A New Examination on the Relationship between Science and Philosophy

   The internal relationship between science and philosophy is undoubtedly one of the central themes in western intellectual circle over the past two thousand years, and with the constant development of both science and philosophy, the basic appearance of this issue is also changing without stop. In this paper, based on some latest results in science and philosophy, we want to make certain somewhat fundamental explorations about this basic issue.

   (I) A Historical Retrospect of the Relationship between Science and Philosophy

   If we take a macroscopic perspective to overlook the internal relationship between science and philosophy, then, we can easily see that, the relationship between them roughly goes through three major phases:

(1) As is generally known, before the 17^th century, science was to some extent a branch of philosophy, and philosophy then constituted the main body of people’s basic world view. At this time, scientific research and philosophical inquiry were often interweaving with each other.

Take some great scholars for example, in ancient Greece, Plato made a series of fundamental contributions in philosophy, and his esteem for idea laid the foundation of rationalism temperament in western culture for more than two thousand years, and meanwhile, he also made some substantial contributions in mathematics, and in them, the most famous one is naturally his school’s classification of five kinds of regular polyhedron (cube, regular tetrahedron, regular octahedron, regular dodecahedron and regular icosahedron) which extensively exist in the natural world. After Plato, the successive Aristotle embodied the different thinking orientation in western culture, who laid the thought foundation of empiricism philosophy; in the classicMetaphysics, he thinks that the particular is prior to the universal; and meanwhile, Aristotle’s basic contributions in science are also widely known and he is the important founder of a series of subjects, including zoology, physics, logic and etc. To conclude, in the representative figures of ancient Greece, they kept intellectual enthusiasm to both philosophy and science simultaneously, and also did groundbreaking significant contributions to both of them. This is the first period of the relationship between science and philosophy.

  (2) When it advances to modern times, the basic relationship between philosophy and science begins to gradually undergo deep-level changes. In the 17^th century, science and philosophy are still concurrently developing and mutually promote. Take Descartes as an example, he thinks that human reason is the source of everything, as he says: “Observing this truth: I am thinking therefore I exist, was so secure and certain that it could not be shaken by any of the most extravagant suppositions of the sceptics, I judged that I could accept it without scruple, as the first principle of the philosophy I was seeking.”[1] Compared with Plato’s rationalism, Descartes pulls the eternal idea in the external objective world into human internal mind’s innate reason, which makes human’s subject status greatly stand out, and thus, he expands the range of philosophy and changes western philosophy’s problem consciousness, and brings modern philosophy into a new stage of epistemology. In the meantime, Descartes’ significant contributions in science are also well known: he systematically develops analytic geometry (Fermat independently gets the basic idea of analytic geometry), and also does many original basic contributions in physics (like momentum conservation law, refraction law of light, Newton’s first law of motion, and so on). After Descartes, Leibniz inherits the rationalism tradition, and he thinks: “For something to be in the understanding it suffices that it can be found there. And the sources or basic proofs of the truths we are discussing can be found there, and only there: the senses can hint at, justify and confirm these truths, but they can’t demonstrate their infallible and perpetual certainty.”[2] Leibniz’s insistence on the importance of innate reason is perhaps not novel in the history of philosophy, and his real ingenious contribution is probably his unique “monad theory” (it’s a pity that the monad theory perhaps does not spark more ideas later on). On the other side, in science, Leibniz is an encyclopedic scholar, and besides the epoch-making contribution in the creation of calculus, he also does important contributions in many fields like biology, geology, medicine, probability, information science and etc.

   At the same time, with the development of science, philosophy and science also begin to show a gradual seperation internal tendency, and at this moment, professional scientists and philosophers appear, for instance, famous philosopher Spinoza lacks basic understanding about science, and also does not make any substantial scientific contribution, while many scientists, like Huygens and etc, also lack basic philosophical knowledge.

   In the 18^th century, all fields of science are developing by leaps and bounds, while the research scope of philosophy is also broad, but it is already difficult to say exactly which scholars make original contributions. At this time, in intelligentsia, the representative figure who is expert at both science and philosophy is undoubtedly Kant, in the book General Natural History and Theory of Heavens, Kant puts forward the nebula hypothesis of star formation, and he is also proficient in natural sciences like natural history, geology, mineralogy, on the other side, in Critique of Pure Reason this eminent magnum opus, Kant makes rich contributions for modern philosophy in many ways.

   But, the basic tendency that philosophy and science detach from each other is more increasing. On one hand, for some German philosophers like Hegel, Schelling, Fichte and so on, and some English philosophers like Hume and Berkeley, they just have broad exposure to philosophy and lack sufficient scientific training, for instance, Hegel once used speculative method to deduce that there exist 7 planets in solar system, which is naturally rather ridiculous in today’s view. On the other hand, for some leading figures in science, like mathematicians Laplace and Lagrange and physicist Ampere, their knowledge structure merely concentrates on scientific fields, and without enough philosophical knowledge.

   In the 19^th century, the intellectual exchange between science and philosophy is more and more weak, but not completely cut off, at this time, famous people among scientists who are proficient in philosophy include Poincare, Mach, and so on. Poincare’s tremendous contributions in mathematics don’t need to detailedly list, and some subjects he founds alone like the qualitative theory of ordinary differential equation and algebraic topology has a far-reaching global impact to modern mathematics, and meanwhile, in philosophy, he is renowned for conventionalism and his philosophical works, like Science and Hypothesis, Science and Method, Last Meditation and etc,  are all widely spread. Mach’s contributions in mechanics are also universally acknowledged, and his fierce criticism to Newtonian Mechanics directly inspires Einstein’s inquiry in theory of relativity, and he also has brilliant contributions in many other areas, including acoustics, optics, thermology, fluid mechanics, electricity, and from the basic fact that the flying speed is named after Mach we can also feel his high status in physics. While Mach’s philosophy, as a branch of positivism and empiricism, has a large impact to Vienna Circle’s logical positivism, and he thinks: scientific laws are fact summation derived from the experiments, and they are created is for people to more easily understand the complex data, and thus, scientific laws are not so much connected with actual natural phenomena as related with human thinking. Though Mach’s this basic view is idealist, the rich contents of his philosophy also contain some enlightenting spiritual elements.[3]

   When human society advances to the first half of the 20^th century, great scientists who have deep cultivation in philosophy include Einstein, Weyl, Whitehead, etc.

   As we know, Einstein has a strong interest in philosophy in his lifetime and also reads many philosophical books, Volume 1 of Collected Essays of Albert Einstein contains many articles related to philosophy, like “View on Kant’s and Mach’s philosophy”, “On Bertrand Russell’s epistemology”, “Physics, philosophy and scientific progress”, “Remark on Engels’ manuscript of Natural Dialetic”, etc, from them, we can easily see: Einstein is very familiar with many people’s philosophical views, like Hume, Mach, Kant and Russell, and the thought essence contained in these works is also integrated into his organic thought system. These energetic philosophical ideas also have a positive impact on Einstein’s scientific innovation, for instance, he once points out Hume’s philosophy’s profound enlightment for his creation of special relativity.

   As one of the greatest mathematicians in the 20^th century, Weyl makes a series of significant contributions in mathematical fields like topology, differential geometry, analytic number theory, Lie group, etc; and meanwhile, he also has broad knowledge in philosophy, and his classic Philosophy of Mathematics and Natural Scienceextensively discusses about epistemology, and quotes views from more than one hundred philosophers and scientists, and deeply explores many related topics. Weyl’s philosophical views are constantly changing in his life, and broadly speaking, go through Fichte’s idealism, Husserl’s phenomenology and transcendental existentialism these three periods.[4] In conclusion, similar to Einstein, Weyl also has a lifelong interest in philosophy.

 (3) From the second half of the 20^th century, the relationship between science and philosophy enters into a new phase. On one hand, the influence of philosophy on science is more weak, on the other hand, whether philosophy itself has any substantial progress also becomes a question. These two basic characteristics determine new changes of their relationship.

   At this time, philosophers with certain scientific mastery are Putnam and Tarski. As is well known, Putnam is proficient in quantum mechanics and general relativity, and meanwhile, he makes a critical breakthrough in Hilbert’s 10^th problem, while Putnam’s philosophical research covers a wide range, involving many branches like language philosophy, philosophy of mind, religious philosophy, etc, and in them, he all puts forward his many new views. While Tarski specializes in topology, measure theory, mathematical logic, set theory, etc, and in 1924 (he was only 23 then), he proposed the Banach-Tarski paradox based on axiom of choice, and this renowned theorem points out: when axiom of choice holds, for a three-dimensional solid ball, we can get two solid balls completely identical to the original ball through a series of rigid transformations. Similar to many logicians, Tarski is also interested in issues like “truth”, and his semantic and logical analyses about truth has a wide influence on linguistic philosophy, it is worth noting that: if we just make analyses about “truth” from epistemology, then are possibly difficult to obtain any substantial new development[5] ; but if we relate it with mathematical logic, then are able to get some enduring objective conclusions.

   While since the second half of 20^th century, major mathematicians, physicists and biologists with a strong interest in philosophy are already few, for many leading scientists like Serre, Grothendieck, Feynman and Chen Ning Yang[6] , they just specialize in science. While it is not accidental that the influence of philosophy to science is gradually weakening, and there are some deep-level basic reasons behind, below, we want to do some preliminary analyses about the roots of this basic phenomenon.

(II)Some Central Themes of Philosophical Epistemology from the Perspective of Modern Science

   With the development of modern science, especially the huge development of 20^th century science, many traditional philosophical themes in the past can be more maturely and deeply understood now, and they at least include the following issues:

  1 About the nature of mathematics. The nature of mathematics has provoked many philosophers’ contemplation, and take Kant for example, in Critique of Pure Reason, he writes: “proper mathematical propositions are always judgements a priori, and not empirical, because they carry along with them the conception of necessity, which cannot be given by experience.” “Arithmetical propositions are therefore always synthetic, of which we may become more clearly convinced by trying large numbers. For it will thus become quite evident that, turn and twist our conceptions as we may, it is impossible, without having recourse to intuition, to arrive at the sum total or product by means of the mere analysis of our conceptions.” [7] Here, Kant emphasizes that mathematics’ basic characteristic as synthetic proposition, and in the following chapters, he want to prove why mathematical propositions as synthetic propositions have general validity, and he thinks that the root of generality of mathematical propositions is that time and space is the so-called “pure form of sensuous intuition” (detailed discussions of it is in the latter part of this paper). From Kant’s example, we can easily see that, many philosophers have been probing “the nature of mathematics” and keep high exploration enthusiasm, then what conclusions do they get? Probably just some hollow literal writings, and these inquiries do not make any substantial impetus to the theme in both depth and breadth, but, the 20^th century mathematics has splendid achievements, here, we just list three subjects:

   (1)Abstract algebra. Compared with higher algebra, the thought system formed by central concepts in abstract algebra, like group, normal subgroup, ring, ideal, field, and so on, is a new language, and it greatly extends the range of algebra and deepens its depth. As to the questions it resolves, field extension theory can solve old problems like trisection of an angle, quadrature of a circle (after field extension theory emerges, the resolution of trisection of an angle is already natural and ripe), while Galois theory’s fundamental theorem can solve deep problems like no roots of nth degree polynomial equation exist. The view of structure permeates the whole abstract algebra, and knowledge points of group like fundamental theorem of group homomorphism and group direct product, of ring like prime ideal and maximal ideal, and of field like field extension, all vividly embodies the structural view of algebra. At the same time, what abstract algebra studies is not merely abstract structure and general concept, it also has many special cases, like the special linear group of group theory, the polynomial ring and integer ring in ring theory, and finite field and construction of field extension in field theory are all vivid, interesting and valuable special cases. Ideal is an elegant and pivotal basic concept in ring theory, but if there is just ideal this single concept and without the support of other important concepts, abstract algebra’s thought system is also definitely thin and hollow, it is through concepts like prime ideal, maximal ideal, Noetherian rings and PID and the deep connections between ring theory and field theory that ring theory’s thought system becomes rich and full. Field extension is a very natural theory, and the basic distinction between algebraic extension and transcendental extension is a fundamental distinction of it, and it can be used as an effective tool to solve trisection of an angle problem also demonstrates the power of treating geometrical problems by algebraic method. (The styles between using analytical approaches to solve geometrical problems and using algebraic ones to solve geometrical problems do exist large differences) Finally, the fundamental theorem of Galois theory is a concluding theorem of abstract algebra, and it reflects the graceful and concise internal connections of intermediate field and automorphism group, and is one of few epoch-making basic breakthroughs in abstract algebra. The operative feature also permeates into the whole abstract algebra, and people who have learned abstract algebra will have a deep feeling about this feature, though operation is not the internal aim of algebra, it is indeed its fundamental overall style. In conclusion, abstract algebra great pushes forward the holistic intension of mathematics.

   (2)Functional analysis. The problem consciousness of functional analysis is rooted in mathematical analysis and higher algebra, and central contents like integral operator, differential operator, Baire category theorem, compact operator all have inextricable internal connections with the previous courses, and are the deepening and extension of related concepts and ideas in the previous courses. As to the questions it resolves, functional analysis also solves many old problems, like Weierstrass’ construction of the function continuous and non-differential at anywhere, which is a miracle in the eyes of 19^th century analysts, but through Baire category theorem, we can have a more natural and deep understanding about it, namely, functions continuous and non-differential at anywhere are second category sets, as another example, for the convergent problem of Fourier series, we just have somewhat elementary treatment in mathematical analysis, while functional analysis has a more profound analysis about it. The structural view in mathematical analysis is still not obvious, while it is somewhat notable in functional analysis; Hilbert space and Banach space are the research objects of functional analysis (as the research topics of functional analysis, important examples like Lp space, lp space, C[a,b] are all Banach space), while important theorems like Hahn-Banach extension theorem, uniform boundness theorem, open mapping theorem, and closed graph theorem characterize the basic properties and internal structure of these spaces. In terms of special cases, functional analysis contains many beautiful examples, and Lp space, Fourier series are all important and beautiful special cases. As an important type of operator, compact operator is the important research topic of functional analysis and it has some important basic properties, as an abstract concept, it generalizes many valuable special cases, and can let us feel the enormous power of continuously generalizing and abstracting in mathematics. Finally, functional analysis also has a far-reaching and broad impact on the subsequent mathematical development, for instance, it provides the basic language for partial differential equation, and also directly and widely permeates into quantum mechanics. 

   (3)Real Analysis. Real analysis is the direct deepening of mathematical analysis, and does not have much thought association with algebra. It originates from some fundamental problems tormenting the mathematical world in the 19^th century analysis, like the integrability of function, exchange of order of integration, and is the direct extension in thought system of mathematical analysis. For some deep questions like integrability of function, mathematicians find out that they cannot effectively resolve it by using sequence language like sequence convergence, and therefore, in real analysis, they invent a series of new language, namely, using set and measure to replace sequence, thereby thoroughly solving these fundamental questions in analysis. As a basic concept in real analysis, measurable set is defined through outer measure and Caratheodory condition and is closely related with elementary set. As we know, Lebesgue measure has basic properties like countable additivity, upper continuity. Real analysis also deeply studies the internal structure of Lebesgue measurable function. Bounded variation function and absolutely continuous function are two kinds of important functions, and they all have good properties (like every bounded variation function has finite derivatives almost everywhere; while the derivative of absolutely continuous function is integrable, and the fundamental theorem of calculus for Lebesgue integration holds now). Real analysis thoroughly resolves the integrability of function, exchange of order of integration and monotone convergence theorem these three basic problems, and lays a solid foundation for modern analysis, and also provides stable operational space for the subsequent courses (like harmonic analysis). As for the overall style, real analysis is an elegant and exquisite course, and there are many graceful and delicate skills, and the basic conclusions it finally gets are also harmonic, quite enchanting.

   The above discussed three subjects all belong to mathematical developments in the first half of 20^th century, and in the 1960s and 1970s, there was a new wave of intellectual revolution in the mathematical world, and more complex and profound subjects like K theory, abstract algebraic geometry and homological algebra rapidly emerged, and they all changed the overall face of mathematics. To sum up, the mathematical world’s holistic understanding about mathematics is rapidly developing, but the philosophical world is somewhat vague about this situation, and thus, their answer to the old question “the nature of mathematics” is almost certain to be empty and superficial.[8] This is naturally a holistic effect brought by philosophical world’s detachment from the mathematical frontiers.

2 Space-time view. In western philosophy, space-time view also has caused much dispute, and as is well known, Kant thinks that time and space are both ‘form of sensuous intuition’, and he argues: “What then are time and space? Are they real existences? Or, are they merely relations or determinations of things, such, however, as would equally belong to these things in themselves, though they should never become objects of intuition; or, are they such as belong only to the form of intuition, and consequently to the subjective constitution of the mind, without which these predicates of time and space could not be attached to any object?”[9] Here, the first view belongs to Newton, the second one belongs to Leibniz, while the third one belongs to Kant.

In terms of the third view that time and space as ‘form of sensuous intuition’, Kant makes some systematic expositions, and his expositions can be divided into “metaphysical exposition’ and ‘transcendental exposition’ these two parts. In them, Kant’s metaphysical expositions about the conception of space have four points: firstly, “space is not a conception which has been derived from outward experiences”; secondly, “space then is a necessary representation a priori, which serves for the foundation of all external intuitions”; thirdly, “space is not discursive, or as we say, general conception of the relations of things, but a pure intuition”; fourthly, “space is represented as an infinite given quantity.” After that, Kant gives the ‘transendental exposition’ of conception of space, and he thinks: “how can an external intuition anterior to objects themselves, and in which our conception of objects can be determined a priori, exist in the human mind? Obviously not otherwise than in so far as it has its seat in the subject only, as the formal capacity of the subject’s being affected by objects, and thereby of obtaining immediate representation, that is, intuition; consequently, only as the form of the external sense in general.”[10]

About Kant’s these abstract expositions, the later philosophers have a lot of discussions, and in them, Russell respectively refutes the four arguments of Kant’s metaphysical expositions of conception of space, and he argues: 1 “According to Kant, the eyes and the mouth exist as things in themselves, and cause my separate percepts, but nothing in them corresponds to the spatial arrangement that exists in my perception.” “Kant holds that the mind orders the raw material of sensation, but never thinks it necessary to say why it orders it as it does and not otherwise.” 2 “I should emphatically deny that we can imagine space with nothing in it. You can imagine looking at the sky on a dark cloudy night, but then you yourself are in space, and you imagine the clouds that you cannot see.” In fact, Kant will also agree with Russell’s this view, and he also does not recognize there exists pure space which can be separated from all materials. 3Kant thinks that the space does not have the concept of various parts, and part of it, the “spaces”, is still the “space” itself, while Russell thinks : “To those who take, as practically all moderns do, a relational view of space, this argument becomes incapable of being stated, since neither ‘space’ nor ‘spaces’ can survive as a substantive.” 4Kant thinks: “Sensuous perception’s infinity should be related with the infinity of space, thus space is not a concept.”[11] While Russell refutes: “It is difficult to see how anything infinite can be ‘given’.” [12] (From Russell’s these multi-angle critiques of Kant, we can see that: compared with Chinese culture, western culture’s perception of space is indeed somewhat speculative, and also touches some basic characteristics of space.)

To conclude, we can see that, though western philosophical world’s speculations about the conception of space have certain depth of thought, their detachment from modern scientific knowledge is also obvious, and if we just walk along the road of philosophy, we probably cannot get some simple and important basic theories (like special relativity) even if we spend several centuries’ time.

About the metaphysical exposition about the conception of time, Kant’s expositions have 5 points: firstly, “time is not an empirical conception”; secondly, “time is a necessary representation, laying at the foundation of all our intuitions”; thirdly, “on this necessity a priori is also founded the possibility of apodeictic principles of the relations of time, or axioms of time in general”; fourthly, “time is not a discursive, or as it is called, general conception , but a pure form of the sensuous intuition”; fifthly, “the infinity of time signifies nothing more than that every determined quantity of time is possible only through limitations of one time lying at the foundation.” As to the transcendental exposition about the conception of time, Kant writes: “Time is nothing else than the form of the internal sense, that is, of the intuitions of self and of our internal state. For time cannot be any determination of outward phenomenon. It has to do neither with shape nor position; on the contrary, it determines the relation of representations in our internal state.”

To sum up, the basic view Kant repeatedly argues is that time and space are both not concepts, but forms of sensuous intuition, namely :“space ad time, as the necessary conditions of all our intuitions, in relation to which all objects are therefore mere phenomena, and not things in themselves, presented to us in this particular manner. And for this reason, in respect to the form of phenomena, much may be said a priori, whilst of the thing in itself, which may lie at the foundation of these phenomena, it is impossible to say anything.”[13] About Kant’s arduous intellectual effort, on one hand, we indeed have full respect, however, compared with the vast achievements of modern mathematics and physics, we can also feel its basic defect. Below, we want to state some significant developments involved with the fundamental characteristics of space and time in modern mathematics and physics:

(1)Special relativity. As is generally known, the concept of space-time in classical mechanics is absolute time-space view, namely, Galileo’s space-time view, and this theory thinks: for all the inertial systems, mechanical laws have the same form, but the validity of this basic space-time view has gradually been questioned with the double impacts of experiment and theory. As one of the experimental bases to lead to special relativity, Michelson-Morley experiment finds out the speed of light is irrelevant to the reference frame, and thus, Galileo’s space-time view shows profound internal conflicts with Maxwell theory. In 1905, Einstein makes creative fundamental solution to the chaotic condition of mechanics theory, and puts forward the simple but hugely influential special relativity, and two basic assumptions of this theory is principle of relativity and principle of constancy of light speed, and from these two basic assumptions, it is easy to deduce Lorentz transformation, which is the central equation of special relativity. From Lorentz transformation, we can deduce length contraction, time dilation, relativity of simultaneity and weight increasing these four basic effects, and meanwhile, the velocity formula of relative movement also correspondingly deepens. Finally, we can also get the extremely important mass energy equation. The above descriptions are probably the main intension of special relativity, and they form an organic thought system, which revolutionizes the Galileo’s space-time view. Though the mathematical deductions of special relativity are simple, and the mathematical tools it uses are just some simple differential and integral calculus, it has a profound physical intension, and also has a comprehensive impact on the subsequent development of modern physics.

(2) Differential geometry, Riemannian geometry and Global differential geometry. As is generally known, the research topics of differential geometry are curves and surfaces, and in them, surface is the major research object. The computation of length of curves has been solved in calculus, and in differential geometry, it introduces simple concepts like curvature and torsion, which characterize some basic properties like bending degree of curve. Similarly, some basic properties of surface, like area, tangent plane, normal vector, also already have precise solutions in vector analysis, while in differential geometry, mathematicians introduce the Guassian curvature to describe the bending degree of surface, and also introduce some other delicate concepts (like developable surface, geodesic curvature, etc) ; basic objects like geodesic line and minimal surface are also central topics of surface theory; later, Gauss discovers that K is an intrinsic quantity through complicated computations, and gets the so-called Gauss’s theorema Egregium, which is a significant discovery and directly catalyzes the birth of Riemannian geometry; Gauss-Bonnet formula is one of the central conclusions in differential geometry, which is a direct generalization of the sum of all the angles of a trianlge is 180 degrees in plane geometry, but has a much wider applicability. To sum up, differential geometry enables people’s understanding towards geometry to have an overall deepening.

Riemannian geometry and global differential geometry also have their own complex contents, and we do not elaborate here.

Generally speaking, as Shiing Shen Chern says, the development of geometry has gone through 5 basic stages, and the first two stages are respectively Euclidean geometry and analytic geometry, and they are already well known now. As to the third stage in the development of geometry, Mr. Chern points out: “The third development is the notion of group, which is a basic structure in mathematics”, “he (Klein) builds geometry on the basis of group: a space has a transformation group, which permits the spatial graph to move from one position to another, and thus, once we have a group, we have a geometry, and then we study the geometric properties of all graphs which are unchanged under this transformation group.” Namely, group theory integrates the discussions of geometry into unified intellectual framework, which greatly improves the ordering degree of the whole field. After it, “Riemann localizes geometry, which is the fourth development of geometry.” “Riemann not only uses coordinates, but also uses the differential of coordinates, and thus localizes Cartesian geometry”, “Riemannian geometry is mainly built on arc length s, and the square of differential of arc length will equal quadratic differential form of the coordinate, and we can use arc length to build a geometry, because we have ds, then can compute the length of the curve connecting these two points, namely, arc length.” What Mr. Chern says is naturally just some simple notions in Riemannian geometry, but can also show the plain original ideas of Riemannian geometry. Finally, “after localization, we also need integration, and also need to extend it to the whole space, which is arguably the fifth development of geometry.” [14] The typical feature of this stage is the wide application of the mathematical tool algebraic topology.

(3)Algebra and geometry. In the review article “Mathematics in the 20^th century”[15] , Atiyah does some explorations about certain basic characteristics of mathematics, and he examines the two pillars of modern mathematics: algebra and geometry. Firstly, he thinks: “Geometry is, of course, about space, of that there is no question. If I look at the audience in this room I can see a lot; in one single second or microsecond I can take in a vast amount of information, and that is of course not an accident. Our brains have been constructed in such a way that they are extremely concerned with vision.” Therefore, Atiyah concludes: “spatial intuition or spatial perception is an enormously powerful tool.” “We try to put them into geometrical form because that enables us to use our intuition. Our intuition is our most powerful tool.” “The human mind has evolved with this enormous capacity to absorb a vast amount of information, by instantaneous visual action, and mathematics takes that and perfects it.” To sum up, Atiyah thinks that modern geometry has close basic connections with human’s spatial intuition, which is an important means for human to understand the world.

While about the nature of algebra, Atiyah thinks that it is related with time, and he says: “Algebra, on the other hand, is concerned essentially with time. Whatever kind of algebra you are doing, a sequence of operations is performed one after the other and ‘one after the other’ means you have got to have time. In a static universe you cannot imagine algebra, but geometry is essentially static. I can just sit here and see, and nothing may change, but I can still see. Algebra, however, is concerned with time, because you have operations which are performed sequentially and, when I say ‘algebra’, I do not just mean modern algebra. Any algorithm, any process for calculation, is a sequence of steps performed one after the other; the modern computer makes that quite clear. The modern computer takes its information in a stream of zeros and ones, and it gives the answer.” Through Atiyah’s clear expositions, we can easily see that, algebraic operations do have essential connections with time.

Atiyah’s analyses about some basic characteristics of geometry and algebra naturally can extend our overall understandings about time and space.

To conclude, modern mathematics and physics have advanced the discussions about time and space to a considerable depth, which is hard to imagine for the speculative philosophers who are not familiar with modern mathematics and physics, furthermore, Kant thinks that time and space are so-called forms of sensuous intuition, and are related with human’s practical activities, which I think is presumably nonsense, because mathematics, time and space are all basic inherent properties of the universe, which are completely irrelevant with human’s subjective practical activities, and also do not have any connection with human’s perceptual experience, and I think this point can be deduced as a final conclusion.

Certainly, western philosophy’s discussions about space-time view sometimes also have deep insights, and Whitehead once expounds Descartes’ philosophy of time and space :“He concieves extension as one fundamental attribute of the material, and we can summarize his notion as this: the ultimate fact is not static substance, but the stream of physical existence. We can name this stream and its content and any part of the fullness of occasional presence as an event: extension is the fundamenal attribute of things, and also the fundamental attribute of process. But the evolution of nature cannot be compressed in a continuous linear time process, and it needs such kind of process without the limit of quantity to fulfil this complete insight.”[16] We can easily see, Descartes’ this basic idea is highly consistent with theory of relativity. In the eyes of scholars under pure eastern culture’s influence, time and space are deeply related with motion, which seems somewhat incredible, but in the profound tradition in western philosophy, the deep discussions about extension and time are already voluminous, and thus, Einstein who is very familiar with western philosophy can put forward theory of relativity is also a natural consequence.

Through the above complicated discussions, we can get the following basic conclusion: the inquiry of time and space issue must be based on broad and deep modern scientific knowledge, and though philosophical dicussions also possibly contain some valuable thought nutritions, they should be in the ancillary position, because philosophical speculations contain many ludicrous views, and meanwhile, if philosophical speculations do not have the assistance of mathematical formulas, then they also will not get any substantial scientific conclusion, and thus, are also hard to have direct impact on human’s material life.

3 Probability. Since ancient times, the philosophical world has done much exploration about the complex theme of the relationship between necessity and probability, while such kind of exploration mainly concentrates in the social areas, for example, Schopenhauer once writes: “The life journey of one person is completely not determined by himself, but decided by other two factors-a series of accidental events and his treatment of these events, and these two factors continuously interact and adjust to each other.”[17] Philosophers’ these discussions are certainly also valuable, but compared with them, the scientific community’s research about probable events is undoubtedly more profound, precise and complex.

As is generally known, in the 1920s, the great mathematician Kolmogorov founded the axiom system of modern probability, and he put probability in the theoretical background of measure theory to do a holistic examination, and an event space is defined as a special measurable set, probability function is defined as a measurable function, and expectation is defined as the integration of probability function, and he further proved the simple and basic large number law. Modern probability also introduces basic concepts like conditional expectation, and these concepts and theorems interweave with each other, which together constitute the complete thought system of probability.

To conclude, the discussions about probability maybe need dividing into two basic parts: in social fields, we need speculative philosophy and science to together explore, while in the natural domain, what we need is just modern science.

4 Quantum mechanics. As is well known, in the 1920s, European intelligentsia bursts forth the exciting revolution of quantum mechanics, which thoroughly reforms Newtonian mechanics. In the theoretical system of quantum mechanics, Heisenberg equation is the foundation of matrix mechanics, while Schrodinger equation is the foundation of wave mechanics, and the significant Dirac equation is the Schrodinger equation considering relativistic effects. In wave mechanics, the integration of the square of wave function is the probability distribution of a particle in one area, and the state space of quantum mechanics is a Hilbert space. Today, quantum mechanics has permeated into the general culture of human society, and many conclusions have become familiar-sounding common sense.

After the birth of quantum mechanics, it also provokes much philosophical discussion, for instance, Heisenberg’s uncertainty principle has provoked extensive discussion about certainty and uncertainty, but, unfortunately, since these so-called philosophical speculations lack efficient support of scientific knowledge, thus, most of them has become empty and does not get certain substantial conclusions.

5 The so-called “how are synthetic judgments a priori possible”. “Synthetic judgments a priori” issue is the central theme of Kant’s epistemology, and in the ‘Introduction’ part of Critique of Pure Reason, Kant raises this question: “How are synthetic judgments a priori possible?”[18] If we translate this seemingly obscure sentence, its meaning is actually simple, namely, mathematics and natural sciences are all synthetic judgments a priori (Kant thinks mathematics is not analytical judgement, 5+7=12, cannot be obtained by analysis, but is related with perceptual experience, thus, is a kind of synthetic judgment), why do they have universal necessity? In other words, the question Kant puts forward here is: why do mathematics and natural sciences have universal applicability? The universal effectiveness of scientific truth (such as mathematical knowledge like partial differential equation, and physical knowledge like statistical mechanics) is an obvious objective fact, which Kant does not doubt, and what he questions here is, why do they have universal effectiveness?

About mathematics’ universal applicability, Kant’s answer is: the foundation of mathematics-time and space, are both ‘form of sensuous intuition’, and they ensure mathematics’ universal necessity, while for the universal necessity of natural sciences, Kant’s answer uses the twelve categories as the theoretical basis.

From the viewpoint of science, Kant’s speculative answer is certainly empty, even ridiculous, and for the reason why mathematics has universal applicability, I think we can only answer it from the inherent characteristic of mathematics itself, for instance, the basic fact that harmonic function has infinite differentiability is the result of strict mathematical deductions, which has nothing to do with space and time as ‘form of sensuous intuition’; every mathematical course starts from several original concepts and original axioms, and the following deductions conform to the strictness of logic, and thus, they certainly have universal necessity. Natural sciences’ universal necessity is also like this.

I think today in the 21^st century, there are few professional scientists who will worry about mathematics’ universal effectiveness, or, natural sciences’ universal effectiveness, because the bedrock of modern science is very solid, and meanwhile, in the exploration process of rigorousness of modern science’s foundation, we should attribute almost all the essential contributions to professional scientists (like in the second crisis of mathematics, Cauchy introduces the basic idea of sequence convergence to characterize the limit, and Weierstrass introduces the fundamental concept uniform convergence to clarify the chaotic condition in function series, while Dedekind builds the axiomatic definition of real number system), which have little to do with speculative philosophers.

Here, one question which really needs inquiring is: why do there exist these beautiful and complex basic laws in the universe? This point is probably what Kant really wants to explore. If we ask: why do there exist these elegant and abstract basic structures in the universe? For this basic question, I think that no scientist can answer it, because before we explore a concrete unknown question, no scientist can guarantee that a certain conclusion (for instance, whether Riemann Hypothesis is correct) must be true, or must be wrong, and only after proofs or experimental observations can we make definite conclusions. The order of universe is very awesome, but, I think nobody can answer why the universe complies with these elegant and abstract basic laws.[19] Certainly, we can get some ambiguous conclusions, for instance, mathematics’ every step of development is very natural: from differential geometry to Riemannian geometry to global differential geometry, the research topics of differential geometry go through a natural extension process, while the deepening of algebraic geometry’s thoughts is also unadorned, from abstract algebra to homological algebra, the deepening of algebra is also dominated by some simple basic ideas. What we can get are just some general conclusions, but the question why do there exist these universal and beautiful internal rules in universe, is never able to completely solve. Here, it is worth adding that, the universe is not that extremely harmonious as we imagine: for instance, in geometry, trisection of an angle cannot be done, as another example, in algebra, polynomial equations of more than five degrees do not have unified root formulas, and moreover, in analysis, most Lp spaces are not Hilbert space, in physics, parity nonconservation is also a simple example. To sum up, the universe is neither that inharmonious nor that absolutely harmonious (as many scientists with strong aesthetic temperament mistakenly think), it is a proper moderation, a proper beauty.

6 Primary qualities and secondary qualities. In the long history of philosophy, the intense debate about primary qualities and secondary qualities has lasted for several hundred years, and Locke first extracts this well-known question, and he writes: “qualities thus considered in bodies are of two kinds. First, there are those that are utterly inseperable from the body, whatever state it is in. Qualities of this kind are the ones that a body doesn’t lose, however much it alters, whatever force is used on it, however finely it is divided.” While “Secondly, such qualities which in truth are nothing in the objects themselves, but powers to produce various sensations in us by their primary qualities, i.e. by the bulk, figure, texture, and motion of their insensible parts, as colours, sounds, tastes, etc.”[20]

The later philosophers generally think that time and space belong to primary qualities, while colours, sounds, tastes belong to secondary qualities. Philosophers think that time and space as the material’s attributes are different from colours and tastes, though they are all material’s attributes, time and space have more objective sociality; while if we think that time and space belong to material’s feature, and are related with perceptual practice, this view is undoubtedly somewhat ridiculous, because time and space are basic properties of the universe, and do not have any perceptual connection with human society, and it is a simple basic fact. Meanwhile, colours, sounds and tastes are probably also excited by material particles, and these objects’ molecules are also objective things, and their connections with individual perceptions are also not essential, and thus, what kind of differences between the so-called primary qualities and secondary qualities does not have too much significance. Certainly, the speculations of primary qualities and secondary qualities have stimulated people’s deep research about many concrete biological problems in seeing, hearing and smelling, which is probably the real value of this debate. Whitehead once comments :“This theory takes part in the battle of modern science. Not only for physics, but also for biology, on guiding scientific research into fruitful fields, this theory has fundamental contributions.”[21] To sum up, the debate between primary qualities and secondary qualities once plays an important role in inspiring scientific research, but if just limited in the scope of philosophical speculations, and not extends the antennas in fields like physics and biology, the meaning of this famous debate probably is not notable.

7 The long debate between empiricism and rationalism. The long-standing debate between empiricism and rationalism is naturally the main line in the developing process of western philosophy, and the views of both sides have fought for hundreds of years. Empiricism’s spokesmen include Locke, etc, and he says: “In that all our knowledge is founded; and from that it ultimately derives itself. Our observation employed either, about external sensible objects, or about the internal operations of our minds perceived and reflected on by ourselves, is that which supplies our understanding with all the materials of thinking.”[22] While rationalism’s spokesmen include Leibniz, etc, and he writes: “everything inscribed on it (the soul) comes solely from the senses and experience; or whether the soul inherently contains the sources of various notions and doctrines, none of these comes from external objects, whose only role is to rouse up the notions and doctrines on suitable occasions.”[23] Here, the differences between the two sides is somewhat obvious, certainly, no matter for Locke or Leibniz, their philosophical systems are both very complicated, which cannot be mechanically differentiated, but the thinking orientations of them do have obvious basic differences.

 While Kant who later enters the historical arena tries to reconcile these two continuously conflicting thought lines. He writes: “Our knowledge springs from two main sources in the mind, first of which is the faculty or power of receiving representations (receptivity for impressions); the second is the power of cognizing by means of these representations (spontaniety in the production of conceptions). Through the first an object is given to us; through the second, it is, in relation to the representation (which is a mere determination of the mind), thought. Intuition and conceptions constitute, therefore, the elements of all our knowledge, so that neither conceptions without an intuition in some way corresponding to them, nor intuition without conceptions, can afford us a cognition.” “We apply the term sensibility to the receptivity of the mind for impressions, in so far as it is in some way affected; and, on the other hand, we call the faculty of spontaneously producing representations, or the spontaneity of cognition, understanding.” “Without the sensuous faculty no object would be given to us, and without the understanding no object would be thought. Thoughts without content are void; intuitions without conceptions, blind.”[24] To sum up, Kant thinks that our knowledge is together constituted by sensibility and understanding, and perceptual knowledge comes from experience, while rational knowledge comes from the integration of our inner thinking, which is the central argument Kant repeatedly emphasizes in Critique of Pure Reason.

Actually, in Locke’s epistemology, there are also expositions similar to Kant’s, and he writes: “how men ,barely by the use of their natural faculties, may attain to all the knowledge they have, without the help of any innate impressions; and may arrive at certainty, without any such original notions or principles.”[25] “The power of thinking is called the understanding, and the power of volition is called the will; and these two powers or abilities in the mind are denominated faculties.”[26] From this, we can easily see, Locke actually also thinks that people have some natural inner abilities and inner psychological structure, but different with Leibniz, he thinks that there are no innate impression nor innate knowledge in human mind. The reason why Locke holds such wise views is not difficult to understand, because human needs understanding concepts to integrate messy external representations, which is an obvious simple fact, and Kant only endows it with enormous speculative depth.

Therefore, people like Locke are actually all difficult to be called real thorough empiricists, and due to the richness of these scholars’ thoughts, thus, they all have an internal thought orientation to fuse experience and reason these two things. If we give an appropriate example of the debate between empiricism and rationalism, one scenario Goethe depicts is perhaps most proper, and he once vividly describes the interesting meeting when he first gets to know Schiller, and he writes: “Not separately, individually study the nature, but creatively, actively, and trying to from the whole to the parts describe the nature. He wants to clarify about this, but does not conceal his suspect, and he couldn’t admit that, such kind of situation, as I have emphasized, stems from experience.” “At that time, I am enthusiastically expounding the plant’s metamorphosis and try to use some typical drawings to let a symbolic plant appear before him. He listens, and watches all this with much interest, with obvious receptivity; but when I finish this talk, he shakes his head and says: this is not experience, but is a view. I am stunned, with some anger.”[27] Here, Goethe’s empirical view and Schiller’s rational view have a severe conflict. Certainly, we can easily know now, both of their basic views have big problems, and a plant is mainly an organism composed of roots, stems, leaves, flowers, fruits, and seeds these six organs, and we need to do systematic scientific research about them, which is perhaps neither experience nor reason, and no matter the concept of experience or the concept of reason, compared with the extremely complex botanical concrete knowledge, are both too empty.

What modern biology can solve is naturally not only this small debate of Goethe and Schiller about plant’s metamorphosis, and what it can resolve are fundamental problems in philosophical epistemology. As stated above, Kant thinks that, human knowledge comes from the composition of sensibility and understanding, and in them, understanding belongs to human’s natural innate ability, and this basic view is naturally plain and right, here, modern biology can provide us with strong arguments. We want to first give a simple example, and in the above quoted article “Mathematics in the 20^th century”, Atiyah writes: “Vision, I understand from friends who work in neurophysiology, uses up something like 80 or 90 percent of the cortex of the brain. There are about 17 different centers in the brain, each of which is specialised in a different part of the process of vision: some parts are concerned with vertical, some parts with horizontal, some parts with color, or perspective, and finally some parts are concerned with meaning and interpretation.” What Atiyah says is certainly just a small conclusion in neurophysiology, though the development of today’s neurophysiology encounters somewhat big obstacles, the concrete results it gets already make the empty discussions in philosophical epistemology eclipsed. As early as 100 years ago, in the era of William James, neurophysiology already gets many definite conclusions; take the vision Atiyah discusses for example, as William James says: “Munk almost immediately declared total and permanent blindness to follow from destruction of the occipital lobe in monkey as well as dogs, and said that the angular gyrus had nothing to do with sight, but was only the center of tactile sensibility of the eyeball.”[28] “He (Munk) was the first to distinguish in these vivisections between sensorial and psychic blindness”; “the first to notice the hemiopic character of the visual disturbances which result when only one hemisphere is injured. Sensorial blindness is absolute insensibility to light; psychic blindness is inability to recognize the meaning of the optical impressions, as when we see a page of Chinese print but it suggests nothing to us. A hemoipic disturbance of vision is one in which neither retina is affected in its totality, but in which, for example, the left portion of each retina is blind, so that the animal sees nothing situated in space towards its right.”[29] “the occipital lobes have frequently been found shrunken in cases of inveterate blindness in man.”[30] To sum up, William James’ expositions about vision are somewhat rich, and these rich knowledge are all rooted in the overall development of neurophysiology.

From the above concrete expositions of physiological knowledge about vision, we can clearly know that, the heated debate about reason and experience in philosophical epistemology must resort to the definite knowledge in biology to resolve, while what biology’s neurophysiology gets is undoubtedly strong knowledge; if we trace the source of Kant’s so-called human intellectual ability, it is naturally controlled by many cells in brain center. Generally speaking, we can get the following basic conclusion: it is too deviod to use ambiguous concepts like sensibility or understanding to describe human’s cognitive process, and they perhaps provide certain exploration frameworks, but, compared with extremely rich concrete neurophysiology knowledge, are definitely somewhat coarse.

The fundamental reason why the philosophical world’ opinions are divided about empiricism and rationalism this central issue is due to neurophysiology’s high complexity and abstruceness, as is well known, the overall field of neurophysiology is very difficult, which possibly cannot be solved even by the 22^nd century. Biology currently is only in its embryonic period, and basic achievements which can support the whole field’s development are not very many, while as the most abstruce field in biology, neurophysiology’s development is even more in the very initial stage. Therefore, neurophysiology’s research has not obtained sufficient research results, which determines that the philosophical world has argued for such a long time on the fundamental problem about whether knowledge comes from experience or reason; considering neurophysiology’s current development, this heated debate probably will still last for some time.

8 The influence of philosophy of science. As we know, the representative figures of philosophy of science include: famous philosopher Karl Popper who holds critical rationalism, the author of the widespread classic Proofs and Refutations: The Logic of Mathematical Discovery Lakatos, historian of science Kuhn who put forwards the original idea of scientific paradigm theory, and Feyerabend who claims scientific relativism. We must point out that, philosophy of science plays certain positive functions in clarifying some basic features of scientific knowledge (like Popper’s ‘falsifiability’), and distinguishing certain trends of scientific development (like mathematical knowledge’s empirical property Lakatos discovers[31] ), etc, thus, philosophy of science also enriches human knowledge domain, and broadens and deepens human’s cognitive perspective. But, for professional scientists, we perhaps do not need too much concrete knowledge in philosophy of science, and as the famous physicist Weinberg says: “The philosophy of science is just about as useful to scientists as ornithology is to birds.” Though this sentence is somewhat biting, it also includes some truth. Because, on one hand, compared with concrete knowledge in modern mathematics and physics, philosophy of science’s theory is somewhat too hallow, on the other hand, knowledge in modern mathematics and physics is already vast and difficult, and scientists already make every effort to learn these knowledge, and do not have spare energy to learn these obscure philosophical ideas. Thus, philosophy of science has certain thought value, but should not be overestimated.

Here, about the influence of philosophy of science, we can more specifically examine the situation in the scientific community. Firstly, as for certain scientific scholars, if we ask some important mathematicians and physicists in the second half of the 20^th century, like Lax, Chern, Selberg, Hirzebruch, Milnor, Smale, Gell-Mann, Feynman, and Landau, whether they have been impacted by philosophy of science. I think they will probably all say that they are not familiar with some philosophers of science, like Popper, Kuhn, Lakatos, Schlick and Carnap, and even are not familiar with well-known philosophers in the 17^th and 18^th century like Kant, Locke and Hume, but, they still do many brilliant scientific contributions, which fully shows that philosophy of science’s actual influence on scientists is actually very small; secondly, for the whole scientific community, as most scientific workers can feel, philosophy of science’s impact on the whole scientific world (mathematics, physics, chemistry, etc) is also weak. (Certainly, some great scientists, like Heisenberg and Schrodinger, have a somewhat strong interest in philosophy, but they are just minor cases, and philosophy’s impact on 20^th century science is somewhat small, which I think is a basic fact most professional mathematicians and physicists will agree with, certainly, this fact itself is not necessarily good, after all, philosophical speculations once played a very positive role in scientific research before the 20^th century, and therefore, about the value of philosophy of science, we should dialectically view.) To conclude, if we combine the facts in many aspects together and comprehensively consider, about the value of philosophy of science, I think it is, to a large extent, more close to liberal art subjects like sociology, philosophical epistemology and intellectual history, while its connection with the scientific world is not very close, namely, the field philosophy of science probably belongs to cross-discipline field between science and humanities, and thus, about its internal value, we also need to respectively consider its complex impacts in natural sciences and humanities, which I think is a basic fact we need to identify.

If summarizing the above complex discussions, we can get three basic conclusions: firstly, the function philosophical epistemology plays in mathematics and physics is already small, while in the perspective of modern mathematics and physics, some fundamental problems the philosophical world has argued for a long time can get somewhat complete answers. Therefore, in mathematics and physics, pure speculative philosophical discussions perhaps are already somewhat meaningless. Nowadays, there exists a universal phenomenon: after some philosophers get certain vague understandings about special relativity, quantum mechanics, algebraic topology and Riemannian geometry, they begin to talk about their so-called philosophical intension, but, it is actually not an easy thing to get precise understandings about certain scientific knowledge, for instance, even for the somewhat simple special relativity, I repeated over fifty times in the process of mastering it; I personally think: before we can solve all the after-school problems in special relativity, one person is not eligible to talk about its so-called philosophical meaning. Secondly, in fields like biology and linguistic, due to the high complexity of neurophysiology, some old philosophical debates will still continue. Thirdly, the universal decline of philosophical epistemology’s influence in the latter part of the 20^th century is a natural result of philosophical world’s detachment from the frontiers of modern mathematics, physics, biology, etc.

Certainly, it is also difficult to affirm that, the philosophical world’s vast discussions about many issues, like time, space, experience, consciousness, etc, are really meaningless, and the basic

phenomenon that leading scientists lack profound philosophical mastery in modern science is also rather regrettable; because the intellectual exchange between science and philosophy once lasts for two thousand years, and it is proved that this intellectual interaction is meaningful (refer to examples like Einstein and Weyl), and the high speculation of philosophical exploration perhaps can still provide us with some valuable spiritual nutrients, and therefore, it is also a quite meaningful thing for professional philosophers to have certain philosophical mastery.

   As a supplement of the discussions about the relationship between philosophical epistemology and modern science in the above, below we want to analyze the intricate connections between experience and scientific research.

   9 Experience and scientific research. When our analytical perspective turns to the intriguing theme about the relationship between experience and scientific research, firstly, we will encounter one popular view, namely: experience is of little value to scientific research; but, Dewey corrects people’s this universal prejudice, and he says: “They indicate that experience, if scientific inquiry is justified, is no infinitesimally thin layer or foreground of nature, but that it penetrates into it, reaching down into its depth, and in such a way that its grasp is capable of extension; it tunnels in all directions and in so doing brings to the surface things at first hidden-as miners pile high on the surface of the earth treasures brought from below.” Using the geologist’s work method as an example, Dewey describes: “The geologist did not leap from the thing he can see and touch to some event in by-gone ages; he collated this observed thing with many others, of different kinds, found all over the globes; the results of his comparisons he then compared with data of other experiences, say, the astronomer’s. He translates, that is, observed coexistences into non-observed, inferred sequences.” Namely, human’s primitive experience is important material of scientific research, and in the process of scientific research, human’s primitive experience is processed, refined and abstracted into some secondary scientific knowledge, in other words, human’s primitive experience is always one of the most important and extensive materials in scientific research. Based on biological knowledge, Dewey continues to analyze: “For the natural sciences not only draw their material from primary experience, but they refer it back again for test. Darwin began with the pigeons, cattle and plants of breeders and gardeners.” “Scientific men, whether they accepted his theories or not, employed his hypothesis as directive ideas for making new observations and experiments among the things of raw experience-just as the metallurgist who extracts refined metal from crude ore makes tools that are then set to work to control and use other crude materials.” Dewey further summarizes the basic relationship between scientific theory and empirical materials: “Theory may intervene in a long course of reasoning, many portions of which are remote from what is directly experienced. But the vine of pendant theory is attached at both ends to the pillars of observed subject-matter. And this experienced material is the same for the scienfic man and the man in the street. The latter cannot follow the intervening reasoning without special preparation. But stars, rocks, trees, and creeping things are the same material of experience for both.” Finally, as the summary of the above complicated arguments, Dewey writes: “wherein experience presents itself as the method, and the only method, for getting at nature, penetrating its secrets, and wherein nature empirically disclosed (by the use of empirical method in natural sciences) deepens, enriches and directs the further development of experience.”[32] In a word, actual empirical materials are fundamentally important for scientific research, which is somewhat inconsistent with our common imagined science’s rationalism feature, but it is indeed a complex  issue requiring our serious consideration.

   In modern physical and mathematical research, the importance of experience is also very notable. Chen Ning Yang once describes great physicist Fermi’s basic research style: “We know that, physics should not be a subject of experts, and physics should be piled from the ground, laying one brick by another, and increasing the height layer by layer. We know that, abstraction should be after the concrete foundational work, and must never be before it.”[33] While in mathematical research, phenomenological theory is also very important in the establishment process of general theory; in terms of group theory, the reason why dihedral group is important is because regular polyhedrons universally exist in nature, while the reason for the importance of wave equation in partial differential equation is also that wave phenomena appear in many natural domains. Therefore, actual world’s experience provides the most basic and most important materials for scientific research, and no matter how abstract and complex the theories are, they should all be built upon the solid foundation of many empirical facts, which is a basic view many accomplished scientists all insist.

(III) The Relationship between Human Society and Experience

   In the above, our comments on the value of philosophical epistemology in scientific research are perhaps somewhat too harsh, when we turn the analytical vision from scientific fields to social fields, what we find out will be a very different overall picture, namely: experience plays a central role in human society.

1 The use of mathematics in economics. Since Marshall, economics starts a grand trend of continuous mathematization; and from the latter part of the 20^th century, the process of economics’ mathematization greatly accelerates, and economic researches using mathematics as the basic tool become a common practice and have gradually converged into the mainstream of economics. The mathematization of economics can be roughly inspected through two commonly used textbooks-Sargent’s Recursive Macroeconomic Theroy, and Varian’s Advanced Microeconomics. It should be noted that, the mathematization of economics definitely has a high value, like the famous Solow model in development economics, which quantitatively depicts the functions capital, labor and technology play in economic development, and such kind of quantitative analysis has certain advantages which qualitative analyses cannot compare with. The mathematization of economics is not empty talk, and these mathematical economical models all precisely characterize certain economic behaviors in the actual domain, and take one fact the financial circle is generally familiar with, Simons once is a brilliant geometer, but he transfers from mathematics to finance after 40, and founds Renaissance Technologies Corporation, working in hedge funds field, and achieves huge success, and his investments are exactly based upon mathematical models and computer programming, thus, this example fully proves the explanatory power of modern economics towards the real world. Nowdays, professions like high-frequency trading based on mathematics are already widely known.

But, economics’ mathematization will possibly lead to another extreme, namely, a blind worship for the scientific method, and this excessively obsessed with science attitude often thinks that all the economic behaviors can be precisely depicted by scientific models, as Hayek says: “During the first half of the nineteenth century a new attitude made its appearance. The term science came more and more to be confined to the physical and biological disciplines which at the same time began to claim for a special rigorousness and certainty which distinguished them from others. Their success was such that they soon came to exercise an extraordinary fascination on those working in other fields, who rapidly began to imitate their teaching and vocabulary. Thus the tyranny commenced which the methods and techniques of the Sciences in the narrow sense of the term have ever since exercised over the other subjects. These became increasingly concerned to vindicate their equal status by showing that their methods were the same as those of their brilliantly successful sisters rather than by adapting their methods more and more to their own particular problems.”[34] People like Comte are good representatives of this stream of thought, and Comte thinks that he has found some universal truths which can be applied everywhere in social fields, and his research method is also highly similar to the method of natural sciences. Hayek is very concerned about such kind of research paradigm of scientism, and he thinks :“The conception of man deliberately building his civilization stems from an erroneous intellectualism that regards human reason as something standing outside nature and possessed of knowledge and reasoning capacity independent of experience.”[35] He further analyzes: “it is only natural that the scientists tend to stress what we do know; but in the social field, where what we do not know is often so much more important, the effect of this tendency may be very misleading. Many of the Utopian constructions are worthless because they follow the lead of theorists in assuming that we have perfect knowledge.”[36] Namely, in social fields, what we do not know is often much more than what we know, thus, it is inevitably futile to construct an all-embracing theoretical system through one people’s limited experience. As is well known, the rationalist philosophy has led to many utopian constructions in modern society, and these utopian constructions often use the so-called scientization as the flag, and hold a rational control view towards society, about this, Hayek criticizes: “The scientistic as distinguished from the scientific view is not an unprejudiced but a very prejudiced approach which, before it has considered its subject, claims to know what is the most appropriate way of investigating it.”[37] For Hayek’s detailed expositions on this significant problem, please refer to his relevant works, and through many significant conclusions found by his lifelong persistent intellectual explorations, we should be able to hold a profound, dialectic and balanced opinion about the mathematization of certain subjects like economics and sociology; we need to know that, many things in human society cannot be integrated into neat and uniform theoretical models, and if we blindly worship the scientific method, we will possibly lose many most precious things in human society (like originality, individual freedom, the strength of emotion, etc).

 About this significant problem, famous philosopher Putnam also holds the same basic view, and he writes: “I argued in the previous lecture that although we do sometimes succeed in constructing good explanatory models of some natural kinds in physics, it is hopeless to seek an explanatory model of the natural kind ‘human being’ (although we may, of course, discover empirical regularities and perhaps even laws about human beings). This is what accounts for the unformalizability of practical knowledge.”[38] Namely, Putnam also thinks that many human behaviors cannot be accurately grasped by using scientific methods. Berlin also thinks alike: “Social and political terms are necessarily vague. The attempt to make the vocabulary of politics too precise may render it useless.”[39]

2 The reason for the importance of experience in economics. As common sense tells us, experience plays a central role in economics, and the reason for producing this basic phenomenon, well known economist Knight thinks, is the enormous complexity of individual behaviours, and he says: “The world is ‘really’ made up of units which not only do not change (atoms, corpuscles, either, or what-not), but whose laws of behaviour are simple and comprehensive. But it is contended that there are so many of these units that the simple changes which they undergo (ideally movements in space alone) give rise to a variety of combinations which our minds are unable to grasp in detail. We have examined this dogma and been forced to the conclusion that whatever we find it pleasant to assume for philosophical purposes, the logic of our conduct assumes real indeterminateness, real change, discontinuity.”[40] Namely, the units of the world we live in are of large number, and their permutations and combinations will result in endless complexity, thus, these changes are impossible to completely describe by mathematical models, and even they can be described, these models are also unable to keep up with the pace of rapidly changing social reality.

This phenomenon Knight reveals has a deeper reason behind it, namely, the extreme broadness of experience in human society; if we say that there is trillions of information in scientific knowledge, then, there is probably also trillions of information in life experience of human society, and these huge amounts of information is also fastly changing, and therefore, it is hard to imagine that any mathematical model can describe such a complex large-scale system. Thus, experience, as a means for human to qualitatively understand the surrounding society, shows a high value, and experience is extremely condensed equations and highly simplified mathematical models, and these equations and mathematical models which exist empirically are undoubtedly powerful tools for individuals to understand the surrounding society, and they can help us to better understand the surrounding world, and about this, Whitehead once says: “our experience, dim and fragmentary as it is, yet sounds the utmost depths of reality.”[41] Furthermore, even in ancient society, life was also a continuous learning process, while in modern society, the range of life experience is ten times more than ancient society, thus, the accumulation of life experience is more difficult and important. Montaigne also writes: “Reason has so many forms that we know not to which to take; experience has no fewer; the consequence we would draw from the comparison of events is unsure, by reason they are always unlike. There is no quality so universal in this image of things as diversity and variety.” “Resemblance does not so much make one as difference makes another. Nature has obliged herself to make nothing other that was not unlike.” “Never did two men make the same judgment of the same thing; and it’s impossible to find two opinions exactly alike, not only in several men, but in the same man, at diverse hours.”[42] What Montaigne describes is naturally a universal and profound basic phenomenon in individual life. To conclude, experience will continue to play a central role in future human life, which is an undoubtful basic fact.

Besides experience has great broadness this evident feature, it also has the basic feature of continuous variability, which also leads to that experience plays a central role in human society. In modern philosophy and modern social sciences, scholars often prefer things with certainty, as Dewey says: “As a result, whatever in capable of certainty is assumed to constitute ultimate Being, and everything else is said to be merely phenomenal, or, in extreme cases, illusory.” Dewey describes the universal mentality that philosophers flee from the coarse and chaotic experience one after another to hide in static and pleasant ordinary things: “Gross experience is loaded with the tangled and complex; hence philosophy hurries away from it to search out something so simple that the mind can rest trustfully in it, knowing that it has no surprises in store, that it will not spring anything to make trouble, that it will stay put, having no potentialities in reserve.” Dewey further points out: “The permanent enables us to rest, it gives peace; the variable, the changing, is a constant challenge. Where things change something is hanging over us. It is a threat of trouble. Even when change is marked by hope of better things to come, that hope tends to project its object as something to stay once for all when it arrives.”[43] The phenomenon Dewey describes naturally does not only fit philosophers, and in real life, the social public also prefers static and stable life, however, our surrounding world is always turbulent, and diverse and chaotic experience is always in a fastly changing process, and therefore, understanding the complex world we live in by the means of experience has become an indispensible basic work and living method.

The importance of experience also embodies in the overall grasp of social basic structure, and in the classic Social Origins of Dictatorship and Democracy, Moore writes: “By itself a quantitative measure of social mobility tells us little about social anatomy and its workings.” He then gives an example: “In the nineteenth-century Prussia the members of the bourgeoisie who became connected with the aristocracy generally absorbed the latter’s habbit and outlook. Rather the opposite relationship held in England. Thus if we did have a technically perfect measure of mobility that gave an identical numerical reading for the amount of fusion in England and Prussia, we would make a disastrous mistake in saying that the two countries were alike on this score. Statistics are misleading traps for the unwary reader when they abstract from the essence of the situation the whole structural context in which social osmosis takes place.”[44] This important fact revealed by Moore through the above specific example is certainly a good warning for the scholars excessively infatuated with quantitative tools.

About the high importance of experience in social fields, other scholars give some other proof ideas, and when the well known scholar Berlin elaborates Mill’s thoughts, he says: “He saw that men differed and evolved, not merely as a result of natural causes, but also because of what they themselves did to alter their own characters, at times in unintended ways. This alone makes their conduct unpredictable, and renders laws or theories, whether inspired by analogies with mechanics or with biology, nevertheless incapable of embracing the complexity and qualitative properties of even an individual character, let alone a group of men.”[45] Namely, Mill thinks that, not only human society’s external experience is very broad and continuously changing, and thus, is difficult to model, but also individual’s internal character and thoughts are also in a constantly changing process, and thus, are also difficult to precisely characterize by scientific method. Combining the complex changes of both the external social experience and internal individual character, we can naturally deepen the understanding about experience’s basic value in human society.

3 The importance of experience in human society. Besides experience’s fundamental importance in economic behaviours and fundamental importance in scientific research these two aspects, it also has some other basic values in human society, and one of them is its value for human perceptual world. In modern society, due to science and technology’s enormous power embodied in practical areas, thus, it often leads to a blind worship towards science, and about this social atmosphere of over admiration about scientific knowledge, Dewey once did profound reflections, and he wrote: “In the assertion (implied here) that the great vice of philosophy is an arbitrary ‘intellectualism’, there is no slight cast upon intelligence and reason. By ‘intellectualism’ as an indictment is meant the theory that all experiencing is a mold of knowing, and that all subject-matter, all nature, is, in principle, to be reduced and transformed till it is defined in terms identical with the characteristics presented by refined objects of science as such. The assumption of ‘intellectualism’ goes contrary to the facts of what is primarily experienced. For things are objects to be treated, used, acted upon and with, enjoyed and endured, even more than things to be known.” Namely, Dewey thinks that, human experience much more ingredients than those can be objectively understood, and many factors in experience are necessarily unable to be completely grasped by scientific cognition, while “all modes of experiencing are ways in which some genuine traits of nature come to manifest realization.”[46] Therefore, the range of experience in human society is much broader than the limited scientific experience.

About the basic phenomenon pan scientism which exists universally in modern society, Chang Hao also makes a similar description: “In the modern world, science is fashionable, and people’s attitude towards science often becomes idolatry, and scientific view then turns into pan scientific view, and the so-called pan scientific view means an attitude believing that the only credible knowledge for human is science, and there is only one standard for science to determine meaning and truth, namely, the check based on sensory experience. This is certainly a very narrow opinion about human experience. Because human experience, in fact, is very rich, and has many levels and many aspects, but the pan scientific view insists that we should not believe what cannot be confirmed by sensory experience.”[47] Obviously, this phenomenon Mr Chang characterizes and worries about is very identical to the basic phenomenon Dewey describes.

About the prevalence of pan scientific view, in The Birth of Tragedy, Nietzsche also made severe criticisms. In this aesthetic masterpiece, he criticizes the modern culture in which people use a scientific attitude to treat life, and he thinks that science’s thinking orientation is: “a man raised above fear of death by knowledge and reason”, “reminding every individual of his purpose, namely, to make existence intelligible and thus apparently justified.” Namely, scientism believes that we can solve all the life’s secrets through scientific exploration, and Nietzsche further depicts: “how an unimaginable universal greed for knowledge through the full extent of the educated world steered knowledge around the high seas as the essential task for every person of greater capabilities, a greed which it has been impossible since then completely to expel from scientifc knowledge, and how through this universal greed a common net of thinking was cast over the entire earth for the first time (with even glimpses of the rule-round workings of an entire solar system).” Therefore, the ultimate effect by using a scientific attitude to treat life is: “mechanism of ideas, judgments, and conclusions has been valued, from Socrates on, as the highest activity and the most admirable gift of nature, above all other faculties. Even the noblest moral deeds, the sympathetic emotions, self-sacrifice, heroism, and that calmness in the soul (so difficult to attain), which the Apollonian Greeks called sophrosyne-all these were derived by Socrates and his like-minded descendants right up to the present from the dialectic of knowledge and therefore described as teachable.”[48] To conclude, in modern society, human’s various perceptual actions all need rational explanations, and the modern psychology based upon physics and physiology is a typical representative in them. While Nietzsche’s basic view is : there are many things in life which cannot be explained by science, and the most central one is the death issue, and scientific knowledge cannot eliminate the gloomy background cast over human society by death, and it will just enable individuals to be indulged in superficial sensory enjoyment, and evades the fundamental death issue. In Nietzsche’s view, the meaning of life cannot be answered by science, and can only be defused through art, and art has a central meaning in answering many fundamental life issues. He thinks: “This is the true artistic purpose of Apollo, in whose name we put together all those countless illusions of beautiful appearances which render existence at every moment in general worth living and push us to experience the next moment.” “The Dionysian shows itself, measured against the Apollonian, as the eternal and primordial artistic force, which summons the entire world of appearances into existence.”[49] Namely, Nietzsche hopes for the two basic factors Apollo and Dionysian in art to solve the fundamental problem of the meaning of life. Nietzsche’s thinking path here also deserves our attention.

Besides Nietzsche, Husserl also refutes the scientism, and he thinks that knowledge about life is equally valuable as knowledge about the objective world like mathematics and physics, and he writes: “The universal transcendence in objective logical level-the universal transcendence of mathematics and all the other transcendent sciences in the usual sense-is founded on a kind of universal transcendence prior to them, namely, the transcendence of pure living world.”[50] Heidegger’s opinions are also similar, and he says: “The human sciences, by contrast, indeed all the sciences that deal with living things, precisely in order to remain disciplined and rigorous, are necessarily inexact. One can, indeed, view living things, too, as magnitudes of spatio-temporal motion, but what one apprehends is then no longer living. The inexactness of the historical human sciences is not a deficiency but rather the fulfilment of an essential requirement of this type of research.”[51]

Putnam also thinks highly of the value of basic things like experience and literature, and he says :“We can only understand the way in which the literature imagination does really help us to understand ourselves and life, on the other hand, and the way in which science does really bear on metaphysical problems on the other, if we have an adequate view of moral reasoning, where, by moral reasoning, I mean not just reasoning about duty or virtue, but moral reasoning in the widest sense-reasoning about how to live.”[52]

Max Weber’s basic view on this central issue is also widely known, and he says :“Who-aside from certain big children who are indeed found in the natural sciences-still believes that the findings of astronomy, biology, physics, or chemistry could teach us anything about the meaning of the world? If there is any such ‘meaning’, along what road could one come upon its tracks?”[53]

To conclude, combining many thinkers’ clear expositions in the above and our daily experience together, the enormous value of many beautiful things like experience and art in human perceptual world is beyond doubt. We should remember one basic truth : the barrenness of mind is sometimes more dangerous than lack of knowledge, and barrenness of mind will possibly lead the individual and society into the road of destruction, and meanwhile, our mind can only be enriched and infiltrated by non-scientific things like experience and art. Dewey once makes a good summary about the importance of social knowledge: “The successful maintenance of democratism strictly requires to use the most efficient method to acquire social knowledge roughly matching our substance knowledge, and invent and use the social project roughly matching our technical ability about material things.”[54] In conclusion, experience has fundamental importance for keeping the overall balance of human perceptual world and then for maintaining human society’s richness and harmony.

4 The fundamental importance of experience in real life. At the same time, the fundamental importance of experience embodies most strongly and evidently in people’s real life; it is easy to understand that, for many individuals living in the real society, their practical lives actualy do not need too much scientific knowledge, like policeman, government official, lawyer, businessman and architectural worker; for them, what they need most is systematic, flexible and delicate life experience. As common sense tells us, most people in real life will actually not passionately discuss and explore scientific knowledge like scientists, and for them, scientific knowledge does not have a core meaning, and what they think and face are mainly many complex issues in work and life, and these issues include clothing problem, traffic issue, household spending, job planning, leisure and entertainment, etc, and they naturally all belong to the category of living experience and work experience, and thus, are all with a strong empirical color, and meanwhile, the range of these life experience is very broad, and these living experience are also hard to be strictly characterized by scientific knowledge, therefore, experience is certainly more important than scientific knowledge in real life. To sum up, considering that in most people’s real life, life experience is so broad and so important, while the importance of scientific knowledge is also not very evident, therefore, the fundamental meaning of experience in actual life naturally stands out.

In conclusion, through the above expositions from several aspects, I think we can somewhat well understand the multi-dimensional basic values of experience in human society, and all of these multi-dimensional values can naturally not be replaced by scientific knowledge, and therefore, experience’s basic meaning in human society is actually very profound, and also very stable.

(IV) A Rethinking on the Relationship between Science and Philosophy

It is easy to see that, the comments on philosophical epistemology in part (II) are somewhat negative, and through the relevant expositions in the above part (III), about the meaning of philosophy this significant theme, we should be able to hold a more sound view, and after the investigations from both the positive and negative sides, here, it is somewhat appropriate to overally evaluate the relationship between philosophy and science.

In the era before the 17^th and 18^th century, philosophy was often regarded as the source of all sciences, and its status was above concrete sciences, as Kant says: “she (metaphysics) was the queen of all the sciences”[55] , but with the enormous development of various scientific fields in the 19^th and 20^th century, philosophy’s this basic positioning has been fundamentally challenged, and most philosophers in the 20^th century has identified this basic fact, take Dewey for example, he writes: “Since they admit that science is sovereign in the knowledge domain, and this includes the entire territory of human experience. This reduced approach excludes one kind of philosophy, and this kind of philosophy thinks that philosophy is superior knowledge than science, and it provides the knowledge about ultimate high-level reality.” But, at the same time, Dewey thinks that philosophy still has indispensbile basic values in modern society, and about it, he says: “Excluding this special type of philosophy does not mean that philosophy itself should be abandoned.” “As for ordinary people, the reason why knowledge itself is important is because it has influence over what he needs to do and what he wants to create. It helps him to clarify his desires, helps him to form his goal, and helps him to get the means of achieving these goals. In other words, there are cognitive facts and principles, and there are also values, and philosophy is basically studying values-it studies the pursued goals of human action.”[56] Namely, Dewey thinks that what philosophy cares about is the value domain, and it can provide individual actions’ desires and goals, while these things cannot be replaced by science, and meanwhile, these desires and goals are also broad and complex, thus, philosophy still has extensive and important values in human society. In conclusion, since the 20^th century, the relationship between philosophy and science has appeared some basic changes, and correspondingly, philosophy also needs to adjust its basic positioning in human society.

In the meantime, famous philosopher Whitehead’s thinking about this theme also deserves our attention; firstly, he explains the basic characteristics of science and philosophy: “The facts so far prove that, in all the living things on earth, science and philosophy only belong to mankind. Both of them emphasize to conceptualize individual facts into the special cases of universal principles. The principles are abstractly understood, while the facts are understood as embodiments of the principles.” He further expounds: “The term ‘curiosity’, in a larger sense (here we use it in this way), means a kind of rational impulse, which hopes to understand the facts separated from the experience, means a rejection of being satisfied with messy facts, or a rejection of being satisfied with pure normal habits. When people understand that every routine is a special case to illustrate certain principle, and every principle can be abstractly demonstrated through its many concrete cases, then science and philosophy make the first step.” Namely, science and philosophy are all devoted to abstracting individual facts into universal general principles, and their differences are: “Science emphasizes the observation about specific situations and induction and generalization, and thereby, makes extensive classification based on the mode of action of concrete things, in other words, classifies them based on their natural law. While philosophy emphasizes general propositions. Since the application range of general propositions is too broad, and thus, they can hardly be classified.” Namely, what philosophy emphasizes are general propositions, while science must be based on concrete empirical facts, and through this division, the value of philosophy then shows up: “They (philosophical systems aimed at containing everything) are methods for human spirit to foster its deeper intuition. Through these systems, isolated ideas get vitality and motion. If without these systems to coordinate, isolated ideas will just accidentally emerge at any moment, and inspire thinking at certain stage, and then wither and die and be forgotten by people. The range of one kind of intuitive knowledge, can only be defined by its coherent degree with many other universal concepts.”[57] Namely, Whitehead thinks that, the value of philosophy is to universally abstract and generalize many phenomena in human living world and natural world, while the abstract conceptual system which philosophy gets has deep and extensive subtle enlightenment towards human life. Obviously, these analyses of Whitehead can also deepen and broaden our basic understandings about the relationship between science and philosophy.

In conclusion, as two basic things in human society, philosophy and science will both continuously develop with the progress of human society, and their destinies will be necessarily intertwined with human’s general destiny.