칸트 철학에서 수학이 갖는 존재론적 위상: 선험적 관념론과 수학적 우주론의 긴장 관계를 중심으로 = The Ontological Status of Mathematics in Kant’s Philosophy: Centering Upon the Strained Relationship between Transcendental Idealism and Mathematical Cosmology

다국어 초록 (Multilingual Abstract)

The main aim of this paper is to bring to light the ‘ontological revolution’ accomplished by Kant’s philosophy of mathematics. In light of the ontological significance of Kant’s philosophy of mathematics, I am going to criticize the ‘principle of mathematical aesthetic’ in contemporary physics. My motive in writing this treatise was a thought that there is a need to be critical of the situation where, while those still inclined toward the ‘Pythagorean-Platonic ideal’, within the community of the 21st-century physics today since the last century, have been resorting to mathematics to devise increasingly abstract or speculative theories, physics has found itself to be indistinguishable from mathematics or mathematical aesthetic. By stating in the introduction of Critique of Pure Reason that “Mathematical judgements are all synthetic,” Kant declared anti-Platonism (KrV, B 14). Mathematics, having drifted along in a Platonic world, was made to descend toward this earth by Kant. This ‘ontological downward movement’ completed by Kant’s philosophy of mathematics is one of the greatest revolutions in the history of western philosophy. Kant returned mathematics in its totality to our empirical world. With Kant’s philosophy of mathematics summed up as “Transcendental Aesthetic” in Critique of Pure Reason-transcendental aesthetic forming the fundamental spirit of transcendental idealism-and with western cosmology composing mathematical cosmologies since that of Pythagoras-Plato up to theoretical physicist Max Tegmark’s “Mathematical Universe Hypothesis” (MUH), transcendental idealism and mathematical cosmology have been in a strained relationship. The principle of mathematical beauty, a long-held ideal traced through Plato back to Pythagoras, has still been wielding a mighty influence on physics in the 21^st century through modern physics. Theoretical physics today, producing increasingly abstract theories depending on by far the highest-level mathematics, is becoming ‘speculative physics’ (against the backdrop of the ideal of unification, understood as the integration of the theory of relativity and quantum theory). Those speculative theories may be exceptional feats of human reason, but they may also be merely ‘mathematical illusions.’ The “Theory of everything” (TOE), the so-called holy grail of contemporary physics, is a “final theory,” which encompasses all phenomena and all particles in the universe and integrates all the forces including gravity (this dream of a final theory, theoretical physicist Marcelo Gleiser defined as “the scientific incarnation of the monotheistic tradition of the West”). TOE, which presupposes the ability to intuit the entire universe, i.e., the divine capability of intuiting outside the boundary of the universe all phenomena in it, is a dream lacking the awareness of the limits of human cognition-this is an implication of physics in Kant’s first antinomy of pure reason. At the point of no possibility of experimental verification, a sizable number of theoretical physicists have a disposition to resort to mathematicalaesthetic intuition to find out a theoretical breakthrough. In other words, what they do is the introduction of the principle of mathematical beauty. For them, the faculty of mathematical-aesthetic intuition is something like a tentacle to stretch out toward the ultimate reality at the point of no possible guidance by sensory intuition. This means that the Kantian concept of the thing-in-itself is to be mathematically reduced or determined through a mathematical idea. For Kant, however, mathematics is a discipline laying the cornerstone of physics as an empirical science; mathematical cognition is the basis of scientific cognition, a principle which Kant named the “axiom of cognition.” This axiom, which belongs to the “mathematical principle” along with the “anticipations of perception,” is the primary principle for legitimate or scientific cognition. The belief that one can find out mathematical beauty in the universe, or the Platonist way of thinking mathematical beauty to be an entity to be discovered, leads to the dogma of ‘Intelligent Design [ID]’ (which is equivalent to the “physico-theological proof,” confuted by Kant). Even Paul Dirac, a professed atheist theoretician, was, enraptured by the power of mathematics, not free from the illusion of the ID. For most theoretical physicists including Steven Weinberg, natural laws are real, unchanging laws. In such a realist position, mathematical order/structure is a substance to be discovered. According to Kant’s transcendental idealism, the outer physical reality is an empirical reality within th limits of cognition; mathematics is not a mystical discipline by which to soar high into a transcendent world or which enables us to see into the ultimate reality or being itself, but rather an entirely immanent science associated with our empirical world. Mathematical aestheticism pervading the academic world of theoretical physics is a demonstration that not a few theoretical physicists have not strictly performed ‘Kantian critique of cognition’. According to Kant’s philosophy of mathematics, humanity’s capability of mathematical cognition cannot reach beyond our phenomenal world. Kant’s philosophy of mathematics, as a reminder of the limits of our knowledge, is the core of Kant’s critical philosophy.