ELSE_COHEN_CH010.qxd 6/23/2005 1:55 PM Page 243 1 Chapter 10 2 3 ATOMS, CATEGORIZATION AND CONCEPTUAL CHANGE 4 5 PAUL THAGARD AND ETHAN TOOMBS 6 University of Waterloo 7 8 Contents 9 10 Abstract 243 11 1. Introduction 244 12 2. Theories of concepts 245 13 3. The ancient concept of an atom 246 14 4. Revival of the concept of the atom 248 15 5. Modern development of the concept of an atom 249 16 6. Theories and meaning 252 17 7. Conclusion 253 18 References 253 19 20 21 Abstract 22 23 This chapter uses the concept of an [ATOM] to discuss ways in which categorization 24 depends on conceptual change. Features of such theoretical concepts are theory-gener- 25 ated rather than observed. They fit much better with the “knowledge approach” to the 26 nature of concepts than to classical, exemplar, or prototype theories. The concept of 27 atom has undergone numerous changes in the history of chemistry, most notably the 28 realization that atoms are divisible and have internal structure. 29 30 31 32 33 34 35 36 37 38 39 40 41 Handbook of Categorization in Cognitive Science, Edited by Henri Cohen and Claire Lefebvre 42 2005 Elsevier Science B.V. All rights reserved 243 ELSE_COHEN_CH010.qxd 6/23/2005 1:55 PM Page 244 244 P. Thagard and E. Toombs 1 1. Introduction 2 3 Conceptual change is an important topic in many areas of cognitive science, including 4 philosophy of science, developmental psychology, and science education. This chapter 5 will discuss the relevance of cognitive processes of conceptual change to questions 6 about categorization, particularly concerning the role of theoretical concepts such as 7 atom, molecule, and element. 8 First some terminological clarification is in order. Philosophers such as Aristotle and 9 Kant have used the term “category” to refer to the most fundamental concepts such as 10 substance, quantity, and quality. We shall, however, follow the standard usage in psy- 11 chology, in which a category is a class of things in the world, for example the class of 12 dogs. Concepts are mental representations that usually correspond to particular words 13 and refer to classes of things in the world. For example, the concept [DOG] corresponds 14 to the word dog and refers to the class of dogs in the world. Categorization is the 15 process of dividing the world into categories, and usually involves constructing con- 16 cepts that provide mental representations of those categories. 17 Most psychological research on categorization involves classes of observable objects 18 such as animals and furniture. In contrast, most philosophical discussion of conceptual 19 change has concerned classes of non-observable objects such as atoms, black holes, and 20 genes. Such objects are called theoretical entities, and concepts that refer to them are 21 theoretical concepts. A crucial part of scientific inquiry involves the formation and 22 improvement of such concepts, which categorize non-observable objects. Categorization is 23 therefore more than dividing up the world based on the observed features of things; in fact, 24 it requires one to create concepts that enable deep explanations of how the world appears 25 by hypothesizing properties of non-observable entities. For example, the ancient Greeks 26 formulated the concept of fundamental particles called atoms in order to explain many 27 facts about the natural world. 28 The development of the concept [ATOM], with the attendant development of concepts 29 such as [MOLECULE] and [ELEMENT], carries numerous lessons for cognitive theories 30 of categorization and conceptual change. We will argue for the following conclusions: 31 1. Concepts such as [ATOM] are crucial for categorizing the world. 32 2. Features of such concepts are theory-generated, rather than observed. 33 3. Definitions are revisable. 34 4. Conceptual change concerning atoms, molecules, and elements results from theory 35 change. 36 5. The concepts of atom, molecule, and element are theoretically intertwined: they 37 changed together as theories of matter developed. 38 6. Meaning is a function of both relations among concepts and indirect relations to the 39 world via experiments. 40 7. Science education, and possibly also developmental psychology, must attend to the 41 complexities of theoretical conceptual change. 42 We will also discuss the mental representations and processes underlying theories, 43 explanations, and mechanisms. ELSE_COHEN_CH010.qxd 6/23/2005 1:55 PM Page 245 Ch.10: Atoms, Categorization and Conceptual Change 245 1 2. Theories of concepts 2 3 We will first consider theories of concepts and then apply one approach to the develop- 4 ment of atomic theory. There are five main theories of the nature of concepts in current 5 cognitive science: classical, prototype, exemplar, neurological, and the “knowledge 6 approach” [Medin (1989), Murphy (2002), Thagard (2005)]. According to the classical 7 theory, a concept is defined by a set of features that are necessary and sufficient condi- 8 tions of its application. For example, a shape is a triangle if and only if it has three sides. 9 Unfortunately, such tight definitions are rare outside mathematics, and are hard to find 10 for ordinary concepts such [DOG] and [CHAIR], let alone for more abstract concepts 11 such as [BEAUTY] and [JUSTICE]. Accordingly, many psychologists, philosophers, 12 and other cognitive scientists have maintained that concepts are prototypes that specify 13 typical features rather than necessary and sufficient conditions. Something is a dog, for 14 example, if it matches many of the typical features of dogs such as having fur and four 15 legs. But something can still be a dog if it lacks a typical feature. On the classical view 16 of theories, categorization is a deductive process of reasoning with necessary and suffi- 17 cient conditions, but on the prototype view categorization is an inductive process of find- 18 ing the best match between the features of an object and those of the closest prototypes. 19 An alternative view of concepts is that they do not consist of general features but 20 rather of stored examples. People who have observed many dogs have their observa- 21 tions stored in memory, and they categorize new objects as dogs based on these exem- 22 plars. The exemplar view is compatible with a neurological view of concepts as patterns 23 of activation in neural networks. If a network stores many examples of a category, then 24 it may have a pattern of activation that arises when similar examples are observed. 25 However, the neural representation view of concepts is also compatible with a proto- 26 type theory, since training a network may produce patterns of activation that correspond 27 to typical features. 28 The most high-level theory of concepts is the “knowledge approach,” according to 29 which concepts are part of our general knowledge of the world, and are learned as part 30 of our overall understanding of it. On this view, concepts are not just a matter of exam- 31 ples or of typical observed features, but also have a crucial explanatory role. For exam- 32 ple, the concept of [DOG] includes features that explain why and how dogs behave as 33 they do. The knowledge approach should be compatible with a neural representation 34 view of concepts as patterns of activation, but requires that the patterns be achieved by 35 processes more complex than just storage of examples or training of connections that 36 represent typical features. 37 We will not consider the relative merits of the different theories for ordinary con- 38 cepts such as [DOG] and [CHAIR], but it is obvious that something like the knowledge 39 approach is crucial for theoretical concepts such as [ATOM]. The Greeks had obviously 40 never observed any atoms; rather, they hypothesized their existence in order to explain 41 the properties and behavior of macroscopic objects. Their mental representation of an 42 atom included the features of being a kind of particle, of having a variety of shapes, of 43 being in motion, and, most crucially, of being indivisible. Like atoms themselves, none ELSE_COHEN_CH010.qxd 6/23/2005 1:55 PM Page 246 246 P. Thagard and E. Toombs 1 of the features of atoms are observable, so they had to be generated as explanatory 2 hypotheses. Thus, the structure of the concept of the atom fits best with the “knowledge 3 approach” to the nature of concepts. 4 The psychological purpose of the mental representation [ATOM] is to stand for a 5 category of things, namely atoms, and to generate explanations of the behavior of all 6 those things that are constituted by atoms. Introducing the concept of an atom was a 7 major kind of conceptual change. The ancient alternative to the atomic theory of mat- 8 ter was the plenum theory, held by Aristotle and others, according to which matter is 9 continuous and therefore can be subdivided without limit. There is no historical record 10 of how the Greeks concocted the concept of an atom, but the most plausible cognitive 11 mechanism is analogical abduction, a process in which puzzling facts are explained by 12 using analogies to generate new hypotheses [Thagard (1988, pp. 60–63)]. For example, 13 the Greeks appear to have arrived at a wave theory of sound by noticing analogies 14 between the propagating and reflecting behavior of sound and the behavior of water 15 waves. Similarly, we conjecture that the concept of an atom is formed analogically by 16 noticing how the properties of big objects derive from their smaller but still observable 17 constituents. A sword, for example, is capable of cutting because it is composed of 18 parts, including a handle and sharp blade.