Kant’s Space-Time and Hawking’s Universe — Kant’s View of Science and Modern Physics

Abstract

Kant is one of the greatest philosophers of all time. Some have said, “Kant is like a reservoir: all the philosophy of the past flows into him, and all the philosophy that comes afterward flows out from him.”[①] Kant’s philosophy has an influence so far-reaching that it is beyond dispute. However, the significance of his doctrine of space and time and his understanding of the natural sciences has been widely underestimated. What I want to show is this: although science appears to have undergone earth-shaking changes, from Newton’s classical system to modern physics represented by relativity and quantum theory, scientific method has not changed qualitatively, and modern people’s understanding of the nature of natural science is not much deeper than Kant’s. Kant’s doctrine of space and time and his view of science are not only of profound historical significance; they also retain profound relevance today. Kant’s philosophy resonates broadly with modern physics, and can still offer important insights for modern people in understanding questions such as “What is scientific truth?”

Main Text

“It is said that Hawking’s natural science, although very different from Newton’s and Einstein’s natural science, is still regarded by Hawking himself as applicable to Kant’s system. Hawking does not believe in God, nor in anything else, but he believes in Kant’s philosophy.” [②]

I have not been able to find any relevant comment by Hawking on Kant, but Hawking often uses Kant’s “antinomy of pure reason” to introduce topics in his lectures[③] and writings:

If the universe really was created, then why did it wait an infinite time before being created? On the other hand, if the universe has existed for an infinite time, why have not all the events that are going to happen already happened, so that history has already come to an end? In particular, why has the universe not reached thermal equilibrium, so that everything has the same temperature?

Kant called this problem the “antinomy of pure reason,” because it seems to be a logical contradiction. There is no way to resolve it, but it only raises a contradiction within the framework of Newton’s mathematical model. In Newton’s model, time is an infinite line, independent of what happens in the universe…[④]

Later we will see the broad resonance between Kant’s philosophy and the modern scientific worldview, but Hawking’s exposition of Kant’s antinomy here is incomplete. Of course, here Hawking is merely borrowing Kant’s name to introduce his own topic, and has no intention of pursuing Kant’s philosophy further. In fact, Kant himself had already answered these contradictions. He pointed out: “The proofs given above for the fourfold antinomy are not a sham; rather, they rest on a presupposition at bottom, namely that appearances, or the sensuous world that comprehends all appearances within itself, are things in themselves.”^{[A507 B535][⑤]} Kant’s “fourfold antinomy” does not pose a problem; on the contrary, it is meant to solve one. It is meant to reveal the presuppositions shared by the old metaphysics that lead to contradiction.

So are time and space finite or infinite? Kant already gave the answer—first he distinguished between “analytic opposition” and “dialectical opposition”: “If one says, for example, that every body is either fragrant or foul-smelling, then there is a third case, namely that it has no smell at all (does not emit any odor), so that the two conflicting propositions can both be false.”^{[A503 B531]} If the pair is “fragrant” and “not fragrant,” then this is a pair of “analytic opposition”; if one proposition is proven correct (or incorrect), the corresponding one can only be incorrect (or correct), respectively (of course, Kant is not saying that judgments of contradictory opposition are always possible). But if the pair is “fragrant” and “foul-smelling,” then this is a pair of “dialectical opposition.” For a pair of “dialectical opposition,” if one can “prove” that both are right, that is tantamount to proving that both are wrong, and it will also indicate that the presuppositions used in “proving” them correct must be problematic.

Whether space and time are finite or infinite is precisely such a pair of dialectically opposed propositions:

Hence if I say: the world in respect of space is either infinite or it is not infinite, then when the first proposition is false, its contradictory opposite “the world is not infinite” is true. In this way I have only eliminated one infinite world, and have not posited another world, namely a finite one. But if I say that the world is either infinite or finite, then both of these can be false. … that is to say, if the world is not given at all as a thing in itself, and therefore neither as infinite nor as finite in respect of its magnitude. ^{[A504 B532]}

Kant thus reveals and demonstrates that “appearances are by no means things existing in themselves”^{[A505 B533]}. With regard to the “totality” of the various parts of appearances, we can say neither that it is finite nor that it is infinite, because appearances can exist in representation only as constituting a successive series of regressions, and such regression is “never absolutely complete, nor given as either finite or infinite”^{[A505 B533]}. Here Kant is not trying to discuss the question of whether time and space are ultimately finite or infinite; rather, he is seeking to demonstrate a more fundamental point about the limits of human cognition, namely, to emphasize the distinction between “appearance” and “thing in itself.”

Modern cosmology holds that space-time is “finite but unbounded,” which can also be understood as the universe being “neither finite nor infinite.” So does this modern scientific theory “confirm” Kant’s view that space-time is neither finite nor infinite? On the surface, that sounds pretty good—this is the “resonance between Kant’s philosophy and modern physics” that I want to describe? Not at all! As I have already said, what Kant wanted to discuss was not the topic of whether time and space are ultimately finite or infinite; what he discussed was how human beings know nature—that is, the question of “What can I know?” concerning the fundamental attitude of science!

Many people think that Kant’s view of natural science is either an error constrained by the limits of his era, or a timeless insight that has, since being “confirmed” by modern science, lost any freshness of meaning, and that it is of course more persuasive to state such views directly in terms of modern scientific “evidence.” For example, Professor Deng Xiaomang argues that “from the modern point of view, there is little that is new in Kant’s interpretation of the Newtonian system based on his own metaphysics. On the one hand, this is because some views have already been confirmed by modern physics (such as the relativity of space, the relation between mass and motion, etc.), and have received a more scientific explanation; on the other hand, it is also because Kant’s views, broadly speaking, still bear the metaphysical atmosphere characteristic of that era.” [⑥] Yet I have already pointed out that the focus of Kant’s philosophy is not those specific “scientific cognitions,” but the mode and limits of “scientific cognition” itself. In this respect, modern people are no more brilliant than Kant!

Richard Feynman, the maverick of modern physics, once reminded those who wish to understand “the nature of physical law” to pay attention to this: “What is newer may not necessarily be more modern. Modern science was built precisely in accordance with the unifying tradition discovered through the law of gravitation.”[⑦] Feynman chose Newton’s law of gravitation as his “case,” rather than the more recent and more “fashionable” laws of electromagnetism, relativity, or quantum mechanics, in order to reveal “the nature of physical law.” This is because, although the scientific theories from Newton to Maxwell, Einstein, Heisenberg, and Hawking underwent many earth-shaking “revolutions,” what Feynman wanted to tell us was the “nature” of physical law—that is precisely to grasp the unchanging things behind scientific revolutions in cognition. And those fundamental things have not undergone any qualitative change since Newton established the mature system of modern physics. Feynman, with great care, warns us that if we want to understand the nature of science, we must not “follow fashions” or be overambitious!

The same warning, in the famous Feynman Lectures on Physics, is expressed through a mockery of “philosophers of relativity”:

When this idea was first made public, it stirred up a great commotion among philosophers, especially the “cocktail-party philosophers,” who said, “Oh, that’s easy, Einstein’s theory shows that everything is relative!” … The fact that “things depend on the frame of reference one uses” was supposed to have had a profound effect on modern thought, and one might well wonder at this, because after all, the fact that things depend on the point of view one takes is so simple that, to discover it, there surely was no need to go rummaging around in the theory of relativity in physics. Anyone walking down the street must certainly understand that everything he sees depends on his frame of reference, because when a passerby walks toward him, what he first sees is his front and then his back; of most philosophies said to derive from relativity, there is nothing deeper than the claim that “one sees a thing differently from the front and from the back”; the old story of several blind men describing an elephant in several different ways is perhaps another example of philosophers’ attitude toward relativity.^[⑧]

Here Feynman is openly ironic toward philosophers who understand relativity too superficially. We need not quibble with Feynman over details; his irony hits the mark—if all one wants is to break dogmatism, there is no need at all to wait for Einstein to appear! In fact, this task had already been accomplished much more brilliantly by Kant.

Let us first look at Kant’s profound insight into the problem of the relativity of space and time:

In all experience there must be something that is sensed; this is the reality of sensuous intuition, and therefore space, in which we are to apprehend motion through experience, must also be described as something sensible, that is, must be described through what can be sensed; this space, as the totality of all objects of experience and itself as an object of experience, is called empirical space. But this space, as material, is itself in motion. Yet a moving space, if its motion is to be perceived, presupposes another extended material space in which it moves; and this material space in turn also presupposes another, and so on ad infinitum.

So all motion as an object of experience is only relative; the space in which motion is perceived is relative space…^[⑨]

Kant regards space as the a priori form of outer intuition, and time as the a priori form of inner intuition. In short, space-time is a “form of intuition.” The unity of space-time depends on causal interaction among objects in order to be realized. “Empty space is not at all something belonging to the existence of things, but only something belonging to the determination of concepts; in this sense empty space does not exist.”[⑩] Therefore, space-time always exists only in relation to the objects within space-time.

However, Kant did not abandon the concept of “absolute space”—“Matter is a movable thing in space. Space, insofar as it itself is movable, is called material space, or also relative space; that space in which all motion must ultimately be thought, and which is therefore itself absolutely at rest, is called pure space, or also absolute space.”[11]—At this point, many people begin to suspect that Kant’s revolution in the concept of space-time did not go far enough. For example, in *A Guide to Kant’s Critique of Pure Reason*, Yang Zutao and Deng Xiaomang point out “the fundamental limitations and errors of Kant’s doctrine of space and time”[12]: first, Kant regarded space and time entirely as a priori forms of intuition already present in people’s subjective minds. Starting from this transcendentalism, all his demonstrations of the “objectivity” of mathematics and sensible knowledge are completely subjective. He restricts the validity of these forms of knowledge to subjective “appearance,” and denies all possibility that they can grasp objective essence (things in themselves) beyond the phenomenal world, in order ultimately to leave room for fideism. In this respect, this theory has again had harmful and negative effects on the healthy development of science. Second, Kant moved Newton’s framework of absolute space-time from the objective material world into the subjective a priori capacities of human beings. Yet he did not change the “absolute” nature of this framework, which greatly discounted the idea of the subject’s active agency in Kant’s doctrine of space and time. Since space and time were from the very beginning already present in the mind in a “straightforward,” Euclidean manner as “a priori forms of intuition,” … but the space-time theories of modern physics hold that Euclidean space is only a special form or limiting form among all possible kinds of space in the universe…

I think that these two “criticisms” are precisely what point to the most precious and profound intention in Kant! The first criticism, which is also the most important implication of Kant’s view of science, I shall discuss later.

Let us first discuss the second criticism, namely the one concerning “absolute space-time.”

First, “the historical development of non-Euclidean geometry did not oppose Kant’s theory; Kant denied that Euclidean geometry is analytic, which means that non-Euclidean geometry is logically possible. The issue is that Kant believed space to be Euclidean as an a priori truth. In fact, space being non-Euclidean is an empirical truth.”[13] Does not the development of non-Euclidean geometry precisely embody the profundity of Kant’s thought? Before Lobachevsky and Riemann, almost everyone thought Euclidean geometry was something beyond dispute, self-evident. Kant alone pointed out that Euclidean geometry is not self-evident, but depends on intuition of space. And in fact this is exactly so: Euclidean geometry is the product of flat space, while non-Euclidean geometry corresponds to pseudospherical or saddle-shaped space. Kant’s deficiency lies only in not having imagined the possibility that “space is not flat.”

Let us now look at why Kant was unwilling to abandon the wording of “absolute space-time.”

Absolute space itself is nothing at all, still less an object; it only means that beyond the space that is given to me, I can at any time think of any other relative space whatsoever. I merely make it into something that contains all given spaces, something in which I represent all given spaces as spaces in motion, and thereby advance toward infinity beyond all given spaces. Since I have this space, though still material, only in thought, and know nothing of the matter that delineates such space, I abstract away from matter, and so space is imagined as though it were a pure, non-empirical, and absolute space. I can compare it with yet an empirical space, and in it imagine the empirical space as moving, and thus it is always regarded as at rest. To make this absolute space into reality means to mix the logical universality of any space with which I can compare every empirical space contained in it into physical universality within the realm of reality, and to misconstrue the ideas of reason.^[14]

Here, Kant has already made it quite clear that within the bounds of “experience” he utterly rejects “absolute space and time” — “absolute space is nothing at all for all possible experience.”[15] Since it is “nothing at all,” why must Kant insist on preserving such a “nothing” in “imagination”? I believe that, on the one hand, similar to the talk of the “thing in itself,” Kant’s insistence that there is something “absolute” that can never be experienced prevents his philosophy, after rejecting dogmatism, from sliding into relativism. The basic aim of Kant’s philosophy is “to rescue scientific knowledge from skepticism”[16], and the dangerous notion that “everything is relative” would make it hard to secure the objectivity of knowledge. On the other hand, “absolute space and time,” as an a priori form of intuition, really do exist in human “imagination”! For example, when we say “gravity bends space,” this “bending” is likewise merely a “form”; the curvature of space is only a convenience for calculation, and compared with treating the effect of curved spacetime as photons being deflected by gravity, it seems more intuitive to regard space as curved. Moreover, before we imagine a curved spacetime, we inevitably need first to have an intuition of flat spacetime: we draw some curves on paper to explain the state of a curved spacetime, just like those exquisite illustrations in The Universe in a Nutshell, yet the reason those curves can help us imagine a “curved” spacetime is that they are first drawn on the “flat” paper serving as the background! It is the same in our thought as well — our a priori intuition of spacetime is always the “flat” Euclidean spacetime! Likewise, we also cannot avoid the fact that what we first possess is the intuition of static space. So, which form of spacetime is ultimately the most fundamental? Kant believed that absolute space and time cannot be experienced and cannot be determined by us at all; what we can determine is only our “a priori intuition.” Therefore we need not argue over “which form of spacetime is absolute”; what is worth discussing is only “which form of spacetime is more convenient for intuition.”

Here, Hawking has a statement quite similar to Kant’s — in order to avoid “spacetime singularities,” Hawking devised a conception called “imaginary time”: “… The spacetime in which the time coordinate of events has an imaginary value is called Euclidean spacetime, because its metric is always positive. … One may think that using imaginary time is just a mathematical method — or, one might say, a trick — for calculating answers about real spacetime,[17]” “So perhaps what we call imaginary time is actually the more fundamental concept, while what we call real time is merely something invented to help us describe the concept of the universe we have in mind. But… scientific theories are mathematical models we use to describe the results of our observations. They exist only in our minds, so questions of this sort are meaningless: which is real, ‘real’ time or ‘imaginary’ time? The only issue is which is the more useful description.”[18]

Since human cognition of nature is always relative and limited, the foundation of the possibility of knowledge cannot be built on experience of appearances. Thus it is necessary to make the object conform to the subject in turn, and to establish some metaphysical principles as transcendental assumptions to ensure the possibility of objective knowledge! “A doctrine of nature that is meant to be intelligent can only be called natural science if the natural laws on which it is based are understood as a priori laws and not merely empirical ones.”[19] “Every mathematical physicist is entirely unable to do without metaphysical principles.”[20] Kant further demonstrated that these assumptions are not only necessary but also reasonable. Here modern science resonates with Kant: as a conceptual forerunner of relativity and quantum mechanics, Poincaré (Jule-Henri Poincaré, 1854—1912, also rendered as Puangkalai), hailed as “the last man to possess comprehensive knowledge of mathematics and its applications,” founded the so-called “conventionalism” of philosophy of science, which holds:

Mathematical quantities … are they discovered by us in nature, or do we ourselves introduce them into nature? … The framework into which we wish to force everything turns out to be one we have ourselves constructed, but we did not create it arbitrarily. One might say that we are made to measure, and therefore we can make the facts fit it without changing the essential things in the facts.

Another framework we impose on the world is space. Whence do the first principles of geometry come? Are they imposed on us by logic? Lobachevsky proved by creating non-Euclidean geometry that this is not the case. Is space suggested by our senses? No, it is not… Does geometry come from experience? Further discussion shows us that this is not so. Therefore we conclude that the first principles of geometry are nothing but conventions. But these conventions are not arbitrary…^[21]

After carefully reading the above passage, it is hard to imagine that Poincaré was not inspired by Kant! Although Kant’s “synthetic a priori judgments” are not exactly identical to Poincaré’s “conventions,” if we match Poincaré’s “framework” with Kant’s “a priori forms,” “conventions” with “transcendental sensibility,” “mathematical quantities, space” with “time, space”… to our astonishment, we discover that the so-called creative insights of the last all-round mathematical genius contain scarcely any novelty compared with Kant more than a century earlier!

The foregoing has focused mainly on expounding the profound implications of Kant’s view of space and time, and on revealing the importance of that view for understanding the modern scientific cosmic outlook. Kant’s view of space and time has not only not become obsolete; it can in fact continually bring new inspiration to modern science! Rather than “chasing the fashion” and showing off philosophy of relativity or philosophy of quantum theory, modern philosophers would do better to listen earnestly to Kant’s advice.

Finally, let us return to the question we set aside earlier: namely, the first of Mr. Yang Zutao and Mr. Deng Xiaomang’s criticisms of the “fundamental limitations and errors of Kant’s doctrine of space and time,” that is, “Kant denies every possibility that human knowledge can grasp objective essence (the thing in itself) beyond the phenomenal world, so as ultimately to reserve a place for fideism.” In fact, the thorough denial of any possibility that human knowledge can grasp objective essence is precisely the most admirable part of Kant’s philosophy.

On the other hand, regarding this question there is another completely opposite evaluation, namely, that Kant’s mistake was not to underestimate the power of human knowledge, but rather to overestimate human beings. For example, Professor Zhao Dunhua believes: “Kant’s epistemology has both a side that accords with natural science and a side that does not… One significance of Copernicus’s replacement of geocentrism with heliocentrism lies in breaking the illusion that human beings are the center of the universe; the ‘Copernican revolution’ launched by Kant in philosophy, however, tries to redefine the central position of man in nature. Here the divergence between transcendental philosophy and natural philosophy has already begun to emerge.”[22]

These two criticisms, taken together, precisely bring into relief the profound significance of Kant’s philosophy from both the positive and negative sides! In fact, Kant’s exaltation of human subjectivity and his restriction of human subjectivity’s powers are both motivated by the same purpose — namely, the fundamental question to which Kant’s entire philosophy ultimately points: “What is man?”

Kant lived in an age when a mechanistic view of nature prevailed. Beginning with Descartes, mechanistic thinking filled people’s minds and became the habitual framework through which they thought about everything: “From Descartes to Newton, from Hobbes to La Mettrie, the machine metaphor dominated the early modern mind; not only the material universe, but also society, animals, and even human beings were regarded as different kinds of machines, lacking any vital impulse.”[23] Spinoza, for example, boasted: “I shall consider the actions and passions of human beings in exactly the same precise manner as if I were considering lines, planes, and solids.” La Mettrie declared: “Let us boldly conclude that man is only a machine, and that the whole world is nothing but a kind of material endlessly combined and transformed.” The consequences of such a mechanized world picture are easy to imagine: the world no longer holds any mystery for human beings, and human beings no longer feel awe toward nature. Moreover, since human beings themselves are machines, respect for human beings is in fact distorted as well; noble virtue can no longer arouse admiration, and the raising of the self’s spiritual level is meaningless. What people pursue is only material achievement — excavation, possession, and conquest.

Under such a cold world picture, the power of human knowledge seems to expand without limit, while human beings themselves become infinitely insignificant! Through mathematical calculation, human beings seem able to understand everything in the entire universe, yet they are less clear than ever about the meaning of their own existence as human beings; human beings themselves, perversely, become the slaves of human knowledge. The problem Kant faced was not merely “to rescue scientific knowledge from skepticism,” but also to rescue morality, faith, value, and meaning from nihilism!

Thus Kant, on the one hand, “by his solemn proclamation that ‘man legislates for nature,’ exalted the freedom of human subjectivity.”[24] On the other hand, and more importantly, he limited the boundaries of knowledge, so that human beings would remain humble before nature!

I have therefore found it necessary to suspend knowledge in order to make room for faith, and dogmatism in metaphysics — that is, the prejudice that would grow in metaphysics without a critique of pure reason — is the true source of all unbelief that obstructs morality, and such unbelief is at all times highly dogmatic. ^[BXXX]

“To honestly and courageously recognize the limits of reason may make philosophy more difficult and dangerous, but this is precisely the best way — if not the only way — to preserve the meaningfulness of human life”[25]

What people often value in Kant’s philosophy is the arrogance of “man legislates for nature,” yet they frequently overlook that while Kant exalted human subjectivity, he also insisted more strongly that human beings must remain humble before nature! Science cannot exhaust nature, human beings cannot dominate nature, and philosophers cannot monopolize knowledge — these are the more important lessons Kant’s philosophy leaves us.

“One decisive significance of Kant’s philosophy is that it insists there are realms human beings are necessarily unable to know, which keeps philosophers humble.” [26]

Even Kant himself repeatedly and proudly proclaimed that “his system surpassed all previous philosophers.” Yet the more important hint he left for people was not philosophical arrogance, but quite the opposite —

… But do you really hope for a kind of knowledge that concerns all human beings, that ought to transcend ordinary understanding and be disclosed to you only by philosophers? The very point you blame is precisely the best proof of the correctness of the foregoing claim, because it reveals something people could not foresee at the outset, namely that nature, in the matters in which people are indiscriminately concerned, has not shown any favoritism in distributing their endowments, and that the highest philosophy, with respect to the ultimate aims of human nature, can bring nothing more than the guidance that human nature itself has already bestowed even upon the most ordinary understanding. ^{[A831 B859]}

Kant tells us that the special thing about philosophy is not that it can make our level of cognition higher than that of ordinary people, or even expand it without limit, but precisely that philosophy can show us the limits of cognition and thereby make us humble. “It is a pity that many philosophers after Kant refused to accept this important implication of his system. On the contrary, the history of metaphysics over the past two hundred years has to a large extent been the history of various efforts to evade this painful implication (only by being humble can one become a good philosopher).”[27]

Kant did not forget to admonish people about the humility of philosophy in The Metaphysical Foundations of Natural Science either. In the book’s final sentence, Kant reminds us: “Thus the doctrine of bodies in metaphysics can neither remain with the conditioned nor comprehend the unconditioned. When it impels the inquirer to grasp the absolute totality of all conditions, there remains nothing else for it to do but to return from the object to itself, not in order to investigate and determine the ultimate boundary of things, but rather to investigate and determine the ultimate boundary of its own proper powers, by means of which it itself is enabled.”[28]

Does limiting the boundaries of knowledge then mean shrinking the space in which knowledge can be used? Kant points out: “On a cursory glance at this work, one might think that its utility is merely negative, namely, never to dare, by means of speculative reason, to go beyond the bounds of experience”^[BXXIV-BXXV]. Kant further notes that once speculative reason is left under no restraint at all, “the result is not an enlargement of our use of reason, but rather a shrinking of it,” because the abuse of speculative reason would threaten and exclude that “pure (practical) use of reason,” becoming an obstacle to that “completely necessary practical use (moral use)” of pure reason. Just as the utility of the police is positive and not negative, so the limitation of speculative reason has a very important positive significance!

On the question of whether knowledge has its limits, the greatest modern scientists would for the most part also agree with Kant:

Feynman said: “Any scientific concept lies on some scale between absolute error and absolute truth, and not at either end. I believe that accepting the idea of uncertainty is extremely necessary, not just for science but for other things as well; I believe that admitting one’s ignorance is of great significance.”[29]

Even Hawking, who had always been committed to finding a “grand unified theory” intended to encompass all physical laws of the universe, finally had to admit at the Beijing International Conference on String Theory on August 17, 2002, that “in the field of physics, there very likely exist laws analogous to Gödel’s incompleteness theorem, so building a grand unified theory that describes the universe is unlikely.”[30]

Einstein was even more explicit: “Anyone who has had a deep experience of victorious progress in this field (scientific inquiry) feels a profound reverence for the rationality displayed in existence. Through understanding, he is completely liberated from the fetters of personal wishes and desires, and thus adopts a humble attitude toward the reason embodied in existence; and this majestic reason, by virtue of its extreme profundity, is beyond human reach.”[31]

Department of Philosophy, Peking University

Hu Yilin

00423019

November 10, 2005

There are two things, the more persistently and deeply we think about them, the more our minds are filled with ever new and ever stronger wonder and awe: the starry heavens above me and the moral law within me.

——Kant

Main Bibliography

[U.S.] Pangsifen / author: The Tree of Philosophy, translated by Zhai Pengxiao, proofread by Wang Lingyun, Guangxi Normal University Press, May 2005

[German] Kant / author: Critique of Pure Reason, translated by Deng Xiaomang, proofread by Yang Zutao, People’s Publishing House, February 2004

[German] Kant / author: The Metaphysical Foundations of Natural Science, translated by Deng Xiaomang, Shanghai People’s Publishing House, January 2003

Yang Zutao Deng Xiaomang / authors: A Guide to Kant’s Critique of Pure Reason, Hunan Education Press, December 1996

[U.S.] Garrett Thomson / author: Kant, translated by Zhao Chengwen, Teng Xiaobing, Meng Lingpeng, Zhonghua Book Company, September 2002

Deng Xiaomang / author: Lectures on Kant’s Philosophy, Guangxi Normal University Press, May 2005

Zhao Dunhua / author: A Brief History of Western Philosophy, Peking University Press, January 2001

[U.S.] Feynman, Leighton, Sands / authors: The Feynman Lectures on Physics (Vol. 1), translated by Zheng Yongling, Hua Hongming, Wu Ziyi, et al., Shanghai Scientific and Technological Press, June 2005

Stephen Hawking / author: The Theory of Everything — The Origin and Fate of the Universe, translated by Zheng Yiming and Ge Kaile, Hainan Publishing House, Sanhuan Publishing House, January 2004

Stephen Hawking / author: The Universe in a Nutshell, translated by Wu Zhongchao, Hunan Science and Technology Press, January 2005

Compiled by Jiang Xiaoyuan and Niu Weixing: Rise of Man — A Reader in Science, Shanghai Education Press, July 2005

[U.S.] R. P. Feynman / author: The Character of Physical Law, translated by Guan Hong, Hunan Science and Technology Press, February 2005

Einstein / author: Writings of Einstein, edited by Xu Liangying and Liu Ming, Zhejiang Literature and Art Publishing House, January 2004

A Brief History of Western Philosophy, by Zhao Dunhua / author, Peking University Press, January 2001

p. 268, Critique A35/B51: time and space … are only “the subjective pure forms of our human intuition”

Critique A34/B50: space and time are “the a priori, formal conditions of all appearances”

p. 273, Critique of the Metaphysics of Morals: The highest law of nature must necessarily lie within us, that is, in our understanding. Selected Readings from the Original Texts of Western Philosophy, vol. 2, The Commercial Press, 1982, p. 286

p. 273 One significance of Copernicus’s replacement of geocentrism with heliocentrism lies in breaking the illusion that human beings are the center of the universe, but Kant’s “Copernican revolution” in philosophy sought instead to redefine humanity’s central place in nature. Here, the divergence between transcendental philosophy and philosophy of nature has already become apparent.

////——What people often value is the arrogance in Kant’s philosophy of “man legislating for nature,” yet they frequently overlook that while exalting human subjectivity, Kant also stressed even more that human beings must remain humble before nature! Science cannot exhaust nature, human beings cannot dominate nature, and philosophers cannot monopolize knowledge—these are the more important reminders left to us by Kant’s philosophy.

Kant, [U.S.] Garrett Thomson / author Zhao Chengwen Teng Xiaobing Meng Lingpeng / translators, Zhonghua Book Company, September 2002

p. 1 Kant … aimed to rescue scientific knowledge from skepticism and to show why metaphysics was destined to fail.

p. 13 Sensibility or understanding alone is insufficient for experience. “Intuitions without concepts are blind, concepts without intuitions are empty.” This is precisely where Kant’s theory transcends both empiricism and rationalism.

pp. 22-23 If something, by analogy and by some existing perceptions, can be connected, then it exists (A225)

p. 25 Kant opposed the view that we can perceive only our own ideas; he believed that we directly perceive objects in space and time that exist independently of us.

p. 26 Thesis of objectivity: the world is composed of objects in space and time, which are unperceived and exist independently of the perceiver. Thesis of transcendental idealism: the world composed of objects in space and time is in some sense transcendentally ideal. The two propositions are both indispensable for the First Critique, yet they seem highly inconsistent. Only by resolving this contradiction can we be properly brought to the center of this critique, which reveals the strange profundity of Kant’s insight.

p. 31 To assert that the form of the world depends on the form of any possible experience does not make the world dependent on the perceiver or perception.

////——The distinction between the “form” of an object and the “existence” of an object.

p. 31 Kant called himself an empirical realist, and he held that spatiotemporal objects are real. They are objectively real because their existence does not depend on us.

p. 41 What Kant argues is that objective time becomes possible through causality. ………….. Cause and effect make before and after possible. The direction of time is made possible on the basis of the reversibility and asymmetry essential to causality.

p. 43 Kant insists that specific causal laws must be discovered in experience, even though we can know a priori that all things indeed have a cause.

p. 46 Physical laws are not the a priori synthetic necessary conditions of experience, but neither are they merely the individual inductive generalizations of experience. They occupy an intermediate position, containing both empirical and a priori elements.

pp. 48-49 The unity of nature requires the unity of space and time; if any part of space or time has no determinate spatial or temporal relation to any other part, then spacetime would not possess unity. In the Third Analogy, Kant holds that since space and time cannot be perceived, their unity must be known through the unity of their content. In other words, the unity of space and time must be manifested through the causal interaction among objects.

p. 52 The historical development of non-Euclidean geometry did not refute Kant’s theory; (////——it was precisely a manifestation of the depth of Kant’s thought) the reason Kant denied Euclidean geometry was that he believed space’s being Euclidean was an a priori truth. In fact, however, space’s being non-Euclidean is an empirical truth.

p. 55 Kant agreed neither with the view of absolute spacetime nor with that of relational spacetime. He located his own position somewhere between Leibniz and Newton.

p. 57 He said that space is the a priori form of outer intuition, while time is the a priori form of inner intuition.

p. 63 Kant’s remedy is to show how the concept of matter can find its application without appealing to absolute space; in this sense, Kant aimed to show how physics can describe the objective world.

p. 68 (Regarding the law of causality) the intermediate position between the purely a priori and the strictly empirical.

p. 69 It is important to emphasize Kant’s rejection of Newton. This led him to seek more operational definitions for core physical concepts. This idea is very important in modern physics; the need to seek an operational definition of simultaneity was a key factor in Einstein’s special relativity.

The Metaphysical Foundations of Natural Science, [German] Immanuel Kant / author Deng Xiaomang / translator, Shanghai People’s Publishing House, January 2003

Translator’s Preface

pp. 5-6 His rejection of “absolute events” was also incomplete: after excluding them from actual experience (from phenomena), he then allowed them to guide people’s scientific research as an “idea.” ////——This is precisely where the profundity of Kant’s thought lies!

p. 6 It was precisely through his agnosticism (on the negative side) and humanism (on the affirmative side) that Kant broke through the seemingly so neat and uniform Newtonian system, even foreshadowing, in some respects, the outlines of the modern physics revolution.

p. 11 With his solemn declaration that “man legislates for nature,” Kant exalted the freedom of human subjectivity.

Text

P9 An intelligible doctrine of nature is entitled to be called natural science only when the natural laws that serve as its foundation are understood as a priori laws, and not merely as empirical ones.

P10 Every mathematical physicist is utterly dependent on metaphysical principles.

P11 In the pure part of the natural sciences, in which metaphysical and mathematical constructions often interact—the physics generalis, or general physics—it is necessary to present in a system the former conception and the principles of the construction of these concepts that accompany it; that is to say, to present the principles of the very possibility of a mathematical doctrine of nature itself, that is, to present the principles of the very possibility of a mathematical doctrine of nature itself.

P12 As long as this metaphysical doctrine of bodies continues to expand and to offer a complete exposition, I believe in it, even if no truly great results have yet emerged from it.

P13 Therefore the concept of matter must be realized through the functions of all four of the above concepts of the understanding (in the four main divisions). (Quantity, quality, relation, modality)

P15 So natural science is generally either a pure or an applied doctrine of motion.

P25 Matter is a moving thing in space. Space that is itself moving is called the space of matter, or relative space; the space in which all motion must ultimately be conceived (and which is therefore itself absolutely at rest) is called pure space, or absolute space.

P26-27 In all experience there must be something that is felt; this is the reality of sensible intuition, and therefore space, in which we are to apprehend motion through experience, must also be described as something perceptible, that is, it must be described by means of something that can be perceived; this space, as the totality of all objects of experience and also as itself an empirical object, is called empirical space. But this space, as a material thing, is self-moving. Yet a moving space, if its motion is to be perceptible, must presuppose another extended material space in which it moves; this material space, in turn, must likewise presuppose yet another, and so on ad infinitum. Therefore, all motion as an object of experience is only relative; the space in which motion is perceived is relative space……

P27-28 Absolute space by itself is nothing at all, and still less an object; it means only any other relative space that I can at any time think alongside the given space. I merely make it into something that contains all given spaces, something in which I take all given spaces as spaces in motion, and press onward into infinity beyond all given spaces. Since I have this space, though still material, only in thought as an expanding space, I know nothing of the matter that delineates such space, and so I abstract from matter; thus space is imagined as a pure, non-empirical, and absolute space. I can compare it with a still empirical space and in doing so imagine the empirical space as moving, and hence it is always regarded as at rest.That which makes this absolute space real. This means mixing the logical universality of any space, which I can compare with every empirical space contained in it, into the physical universality within the realm of reality, and thereby misconstruing the idea of reason.

P40 Absolute space is nothing for all possible experience.

P41 But here I posit all motion as rectilinear motion. For when it comes to curvilinear motion, since it is not equal in every respect, whether or not we are entitled to regard the body as moving (for example, the earth’s daily rotation) and the surrounding space (the starry heavens) as at rest, it must be treated specially with respect to its effect.

P190 Empty space does not belong at all to the existence of things, but only to the determinacy of concepts; in this sense, empty space does not exist.

P194 (last sentence) Therefore the metaphysical doctrine of bodies can neither remain with the conditioned nor comprehend the unconditioned. When it impels the inquirer to grasp the absolute totality of all conditions, there remains nothing else for it to do than to turn back from the object to itself—not in order to investigate and determine the ultimate bounds of things, but in order to investigate and determine the ultimate bounds of its own proper power, the power on which it relies.

Lectures on Kant’s Philosophy, by Deng Xiaomang /author Guangxi Normal University Press, May 2005年5月

P11 Scientific knowledge is in fact a product of the subject, established by the subject; thus the objective is also subjective, and the subjective can in this sense also be regarded as objective.

P12 The objectivity and reliability of a system of knowledge do not lie in its reflecting an external object—that object is not the object of cognition—but the scientific system constructed by the web of knowledge is after all in conformity with the objects and object-concepts that we ourselves have constructed. ………… There is one difference between Kant and Hume: Hume held that whether things-in-themselves exist is also unknowable, whereas Kant held that things-in-themselves do exist, but cannot be known.

P15 This is Kant’s “Copernican revolution” in epistemology. He reversed the relation between subject and object: it is not the subject that conforms to the object, but the subject that establishes the object and the object that conforms to the subject. In this way, he found a new foundation for scientific knowledge.

P22 We think knowledge has two levels: one is sensory knowledge, the other rational knowledge. In fact, these are different aspects of the same kind of knowledge; sensory knowledge………… Kant believed that any kind of knowledge simultaneously has these two levels, and if one level is lacking, it cannot count as knowledge.

P68 So some people say that Kant is like a reservoir, into which all earlier philosophy flows, and from which all later philosophy flows out.

The Feynman Lectures on Physics (Vol. 1), [U.S.] Feynman, Leighton, and Sands /authors; Zheng Yongling, Hua Hongming, Wu Ziyi, et al. /trans., Shanghai Scientific and Technical Publishers, June 2005年6月

P168 When this idea was revealed to the world, it caused quite a stir among philosophers, especially among those “cocktail-party philosophers,” who said: “Oh, it’s very simple, Einstein’s theory shows that everything is relative!” … “The fact that things depend on people’s frame of reference” was then imagined to have exerted a profound influence on modern thought. One might well feel puzzled by this, because after all, the fact that things depend on one’s point of view is so simple that, in order to discover it, there surely would have been no need to go looking for trouble in the theory of relativity in physics. Anyone strolling down the street must surely understand that everything he sees depends on his frame of reference, because when a passerby approaches him, he first sees the front of the person and only then the back; in most philosophies supposedly derived from relativity, there is nothing more profound than the statement that “one looks different from the front than from the back.” The old story of several blind men describing an elephant in different ways is perhaps another example of philosophers’ view of relativity.

////——Here Feynman is speaking with a mocking tone toward philosophers who understand relativity too superficially. We need not nitpick the details with Feynman; his satire hits the mark. If the goal were merely to break dogmatism, there would have been no need to wait for Einstein’s appearance at all—this task had already been accomplished far better by Kant much earlier.

A Theory of Everything——The Origin and Fate of the Universe, by Stephen Hawking /author, Zheng Yiming and Ge Kaile /trans., Hainan Publishing House and Sanhuan Publishing House, January 2004年1月

P90 Imaginary time…… A spacetime in which the time coordinate of events takes imaginary values is called Euclidean spacetime, because its metric is always positive. ……………… One may take it that using imaginary time is merely a mathematical method—or, one might say, a trick—for calculating the answer concerning real spacetime; however, there may be more to it than that. In fact, it may well be that:Euclidean spacetime is the basic concept, and what we regard as spacetime is the fictional construct indicated by our imagination.

P95 This may suggest that what is called imaginary time is actually the fundamental time, while what we call real time is merely a creation of our minds.

So perhaps what we call imaginary time is in fact the more basic concept, and what we call real time is instead merely an invention devised to help us describe the concept of the universe in our minds. But… scientific theoretical knowledge is a mathematical model we use to describe our observational results. It exists only in our heads, and thus a question like this is utterly meaningless: which is real, “real” time or “imaginary” time? The only question is which description is more useful.

P125(Marginal note) At the Beijing International String Theory Conference on August 17, 2002, Hawking conceded that in the field of physics there very likely exist laws analogous to Gödel’s incompleteness theorem, and therefore it is unlikely that one can establish a grand unified theory describing the universe.

A Universe in a Nutshell

P34……If the universe was indeed created, then why did it wait an infinite time before being created? On the other hand, if the universe has already existed for an infinite time, why has not every event that is going to happen already happened, so that history has already come to an end? In particular, why has the universe not yet reached thermal equilibrium, so that all things have the same temperature? Kant called this problem the “antinomies of pure reason,” because it seems to be a logical contradiction; there is no way to resolve it, but it is only a contradiction raised within the framework of Newton’s mathematical model. In Newton’s model, time is an infinite line, independent of what happens in the universe…………

////——A507B535 The proofs of the four antinomies above are not a scam; rather, there is a presupposition at the root of them, namely that phenomena, or the sensory world that contains all phenomena within itself, is the thing-in-itself.

P80 The idea that the universe has multiple histories sounds like science fiction, but it is now widely accepted as scientific fact.

The Rise of Man—A Reader in Science, Jiang Xiaoyuan and Niu Weixing, eds. Shanghai Education Press, July 2005

Poincaré: “Hypothesis Not Only Necessary, but Reasonable”: Mathematical quantities… are they discovered in nature by us, or are they introduced into nature by ourselves? … The framework into which we want to force everything turns out to have been constructed by ourselves, but we do not create it arbitrarily. One might say that it is made to measure, and thus we can make facts fit it without altering what is essential in the facts. Another framework that we impose on this world is space. Whence do the first principles of geometry come? Are they imposed on us by logic? Lobachevsky proved, by founding non-Euclidean geometry, that they are not. Is space suggested by our senses? No, it is not… Does geometry come from experience? Further discussion shows us that this is not the case. Thus we conclude that the first principles of geometry are nothing but conventions; however, these conventions are not arbitrary…

////——The view that mathematics is a kind of a priori synthetic judgment is one of Kant’s original insights.

The Nature of Physical Law, by [U.S.] R·P·Feynman, trans. Guan Hong, Hunan Science and Technology Press, February 2005

P2 The most up-to-date things may not necessarily be the most modern. Modern science was built precisely according to the unified tradition discovered under the law of gravitation.

The Big Bang Theory—Quantum Physics and Cosmology, by John Gribbin, trans. Lu Jufu, Shanghai Scientific and Educational Press, July 2000

P175……the standard model of the universe, the current “best choice” in cosmology…… ……But a model can never tell us what must happen in the real universe. I will give a description and take it as the history of our universe; that is the only coherent way. But please keep in mind,that this description actually applies only to a mathematical-model universe, a model universe that bears a striking resemblance to the universe we know today…

Einstein Writings, by Einstein, ed. Xu Liangying and Liu Ming, Zhejiang Literature and Art Press, January 2004

P67 “The Religious Spirit of Science” You would have a hard time finding among deeply accomplished scientists one who does not have his own religious feelings.

P73 “Science and Religion” Anyone who has had a profound experience of making victorious progress in this field (scientific inquiry) will feel adeep reverence for the rationality revealed in existence. Through understanding, he is completely liberated from the fetters of personal wishes and desires, and thus holds ahumble attitude toward the majesty of reason embodied in existence, a majesty whose profoundness is so extreme that, for human beings, it is something one can look up to but never reach.

The Tree of Philosophy

P70 Critique of Pure Reason BXXX “…” — Honestly and courageously recognizing the limits of reason may make philosophy more difficult and more perilous, but it is precisely the best way (if not the only way) to preserve the meaningfulness of human life

P 71 Kant also distinguishes two kinds of ignorance (CPR 605~606). Our contingent ignorance of empirical things ought to be able to inspire us to go beyond the realm of knowledge and toward the practical aim of philosophizing, namelyto live a better life.

“The Pure Critique”

P628 A831 B859 ……But do you really want a kind of knowledge that concerns all human beings, that ought to go beyond common understanding and be disclosed to you only by philosophers? The very point you criticize is precisely the best proof of the correctness of the foregoing claim, for it reveals something people could not have foreseen at the outset: that nature, in matters in which people are equally concerned, shows no partiality in distributing its gifts, and that the highest philosophy, with regard to the fundamental purposes of human nature, can contribute nothing more than the guiding function that human nature has already bestowed even on the most ordinary understanding.

“The Tree of Philosophy” P72 One decisive significance of Kant’s philosophy is that it insists there is a realm human beings are necessarily unable to know, and this keeps philosophers humble. ////—Even though Kant himself repeatedly and proudly declared that his system surpassed all previous philosophers.

“The Tree of Philosophy” P73 In other words, what is special about philosophy does not lie in allowing us to proudly claim that we possess a higher level of cognition than ordinary people, but in showing us the limits of all our cognition, thereby making us humble. Unfortunately, many philosophers after Kant refused to accept this important implication of his system. On the contrary, the history of metaphysics over the past two hundred years and more is, to a large extent, precisely the history of various attempts to evade this painful implication (only by being humble can one become a good philosopher).

P19 BXXIV-BXXV But if one asks what sort of legacy such a metaphysics, clarified by critique and thereby also brought into a lasting state, is intended to leave to posterity, then what exactly is it? At a cursory glance at this work, one might think that its use is nothing but negative: never to risk, by means of speculative reason, going beyond the bounds of experience. And indeed this is also the first use of such metaphysics. But this use will immediately become positive as well, once we note that the principles which speculative reason ventures to use to go beyond its bounds, if examined more carefully, have as their unavoidable consequence not an extension of our rational employment but a reduction of it, because these departures from reality threaten to bring its…………

P22 BXXX I had to suspend knowledge in order to make room for faith, and the dogmatism of metaphysics, that is, the prejudice that would arise in metaphysics without a critique of pure reason, is the true source of all that faithlessness that obstructs morality; and such faithlessness is always highly dogmatic.

P413-P414 Distinguishing contradiction from dialectical opposition

   A503B531 If someone says that every body is either fragrant or foul-smelling, then there is a third possibility, namely that it has no odor at all, so that these two mutually conflicting propositions can both be false.

   A504B532 Therefore, if I say: the world in space is either infinite, or it is not infinite, then when the first proposition is false, its contradictory opposite “the world is not infinite” is true. In this case I have merely ruled out one infinite world, but have not posited another world, namely a finite one. But if I say instead that the world is either infinite or finite, then both of these may well be false. For in this opposition I not only cancel infinity, and along with infinity perhaps also cancel the whole separate existence of the world, but also add…………, that is to say, if the world is not given at all as a thing in itself, and therefore with respect to its magnitude ought neither to be given as infinite nor as finite.

   A505B533 If this world is conditioned at every point, then it can never be given as a whole, and therefore the world is by no means an unconditioned totality, and so not existent as such a totality, neither with infinite magnitude nor with finite magnitude.

   A507B535 The proofs above concerning the fourfold antinomy are not a trick; rather, they rest fundamentally on a presupposition, namely that the appearances, or the sensible world that includes all appearances within itself, is the thing in itself.

A Guide to Kant’s Critique of Pure Reason, Yang Zutao Deng Xiaomang / eds., Hunan Education Press, December 1996

P328 Regard the cosmological ideas of pure reason merely as “regulative” principles, not as “constitutive” principles.

P330 In other words, when we employ the regulative principles of pure reason, we use them “as if” we were determining things in themselves, whereas in fact we are only bringing about the effect of promoting our continual inquiry within the field of experience.

P97 Kant, by analyzing space and time, was the first to establish a standard for truly scientific knowledge: a standard that both highlighted the fact that scientific knowledge must take sensible intuition as its object, and at the same time emphasized that such knowledge must possess universal necessity or objective reality (in Kant’s sense). From that point on, natural science was freed from the entanglement of old metaphysics and skepticism, found signposts on the epistemological road ahead, and set out on a path filled with confidence yet without losing caution. This was a sign that modern scientific thought had broken away from blind groping and reached self-consciousness.

P98-P99 The fundamental limitations and errors of Kant’s doctrine of space and time.　　I. Kant viewed space and time entirely as forms of intuition a priori inherent in the human subject. Starting from this transcendentalism, all his arguments for the “objectivity” of mathematics and sensory knowledge are thoroughly subjective; he restricts the validity of these kinds of knowledge to subjective “phenomena” and denies them any possibility of grasping objective essence (the thing in itself) beyond the phenomenal world, ultimately so as to reserve a place for fideism. In this respect, this theory also had harmful and negative effects on the healthy development of science.　　II. Kant transferred Newton’s absolute framework of space and time from the objective material world into the human subject’s a priori capacities. Yet he did not alter the “absolute” nature of this framework, and this greatly discounted the idea of subject activity in Kant’s doctrine of space and time. Since space and time from the outset exist ready-made in the mind as “forms of intuition a priori” in a “flat,” Euclidean manner,…………, but the theory of space and time in modern physics holds that Euclidean space is merely a special form or limiting form among all possible spaces in the universe……

---

[①] Deng Xiaomang: *Lectures on Kant’s Philosophy*, Guangxi Normal University Press, 2005 edition, p. 68

[②] Ibid., p. 30

[③] For example, in the opening words of the lecture “M-Theory Cosmology” at the International Conference on String Theory on August 13, 2002.

[④] Stephen Hawking: *The Universe in a Nutshell*, translated by Wu Zhongchao, Hunan Science and Technology Press, 2005 edition, p. 34

[⑤] The author uses *Critique of Pure Reason*, translated by Deng Xiaomang and edited by Yang Zutao, People’s Publishing House, February 2004 edition. Hereafter, all quotations from *Critique of Pure Reason* are marked directly in the text with the original edition’s pagination in the form “[A507 B535]” (indicating p. 507 of the A edition and p. 535 of the B edition).

[⑥] Deng Xiaomang: *Lectures on Kant’s Philosophy*, Guangxi Normal University Press, 2005 edition, p. 5

[⑦] R. P. Feynman: *The Character of Physical Law*, translated by Guan Hong, Hunan Science and Technology Press, 2005 edition, p. 2

[⑧] Feynman, Leighton, and Sands: *The Feynman Lectures on Physics, Volume I*, translated by Zheng Yongling, Hua Hongming, Wu Ziyi, et al., Shanghai Scientific and Technical Publishers, 2005 edition, p. 168

[⑨] Immanuel Kant: *Metaphysical Foundations of Natural Science*, translated by Deng Xiaomang, Shanghai People’s Publishing House, 2003 edition, pp. 26-27

[⑩] Ibid., p. 190

[11] Ibid., p. 25

[12] Yang Zutao, Deng Xiaomang: *A Guide to Kant’s Critique of Pure Reason*, Hunan Education Press, 1996 edition, pp. 98-99

[13] Garrett Thomson: *Kant*, translated by Zhao Chengwen, Teng Xiaobing, and Meng Lingpeng, Zhonghua Book Company, 2002 edition, p. 52

[14] Immanuel Kant: *Metaphysical Foundations of Natural Science*, translated by Deng Xiaomang, Shanghai People’s Publishing House, 2003 edition, pp. 27-28

[15] Ibid., p. 40

[16] Garrett Thomson: *Kant*, translated by Zhao Chengwen, Teng Xiaobing, and Meng Lingpeng, Zhonghua Book Company, 2002 edition, p. 1

[17] Stephen Hawking: *The Grand Design: The Origin and Fate of the Universe*, translated by Zheng Yiming and Ge Kaile, Hainan Publishing House and Sanhuan Publishing House, 2004 edition, p. 90

[18] Ibid., p. 95

[19] Immanuel Kant: *Metaphysical Foundations of Natural Science*, translated by Deng Xiaomang, Shanghai People’s Publishing House, 2003 edition, p. 9

[20] Ibid., p. 10

[21] Poincaré: “Hypotheses are not only necessary, but reasonable,” in Jiang Xiaoyuan and Niu Weixing (eds.), *The Ascent of Man—A Science Reader*, Shanghai Education Press, 2005

[22] Zhao Dunhua: *A Brief History of Western Philosophy*, Peking University Press, 2001 edition, p. 273

[23] Stephen Best and Douglas Kellner: *The Postmodern Turn*, translated by Chen Gang et al., Nanjing University Press, 2002 edition, p. 263

[24] Immanuel Kant: *Metaphysical Foundations of Natural Science*, translated by Deng Xiaomang, Shanghai People’s Publishing House, 2003 edition, translator’s preface, p. 11

[25] R. P. Thomson: *The Tree of Philosophy*, translated by Zhai Pengxiao, proofread by Wang Lingyun, Guangxi Normal University Press, 2005 edition, p. 70

[26] Ibid., p. 72

[27] Ibid., p. 73

[28] [Ger.] Immanuel Kant, The Metaphysical Foundations of Natural Science, trans. Deng Xiaomang, Shanghai People’s Publishing House, 2003 ed., p. 194

[29] Feynman: The relationship between science and religion, see [R. P. Feynman: The Pleasure of Finding Things Out, trans. Zhang Yuhu, Hunan Science and Technology Press, 2005 ed., p. 257

[30] Stephen Hawking: A Theory of Everything—The Origin and Fate of the Universe, trans. Zheng Yiming and Ge Kaile, Hainan Publishing House and San Huan Publishing House, 2004 ed., marginal note on p. 125

[31] Einstein: “Science and Religion,” in Collected Writings of Einstein, ed. Xu Liangying and Liu Ming, Zhejiang Literature and Art Publishing House, 2004 ed., p. 73

Translated from the Chinese original with AI assistance. The original text is authoritative.

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