Of Philosophical Study in the 20thCentury
As an old subject, like many other subjects, the study of philosophy is still continuously expanding and deepening in the 20thcentury, and in this process, it evolves some new branches (such as logical positivism, philosophy of science, existentialism, etc), and also spawns many important new ideas, which all show that the 20th-century philosophy is still full of vitality and energy, and modern philosophy also becomes a wide-ranging field; but, these many-sided new developments also result in certain chaos of philosophy, and thus, it will be a quite meaningful thing to do some systematic and deep combing and discussions about 20th-century philosophical study. In this paper, we prepare to do some investigations about the academic thought and general characteristic of 20th-century philosophy, and meanwhile, we will also incorporate some new views of our own.
(I) Some Branches of 20th-Century Philosophy
Compared with the 18thand 19thcenturies, there are certainly more philosophical branches in the 20thcentury, and as is well known, the philosophical branches in the 18thand 19thcenturies are somewhat few, and no matter for German philosophy, English philosophy, French philosophy or American philosophy, it is all so, while the 20th-century philosophy has a large number of branches and scholars; therefore, in this part, we firstly prepare to do some analyses, arrangements and discussions about these philosophical branches.
1 Frege, Whitehead and Russell’s logical study.The development of modern logic is a long and somewhat complex process, and many scholars make important contributions, among them, as one of the founders of mathematical logic, Frege does brilliant contributions. One basic characteristic of Frege’s study is to use logical symbols to quantitatively study many logical problems, which is quite different from the literary study of many scholars; to better understand the research characteristic of Frege, we want to discuss one specific problem, namely, the “universality” problem.
We firstly give a judgment:
| α Ф(α)
It means the following judgment: no matter what the variable is, the function is always a fact.
The horizontal line left to the concavity is content line, and it means that no matter what valueαis,Ф(α)is always valid; the horizontal line right to the concavity is the content line ofФ(α),and here we must substitute definite things atα.
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Through| α X(α) denies: no matter what valueαis,X(α)is always valid. But this does not deny: we can giveαa valuesuch thatX()is a fact.
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| A
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α X(α)
means that the situation we confirm α X(α)and deny A does not exist, but it absolutely does not deny the situation in which we affirmX()but deny A: because as we see in the above, we can affirmX() but deny α X(α).Thereby, here we cannot substitute any value at α, and also does not harm the validity of this judgment. It illustrates that why the concavity with German letter is necessary: it limits the range of universality this letter represents.
A Latin letter can use the content of the whole judgment as its range, and then it does not need the concavity of content line.
A Latin letter can always substitute a German letter which does not exist in a judgment, and here the concavity should follow the judgment bar. For example, we can use
| α X(α)
To replace
| X(a),
Ifαmerely exists in the variable ofX(α).
Similarly, it is obvious that, if A is a function, and a does not appear, and if a is just in the variable ofФ(a),then from
| Ф(a)
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A
We can deduce
| α Ф(α)
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A
If we deny α X(α),then it is necessary to give a one value which deniesФ(a).Thus, if we deny α X(α)and affirm A, then it is necessary to giveαone value which will affirm A and denyФ(α).
But for
| Ф(a)
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A
We cannot do this: because it means, no matter what a is, we all exclude the situation denyingФ(a)and affirming A.
Now we investigate several symbol combinations
| α X(α)
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It means people can find something, for example,,which can denyX().Thereby, it can be translated into: “There are some things, and they do not have property X.”
| α X(α)
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Its meaning is different, and it means: “no matter whatα is,we can always denyX(α)”, or“there are no things which have property X”;or we call the thing which have property X as X, then it means “there are no X”.
| α P(α)
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X(α)
Means: “no matter what is atα,there are no situation denyingP(α)and affirmingX(α)”.Thus here the following situation is possible, for some values ofα,they can affirmP(α)and affirmX(α),for some other values, affirmingP(α)and denyingX(α),and for some other values, denyingP(α)and denyingX(α), and it can be translated as: “If one thing have property X, then it also has property P”,or “every X is P”,or “all X are P”.
It is exactly the way to express causal links.
| α P(α)
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ψ(α)
means: “ We can not give suchα,which affirm bothP(α) andψ(α).”Which can be translated as: “For things which have propertyψ, they do not have property P”,or “no ψ is P”.[1]
From these quotations, we can easily see, Frege’s logical research has a strong mathematical characteristic, and they are all expressed through logical symbols, and these research are also somewhat systematic and deep, which all have far-reaching impacts on the subsequent research of mathematical logic.
Whitehead also makes somewhat large contribution in logic; firstly, by carefully reading his books, we can know, he has a good logic foundation and can do many complex and difficult symbolic proofs, and meanwhile, he is also mainly responsible for the mathematical part ofPrincipia Mathematica.AboutPrincipia Mathematicathis classic logical work, since it is very long, and thus, we think, scholars who can truly finish reading it and understand it are actually very few; for example, though Quine and Carnap also often discuss aboutPrincipia Mathematica,they probably just understand part of it, while only few scholars like Godel truly understand this book. Meanwhile, as for Whitehead’s philosophical research, his academic and thoughtful quality is not sufficient, for example, he is not very familiar with many basic problems in philosophy, such as thinking and being, language reference, the relationship between experience and reason, etc, and the philosophical problems he deals with are probably some marginal and unimportant problems. To conclude, Whitehead’s logical and philosophical research is somewhat broad, and also has certain value.
Russell also makes certain contribution in logic, such as the description theory; to know the basic characteristic of his logical study, below, we want to quote his one passage: “Let us assume that we know the five formal principles of deduction enumerated inPrincipia Mathematica.(M. Nicod has reduced these to one, but as it is a complicated proposition, we will begin with the five.) These five propositions are as follows:-
(1) ‘p or p’ implies p-i.e.if either p is true or p is true, then p is true.
(2) q implies ‘p or q’-i.e.the disjunction ‘p or q’is true when one of its alternatives is true.
(3) ‘p or q’ implies ‘q or p’.This would not be required if we had a theoretically moreperfect notation, since in the conception or disjunction there is no order involved, so that ‘p or q’ and ‘q or p’ should be identical. But since our symbols, in any convenient form, inevitably introduce an order, we need suitable assumptions for showing that the order is irrelevant.
(4) If either p is true or ‘q or r’ is true,then either q is true or ‘p or r’ is true. (The twist in this proposition serves to increase its deductive power.)
(5) If q implies r, then ‘p or q’implies ‘p or r’.”[2]
In this passage, Russell mainly discusses about some basic types of deductive method, and from it, we can see, he can make certain symbolic deductions, and his expositions are also somewhat systematic. On the other hand, through reading Russell’s mathematical works, we can also see, Russell’s logic foundation is not very deep, and he can do certain symbolic reasoning, but can not do some complex and deep symbolic computations and proofs, which is also a fact we need to know. To conclude, about Russell’s logical study, we need to dialectically view.
2 Quine, Carnap and Ayer’s logical philosophy and language philosophy. As is well known, logical philosophy and language philosophy form a large area of 20th-century philosophy, and there are also many important scholars (like Austin, etc), here, we just want to discuss about Quine, Carnap and Ayer these three representative figures’ relevant academic research.Generally speaking, the range of Quine’s logical philosophy and language philosophy is broad, and quite systematic and deep, and also has good originality. About his language research, we want to firstly quote his one passage: “I have argued that we can use singular terms significantly in sentences without presupposing that there are the entities which those terms purport to name. I have argued further that we can use general terms, for example, predicates, without conceding them to be names of abstract entities. I have argued further that we can view utterances as significant, and as synonymous or heteronymous with one another, without countenancing a realm of entities called meanings.”[3]In this paragraph, Quine thinks the logic of language is decided by the essence which language expresses, and has little to do with the formal usage it adopts; from this paragraph, we can see, Quine’s language and logic research are infiltrated together, and he uses the mindset of logic to examine language problem, which is an important characteristic of Quine’s research. About his logical research, the following paragraph is representative: “The operator may be read ‘the class of all objects x such that’. The class ---is definable, by description, as the class y to which any object x will belong if and only if ---; symbolically, .(β)(α)((α∈β)≡Φ). Further the class {x} whose sole member is x, and the class {x, y} whose sole members are x and y, are definable thus: {α} for β (β=α) {α, β} for γ (γ=α) ∨(γ=β).”[4]Here, Quine defines a new logical symbol-class, and he uses strict logical symbol to define this operation, and from it, we can know, Quine’s logical research is conducted through symbolic reasoning, and meanwhile, his these logical research also has quite originality, and has definite thoughtful substance. To sum up, Quine’s logical philosophy and language philosophy have high originality, and are also somewhat systematic and rich, thus, also deserve our deep reading and study.
The quality of Carnap’s logical philosophy and philosophy of science is also high, and the range of problems he discusses is also extensive, systematic and profound, which involves many aspects such as logic, epistemology, philosophy of science, semantics, etc, and also has certain originality; to better know his logical foundation, we want to firstly quote his one passage with symbolic contents: “
a. +(1) pÉp∨q.
(2) qÉp∨q.
(3) qÉ(pÉq).
(4) ~pÉ( pÉq).
b. +(1) p.qÉp.
(2) p.qÉq.
+c.
d. +(1) (p∨q). ~pÉq.
+(2) (p∨q). ~qÉp.
+(3) (pÉq). pÉq.
(4) pÉ[(pÉq)Éq].
(5) (pÉq).~qÉ~p.
e. + (1) (p≡q)É(pÉq).
+(2) (p≡q)É(qÉp).
(3) (p≡q)É(~pÉ~q).
(4) (p≡q)É(~qÉ~p).
(5) (p≡q).pÉq.
(6) (p≡q).qÉp.
(7) (p≡q). ~pÉ~q.
(8) (p≡q). ~qÉ~p.
f. (1) (pÉq)É(p∨rÉq∨r).
(2) (pÉq)É( p.rÉq.r).
(3) (pÉq)É[ (rÉp)É(rÉq)].
(4) (pÉq)É[ (qÉr)É(pÉr)].
(5) (pÉq).( p∨r)Éq∨r.
+(6) (pÉq). (qÉr)É(pÉr).
(7) (p≡q).(p≡r)É( q≡r).
(8) (p≡q).(q≡r)É( p≡r).
g. (1) (p≡q)Ép∨r≡q∨r.
(2) (p≡q)É(p.r≡q.r).
(3) (p≡q)É[ (pÉr)≡(qÉr)].
(4) (p≡q)É[ (rÉp)≡(rÉq)].
(5) (p≡q)É[(p≡r)≡(q≡r)].
h. (1) (pÉq). (rÉs)É(p∨rÉq∨s).
(2) (pÉq). (rÉs) . (p∨r)Éq∨s.
i. (1) qÉ(p≡p.q).
(2) ~qÉ(p≡p∨q).”[5]
In this symbolic deduction, Carnap mainly discusses about the tautologies problem, namely, no matter what propositions p, q, r, s are, the above deductions are always true. From this quotation, we can evidently feel that Carnap’s logical foundation is somewhat profound, and he can do some complex and deep deductions, which is more professional than the above Russell’s logical reasoning; if we compare Carnap’sIntroduction To Symbolic Logic and Its Applicationsand Russell’sIntroduction to Mathematical Philosophythese two logical books, we can also easily see, Carnap’s logic is deeper than Russell. If comparing with Quine, we can know, what Carnap mainly cares about are logical philosophy and philosophy of science, etc, while for language philosophy, he also studies from the logical viewpoint, and not like Quine’s method which emphasizes the substantial analyses of language intension (such as the complex relationship between translation and meaning), namely, his language philosophy is somewhat worse than Quine; on the other hand, Carnap’s logical and mathematical foundations are better than Quine, and his symbolic deductions are more systematic and deep than Quine, and he also know more scientific knowledge such as physics (relativity) than Quine; in a word, the knowledge background and research style of these two important philosophers has somewhat large difference. In general, Carnap’s logical philosophy and philosophy of science also have many valuable places.
Ayer’s logical positivism also has certain influence in the 20th-century philosophical world, and his has many philosophical works, and their quality is also relatively high, but, as an overall characteristic, we think, Ayer’s originality in philosophy is not sufficient; for example, about the property of knowledge, he writes: “Much the same applies to the cases where knowing is a matter of knowing how. Certainly, when people possess skills, even intellectual skills, like the ability to act or teach, they are not always consciously aware of the procedures which they follow. They use the appropriate means to attain their ends, but the fact that these means are appropriate may never be made explicit by them even to themselves. There are a great many things that people habitually do well, without remarking how they do them. In many cases they could not say how they did them if they tried. Nor does this mean that their performances are unintelligent.”[6]Here, Ayer discusses about the general characteristic of knowledge, and he thinks not only things people are clearly aware of can be called knowledge, and there is much knowledge which is not explicitly expressed by language and consciousness, but is also intelligent, and Ayer’s this view is certainly somewhat reasonable. But, we can also know, about the philosophical problem of knowledge’s characteristic, it is a basic problem which has been repeatedly discussed by people since Plato and Aristotle, and in modern times, many people such as Descartes, Locke and Leibniz also have discussed about it, and it is actually already a somewhat old problem, while Ayer seems not to add many essential new insights. To conclude, Ayer’s philosophy emphasizes on the extensive and complex interrelations between knowledge, experience, logic and language, etc, which roughly belongs to the epistemology category, and is not very interested in ontological problems, which all reflect the general feature of British and American philosophy; but, as for originality, he is relatively worse than Quine and Carnap.
3 Husserl, Heidegger and Gadamer’s phenomenology, existentialism and hermeneutics.Broadly speaking, the phenomenology, existentialism and hermeneutics of Husserl, Heidegger and Gadamer are also important branches of 20th-century philosophical world, and also have high academic value. Firstly, as for Husserl, his phenomenology stems from his critical reflection of scientific knowledge, which is consistent with Nietzsche’s view; the basic starting point of his theoretical system is clear, namely, he thinks scientific knowledge (such as physical knowledge and biological knowledge) is object which can be checked, while behind these scientific knowledge, there is still one kind of transcendental knowledge, namely, the knowledge of real life, and because they belong to the field of ontological phenomenology, and thereby is better than empirical scientific knowledge, and is more important, as he says: “Whatever may be the chances for realizing, or the capacity for realizing, the idea of objective science in respect to the mental world (i.e., not only in respect to nature), this idea of objectivity dominates the wholeuniversitasof the positive sciences in the modern period, and in the general usage it dominates the meaning of the word ‘science’. This already involves a naturalism insofar as this concept is taken from Galilean natural science, such that the scientifically ‘true’, the objective, world is always thought of in advance as nature, in an expanded sense of the word. The contrast between the subjectivity of the life-world and the ‘objective’ the ‘true’ world, lies in the fact that the latter is a theoretical-logical substruction, the substruction of something that is in principle not perceivable, in principle not experienceable in its own proper being, whereas the subjective, in the life-world, is distinguished in all respects precisely by its being actually experienceable.”[7]To sum up, Husserl’s phenomenology emphasizes the importance of life-world this phenomenological field, and the focal point is the empirical and objective reflection on scientific knowledge, and he thinks the overemphasis of the importance of scientific knowledge will result in that people overlook the broad experience contained in life-world; obviously, Husserl’s these views have great illumination for the subsequent Heidegger, etc, because one of the central ideas of Heidegger is also the reflection on modern scientific knowledge.
Heidegger’s existentialism also has extensive and profound impacts on the 20th-century art and philosophy, and about the basic problem existentialism faces, he once writes: “Furthermore, in each case Dasein is mine to be in one way or another. Dasein has always made some sort of decision as to the way in which it is in each case mine [je meines]. That entity which in its Being has this very Being as an issue, comports itself towards its Being as its ownmost possibility. In each case Dasein is its possibility, and it ‘has’ this possibility, but not just as a property [eigenschaftlich], as some present-at-hand would. And because Dasein is in each case essentially its own possibility, itcan,in its very Being, ‘choose’ itself and win itself; it can also lose itself and never win itself; or only ‘seem’ to do so. But only in so far as it is essentially something which can beauthentic-that is, something of its own-can it have lost itself and not yet won itself.”[8]The meaning of Heidegger’s this passage is clear, namely, he wants to investigate the various living modes of man as Dasein, hence identify the best and most authentic types, and for this, he does many analyses. On the other hand, Heidegger’s philosophy mostly centers around existentialism, and rarely involves other aspects such as epistemology, history, law, politics and logic, which shows that the range of his writing is not very broad, and I think this point is not difficult to know.
Gadamer’s hermeneutics also has rich and profound intension, and his hermeneutics emphasizes the inheritance of traditional things, but he thinks, in this process, we need to use dialogue and imagination to proactively and critically treat these handed down things, and should keep an open attitude; as a good illustration of the basic idea of his hermeneutics, he once says: “It is not only that historical tradition and the natural order of life constitute the unity of the world in which we live as men; the way we experience one another, the way we experience historical traditions, the way we experience the natural givenness of our existence and of our world, constitute a truly hermeneutic universe, in which we are not imprisoned, as if behind insurmountable barriers, but to which we are opened.” “A reflection on what truth is in the human sciences must not try to reflect itself out of the tradition whose binding force it has recognized. Hence in its own work it must endeavor to acquire as much historical self-transparency as possible. In its concern to understand the universe of understanding better than seems possible under the modern scientific notion of cognition, it has to try to establish a new relation to the concepts which it uses. It must be aware of the fact that its own understanding and interpretation are not constructions based on principles, but the furthering of an event that goes far back. Hence it will not be able to use its concepts unquestioningly, but will have to take over whatever features of the original meaning of its concepts have come down to it.”[9]In this paragraph, Gadamer’s view towards tradition and hermeneutics is clear, namely, he thinks we all live under the long tradition which have handed down, but we also should not blindly accept the tradition’s all contents, while should critically and openly inherit them, and only in this way can we absorb their pith and spiritual essence. By using the basic idea of hermeneutics, Gadamer does extensive and profound investigations about many things such as science, philosophy and art, and they are also greatly inspiring.
4 French philosophy of Sartre and Merleau Ponty.As is widely known, French philosophy is greatly impacted by German philosophy, and has large difference in style with British and American philosophy, for example, few French philosophers discuss about epistemological problems such as logic, language and science, while French philosophy’s correlations with art and literature are closer; here, we prepare to take Sartre and Merleau Ponty these two people as example and discuss about the general style and academic meaning of the 20th-century French philosophy. Sartre’s existentialism has certain impact on the 20th-century politics, literature and philosophy, and it is what we all know, but, compare with Heidegger and etc, his academic level is somewhat worse, for example, he once writes: “If the being of phenomena is not resolved in a phenomenon of being and if nevertheless we can not say anything about being without considering this phenomenon of being, then the exact relation which unites the phenomenon of being to the being of the phenomenon must be established first of all. We can do this more easily if we will consider that the whole of the preceding remarks has been directly inspired by the revealing intuition of the phenomenon of being. By not considering being as the condition of revelation but rather being as an appearance which can be determined in concepts, we have understood first of all that knowledge can not by itself give an account of being; that is, the being of the phenomenon can not be reduced to the phenomenon of being. In a word, the phenomenon of being is ‘ontological’ in the sense that we speak of the ontological proof of St. Anselm and Descartes. It is an appeal to being; it requires as phenomenon, a foundation which is transphenomenal. The phenomenon of being requires the transphenomenality of being.”[10]In this passage, Sartre is discussing about the nature of being, and he thinks only static observing cannot provide reason for being, and being still needs a transphenomenal foundation, namely, the being’s action, and he thinks only by human’s proactive action can individual get the authentic living method, and here, the views Sartre expresses are somewhat clear. But, from this paragraph, we can also see, compared with Heidegger’s thoughts, Sartre is worse in certain aspects such as speculation of words, logic of thought and academic depth, namely, the academic and professional quality of Sartre’s thoughts is not sufficient.
Merleau Ponty’s phenomenology also has certain influence in French philosophical world, and his phenomenological research has certain academic foundation, and the aspects involved are somewhat broad, but his depth of thought is also not enough; for example, he writes: “Once introduced, the notion of sensation distorts any analysis of perception. Already a ‘figure’ on a ‘background’ contains, as we have seen, much more than the qualities presented at a given time. It has an ‘outline’, which does not ‘belong’ to the background and which ‘stands out’ from it; it is ‘stable’ and offers a ‘compact’ area of colour, the background on the other hand having no bounds, being of indefinite colouring and ‘running on’ under the figure. The different parts of the whole-for example, the portions of the figure nearest to the background-possess, then, besides a colour and qualities, a particularsignificance.”[11]Merleau Ponty’s this paragraph discusses about sensation and perception, which is not a very fresh philosophical problem, and many philosophers have already discussed about it, and moreover, we can also see, compared with works likeCritique of Pure Reason(1781) by Kant in the 18thcentury orThePrinciples of Psychology(1890) by William James in the 19thcentury, Merleau Ponty’s related thoughts not only do not achieve progress, but also have certain retrogression. To conclude, about Merleau Ponty’s philosophical research, we think it has certain academic value, but also should not be overestimated.
5 Popper, Kuhn and Lakatos’s philosophy of science.Philosophy of science by Popper and etc also has a large impact on the 20th-century scientific and philosophical world, certainly, considering the realistic fact, its impact on philosophy is bigger than scientific world. Firstly, as for Popper, the range of his exposition is much broader than Kuhn and etc, and is also somewhat systematic and coherent, as an example, about the basic condition scientific theory should satisfy, he once says: “In order to make this idea a little more precise, we may distinguish three requirements which our empirical theoretical system will have to satisfy. First, it must be synthetic, so that it may represent a non-contradictory, a possible world. Secondly, it must satisfy the criterion of demarcation, i.e. it must not be metaphysical, but must represent a world of possible experience. Thirdly, it must be a system distinguished in some way from other such systems as the one which represents our world of experience.”[12]In this passage, Popper thinks that scientific theory should be synthetic, and should be the constructed product of human mind, but it also must fit with the empirical field, and must have objective verifiability, and thus, only by combining human mind’s subjectivity and construction and objective experience’s verifiability together can we get a good scientific theory, and Popper’s this view is somewhat profound. Certainly, the contents of Popper’s philosophy of science are very complex, involving many different problems such as probability, quantum theory, relativity, language, induction, etc, which can not be clearly articulated by a few words, while these ideas also have high academic value.
In terms of Kuhn and Lakatos’s philosophy of science, their works also have substantial intension, and have good academic foundations, though their impact on professional scientists is somewhat small, they also extend and deepen the range of human thought, and thereby, have certain academic meaning. Generally speaking, the impact of philosophy of science mainly embodies in humanity and social sciences, for example, they have a large impact on intellectual history, politics, economics and sociology, while their actual impact on the scientific world is somewhat small; the emergency of this basic phenomenon is not accidental, below we will discuss about the cause of this issue.
Finally, we also want to discuss about the interrelation between philosophy of science and logical philosophy this interesting problem; if we take specific philosophers as example, Carnap are interested in both philosophy of science and logical philosophy, while Popper is mainly interested in philosophy of science, but not good at logical philosophy, Quine is familiar with logical philosophy, but does not know much philosophy of science; in conclusion, from these philosophers, we can know, philosophy of science and logical philosophy have overlapping places, but also have many their own features. In general, logical philosophy pays more attention to problems such as logic’s symbolic deductions and language’s logical form, while the scope of philosophy of science’s concern is broader, and it cares about scientific knowledge’s developing feature, theoretical basis, philosophical meaning, etc; in a word, these two different fields are both somewhat broad, and also have their own academic feature and internal value.
6 Political philosophy and ethical philosophy.
(II) The Connections between Modern Philosophyand Natural Sciences
As people’s general common sense, philosophy and natural science always have close connections, and among them, scientific subjects which have the closest relationship with philosophy are probably mathematics, physics and biology these three fields; but, different from the 18thand 19thcenturies, in the 20thcentury, the relationship between philosophy and natural sciences undergoes some fundamental changes, below, we want to analyze the complex correlation between the 20th-century philosophy and natural sciences.
1 The scientific background of philosophy.In the 17thand 18thcenturies, the connection between philosophy and science is very direct and close, for example, Descartes (1596-1650) and Leibniz (1646-1716) are both important philosophers and important mathematicians, and in the 20thcentury, such kind of person does not exist. The basic reason behind this phenomenon is simple, namely, in the past three, four centuries, though the depth and breadth of philosophy does not increase much, the breadth of science enlarges a lot, and the depth also greatly deepens; we can roughly think, the range of science in the 19thcentury is already more than twice than the 17thand 18thcenturies, while the 20th-century scientific knowledge is also twice than the 19thcentury, which directly results in that scientific research becomes more and more profound and difficult, and therefore, it becomes increasingly difficult for philosophers to master modern science.
As a concrete illustration of the above phenomenon, we want to give an appropriate example, namely, the mathematician Leray’s work. As a great mathematician, Leray does many profound works in topology and partial differential equation, and they include: in 1934, Leray and Schauder cooperated to generalize Brouwer’s fixed point theorem and its mapping degree theory into Banach space and form the topological degree theory, and they also built the Leray-Schauder principle; through this tool, using mapping degree to estimate the fixed point of the completely continuous operator, they could get the solution of certain complex high order partial differential equation, which has become the standard tool to study nonlinear partial differential equation. In 1945, to make connections between the local property of continuous mapping and global cohomology, Leray first introduced sheaf theory and cohomology whose coefficient is sheaf, and after the modification of Weil, Cartan and Serre, it becomes the most efficient method to treat complex space. In 1946, for the need of studying homotopy of fiber bundle, Leray introduced locally compact space and spectrum sequence with compactly supported cohomology continuous mapping, namely, the Leray spectrum sequence, and used it to compute the homology of fiber space, and got profound results. From 1957-1964, Leray did a series of research about strongly hyperbolic operator, and generalized F John’s method to strongly hyperbolic operator. In general, Leray made important contributions in many aspects such as boundary value problem, fixed point theory, hyperbolic partial differential equations and Lagrangian analysis. Form this example, we can see, Leray’s mathematical works are profound and extensive, and even for professional mathematicians, it is also very difficult to understand his relevant research, while for philosophers, it is almost impossible to understand his work; to sum up, mathematicians are working as hard as they can to understand works by Leray and etc, and they do not have energy to study much obscure knowledge of modern philosophy. To conclude, philosophy’s detachment from modern science is not accidental, and the fundamental reason is that modern science is becoming increasingly broad and profound. Certainly, on the other hand, due to some philosophers of science such as Carnap, Popper and Reichenbach, though the direct influence of many research results of modern science on philosophy is weakening, their indirect influence on philosophy is still very extensive and strong.
2 The difference between mathematics and logic.As stated above, some philosophers are keen on studying logic, and the extensive usage of mathematical logic and logical thinking method is also a basic characteristic of the 20th-century philosophy; but, from the perspective of mathematics, logic is just a marginal branch of mathematics, and no matter in depth or breadth, it cannot be compared with some major mathematical branches such as analysis, algebra, geometry and topology.Here, we can take some specific logicians as example: Turing is a good logician, but his level cannot be said too high, Godel’s academic achievement is better than Turing, but also cannot be said too great, namely, these important logicians’ academic contributions are far from some mathematicians like Poincare, Hadamard and Weyl.In a word, compared with other mathematical branches, logic is just a somewhat shallow field, and also somewhat narrow, and I think it is meaningful for philosophers to know this basic fact.
3 About modern philosophers’ scientific foundation. One basic feature of modern philosophical book is that many works are all literary; for example, when we see the title of Husserl’s Logical Investigation, we will probably think there should be many symbolic things in it, but when we browse this book’s contents, we can see, there are almost no symbolic deductions in this whole work; for example, Husserl once says: “The concept of pure logic so far developed covers a theoretically closed circle of problems, essentially relate to the idea of Theory. To the extent that no science is possible without grounded explanation, i.e. without theory, pure logic covers the ideal conditions of the possibility of science in general in the most general manner. It must, however, be noted that logic so regarded does not include, as a special case, the ideal conditions of empirical science in general.”[14] What Husserl discusses here is the nature of logical concept, and his these words are certainly reasonable, but not symbolic. Ayer’s situation is also similar, for example, when we see the title of The Problem of Knowledge, we will often think that there are some symbolic contents, but this book is actually also mostly literary. Certainly, it should be noted that, Husserl has certain scientific foundation, and he receives the mathematical PhD degree from University of Vienna in 1883, and his doctoral thesis is “The variational theory of calculus”, but, the mathematical symbolic contents in his works are not many.
Here, we also want to examine other philosophers’ scientific mastery. As for Carnap, though he has studied relativity, and writesThe Philosophical Foundation of Physicsthis work, in fact, he can not understand most contents of general relativity, because general relativity is based on Riemannian geometry, while Carnap does not quite know Riemannian geometry. Russell’s situation is roughly also like this, for example, inThe Analysis of Matter, he discusses about many physical contents, such as the “quantum theory” in chapter IV, “general relativity” in chapter VI, and “Weyl’s theory” in chapter X, but his understandings towards these physical theories are all superficial, and just with a vague impression, for example, he once writes: “Riemann’s work, as well as that of Faraday and Maxwell, belongs, like the theory of relativity, to the development of the view of the physical world as a continuous medium, which has, from the earliest times, contested the mastery with the atomic view.”[15]In fact, about the mathematical and physical knowledge in this paragraph, such as Riemannian geometry and Maxwell’s electromagnetic theory, Russell all does not really understand.
Considering various kinds of situation, if comparing the scientific foundation of modern philosophers, we think, it will probably be the following order:
Carnap, Putnam, Frege > Russell, Husserl > Ayer
Certainly, in general, these philosopher’s scientific foundations are far from professional scientists, and compared with some important scientists in the 20thcentury, such as Dirac, Grothendieck, Wiener and Wiles, no matter in breadth or depth, modern philosophers’ scientific mastery is far from them. However, conversely, professional scientists also do not quite know some problems these philosophers discuss, such as logic, language, ontology, positivism, existentialism, empiricism and etc, because they lack professional knowledge in philosophy, and I think this point is also not difficult to understand. To sum up, knowing these basic facts will be quite meaningful for us to understand the general feature of 20th-century philosophy.
(III) The Connections between Modern Philosophyand Humanity and Social Sciences
All along, philosophy also has extensive and close connections with humanity and social sciences, which is also a fact we are familiar with; about the relationship between philosophy and social sciences, Hegel once says: “But men do not at certain epochs, merely philosophize in general, for there is a definite Philosophy which arises among a people, and the definite character of the stand-point of thought is the same character which permeates all the other historical sides of the spirit of the people, which is most intimately related to them, and which constitutes their foundation. The particular form of a Philosophy is thus contemporaneous with a particular constitution of the people amongst whom it makes its appearance, with their institutions and forms of government, their morality, their social life and the capabilities, customs and enjoyments of the same.” “The history of the other Sciences, of culture and above all the history of art and religion are, partly in regard to the elements contained in them, and partly to their particular objects, related to the history of Philosophy.”[16]Hegel’s this passage makes a good explanation about the complex and profound relationship between philosophy and social sciences. To conclude, philosophy needs to carefully consider the situation in social field, including many aspects such as politics, economy, society, art, religion and law, because these aspects all contain many meaningful philosophical problems (like social justice, individual’s ethical norm, aesthetics, etc), while if cutting off the extensive connections between philosophy and social field, philosophical research will become water without the source.
Take the specific philosophers as example, they also can well embody the extensive correlations between modern philosophy and social sciences; for example, Heidegger and Sartre’s existentialism has certain impact on political practice, Dewey’s education and politics also comes from the observation and thinking about real social life, Quine’s language philosophy stems from the systematic reflection of many language phenomena in real life, Dworkin and Rawls’s works in political philosophy also reflect many actual problems in their time. Take the philosophical branches as another example, some important philosophical branches in the 20thcentury, such as language philosophy, ethical philosophy, existentialism and hermeneutics, also all use various relevant issues in actual life as their empirical foundation. In conclusion, obviously, many problems in social science field also constitute part of driving force for the development of modern philosophy.
(IV) Aboutthe General Property of Philosophy
Finally, as an appropriate summarization, we also want to discuss about the general property of philosophy; people often say that, philosophy is the subject of world view, while to form a complete world view, philosophy needs to comprehensively consider the complex situation in both natural sciences and humanity and social sciences, and as the ancient Chinese thinker Chuang Tzu says: “Appreciating the beauty of the world, analyzing the reason of everything, and examining the ancient people’s thoughts. If one people can possess the completeness of the world, then he can be called saint.”[17]Chuang Tzu’s these words do a good generalization about the holistic property of philosophy. In philosophers’ view, only after the deep study about many problems in the natural world and social field can one people get a mature and wise view towards life and universe, and can he get true wisdom, which is perhaps the goal philosophers always pursue from ancient to modern times.
Generally speaking, philosophy has both natural science attribute and social science attribute, and is the combined product of them, thereby, for philosophers, it is often insufficient to just study one side of them; for example, about “truth” this important philosophical problem, we can evidently feel this double attribute of philosophy. As is widely known, philosophers like discussing the feature and meaning of truth, while around “truth”, philosophers also have had many intense debates; in general, we think, for scholars in different fields, there are at least the following five kinds of conceptions of truth:
1 Logical positivism’s truth. In the eyes of logical positivists like Carnap, only facts which can be reduced to basic empirical propositions are truth, and the others are not objective truth, and as Carnap says: “The system which is formulated in this book takes as basic elements the elementary experiences. Only one basic concept is used, namely a certain relation between elementary experiences (recollection of similarity). It is then shown that the other concepts, e.g. the different senses, the visual sense, visual field places and their spatial relations, the colors and their relations of similarity, can be defined on this basis.”[18]We can easily see, it is one kind of truth which is mathematical and has strong natural science feature.
2 Pragmatism’s truth. In the eyes of pragmatists like William James, things which can be checked and used in practice are truth, and the other things are not truth, and as he says: “True ideas are those that we can assimilate, validate, corroborate and verify. False ideas are those that we can not. That is the practical difference it makes to us to have true ideas; that, therefore, is the meaning of truth, for it is all that truth is known-as.”[19]
3 Existentialism’s truth. While in the eyes of existentialists like Heidegger, truth is another thing, namely, the freedom to achieve one’s authentic condition is truth, and as Heidegger says: “The essence of truth reveals itself as freedom. The latter is ek-sistent, disclosive letting beings be. Every mode of open comportment flourishes in letting beings be and in each case is a comportment to this or that being. As engagement in the discourse of beings as a whole such, freedom has already attuned all comportment to beings as a whole.”[20]Obviously, Heidegger’s this view is roughly a conception of truth with social science attribute.
4 Natural scientists’ truth. For natural scientists engaged in scientific research, the definition of truth is normally simple and clear, namely, conclusions which can be objectively checked and can be derived from rigorous logic are truth, for example, Gauss’s differential geometry, abstract algebra, statistical mechanics and Maxwell’s electromagnetic theory are all truth.
5 Social scientists’ truth. Many social scientists also often like saying that he is pursuing truth, such as jurist, economist, political scientist, historian, etc, and the truth in their eyes are probably some objective legal, economic and historical facts, or some somewhat true abstract theories.
To conclude, in terms of truth, we can evidently feel that philosophy actually has the double attribute of natural science and social science: the truth problem involves both many facts in natural science and many situations in social field, and only by comprehensively considering these two aspects can we get somewhat reasonable views. In a broader sense, general philosophical research also often needs to consider many situations in both natural science and social science these two different fields.
Certainly, it is somewhat difficult for philosophical research to include both natural science and social science, because these two fields are both broad and complex, and it will cost one people huge energy to well master them; if looking from the specific philosophers, Aristotle, Descartes, Kant, James, Russell, Husserl have profound attainments in both natural science and social science, while Hegel, Dewey, Heidegger and Nietzsche are not very proficient in natural science, and just know humanity and social sciences, namely, in the exploration of the natural world and society, different philosophers’ knowledge background and problem consciousness have large difference. In general, as the subject of world view, philosophy needs to consider the complex situations in both natural sciences and social sciences these two broad fields, and I think 20th-century philosophy also makes many contributions in these problems.
[1]The above contents can refer toConceptual Notation and Related Articles, Chapter I, Section 11, 12, Oxford University Press, 1972. Frege’s analyses about these issues are more complex and systematic than our quotations here, and interested readers can refer to the relevant expositions in the original work.
[2]Introduction to Mathematical Philosophy, Chapter XIV, “Incompatibility and the Theory of Deduction”, pp. 149, 150, Dover Publications, Inc, 1993.
[3]From a Logical Point of View, Chapter I, p. 12, Haper & Row, Publishers, 1963.
[4]See the above book, Chapter V, p. 87.
[5]Introduction To Symbolic Logic and Its Applications, Chapter A, “The simple language A”, p. 27, Dover Publication, Inc. 1958.
[6]The Problem of Knowledge, Chapter I, “Common features of knowledge”, p. 8, Macmillan & Co. LTD, 1956.
[7]The Crisis of European Sciences and Transcendental Phenomenology, Part III, Section 34, p. 127, Northwestern University Press, 1970.
[8]Being and Time, Chapter I, Section 9, “The Theme of the Analytic of Dasein”, p. 68, Blackwell Publishers Ltd, 1962.
[9]Truth and Method, “Introduction”, XXIII, Continuum Publishing, 2004.
[10]Being and Nothingness, Introduction, Section II, “The phenomenon of being and the being of the phenomenon”.
[11]Phenomenology of Perception, Chapter 2, “‘Association’ and the ‘projection of memories’”, p. 15, Routledge, 2002.
[12]The Logic of Scientific Discovery, Part I, Chapter I, Section 5, “Experience as a method”, Routledge, 2002.
[13]Taking Rights Seriously, Introduction, pp. VIII, IX, Harvard University Press, 1978.
[14]Logical Investigations, Volume I, Chapter XI, Section 72, p. 160, Routledge, 2001.
[15]The Analysis of Matter, Chapter II, “Pre-Relativity Physics”, p. 22, Routledge, 1992.
[16]Lectures on the History of Philosophy, Volume I, “Introduction”, B, pp. 53-55, University of Nebraska Press, 1995. In this part, Hegel also discusses spirit of the age and spirit of the people, and these expositions have a large impact on the later social thoughts and philosophical thoughts.
[17]Chuang Tzu, “Heaven”
[18]The Logical Structure of the World, “Preface to the second edition”, p. VII, University of California Press, 1969.
[19]Pragmatism, Lecture VI, p. 201, Longmans Green and Co., 1922.
[20]Pathmarks, “On the Essence of Truth”, p. 147, Cambridge University Press, 1998.