My dissatisfaction with the translation-failure interpretation of incommensurability and the Quinean notion of conceptual schemes is not only caused by the many theoretical difficulties they face, but is also due to the observation that they are unable to elucidate many classical confrontations between alleged incommensurable theories or languages. Some of classical incommensurable cases that I have in mind are: Aristotelian physics versus Newtonian physics; Newtonian mechanics versus Einsteinian relativistic mechanics; Lavoisier’s oxygen theory versus Priestley’s phlogiston theory of combustion; Galenic medical theory versus Pasteurian medical theory; Newton’s view versus Leibniz’s view of space-time; Ptolemaic astronomy versus Copernican astronomy; quantum mechanics versus pre-quantum mechanics, and so on. My presuppositional interpretation emerges in a close reading of those celebrated cases of incommensurability.
How should we understand and explain these classical cases of incommensurability? Specifically, how can we identify the conceptual disparity between the incommensurables? What is the hallmark of these conceptual confrontations, and what are their genuine sources? These familiar conceptual confrontations are, to me, not confrontations between two scientific languages with different distributions of truth-values over their assertions due to the radical variance of the meanings (sense and reference) of the terms involved, but rather are confrontations between two languages with different distributions of truth-value status over their sentences due to two incompatible sets of metaphysical presuppositions underlying them. Consequently, a communication breakdown between the proponents of two incommensurable theories is not signified by the untranslatability between the languages of the theories, but is rather indicated by the occurrence of a truth-value gap between the languages.
The above insights are derived from two case studies. One is a not-yet-well-known study comparing contemporary Western medical theory and traditional Chinese medical theory; the other is the well-known debate on the absoluteness of space between Newton and Leibniz. I choose the first case because both theories arise from two highly developed and sophisticated cultural and intellectual traditions so disparate that cross-language communication between them often breaks down. I will show in the later chapters that this case represents an extreme in which two scientific languages are radically incommensurable. By comparison, the second case represents a moderate version of incommensurability.
Traditional Chinese medical theory (hereafter CMT) emerged more than two thousands years ago. It is still practiced widely inside and outside of Pan-Chinese culture and is very successful today. During its more than 2000-year development, CMT has established a complete conceptual system including its own physiological theory, pathological theory, diagnosis, and treatments. Its physiological and pathological basis consists of the yin-yang doctrine, the five-elements doctrine, the viscera doctrine, and the jingluo doctrine. Z. Lan has a clear and concise summary of these doctrines worthy of full quotation:
The yin-yang doctrine takes the human body to be a unity of opposites. It is composed of two parts, the yin part and the yang part. The yang part includes the upper, exterior, back, outer side, and the six hollow organs, while the interior, the abdomen, the inner side, and the five solid organs belong to the yin part. There are further divisions within individual organs such as the heart and the liver.
The theory of five elements holds that everything is made of five different elements: metal, wood, water, fire, and earth. One of these elements is found in each of the five solid organs of the human body: wood in the liver, fire in the heart, metal in the lung, earth in the spleen, water in the kidney. These organs are inter-related. The kidney essence nourishes the liver, the liver stores blood which is supplied to the heart, the heat generated by the heart warms the spleen, the spleen extracts vital substances from water and cereals to feed the lung, and the lung, in turn, assists the kidney by keeping the kidney fluid pure.
Pathological changes in one organ affect the other solid organs, the limbs, the bones, the five sensory organs, the nine orifices, the tendons, and the blood vessels. These interactions are governed by the viscera-state doctrine. According to this doctrine, the eye is the orifice leading to the liver, the tongue leads to the heart, the ear to the kidney, the nose to the lung, and the mouth to the spleen. As a result, eye disease is treated by clearing away the liver fire, kidney stone by compressing the ear, and so on. (Lan, 1988, pp. 229-30)
Applying the above theories or doctrines to medical practice and health care, CMT has its own unique way of diagnosis and treatment. According to the yin-yang doctrine, it is the balance between the yin and yang parts of the human body that ensures its normal working and health. Loss of the yin-yang balance of the human body invites evils that lead to diseases. All symptoms related to diseases are classified as eight principal syndromes, which can be grouped further into four matched pairs: the yin versus the yang syndrome, the superficial versus the interior syndrome, the cold versus the heat syndrome, and the asthenia versus the sthenia syndrome. Of the eight principal syndromes, the yin and the yang are the leading ones. The yin syndrome governs the superficial, the asthenia, and the cold syndromes, while the yang syndrome controls the interior, the sthenia, and the heat syndromes. Therefore, all diseases arising from loss of the yin-yang balance can be diagnosed as the result of either a yin syndrome or a yang syndrome.
Treatment is a matter of restoring the balance between the yin and the yang inside of the human body. Different principles of treatment are applied to the different syndromes, such as the cold-heat principle, the asthenia-sthenia principle, and the yin-yang principle. For example, when an excess of the yin leads to a weakness of the yang, which is diagnosed as the yin syndrome, herbs and other healing techniques (such as acupuncture and moxibusion, cupping, Qigong2) are administered to restore the yin-yang balance by making up the deficiency of the yang. As another example, CMT holds that the spleen is responsible for transport and conversion. The spleen affects the upward movement of vital substances and controls blood. Many spleen diseases (the important symptoms of which are abdominal distension, loose stools, inappetence, phlegm-retention, oedema, diarrhea, blood in stools, and so on) are caused by the imbalance between the yin and the yang within the spleen, which is manifested as either an asthenic or a sthenic spleen. The cure for these diseases lies in the nourishment of the spleen to restore the yin-yang balance.
In addition, traditional CMT regards the human body as one part of an organic universe in a process of constant transformation in which everything is interrelated and interacted. There is mutual influence between the human body and Heaven (as Nature or the Universe). Therefore, many symptoms can be attributed to the associations between natural forces and changes—which represent the yin or the yang principles of the universe—and the yin-yang parts of the human body that are supposed to correspond to the former. For example, according to Han Confucians, when Heaven is about to make rain (representing the yin) fall, people feel sleepy. This is because when the yin force in Heaven and Earth begins to dominate, the yin in the human body responds. In this way, the association between the yin and rain causes increased sleepiness in people.
From the above brief summary of traditional CMT, we can see that the physiological and pathological theories and the medical concepts of CMT are systematically different from those of contemporary Western medical theory. The former is holistic while the latter is analytic. In addition, both medical theories have very different systems of medical categories. Although CMT has some equivalents (as far as the referents are concerned) for certain Western anatomical terms—such as ‘heart’, ‘liver’, ‘spleen’, ‘lung’, ‘kidney’ (the so-called five solid organs), and ‘gallbladder’, ‘stomach’, ‘large intestine’, ‘small intestine’, ‘bladder’, and ‘triple warmer’ (the so-called six hollow organs)—the physiological and pathological connotations of these terms are not the same. The functions of corresponding referents are believed to be totally different. This is because the organs in CMT are as much physiological and pathological entities as they are anatomical entities. Take the heart as an example:
In Chinese theory, the heart is not only an anatomical entity; it is part of the nervous system and can perform some of the functions which Western theory attributes to the cerebral cortex. The heart not only gives force to the circulation of the blood but also controls the mental and emotional faculties. The Chinese heart is similar to the Western heart in respect of its cardiovascular function. But it differs in its relationship to the cerebral cortex. One consequence of this difference is that Chinese pathology tends to be holistic whereas Western theory tackles medical problems at the molecular and cellular level. (Lan, 1988, p. 231)
CMT is hardly intelligible to most Western physicians. They are very skeptical of Chinese medicine and even regard Chinese physicians as medicasters. Many Western physicians claim that Chinese medicine sounds strange and alien to them. As one Western physician complains, the sentence, ‘The loss of balance between the yin and the yang in the human body invites evils which lead to diseases’, sounds as nonsensical to him as the utterance, ‘ooh ee ooh ah ah’ does. What causes such an apparent communication breakdown between the two medical language communities? One might say that the failure of understanding is caused by the fact that Western physicians are unable to understand many terms used by CMT, such as ‘the yin’ and ‘the yang’. Because of this, they cannot translate the sentences of CMT into their own language. Such untranslatability sets obstacles for understanding and thereby leads to a communication breakdown between the two communities.
However, untranslatability is not the issue at hand here. The Westerner does not lack expressions to convey many central concepts of CMT. For example, the two central notions of CMT, the yin and the yang, could be formulated in English as follows: The yin and the yang are two fundamental elements, forces, or principles in the universe. The yin, which represents the negative, passive, weak, and destructive side of the universe, is associated with cold, cloud, rain, winter, femaleness, and that which is inside and dark. The yang, which represents the positive, active, strong, and constructive side of the universe, is associated with heat, sunshine, spring and summer, maleness, and that which is outside and bright. Of course, the terms ‘yin’ and ‘yang’ have different connotations in different schools of Chinese philosophy. To Tung Chung-Shu, for example, the yin and yang are two kinds of ch’i, which has an exceptionally varied number of meanings in the Chinese language and philosophy. But this is not the problem of translation, but rather the issue of different philosophical interpretations of the concepts. Furthermore, the meanings of the terms ‘yin’ and ‘yang’ in Chinese medical theory are relatively limited. We can use the above plain definitions to convey their basic meanings in English. Then, the English sentence,
(4) The association of the yin and rain makes people sleepy,
is a close translation of the original Chinese sentence.
However, the defenders of the untranslatability thesis might quickly point out that the above argument confuses two different kinds of languages—the theoretical language used to formulate Western medical theory and the natural language used to code the theory. To say that CMT (which is written in ancient Chinese) can be translated into English is not the same thing as to say that the theory can be translated into the language of Western medical theory. The thesis of untranslatability is about the impossibility of translation between two scientific languages. It cannot be applied to, without further qualification, the impossibility of translation from one scientific language into one natural language.
I agree that the literal translation between the two medical languages cannot be done, for many reasons. Let me mention only one of them: because the two languages have sufficiently disparate medical category systems. To have an exact translation from Chinese medical language into Western medical language, we have to alter the whole taxonomic structure of the target language (the Western medical language) and extend dramatically its semantic resources by semantic enrichment. That means that we have to change the whole target language, which is not permissible for a literal translation.
The real issue is, however, that such untranslatability between the two languages does not ensure the failure of understanding between the two language communities; for translatability is not necessary for understanding. Without appealing to translation, the Western physician can still manage to understand Chinese medical theory by language-learning. In fact, there are many people from the West studying Chinese medicine in China today. Many Western medical practitioners successfully adopt ancient Chinese healing techniques in their clinical practice in the US. As one Western physician said, after he learnt the theory, there is no longer ‘ooh ee ooh ah ah’ about it. Sentences that used to be senseless suddenly turned to being perfectly understandable.
In either case, the difficulty of the intertranslation between the two languages is not exactly a barrier to the achievement of cross-language understanding.
If untranslatability between Chinese medical language and Western medical language cannot account for the failure of understanding and communication breakdown between the two language communities, then two questions remain. First, what does the real difficulty of mutual understanding and communication between the two language communities derive from? Second, could we identify a strong linguistic correlate, if any, of such problematic understanding?
The answer to the first question lies in the following observations. Let us first consider the case in which Chinese medical language can be translated into modern English (not into Western medical language). Even so, Westerners who are not familiar with the traditional Chinese mind and the pre-modern Chinese way of thinking would still be left in a fog. Even supposing that they know the general meanings of the terms, ‘the yin’ and ‘the yang’, the question still remains, what is the point of what is expressed by a sentence such as (4) or (5)?
(5) All diseases are due to the loss of the balance between the yin part and the yang part of the human body.
What is the (cognitive or empirical) content asserted by (5)? What is the point of what is being presented or argued by (4) or (5)? It is not the words of (5) that Westerners cannot make sense of, but the mode of reasoning or the way in which the assertion is made and defended is entirely alien to them. Besides, it is based on a whole system of categories that is hardly intelligible to Westerners. Without grasping the unique mode of reasoning and the categorical system underlying the sentence, one cannot understand it effectively. Due to the lack of an alternative— since Westerners can identify neither the underlying way of thinking nor the category system embedded in CMT—Westerners have to approach it from the mode of reasoning and the category system of their own time with which they are familiar. Westerners would naturally try to project their own way of thinking and categories onto what they try to understand. Such a projective way of understanding would distort the Chinese text and lead to the failure of genuine understanding, and thereby a communication breakdown. This is exactly what happens when Westerners feel lost when reading sentences like (4) and (5).
Let us turn to another case in which a literal translation between the two medical languages is not available, but one side can understand the other by language-learning. In general, language-learning is a process in which the learner is not just trying to understand some individual words of an alien language, but also trying to understand the language as a whole. In our case, the language as a whole that Westerners should learn is not only the theoretical language employed by CMT, but also the Chinese language used to code it. This is because ancient Chinese philosophy had such a strong influence on the formation and development of Chinese civilization that it left its print on almost all aspects of Chinese culture and institutions. Even today, the life of the Chinese people is permeated with Confucianism and Taoism. The Chinese language, as the linguistic representation of this great civilization, is no exception. Of course, one might argue the other way around: It is not ancient Chinese philosophy that shaped Chinese civilization and its language, but it is Chinese civilization, especially its language, that shaped ancient Chinese philosophy. I do not know how to cut into this circle, but one thing is clear: There is an intrinsic connection between the Chinese language and Chinese philosophy. For example, suggestiveness, instead of articulateness, is the particular way in which Chinese philosophers expressed themselves. Ancient Chinese philosophers were accustomed to express themselves in the form of aphorisms, apothegms, allusions, and illustrations. Chinese, as a pictographic and ideographic language full of imagination, is the ideal vehicle to convey the suggestiveness of the sayings and writings of Chinese philosophers. Strictly speaking, the rich content and implications of Chinese philosophy can be formulated precisely (without loss and distortion) in Chinese only. On the other hand, the Chinese language is fully loaded with Chinese philosophical ideas. Many concepts of Chinese philosophy have become the common vocabulary of Chinese, such as the yin and the yang, Tao, etc. For example, in Chinese the penis is called the yang zhui (the positive tool); the vagina is called the yin tao (the negative way). Even the terms in modern science still adopt the yin-yang division. The positive electrode is called the yang ji; the negative electrode is called the yin ji. As I will argue in detail in chapter 10, the pre-modern Chinese way of thinking and its underlying cosmology, which are embedded within CMT, were rooted in and developed from ancient Chinese philosophy. Due to the internal connection between Chinese philosophy and the Chinese language, the pre-modern Chinese way of thinking is embedded in the Chinese language. For this reason, to learn CMT, one had better learn it in Chinese. (Of course you can learn it in English. But to do so is akin to tasting Chinese food in a Chinese restaurant in the US that does not serve authentic Chinese food.) I will call the language of CMT coded in Chinese the language of Chinese medical theory as a whole, or the Chinese Medical-Language, in brief, below.
The Chinese Medical-Language reflects a unique belief system and embodies a specific form of life. One effective way to understand this language (if one could do so) is to immerse oneself into its unique belief system and its form of life as adopted by the native speaker living in the pre-modern period of China. During its long historical development, this set of beliefs and the form of life associated with the language have been internalized into the language3 and have formed their own specific mode of reasoning or rational justification (known as the associated way of thinking) as well as their own specific categorical framework.4 Therefore, this language is fully intelligible to Westerners only if they are able to grasp its specific mode of reasoning and categorical framework embedded in the language.5 For Westerners to understand effectively the Chinese Medical-Language, they have to get sufficiently into the pre-modern Chinese way of thinking and categorical framework, which are barely recognizable by and hardly intelligible to most contemporary Westerners.
After understanding the words and grasping the mode of reasoning as well as the categorical framework of the Chinese Medical-Language, Westerners can understand the language quite well. If Westerners were physicians, they would eventually become bilinguals, in our case, bi-medical practitioners. However, a bi-medical practitioner (who can speak both medical languages) is not necessarily a meda-medical practitioner (who can speak a metalanguage with the two medical languages as its sublanguages). Such bi-medical practitioners who live in the boundary between the two language communities often find themselves in an awkward situation. They can eventually understand the Chinese Medical-Language by getting into the pre-modern Chinese way of thinking, but, at best, they can start talking the pre-modern Chinese way only if they become alienated or dissociated from the modern Western way of thinking practiced in their own time. Westerners cannot hold both languages side-by-side in mind to make a point-to-point comparison. They cannot think in both languages at the same time. They cannot use one language to understand the other or incorporate one language into the other.
There has been an interesting initiative, suggested by the Chinese government and medical professional organizations, aimed at incorporating Western medical theory into CMT under the goal of developing traditional CMT. Many Chinese physicians and researchers thought that Chinese and Western medicine might (or should) complement one another so that one makes up for the disadvantages of the other. They called this initiative the Combination of Chinese and Western Medicine (CCWM). Encouraged (actually, required) and funded by the Chinese government, many hospitals and research institutions established research branches of CCWM. In the 1970s, it was even suggested that the yin-yang doctrine could be explained in terms of the Western theory of regulation (C-AMP and C-GMP), but it soon became obvious that the Western theory of regulation cannot be used to substitute for the yin-yang doctrine. The holistic framework of CMT cannot be assimilated into the atomistic framework of Western medical theory. For example, the physiological basis of the viscera doctrine cannot be found in the workings of C-AMP and G-AMP, or nucleic acid. After about thirty years of experiments, it became clear that CMT could not be incorporated into Western medical theory. The same conclusion applies to the opposite incorporation from Western medical theory into its Chinese counterpart. We cannot locate a common theoretical ground to combine the two into one coherent theoretical system.
Of course, the failure of the theoretical integration of Chinese and Western medicine does not mean that our bi-medical practitioners cannot apply both theories and ways of treatment in their clinical practice. Actually, what a bi-medical practitioner does, under the name of CCWM, is just that: either to apply different medical theories to treat different diseases, or to combine both healing techniques (not the two theories) to speed up healing of the same disease. What these bi-medical practitioners have done is not to adopt both theories at the same time, but to move back and forth between the two theories according to their needs in different situations.
In sum, full communication between Chinese and Western medical communities is hardly attainable. A communication breakdown between them is not due to the difficulty of translation, but rather is either due to one side failing to grasp the mode of reasoning and the categorical framework of the other language (hence lack of understanding) or is due to the lack of compatible modes of reasoning or matchable category systems between the two languages (even if understanding can be restored by language-learning). In this sense, we say that the two medical languages are incommensurable.
How can we identify a failure of understanding and a communication breakdown between the two languages? To say that the underlying modes of reasoning or categorical frameworks of the two languages are incompatible does not help, since those attributes are not something that can be easily identified.
As an example, imagine that a Chinese physician Dr Wong, when asked why people tend to become sleepy on rainy days, claims:
(4) The association of the yin and rain makes people sleepy.
What is a likely response of a practitioner of Western medicine, say, Dr Smith? To see his possible responses, we need to consider two different hypothetical situations.
First, let us suppose that Dr Smith knew nothing about CMT and had no background in Chinese culture, philosophy, and language. Suppose further that he was told the meaning of the term ‘the yin’ by a definition which we have given before. Under these suppositions, he would certainly not say, ‘No, what you have said is simply false’. He could not understand (4) since he could not grasp the way in which the assertion was proposed and justified. The content of the sentence lies outside his conceptual reach. It is not even clear for him whether the sentence really asserts anything. It is, hence, very likely that he would say something like: ‘I do not know what you are talking about’ or ‘What is the point of what you are saying?’ The implication behind these responses is that the question of whether the assertion (4) was true or false simply did not arise. For Dr Smith to claim that it was true or false presupposes that he understood the sentence. This is excluded by our suppositions. (4) is nonsense to him and cannot be answered in the way the question is put to him.
Secondly, let us suppose that Dr Smith happened to know CMT and the yinyang doctrine in ancient Chinese philosophy, and was also able to comprehend the pre-modern Chinese mode of reasoning. Suppose further that he did not adopt the yin-yang doctrine and the corresponding mode of reasoning. If we asked him whether he thought Dr Wong’s assertion is true or false, whether he agreed or disagreed with it, would he directly deny the assertion by replying, ‘No, (4) is false’? I do not think so for the following reasons. We can reformulate the suggested Dr Smith’s answer as follows:
(6) It is false that the association of the yin and rain makes people sleepy.
Then, both (4) and (6) somehow strongly ‘suggest’ or ‘imply’ (more precisely, ‘presuppose’) a third sentence:
(7) There is a fundamental element, force or principle in the universe, namely, the yin, and there is a pre-established connection between the human body and natural forces.
Therefore, Dr Smith (suppose that he is a critical thinker and is able to sense the implication behind such an answer) cannot simply deny (4) on its face; for such a denial seems to set a trap for him (recall the infamous question, ‘Do you still beat your wife?’). Therefore, he will hesitate to deny (4) directly.
Dr Smith’s uneasiness about how to answer (4) could have been strengthened further if he had realized the difference between the truth-value status of sentence (4) and a syntactically similar sentence:
(8) The association of the falling of the American stock market and rain makes people sleepy.
It is intuitively recognizable that (8) is untrue in a way which is different from the non-truth of (4). The non-truth of (4) is due to the failure of its ‘felt implication’, namely, (7). But the non-truth of (8) is caused by a false connection between unrelated events. Therefore, it is possible for the negation of (8) (It is false that the association of the falling stock market makes people sleepy) to be true while the negation of (4), namely, (6), is untrue.
In addition, due to his uneasiness about answer (6), Dr Smith will very likely respond to the question by saying, ‘I do not think I can answer the question since there is no such thing as the yin’. To assert that there was no such thing as the yin is certainly not to contradict (4). He is rather giving a reason for saying that the question of whether (4) is true or false did not arise.
In both situations, we reach the same conclusion: For the Western physician, the question of whether (4) is true or false simply does not arise. A similar analysis can be extended to other core sentences of CMT. Either Western physicians fail to understand these sentences due to a failure to grasp the mode of reasoning and thereby cannot assign truth-values to them; or even if they are able to understand these sentences they are still not willing to assign truth or falsity to them because they do not adopt the underlying mode of reasoning and related doctrines. There is no way to match what the Chinese physician wants to say to anything the Western physician wants to say at the theoretical level. The confrontation between the two medical theories does not lie in the sphere of disagreement or conflict of the sort arising when one theory holds something to be true that the other holds to be false (logical inconsistency). The difference between them is not that Western medical theory has a different theory of the operation of the yin and the yang from that of its Chinese counterpart, or that the Chinese physician says different things about, say, bacteria and viruses. Rather, the difference lies in the fact that one side has nothing to say about the other. When Dr Wong diagnoses a disease as an excess of the yin within the spleen, it is not that Dr Smith thinks that Dr Wong is making a mistake in diagnosis or a false assertion, but that he simply cannot assign any truth-value to it at all. He has nothing to say about it. It is not that they say the same thing differently, but rather that they say totally different things. The key contrast here is between saying something (asserting or denying) and saying nothing. The Western physician can neither assert nor deny what the Chinese physician claims.
Consequently, Western physicians do not regard as false many core sentences of the language of CMT; they simply cannot assign truth-values to those sentences because their contents lie outside their conceptual reach. They had better keep silent about what they cannot grasp. Thus, a truth-value gap occurs between the two medical languages. It is this truth-value gap that indicates semantically that we encounter two alternative medical conceptual schemes embodied by the theories and that the communication breaks down between the two medical communities.
For a comparison, let us turn our attention to a classical debate within the same cultural and intellectual tradition—the Newton-Leibniz debate on the absoluteness of space.
Newton thinks that classical three-dimensional Euclidean space describes an independently self-existing physical space. The world of physical bodies and events, for a Newtonian, can be pictured as if it moves through a self-existing empty spatial continuum, as a ship moves through a pre-existing absolutely static ocean. All the physical and geometrical properties of Newtonian space exist independently of configurations of the physical bodies within it. To visualize Newtonian absolute space,
Imagine an empty space without any physical bodies, where each point has an identity of its own. You may stick imaginary labels on these points, naming each. After putting bodies into the space, each will occupy at any given time a certain region, i.e.—a certain set of space-points. (Gaifman, 1984, p. 324)
On the contrary, Leibniz rejects the absoluteness of space. For a Leibnizian, Euclidean space does not describe an independently existing physical space, although it might correspond to the structure of spatial relations in our world. There is no such self-existing empty space. Instead, space is determined by physical body configurations. Leibniz holds that ‘space is nothing else than the order of existing things’, ‘the order of bodies among themselves’, or ‘an order of things which exist at the same time’ and thus, it is not ‘something in itself; it ‘has no absolute reality’, but it is ‘something merely relative’ to body configurations within it.7
For comparison, imagine that we are able to move the whole configuration of bodies in a space, if any, keeping all distances between bodies and body parts constant. For Newtonians, the worlds before and after the movement will be different since each body in the configuration, after the movement, occupies a different region in absolute space. For Leibnizians, it will be the same world, since the configuration of bodies remains unchanged before and after the movement. Actually, it is not even possible, for Leibnizians, to move the same body configuration in a space because this presupposes the existence of absolute space.
The controversy about the absoluteness of space between Newton and Leibniz has become common knowledge among historians and philosophers of science. But as H. Gaifman points out, the question still remains concerning the real meaning of the debate. What is the real difference between Newton’s framework of space and that of Leibniz’s? To say that Newton believes in absolute space but Leibniz does not is of no big help, unless the notion of absolute space can be given a precise definition. But what we have right now is at most the illustration of it. Furthermore, people have many different ways of visualizing a given state of affairs, or can picture the same world in different ways. For example, what is the difference between saying ‘the car is moving toward me and saying ‘I am moving toward the car’? What difference does it make if you visualize natural numbers as a horizontal series going from left to right, but I visualize them as going up vertically? Perhaps the debate about the absoluteness of space is only restricted at the metaphorical or even psychological level? Therefore, it is Leibniz’s burden to justify his rejection of Newtonian absolute space by showing that the difference between Newton’s and his own picture of the spatial world is real and not just a difference involving favored ways of visualizing the same spatial world.
Leibniz’s way of justifying his framework of space has proven to be effective. Leibniz does not attack the Newtonian notion of absolute space head-on by directly addressing the question, ‘Is there a self-existing empty space?’ Instead, Leibniz questions the truth-value status of some core Newtonian sentences about comparison of positions of a given body at different times under the supposition that the whole body configuration remains the same so that the body’s position with respect to other bodies is unchanged (supposition C). The following sentence in modal form represents one such core Newtonian sentence.
(9) The body b at time t could have located in a different place.8
Put (9) in a non-modal form:
(10) The spatial location of the body b at time t1 is different from its location at time t2.9
(9) and (10) are two core Newtonian sentences because they presuppose the existence of Newtonian absolute space. In other words, (9) and (10) are true or false only if (11) is true.
(11) Newtonian absolute space exists (a self-existing empty spatial continuum, all the physical and geometrical properties of which exist independently of different configurations of the physical bodies within it.)
To admit that (9) and (10) are true or false is actually to claim the existence of Newtonian absolute space. Therefore, Newton’s belief in absolute space can be expressed by admitting comparisons of positions of a given body at different times as factually meaningful. In this way, Newton’s position of absolute space can be redefined precisely as an affirmation of the truth-or-falsity of core Newtonian sentences like (9) and (10).
Leibniz challenges the Newtonian notion of absolute space by questioning the truth-value status of these core Newtonian sentences like (9) and (10). In Leibniz’s view, (10) is truth-valueless under supposition C. For a Leibnizian, these Newtonian sentences would be true or false if relative to a frame of reference. It is meaningful, for Leibniz, to ask whether the distance between two bodies changes at different times; or, more generally, whether the spatial locations of a given body relative to a given system of bodies (used as a frame of reference) are different at two different times. However, one cannot speak of the absolute change of locations independently of a body configuration. Here, Leibniz presents his own position as denying that the above Newtonian sentences have truth-values and thereby rejects the existence of Newtonian absolute space.
In short, here is the real issue of the Newton-Leibniz debate on the absoluteness of space: Certain sentences of the Newtonian language, which have truth-values within Newton’s framework of space, lose their truth-values when considered from Leibniz’s point of view.
To reconstruct the Newton-Leibniz debate on a more exact level, we need to identify precisely the set of sentences that have truth-values in the Newtonian language and the set of sentences that have truth-values in the Leibnizian language. To do so we need to formalize the two languages in question. Gaifman provides us with the following formal language that can be modified to serve our purpose.
Euclidean language LE Let us first set up a formal language LE, which treats space and time directly as primitives, to describe the ‘pure’ spatio-temporal structure. LE is a many-sorted language. It is composed of the following factors:10
(a) A pure mathematical part, in which we can speak about real numbers, numerical functions, and constants, and whatever mathematics we wish.
(b) Time terms (constants and variables) u, u1... v, v1 ... ranging over time points.
(c) Space terms (constants and variables) x, x1... y, y1... ranging over space points in a three-dimensional Euclidean space.
(d) (i) Temporal predicate <t for temporal precedence (‘ t1 <t t2 ‘ asserts that the time point T1 precedes the time points t2); (ii) equality symbols ‘ =t ‘, ‘ = s ‘ for time and space, respectively (for example, ‘ u =t v ‘ states that the time-point u is equal to the time-point v).
(e) Quantifiers and the usual sentential connectives.
Holding these factors, all the concepts and axioms of elementary geometry can be formulated in LE, including the axioms of elementary real number theory, the axioms that space is a three-dimensional Euclidean space, and that the time line is a Euclidean line. These are classical Euclidean axioms of space and time.
Both Newtonians and Leibnizians would regard these classical Euclidean axioms as general truths. Newtonians and Leibnizians should have no disagreement about the truth-value status of the sentences of LE. Therefore, all the sentences of LE, which we call the class of sentences SE, are true or false for both Newtonians and Leibnizians. As long as both work within LE, no incongruity arises between them.
Newton’s language LN Extend LE to LN by introducing physical bodies and events.11 This means adding two more types of names and two more function symbols to the five factors of LE:
(f) Proper names of particular material bodies b1, b2 ... and proper names of particular events e1 e2...
(g) Two function symbols, a unary ‘τ’ and a binary ‘σ’ Here, x(e) denotes the time point of the event e while o (b, t) denotes the center of gravity of the body b at the time t.
Based on the above conventions, the Newtonian framework of space and time can be expressed as the following three claims:12
(Nl) The usual rules of first-order logic apply in LN.
(N2) Classical Euclidean axioms for space and time are valid.
(N3) All the sentences of LN, which we call Newton’s class of sentences SN, are candidates of truth-or-falsity.
Of the three claims, N3 is the most significant for Newton’s notion of absolute space. Actually, N3 is the precise expression of Newton’s belief in absolute space. This is because many core sentences of LN, more specifically, a set of sentences within LN but outside LE, presuppose the existence of absolute space. Take sentence (10) as an example again. If b is a physical body and e is an event, then for Newton, τ(e) is an absolute time-point and σ(b, τ(e)) is an absolute space-point. Then, in Newton’s conception of space, the question, ‘Is the location of the body b at time t different from its location at time t2 (under supposition C)?’ has a determinate yesor-no answer since the corresponding sentence (10) is true or false. Reformulating (10) in our formal language into (12):
(12) σ(b, τ(e1))≠ σ(b,τ(e2))
(12) asserts that the space-points of b at the time of event e1 and at the time of event e2 are different. According to Newton, (12), like (10), is a candidate for truth-or-falsity. In contrast, for Leibniz, space-points indicate only relative positions at a given time. Hence, (12) is true or false only if the configuration of physical bodies, including the body b, has changed. In other words, (12) is truth-valueless unless this precondition is satisfied.
From the examples we can see that certain atomic sentences, such as (12), that are true or false in relation to Newton’s conception of space will be regarded as truth-valueless in relation to Leibniz’s conception of space. That means that Leibniz would reject N3. According to Leibniz, some sentences of LN do not have truth-values. In this way, the disagreement between Newton’s and Leibniz’s conceptions of absolute space can be reduced to the disagreement about the truth-value status of certain core Newtonian sentences about the positions of physical bodies.
Leibniz’s language Lz We can further identify the language which determines the class of sentences SL, which are true or false based on Leibniz’s conception of space. First, it is technically convenient to eliminate the variables of space terms. This is because the Newtonian conception of space is fully expressible in a sublanguage of LN in which no variables of space terms exist. Let KN be the sublanguage of LN obtained by omitting from LN the variables of space terms. Thus, every possible fact expressible in LN is expressible in KN. Accepting Newton’s framework of space amounts to accepting all the sentences of KN as true or false. Second, let Lz be the sublanguage of KN obtained by imposing the following restriction: An inequality whose sides are occupied by the terms of space terms cannot figure in a formula unless the body configuration has changed. Thus Leibniz’s space-time ontology can now be expressed precisely as an affirmation of the truth-or-falsity of all the sentences of Lz.
In sum, within the Newtonian framework of space, every sentence of LN and KN (a sublanguage of LN) is true or false. In contrast, within Leibniz’s framework of space, all the sentences of Lz, which we call Leibniz’s class of sentences SL, are candidates for truth-or-falsity. As to the sentences of LN and KN that are not in Lz, they are neither true nor false from Leibniz’s point of view unless they, by some agreed conventions, can be translated and reread as sentences of Lz. Thus, the substantial difference between the Newtonian and the Leibnizian languages of space consists in a different assignment of the truth-value status of the sentences of LN that are not in LZ, namely, the class of sentences SN-SL. In other words, there is a truth-value gap between the Newtonian and the Leibnizian languages of space as to the class of sentences SN-SL.
The confrontation between the Newtonian and the Leibnizian languages of space seems to be very different from the confrontation between Chinese and Western medical languages. The Leibnizian language Lz is a sublanguage of the Newtonian language LN. The Newtonian and the Leibnizian languages have a great deal of overlap while the languages of Chinese medical and Western medical theories are radically disparate. Both the Newtonian and the Leibnizian languages have much common ground: both contain the Euclidean language LE as sublanguage; both share the same category system; both are embedded in the same intellectual tradition with the same mode of reasoning; and so on. Because of these commonalties, the Leibnizians can identify and understand the underlying presupposition of the Newtonian language, namely, the existence of Newtonian absolute space. Consequently, each language is perfectly intelligible to the other. In addition, the Leibnizians have some translation that gives the ‘true meaning’ of the claim for every testable Newtonian claim about the actual world. A major source of the divergence between the two languages consists in whether two ostensibly different descriptions in terms of relations to space-time points correspond to two possible worlds or just one.
Irrespective of these commonalities, the confrontation between the two languages is still ontologically significant. In general, one can understand a language without affirming it just as one can understand a fiction story without believing in the reality of the events described. Indeed, one’s rational rejection of a language is often based on one’s comprehension of the language. Modern physicists understand very well what the sentences in the language of Newtonian mechanics pretend to express, yet they deny that they describe objective reality. In this sense, a rational confutation seeks understanding. In our case, although the Leibnizians are able to identify and comprehend the underlying presupposition of the Newtonian language, i.e., the existence of absolute space, they categorically deny its truth. This is the reason why the Leibnizians regard the set of sentences SN-SL (actually, but not potentially) truth-valueless.
However, cross-language understanding does not guarantee successful cross-language communication. The existence of a truth-value gap between the Newtonian and the Leibnizian languages due to the denial of the underlying presupposition of the Newtonian language signifies that the full communication between the two language communities is at risk. Both sides cannot engage in a full communication although they appear to ‘talk’ with one another. A Leibnizian who can understand the Newtonian language is actually bilingual, not metalingual. Such a bilingual faces many difficulties during communication. The communication between the two language communities is incomplete. Of course, compared with the communication breakdown between Chinese and Western medical communities, the communication breakdown between the Newtonians and the Leibnizians is moderate in nature.
For a further illustration, let us take a look at another similar case study from Gaifman (1984), the Newton-Einstein debate on the absoluteness of time. Consider the following two sentences about simultaneity and precedence:
(13) Event e1 and event e2 are simultaneous: τ(e1) = τ(e2).
(14) Event e1 precedes event e2: τ(e1) < τ(e2).
These two sentences make perfect sense and are true or false in Newtonian physics. Newton pictured the world of events and physical bodies as if it moved through a self-existing empty time consisting of an ordered line of time points that are independent of any event. Thus, we can redefine Newton’s position as an affirmation of the truth of sentences (13) and (14).
However, according to relativity theory, precedence may depend on the coordinate system from which the events are viewed. More precisely, if in some coordinate system the events are separated by distance d and time Δt and d > c × Δt (c = light velocity)13 then their temporal order depends on the coordinate system. Therefore, to ask the questions, ‘Does event e1 precede e2?’ or ‘Are e1 and e2 simultaneous?’ without specifying a coordinate system is to ask factually meaningless questions. Thus, (13) and (14) have no truth-values from the relativistic point of view.
The difference between Newtonian and relativistic physics ‘is often described by saying that in Newtonian physics we have an absolute time ordering and in relativistic physics we do not. But the more precise way of expressing the difference is by pointing to the sentences whose true-or-false status differs from one theory to another’ (Gaifman, 1984, p. 321). Actually, this is the way Einstein treats the concept of time. Einstein does not directly address the question, ‘Does there exist an absolute time ordering?’ Instead, his analysis of the concept of time focuses on the factual meaning of the assertions about the simultaneity of spatially separated events. Einstein told the physicists and philosophers: You must first say what you mean by simultaneity. You can answer it by showing how N5 is tested. But in so doing you will find that you have to specify a coordinate system in which these events happen. It will soon become clear that to ask the question, ‘Are event ei and event e2 simultaneous?’ without specifying a coordinate system is to ask a factually meaningless question. Only relative simultaneity can be admittedly established; there is no such thing as absolute simultaneity. The concept of absolute simultaneity presupposes the existence of an absolute time ordering. Therefore, the disagreement on the truth-value status of some substantial sentences, for example, (13) and (14), can be used to represent the real difference between Newton’s and Einstein’s concepts of time.
1 The current case study mainly refers to Z. Lan (1988) which gives a brief summary of the main characteristics of Chinese medical theory. Also see Beijing College of Traditional Chinese Medicine (1978) for a complete introduction to traditional Chinese medicine.
2 Qigong (pronounced as Ch’i kung) is a combination of breathing and mental exercises performed to create vital energy within the body.
3 By ‘the language’ here I mean the Chinese Medical-Language. It might be doubtful whether ancient beliefs and forms of life really survive ‘internalization into’ a natural language, in our case, contemporary Chinese language.
4 I will illustrate the formation of the pre-modern Chinese mode of reasoning and its content in detail in chapter 10.
5 For further arguments for the necessary role of modes of reasoning and categorical framework in effective understanding, please see chapter 12.
6 This case study is adapted from H. Gaifman, 1975 & 1976, 1984. Gaifman uses the case to illustrate his Wittgensteinian explication of the notion of ontology.
7 Gaifman’s discussion of the debate between Leibniz and Newton about the absoluteness of space is based on the Clarke-Leibniz letter exchange. Clarke did his debating for Newton while Newton supplied the arguments.
8 Another similar formulation of (9) without appealing to supposition C would be: An object in an otherwise empty space could have been located at any number of different spatial points.
9 We could express a similar Newtonian sentence without appealing to supposition C as follows: An object in an otherwise empty space is at rest.
10 Gaifman, 1975 and 1976, pp. 54-5; 1984, pp. 324-5.
11 The Leibnizian language is a sublanguage of the Newtonian language. The Leibnizians can extend their language in the same way. In essence, we introduce a coordinate system onto the set of actual events (or possible events for some relationalists) that allows us to refer to specific events and objects and to describe temporal and spatial relations and distances of them.
12 Gaifman, 1975 and 1976, p. 56.
13 In this case, events are ‘spacelike’ separated or they could be connected only by signals or objects going faster than light.