Conceptual Comparison and Conceptual Innovation

Harold I. Brown

Presented at:
International Congress on Discovery and Creativity
University of Ghent, Belgium
14 May to 16 May 1998
To be published, persumably, in proceedings of the congress

The guiding idea of this paper is that discussions of comparisons of concepts across theories (individuals, historical periods, cultures) and the introduction of new concepts must be based on an account of how the content of concepts is determined. I will sketch a theory of concepts based on the work of Wilfrid Sellars, although with several modifications.1 Then I will illustrate the application of this theory in two cases. First, I will compare the concepts of earth, water, and air as they appear in Aristotelian physics and in Galileo. Second, I will consider the concept of an isotope, an example of a new concept whose introduction is fairly well localized in the history of chemistry. There are two general conclusions that I want to draw from this discussion. First, a Sellarsian approach provides a specific set of tools for comparing concepts and introducing new concepts. Second, major conceptual change can take place while maintaining a great deal of continuity with existing conceptual resources.

One central theme of Sellars' theory of concepts is that concepts occur only as members of systems of interrelated concepts. At least part of every conceptžs content is determined by implications which hold between that concept and other concepts in the system. While holistic, this view should be read as a local holism. It does not require that all concepts link together into a single massive conceptual scheme. Rather, each of us deploys many different conceptual systems that have a variety of relations to each other. I have concepts that I use for thinking about poker, and some of these concepts have close ties to concepts that I use for thinking about other card games, and perhaps other games; but they have little connection with concepts that I use for thinking about carpentry or plate tectonics. I also have two conceptual schemes for thinking about space and time -- one from everyday experience and one from relativity theory. There are close and complex relations among the concepts in the two schemes, and there are good reasons for describing both as systems of space and time concepts.2 Still, they can be treated as distinct conceptual schemes and I can shift from to the other without confusing them.

Although implications are involved in determining the content of every concept, they are not always the complete story. Sellars distinguishes three types of conceptual systems. First, formal concepts -- concepts of logic and pure mathematics -- are wholly determined by the implications in which they play a substantive role.3 There is no more or less involved in the concept of conjunction than is captured by the characteristic inferences that depend on this operator. Classical and intuitionist negation are similar, but not identical, concepts and their similarities and differences are completely determined by the implications in which they play an essential role.4

Second, there are descriptive concepts -- these are among the most common concepts of everyday life and science. The content of these concepts is determined by a combination of implications and what Sellars calls "entry transitions." The idea is that there are paradigm instances of these concepts, and mastering a descriptive concept requires learning to recognize these cases. For example, to master the concept of a table I must learn conceptual relations such as that tables are furniture, manufactured objects, and commonly used for holding other objects at a convenient height; and I must also learn to spontaneously recognize typical tables as tables. If I have learned to parrot expressions such as "All tables are furniture" but cannot recognize a typical table, then I have not mastered this concept. Nor have I mastered the concept if I have learned to say "table" on encountering a typical table, but do not have the concepts of furniture or manufactured objects. We have here a key contrast with empiricist theories, which hold that mastery of a concept such as red requires only that I be able to correctly identify instances of red. On typical empiricist accounts, I might learn the concept red without acquiring any other color concepts, or the concept of a color, or indeed any other concepts at all. For Sellars, mastery of a concept always requires mastery of other concepts, but in the case of descriptive concepts more is required. Sellars describes the additional element as an "entry transition" to underline a key point of his account: When we subsume an item under a concept we are making a transition from noticing that item into a conceptual system.

Third, there are normative concepts which have their content determined by a combination of implications and "departure transitions" -- spontaneous moves from thinking about a concept to action in the world. To go from thinking of sitting on a chair to actually sitting would be one example of a departure transition, but the most important application of departure transitions occurs in Sellars' account of normative concepts. Sellars holds that normative concepts enjoin action, and that mastery of such concepts requires that I at least have a tendency to carry out this action.

It seems clear that we should add a fourth type of concept to this scheme since many concepts have both descriptive and normative aspects. Truth is a good example: saying that a proposition is true involves both a descriptive claim about that proposition and an injunction to believe and be prepared to act on that proposition. However, for the remainder of this paper I will be concerned only with descriptive concepts.

I now want to note two respects in which I am going to depart from Sellars' own practice. The first concerns a tendency, which he shares with many others, to use the terms "conceptual system" and "language" interchangeably, and to describe entry and departure transitions as moves between language and the world. One reason for avoiding this usage is that I do not want to make any assumptions about whether non-linguistic beings have concepts. In addition, this practice tends to limit our scope in discussing descriptive concepts. I want to pursue the thesis that whenever we have a body of beliefs about some subject matter, those beliefs are embodied in a system of descriptive concepts. One subject about which we have such beliefs is language. For example, a set of grammatical concepts is a conceptual system used to describe certain aspects of languages. When we recognize a word as a noun, we are making a entry transition from a bit of language into a system of grammatical concepts, and it is awkward, at best, to describe this as a transition from the world into language. To achieve the level of generality I wish to pursue, I will talk of "conceptual systems" and their "extra-systemic" subject matter -- where that subject matter is external to the system of concepts that is used to describe it. And I will take entry transitions to be transitions from a specific domain into the conceptual system we use to describe that domain.

My second departure from Sellars' practice is more significant, but the story is more complex. Sellars typically discusses concepts in psychological terms and the development of appropriate habits plays a central role in these discussions. Sellars' entry transitions are habits that take us unreflectively from noticing an item to thinking of a concept. In addition, where I have spoken of "implications" among the concepts in a system, Sellars talks of habitual "inferences." Further, when Sellars talks about mastering a concept, he is usually concerned with developing these habits. Now this psychological focus derives from Sellars' naturalistic view that concepts exist only in cognitive agents so that without such agents there would be no concepts. In addition, there are two main reasons for the emphasis on habits. First, Sellars is concerned with understanding concepts as tools by which we find our way around in the world, and this practical focus often requires that we respond to situations swiftly. We accomplish this by embodying our concepts in habits. Second, as Sellars points out (1963, p. 321), his holism generates a problem about how concept-learning ever gets started. Sellars holds that genuine mastery of a concept requires not only that we use the concept appropriately, but that in doing so we are obeying rules, formulated in a metalanguage, that govern the use of these concepts. Stated in his characteristic linguistic idiom, this suggests that in order to learn a language we must first learn the metalanguage, and this would seem to make it impossible for language learning to get started. Sellars' response is that -- at least initially -- we learn concepts in two stages. First, we develop habits that are reinforced in a social setting. Only later do we come to understand the rules that govern these habits and move to full competence in the use of these concepts.

Now the concern with habits is not relevant to the present paper. Sellars' second stage in concept learning involves a considerably more sophisticated mastery of concepts than is required when young children are first learning concepts, and we are working on this sophisticated level when we study concepts and propose new concepts. Moreover, when we are engaged in these activities, we treat concepts as abstracted from whatever embodiments they have in habits. Indeed, when we contemplate conceptual change or examine the conceptual system of an abandoned scientific theory, we regularly master concepts without learning to apply them habitually. Sellars seem to recognize this point even while he is emphasizing the desirability of embodying concepts in habits. For example, he writes:
suppose that 'phi' and 'psy' are empirical constructs and that their conceptual meaning is constituted, as we have argued, by their role in a network of material (and formal) moves. Suppose that these moves do not include the move from 'x is phi' to 'x is psy'. Now suppose that we begin to discover (using this frame) that many phi's are psy and that we discover no exceptions. At this stage the sentence 'All phi's are psy' looms as an 'hypothesis', by which is meant that is has a problematical status with respect to the categories of explanation. In terms of these categories we look to a resolution of this problematical situation along one of the following lines.
  1. We discover that we can derive 'All phi's are psy' from already accepted nomologicals. (Compare the development of early geometry.)
  2. We discover that we can derive, 'If C, then all phi's are psy' from already accepted nomologicals, where C is a circumstance we know to obtain.
  3. We decide to adopt -- and teach ourselves [italics mine] -- the material move from 'x is phi' to 'x is psy'. In other words, we accept 'All phi's are psy' as an unconditionally assertable sentence of L, and reflect this decision by using the modal sentence 'phi's are necessarily psy'. This constitutes, of course, an enrichment of the conceptual meanings of 'phi' and 'psy'. (1963, p. 357)
Note the two main steps in Sellars' third case. First we conclude that all phis are psy and modify phi to include this condition; second, we undertake to adjust our habits so that we will spontaneously infer psy from phi. But this second step requires that we already grasp the relevant concepts before we decide to teach ourselves the new inference.

In order to discuss concepts on this reflective level, we must make some changes at least in Sellars' terminology. One change is straightforward, and I have already made it: talking of implications rather than inferences. This change includes recognition that there may be more involved in a conceptual system than its users have so far recognized -- a point that is implicit in Sellars' cases (a) and (b). Exploration of these implications is an important form of research and one possible source of reasons for engaging in conceptual change. Russell's discovery that classical set theory is inconsistent provides a striking illustration.

A more complex problem faces us in the case of entry transitions. The notion of an habitual move will be replaced by the requirement that the content of a descriptive concept include an account of the criteria for an item to be instance of that concept. Such criteria will be internal to the conceptual system, rather than a direct link between that system and extra-systemic items, and will provide an account of how that link is to be established. For example, in discussing the concepts of Aristotelian physics we need an account of the cases that an Aristotelian would spontaneously identify as instances of, say, violent motion. The need for such criteria is also clear when we are introducing a new concept that may not have any instances. I will, however, continue to use Sellars' term "entry transition" for this aspect of descriptive concepts.5

This leaves Sellars' general thesis that concepts exists only as items in cognitive agents, with which I agree. An immediate consequence is that our psychology and biology provide a major constraint on the acceptability of a theory of concepts. A theory that attributes to concepts properties that cannot be embodied in human biology and psychology cannot provide either a correct account of human conceptual development or a set of recommendations for how we should endeavor to introduce new concepts. Nevertheless, this issue can be left aside in the present context. For purposes of analysis, concepts can be treated as abstract structures apart from their actual embodimentsžalthough this approach leave open the possibility that our results may be undermined by evidence from psychology or biology.6

I turn next to a central and controversial feature of Sellars' account of descriptive concepts. As was indicated in the earlier quote, Sellars holds that when we firmly accept the empirical generalization "All A are B" we build the implication from A to B into our concept of A. The generalization, which is in the metalanguage governing this system of concepts, now functions as a material rule which, along with formal rules, license the implications associated with A. Sellars says surprisingly little about the analytic/synthetic distinction, but he does deny that this is a distinction between propositions that are determinative of the content of concepts and those that are not.7 In effect, Sellars holds that the concept of an A embodies all of our firm beliefs about As and that we change our concepts when these beliefs change. The view that material rules enter into the content of concepts has several immediate consequences: conceptual change is more common than many philosophers take it to be, and the dividing line between change of concept and change of belief is extremely vague. It also follows that conceptual diversity is more common in a community than it is often taken to be by philosophers. But this diversity does not generate massive failures of communication because the differences between concepts in a population may be small. Differences between two descriptive concepts can consist of differences in accepted implications, entry transitions, or both. At the same time, we have here a basis for introducing new concepts by making systematic changes in entry transitions and implications of existing concepts.8

I now want to enrich the Sellarsian theory of concepts by extending the scope of an idea that Sellars deploys only in a specific case. Sellars argues that new entities are introduced by analogy with familiar entities: the new entity is conceived of as identical with familiar entities in some respects, but having additional properties, or lacking properties of those familiar entities. For example, molecules can be introduced as very small spheres, like billiard balls, but lacking color and temperature while being capable of completely elastic collisions. Moreover, such analogies are not limited to first-order properties. The common analogy between successive moments time and points on a directed line is based on properties of the ordering relation. The introduction of a new entity is always accompanied by a "metalinguistic commentary" in which we explain the identities and differences between the new entity and whatever provides the basis of the analogy (1963, ch. 5, 1965).

Now the introduction of a new entity amounts to the introduction of a new concept, and Sellars is here describing a process by which we introduce new concepts by analogy with available concepts. But analogous concepts are just concepts that are the same in some respects and different in others, and there is no reason why the process need be restricted to cases concerning entities. New concepts of any kind can be introduced by such analogies with existing concepts. In the case of descriptive concepts these analogies can involve identities and differences in implications and in entry transitions. We may also compare concepts from competing or successive scientific theories by exploring such analogies.9 Such discussions are always metalinguistic, and I will take Sellars' notion of a metalinguistic commentary as a prototype for all discussions of concepts. When we are carrying out such discussions we have available all of the language and concepts that are required to achieve this level of cognitive sophistication.

Once we look at concepts from this metalinguistic perspective, another point that Sellars alludes to from time to time comes into focus. Each of our scientific concepts has been introduced to do a specific cognitive job. Indeed, one reason for introducing a new concept is that we come to recognize the need for a cognitive job that was previously not recognized; Newtonžs distinction between weight and mass provides one example. At the same time, we drop concepts when we reject the cognitive jobs that they had been introduced to carry out. Rejection of the traditional distinction between a terrestrial and a celestial realm is an example. Now Sellars never develops this idea or integrates it into his overall theory of concepts. Strictly speaking, when Sellars writes of a "conceptual role" he means just the appropriate combination of implications and entry (or departure) transitions.10 I suspect that this is a direct result of his focus on the active use of concepts and their embodiment in habits, since to master a concept in use we need learn only its implications and transitions. But once we move to reflective discussions of our concepts, consideration of the role a concept plays in our cognitive economy provides a key part of an account of that concept, and comparisons of conceptual roles provides an additional dimension for comparing conceptual systems.

The upshot of this sketch is that a Sellarsian approach provides us with three specific dimensions to work along when we are analyzing a descriptive concept, proposing new concepts, and comparing concepts from different scientific theories: implications, entry transitions, and what I will call "conceptual roles." I want to illustrate the power of this approach by applying it, first, to the comparison of a set of concepts from Galileo's physics with a related set from Aristotle, and then by examining the introduction of the concept of an isotope.

An essential part of Galileo's dynamical theory, as developed in his Dialogue on the Two Chief World Systems, is a distinction between the elements of earth, water, and air, where these are characterized by their dynamical properties.11 I will sketch Galileo's account of these concepts and then use the Sellarsian approach to compare them with the versions that occur in Aristotležs physics. Earth, according to Galileo, is characterized by three kinds of natural motion plus the ability to sustain an impressed motion. A natural motion is a motion that an object pursues when not constrained or acted on by an external force. One of these is the motion of an object to its natural place. This accounts for the fall of unsupported objects and is worthy of further exploration, but I will focus here on the two additional natural motions that Galileo introduces.12 There are two such motions: a daily motion around the center of the planet and an annual motion around the sun. Thus Galileo requires no special explanation for the daily rotation and annual revolution of the planet: these are simply the natural motions of the predominant element in its composition. This doctrine of natural motion provides the basis for Galileo's response to several standard anti-Copernican arguments. For example, in the case of the tower argument Galileo argues that the fact that a rock dropped from the top of a tower lands at the base is compatible with a rotating earth because the rock, an earthy object, engages in the natural daily rotation of the earth, and thus maintains its relative location with respect to the tower as it falls. Nor does it follow from Copernicanism that an arrow shot vertically would land far to the west of the archer because of the earth's annual motion. For the arrow, another earthy object, shares that natural motion.

Impressed motion occurs when an object is pushed into some non-natural motion by an external force; projectile motion is the key case. Earthy objects sustain an impressed motion, and this is the basis for Galileo's prediction that a rock dropped from top of the mast of a moving ship would land at the foot of the mast, not at the rear of the ship, as Aristotelians predicted.13

Now consider water. According to Galileo, water does not share in the natural motion of the earth, but does sustain an impressed motion. This is the dynamical basis for Galileo's theory of the tides, which he considered a particularly powerful argument for the motion of the earth. Because of the double motion of the earth, water confined in an ocean basin is subject to a pair of continually changing impressed motions. The water tends to sustain these impressed motions, and tides result from the sloshing of the water in its basin.

Air does not share the natural motion of the earth and does not sustain an impressed motion. There is a pair of anti-Copernican arguments that concern the air: if the earth rotates from west to east, we should experience a continual wind blowing from east to west; and, as a result of the earth's annual motion, the earth should leave the air behind. Galileo replies that the air is drawn along with the earth because it is trapped by the roughness of the earth, and also because it is mixed with "earthy vapors." But while this will explain why we do not lose our atmosphere or experience a constant wind over land, Galileo contends that we do find exactly the predicted wind over the oceans. An apparent counter-instance to Copernican astronomy is thus turned into a confirmation.

Let us compare Galileo's concepts of earth, water, and air with their Aristotelian counterparts. First, these concepts play similar roles in the two frameworks. In both cases, the concepts pick out basic kinds of entities in the terrestrial world, and these entities are characterized in terms of their dynamical properties. By the same token, the concept of natural motion plays similar roles in the two frameworks -- it captures how a type of object moves when it is not being forced or restrained. Second, with regard to entry transitions consider, first, identifications of a sample as earth, water, or air. Here we find complete agreement between the two frameworks. However, the story becomes a bit more complex when we turn to the concept of natural motion. In the case of earth, Galileo includes two kinds of natural motion that have no place in an Aristotelian framework. But these new natural notions pertain only to earth, so Galileožs account of natural motions for air and water would presumably agree with Aristotležs. On the other hand, there would be no Galilean entry transitions to the concept of violent motion since this concept, which Aristotle defines as a contrary to natural motion, does not exist in Galileo's conceptual scheme.

The deepest differences between the two frameworks comes out when we look at implications. For example, since Galileo drops the concept of violent motion, the implications associated with this concept in the Aristotelian framework vanish. This is a particularly important change because it is Aristotle's definition of natural and violent motion as contraries that yields the supposedly a priori truth that no object can be moving simultaneously in a horizontal and a vertical direction. Dropping this fundamental contrast opens up logical space for multiple kinds of natural motions, for the simultaneous occurrence of natural and impressed motion, and for multiple impressed motions in a single object at the same time. This is only a cursory discussion, but it is sufficient to support the thesis that when we examine Galileo's system of dynamical concepts using the tools of our Sellarsian theory of concepts, we can see that at least parts of this system constitute a systematic alteration of Aristotležs dynamical concepts. I urge that this kind of detailed comparison is considerably more informative than attempts to give simple "Yes" or "No" answers to such questions as whether the two systems are commensurable.

Now consider the concept of an isotope, a new concept that was introduced into chemistry when it became clear that a new conceptual role was required. Here is the relevant background. The thesis that a characteristic weight is the defining feature of each chemical element was central to nineteenth-century chemistry. This view had been introduced by Dalton, was embodied in Prout's thesis that each element is compounded out of hydrogen atoms, and provided a major part of the conceptual the basis for locating elements on the periodic table. Anomalies appeared throughout the century, so that by 1886 Crookes put forward the "audacious" but testable speculation that the weight standardly associated with an element was that of the majority of its atoms, and that some might have slightly different weights (Bruzzaniti and Robotti 1989, p. 309). Still, the prevailing view was that variant atomic weights associated with a specific element indicated failures of chemical analysis.14 The proposal that chemically identical pure samples could differ in weight involved a deep change in chemical thought. As Soddy noted, it undercut a central research project of nineteenth-century chemistry:
There is something, surely, akin to if not transcending tragedy in the fate that has overtaken the life work of that distinguished galaxy of nineteenth-century chemists, rightly revered by their contemporaries as representing the crown and perfection of accurate scientific measurement. Their hard-won results, for the moment at least, appears as of as little interest and significance as the determination of the average weight of a collection of bottles, some of them full and some of them more or less empty. (1932, p. 50)

The main impetus for introducing this change came from the recently discovered phenomenon of radioactivity. By 1913, through the work of several researchers, it had become clear that transformations occurred in which an element emitted an alpha particle and two beta particles (in any order). This left its slot in the periodic table unchanged while its weight dropped by four units (Fajans 1913, Soddy 1913b).15 This led Soddy to propose a new basis for locating elements on the periodic table.16 He believed that the nucleus contained both electrons and protons and that the difference between these -- the "intra-atomic charge" -- provided the proper criterion.17 Isotope is a new concept; let us consider its introduction from our Sellarsian perspective.

The concept of an isotope marks a new conceptual role, one which was not only unnecessary in the pre-existing system of chemical concepts, but actually precluded. Previously, the concept used to describe each element implied a characteristic weight, and while not every weight is an atomic weight, every atomic weight implied a specific element. Both of these implications were dropped when the new role was introduced: now an element could have different weights, and different elements could have the same weight. As a result of these changes, implications between a weight and location on the periodic table were dropped and replaced by a new mutual implication between location on the periodic table and net nuclear charge. Yet the set of implications that constituted most of the existing body of chemical knowledge stood unaltered. Indeed, the arrangement of elements in the periodic table was not affected, even while the conceptual basis of this ordering was undercut. In addition, all results of standard chemical and spectroscopic analyses remained unchanged. Even the vast majority of implications among elements and physical properties endured, although those explicitly involving considerations of atomic weight, such as density and diffusion rates, had to be reconsidered (cf. Soddy 1932, p. 44).

These changes in implications are directly reflected in changes in entry transitions, i.e., in the tests for specific elements and isotopes. Measurements of weight were greatly reduced in significance, and new tests were needed to distinguish isotopes of an element. In effect, these required the ability to detect small weight differences in chemically indistinguishable samples, and the most important technique was soon embodied in Aston's mass spectrograph. In addition, the newly discovered property of the half-life provided a means of recognizing different isotopes of an element -- as well as a new means of distinguishing among radioactive elements. These were radical changes, yet it is striking how much accepted chemical practice and knowledge remained unchanged even while their foundation was being radically restructured.18

These examples bring us to the two conclusions announced at the beginning of this paper. First, the Sellarsian theory of concepts provides a systematic approach to the analysis of conceptual innovation and conceptual change, in particular, to sorting out what changed and what remained essentially the same in specific cases. It also provides a guide to the process of introducing new concepts. Second, and more generally, when we approach specific changes from this perspective, we see clearly that change is not an all-or-nothing phenomenon, and that radical conceptual change in a field is quite compatible with a great deal of stability. These stable elements provide the basis for carrying out conceptual innovation in a coherent manner and for debating the merits of a new framework.

Notes

1 See Brown (1986) for a more detailed account.

2 See Sellars (1973, 1974) for discussion of this and related examples.

3 The point about a substantive role is required because an operator such as negation may be carried along through a series of implications that do not depend on this operator; these implications are not relevant to the content of this concept.

4 These roles are not completely captured by the customary introduction and elimination rules. In accord with Sellars' overall approach, we should not thing that the propositional operators can be specified one by one. For example, De Morgan's laws play an essential role in determining the classical concepts of negation, disjunction, and conjunction.

5 This is only an introductory sketch; the full story is considerably were complex. For example, a charged particle may have a standard signature in a detector, but the reasons for believing that an uncharged particle passed through the detector may be just the absence of any charged particles in a particular context. Moreover, many cases require statistical analysis to determine if a particular particle passed through the detector. Consider the concept of the top quark. This concept is well understood by physicists, and they have evidence that the concept is instantiated. But this evidence does not include any single detector output indicating that the particle occurred. Rather, it consists of a body of data for which the occurrence of a top quark one of a set of possible explanations, plus an argument to show that the probability that none of these cases involved a top quark is incredibly low. Most of Sellars' examples concern simple observables and the extra-systemic side of an entry transition is usually an instance of the concept. But Sellars is aware that these more complex cases exist (e.g., 1963, p. 316) even though he does not consider any in detail.

6 I have developed this paper so that it is neutral between a necessary-and-sufficient-conditions view of concepts and a view of concepts as having open texture. The former thesis requires that examples of conceptual change be viewed as cases in which one concept is replaced by a different concept, but this does not alter the point that we can still explore similarities and differences between a concept and its replacement. Still, an open-textured view seems more appropriate for a naturalistic approach since it allows for the idea that we often introduce concepts in response to current needs without thinking through many of their ramifications until a need to do so arises.

7 This amounts to the proposal that we make certain changes in the traditional system of epistemic concepts. Quine's rejection of the distinction is another proposal of this kind. See Brown (1991) for further discussion.

8 Sellars has many reasons for adopting this approach. 1. One reason derives from his view that concepts guide our action in the world. We build our firm beliefs about items into the associated concepts in order to assure that we respond appropriately to items when we encounter them. 2. The approach provides a way of absorbing a point that has been argued, in different ways, from Kant to Kuhn and beyond: Fruitful scientific research requires the acceptance of propositions that are not analytic but that are protected from empirical refutation, at least for a time. These propositions play a central role in providing the conceptual framework within which research takes place. In Sellars' version, this results in propositions that are non-analytic, but true ex vi terminorum (cf. 1963, ch. 10). 3. The view is a central part of Sellars' project of analyzing causal claims as metalinguistic claims about our descriptive concepts. He proposes that we reformulate the problem of induction as a concern with our decisions to accept specific empirical correlations and then build them into our concepts. As a result, accepting a material rule is equivalent to believing a causal necessity (cf. 1958). 4. The approach also provides the basis for an account of how we can learn concepts in a piecemeal fashion, elaborating a concept as we learn more about what features are included in it in our society. 5. Most important, for present purposes, we will see that the view is an integral part of an account of how we can introduce new concepts by building on available concepts, and learn older concepts by backtracking from current concepts to those from which they were historically derived.

9 We may even be able to approach concepts from another historical or contemporary human society by mapping out analogies with our own concepts.

10 In one place Sellars seems to explicitly reject the notion of a conceptual role that I am introducing. Discussing the German name Sokrates, Sellars writes: "One is tempted to say that the function in question is that of being used to refer to a certain Greek philosopher. But it is a mistake to tie the semantical concept of a reference too closely to referring as an illocutionary act." (1974, p. 428.)

11 Galileo expresses doubt that fire is an element. See Brown (1976) for further details and references.

12 While Galileo holds that fall occurs because an object is moving to its natural place, his account of natural place is significantly different from Aristotle's.

13 Galileo's replies to the major physical arguments against a moving earth appeal to natural motion, not impressed motion. This has an intriguing consequence for the ship experiment -- which Galileo did not do and apparently had no interest in actually doing. If Galileo is correct and the object falls at the foot of the mast, the experiment supports the Copernican view since it would show that an object is capable of engaging in multiple motions simultaneously. If this is the case for an impressed motion, the point holds a fortiori for nature motion. If the rock were to fall at the rear of the ship we would have an empirical challenge to Galileo's account of impressed motion, but no significant argument against the Copernican view since Galileo's defense of that position depends only on natural motion.

14 In other words, the thesis that elements are characterized by their weight played the role of a guiding assumption (cf. Laudan et al 1986): A variety of chemical tests were used to identify elements, and samples initially identified as the same element could exhibit different atomic weights, but this was not considered evidence against the thesis that elements are characterized by weight. Instead, such cases were interpreted as evidence that impurities were still present.

15 Throughout this period it was assumed that electrons make no significant contribution to an element's weight, although it was recognized that electrons do have mass. Thus beta decay was treated as involving no change of weight.

16 As Soddy noted, the same proposal was made slightly earlier by van den Broek (1913), although his concerns were ddferent: he was attempting to bring the periodic table into accord with the thesis that all elements were built up out of halves of alpha particles.

17 Clearly, the concept of an intra-atomic charge is not the same as the modern concept of atomic number because it assumes a view of the nucleus that is now rejected and, as a result, it is calculated in a way that makes no contemporary sense.

18 The concept of an isotope is just one locus of this rethinking. The research leading to this new concept came to a head in 1913, just a few months before Bohr's new theory of the atom was published.

References

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