the same thing had been said by Russell in Introduction to Mathematical Philosophy (1919): “Mathematics is the subject in which we do not know what we are talking about, nor whether what we are saying is true.”
III. Professor Yang-Hui He, you have made a great synthetic survey of the history of modern mathematics, as important as Iain McGilchrist’s survey of the neuro-physiology of cognition in his books. But you both have done nothing but finally confirm Kant’s stereoperspectival epistemology, which says that we always look at the world and the things around us from two orthogonal perspectives, one synthetic (transcendental, purely theoretical) and the other analytic (empirical).
McGilchrist metaphorically calls the synthetic perspective the “Master’s perspective” and attributes it to the right hemisphere of the brain, and the analytic perspective is called the “Emissary’s perspective” and he shows with overwhelming neuro-physiological evidences that it is specific to the left hemisphere.
You metaphorically call the two perspectives “top-down mathematics” and “bottom-up mathematics”. Then you show that the same pattern repeats itself between mathematics and physics. Mathematics (and theoretical physics) is the top-down perspective and experimental physics is the bottom-up perspective – if I understand you correctly. If so, then I am very glad, because you have brought me with this yet another scientific confirmation of everything I have written so far about Kantian epistemology in my books.
In “Critical Introduction. On the Possibility of Metaphysics as Science in Kantian Critical Philosophy” (2004), not yet translated into English, I metaphorically call the top-down epistemological perspective the “bird’s perspective” and the bottom-up perspective the ”mole’s perspective”.
In “Open Letter to Iain McGilchrist / I. On Iain McGilchrist’s Implicit Physiological Confirmation of Kantian Stereoperspectival Epistemology” (2024) I first call Kantian epistemology a stereoperspectival epistemology precisely to emphasize the Kantian idea that the two perspectives or sources of knowledge (empirical intuition, respectively concepts, ideas and synthetic a priori judgments) despite their independence (orthogonality) are not mutually exclusive, but that authentic knowledge can only be achieved through their concurrence. Exactly what Iain McGilchrist pointed out about the specialization, competition and collaboration of the two cerebral hemispheres.
McGilchrist himself quotes at one point the famous Kantian phrase from the Critique of Pure Reason: „Gedanken ohne Inhalt sind leer, Anschauungen ohne Begriffe sind blind.“
A century after Kant, Einstein would say the same thing: “Insofar as the laws of mathematics are certain, they do not refer to reality; and insofar as they refer to reality, they are not certain.”
Without physics, math would be meaningless. Without mathematics physics would be nothing but a grope in the dark.
Physics must give mathematics an empirical content and mathematics must give physics an intelligible form.
Kantian transcendental aesthetics is the epistemological paradigm of all modern sciences. This has only become obvious nowadays, two centuries after Kant.
I started advocating these ideas back in 1986, with my undergraduate thesis in physics, but to this day no one has taken any notice. Pretty sad, isn’t it? Not for me, but for modern science and philosophy.
Kantinomus Verlag 