Einstein once said that "thinking without the positing of categories and of concepts in general would be as impossible as is breathing in a vacuum." His remark echoes a long tradition of Western philosophy arguing that our experience and knowledge are structured by a framework of categories or general concepts. The categorical framework contains our most basic and general presuppositions about the intelligible world and our status in it. It is not imposed externally but is already embodied in our objective thoughts as oxygen is integrated in the blood of breathing organisms. Since the categories subtly influence our thinking, it is as important to examine them as to test whether the air we breathe is polluted. Philosophers from Aristotle to Kant have made major efforts to abstract them from our actual thoughts, articulate and criticize them.
This book continues my effort to uncover the categorical framework of objective thought as it is embedded in scientific theories and common sense. Scientific theories contain some of our most refined thoughts. They do not merely represent the objective world, they represent it in ways intelligible to us. Thus while their objective contents illuminate the world, their conceptual frameworks also illustrate the general structure of theoretical reason, an important aspect of our mind.
As a physicist who turns to philosophize, I naturally started by examining relativity and quantum mechanics. Many general concepts, including the familiar notions of object and experience, space-time and causality, seem problematic when physics pushes beyond the form of human observation and analyzes matter to its simplest constitutive level. Quantum and relativistic theories have been used by many philosophers to argue for the impossibility of invariant categories. I contested their arguments in How is Quantum Field Possible? There I compared the conceptual frameworks of quantum field theory underlying elementary particle physics, general relativity for the large-scale structure of the universe, and our everyday thinking about the world. Their topics vary widely, but they share a common categorical structure. Modern physical theories reject many specific everyday opinions about particular objects and properties but retain the general common-sense notions of object and property. They do not abrogate the seemingly problematic categories but make the categories explicit and incorporate them within themselves, effectively clarifying and consolidating the general presuppositions that we tacitly understand and unreflectingly use in our daily discourse.
After quantum and relativistic physics, the next obvious stop is statistical mechanics. Most advancement in statistical mechanics occurs in condensed-matter physics, which investigates the microscopic structures of solids and liquids. A solid or a fluid is a many-body system, a complex system made up of a great many interacting constituents of similar status. The many-body theories in condensed-matter physics provide a conceptual framework that unites the microscopic and macroscopic descriptions of large composite systems without disparaging either.
Guided by the philosophical aim of seeking general patterns of thought, I realize that many-body theories address a major problem that has concerned philosophers since the debate between the Greek Eleatics and Atomists. How do we explicitly represent the composition of a large system while preserving the integrity of the system and the individuality of its constituents? The importance of the problem is evident from the diversity of circumstances in which it arises. Hobbes' Leviathan and Leibniz's Monadology offer disparate solutions in different contexts, and their answers have many competitors. The problem persists today, so does the polarity in solutions. Large-scale composition is highly complex. Crude models unable to handle the complexity conceptually sacrifice either the individual or the system. Even worse, the expedient sacrifice is sometimes interpreted as "scientific" justifications for various ideologies. Such simplistic models and interpretations have practical consequences besides undermining the credibility of science. The modern individualistic and egalitarian society is a many-body system, and the tension between the individual and the community lurks beneath the surface. What concepts we use to think about the situation affect our perception of ourselves and the society in which we participate, and our perception influences our action. We can clear up some conceptual confusion by a careful analysis of scientific theories to see how they represent composition and what assumptions they have made in their representations.
Many-body systems are the topics of many sciences, for they are ubiquitous in the physical, ecological, political, and socioeconomic spheres. If there is indeed a categorical framework in which we think about them, then it should not be confined to physics. To maintain the generality and broad perspective befitting philosophy, I decided to diversify. I looked for sciences of many-body systems that have developed reasonably comprehensive theories. After a little survey I chose to learn economics and evolutionary biology to sufficient depth so that I can analyze their theories, compare their conceptual structures to that of statistical physics, and extract the common categorical framework. I always have a strong interest in these fields and seize the opportunity to find out what their researchers are doing.
The parallel analysis of theories from economics, evolutionary biology, and statistical physics does not imply that the social and biological sciences ape physics or are reducible to it. Science is not like a skyscraper in which the upper floors rest on the lower; it is closer to an airport in which the concourses function as equals. I draw analogy among the sciences. Analogy is instructive not because it patterns the strange in terms of the familiar but because it prompts us to discern in the familiar case a general idea that is also applicable to unfamiliar situations. For example, the comparison of the perfectly-competitive market theory in microeconomics and the self- consistent field theory in physics does not explain consumers in terms of electrons or vice versa. It brings out a general theoretical strategy that approximately represents a complex system of interacting constituents as a more tractable system of noninteracting constituents with modified properties responding independently to a common situation jointly created by all. The theoretical strategy is widely used, but the rationale behind it is seldom explained in the social sciences. Consequently social theories using it often spawn ideological controversies over the nature of the independent individuals and their common situation. The controversies can be cleared up by drawing the analogy with physical theories in which the theoretical transformation between the original and approximate representations is explicitly carried out, so that we can see plainly the assumptions involved and the meaning of the resultant individuals.
A significant portion of this book is devoted to the presentation of scientific theories and models that serve as the data for conceptual analysis. Due to the complexity of many-body systems, the sciences rely heavily on idealization and approximation, and each splinters into a host of models addressing various aspects of the systems. I try to lay bare the assumptions and presuppositions behind the models so that the readers can assess their claims, which are often culturally influential. Besides clarifying general concepts, I hope the book will stimulate more dialogue among scientists in various fields, not only about what they are studying but how they are proceeding with it. Therefore I try hard to make the material intelligible to a general reader, presenting the conceptual structures of the sciences as plainly as I can, using as little jargon as possible, and explaining every technical term as it first appears. Since the book covers a wide range of material, I try to be concise, so that the major ideas stand out without the cluttering of details.
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