Higher taxonomy and higher incommensurability

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TAXONOMY IN THE SCIENCES Higher Taxonomy and Higher Incommensurability Daiwie Fu * In a series of recent papers, some of them unpublished, Thomas Kuhn has begun to use a new set of concepts to discuss the old thesis of incommensurability, which was introduced in the controversies initiated by him and Paul Feyerabend in the 1960s. As Kuhn himself admits, he now discusses issues in the philosophy of science less and less in terms of ‘paradigm’, and more and more in terms of ‘taxonomy’ or lexicons. Already there are papers discussing Kuhn’s recent ‘taxonomic turn’, as it has been aptly named by Carl Hempel.’ Instead of taking issue with these papers on Kuhn’s recent arguments about taxonomy, taxonomic kinds and the implications of the thesis of incommensurability, I intend to borrow critical ideas in them as a point of departure in this paper in order to re-examine the formulation of Kuhnian incommensurability itself. Rather than a negative criticism of Kuhn’s new arguments, my thesis in this paper is that Kuhn’s original intuitions about incommensurability can be pushed to a ‘higher’ level, one that philosophers of science have usually ignored but that is very important for historians of science. By extension, this higher-level incommensurability can also be explicated by a higher-level notion of taxonomy. From the taxonomy of a specific scientific discipline in a specific historical context, we can ascend to a general taxonomy of the ‘knowledge’ held by a group of scientific communities in a specific historical context. As we shall see later, the taxonomy of a discipline may shift, not only as a result of internal changes, but also as a result of changes in its relation to other disciplines that share some of its terms. In his paper ‘Working in a New World: the Taxonomic Solution’,’ Ian Hacking gives a detailed explanation of Thomas Kuhn’s recent ideas on ‘taxonomic kinds’.3 *Institute of History, National Tsing-Hua University, Hsinchu, Taiwan. Received 19 January 1994; in revised form 16 August 1994. ‘Carl G. Hempel, ‘Thomas Kuhn, Colleague and Friend’, in P. Horwich (ed.), World Change: Thomas Kuhn and the Narure of Science (Cambridge. MA: MIT Press, 1993). pp. 7-8. *Ian Hacking, ‘Working in a New World: the Taxonomic Solution’, in P. Horwich (ed.), World Change: Thomas Kuhn and the Nature of Science. (Cambridge, MA: M.I.T. Press, 1993). 3The following extremely rough sketch of Hacking’s paper and the quotation are from the original draft of his paper delivered at the conference on ‘Thomas S. Kuhn’s Impact on Current Work in the History and Philosophy of Science’ in honour of T. S. Kuhn at MIT in May 1990. With revisions and clarifications, Hacking’s paper, with the same title, appeared as in note 2. Similar discussions of ‘poison’ and real kinds occur in pp. 299-301 of the 1993 published collection. For Kuhn’s recent papers and drafts concerning

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Stud. Hist. Phil. Sci.. Vol. 26, No. 2, pp. 273-294, 1995 Copyright 0 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0039-3681/95 $9.50 + 0.00

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Kuhn’s kinds turn out to be very similar to Mill’s ‘real kinds’ except for several critical points. In short, Kuhn’s kinds can be characterized are taxonomic,

by the following features: (i) they

which means that no object can be a member of two distinct kinds

unless one kind is properly contained

in the other; (ii) they have ‘infimae species’,

which means that trees of natural kinds terminate;4 and (iii) they are projectible, which means that we should be able to use them in making generalizations or forming expectations about the future. Once we fix the conditions of Kuhnian taxonomic kinds, Kuhn’s thesis of incommensurability Incommensurability/untranslatability

(couched in these terms) follows naturally. occurs when any of the above three conditions

are violated in an attempt to translate a kind term of the old paradigm: e.g. when a a scientific kind in the new science, or when a kind sub-divides a kind in the new science that has no sub-kinds. In his critical discussion of Kuhn’s taxonomic kinds, however, Hacking raised an important question, or counterexample. kind overlaps

Arsenic and hemlock are both poison, but one is mineral and one is vegetable, thus violating any sort of taxonomy, if the set of poisons were a natural kind. Hacking asks: Why isn’t poison a natural kind? Poisons are not notably a&-factual nor artificial. The word ‘poison’ is projectible. Forensic science deploys it in contrary to fact conditionals powerful enough to free one man from jail and to electrocute another. Does it occur in statements of laws of nature? Perhaps not, but to show that we would have to be more precise about ‘laws of nature’ than the most deft of the logical empiricists. We can’t glibly say that this is no term of science, because there is a science of poisons, toxicology.

Hacking’s way of solving this problem is to invoke Mill’s notion of ‘real kinds.’ In order to be a real kind according to Mill, a substance must have a virtually inexhaustible we distinguish

number of properties that are not consequences

of the marks by which

it. Thus there is at least one important difference between arsenic and

poison. Whereas there may be an inexhaustible

number of things to find out about

arsenic, there is nothing in particular which is common to poisons except that which puts them in the class of poisons in the first place: the potential for killing people after being ingested. Therefore, Hacking suggests that Kuhn’s kinds should be real kinds, taxonomic kinds, kinds with infimae species. I am not sure that resorting to Mill’s idea of real kinds provides us with a good way to handle problems

like toxicology,

not to mention

that Mill’s notion of real

‘continued

natural kinds and taxonomic

structures, see T. Kuhn, ‘The Presence of Past Science’, The Shearman Memorial Lecture (London: University College, London, 1987); ‘Possible Worlds in History of Science’, in S. Allen (ed.), Proceedingsof Nobel Symposium65, (Berlin: de Gruyter, 19891, pp. 9-32; ‘The Road Since Structure’, Presidential Address to the Philosophy of Science Association, in A. Fine. M. Forbes and L. Wessels (eds) PSA 1990 (East Lansing, MI: PSA, 19901, vol. 2, pp. 3-13. 4‘Infimae species’ are natural kinds that have no subsets that are natural kinds. The infimae species is the ‘lowest’ level in the classification tree, and cannot be a genus.

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kinds is problematic itself, as noticed by C. S. Peirce and Hacking himself.5 In an important recent paper on kinds (1992),6 Jed Buchwald followed up on Hacking’s question, but he sees the problem from a different and actually more interesting perspective. Buchwald considers whether a particular object in the present lexicon might fall into kinds that belong to ‘completely different areas of inquiry’:7 A liquid might for example be considered solely in respect to its viscosity for determining what kind of hydrodynamic entity it is; the same liquid might be considered in respect of its effects on the phase of reflected light in considering what kind of optical object it is. These two groupings of kinds-hydrodynamic and optical-might very well have nothing at all to do with one another.. . . What one cannot have is a hydrodynamic object that falls simultaneously into hydrodynamic kinds that are not nested. Of course it is certainly possible that optical and hydrodynamic behaviour might eventually be brought together (by e.g., linking molecular structure to both hydrodynamic and to optical properties), but if this does happen then the kinds will have to be reconstructed to prevent overlap. In short, the problem Hacking has been trying to solve-that of the apparent overlap in taxonomies-by distinguishing the real kinds from others, Buchwald reconsiders from another direction by measuring the ‘distance’ between two taxonomies. It seems to me that this problematic of distance between taxonomies points to an important aspect of incommensurability to which Kuhn’s recent discussions have not devoted enough attention. This problem actually leads to a higher level of incommensurability, which, I believe, also has important implications regarding Kuhn’s recent treatment of the issue of translation.* Let me first address this problematic from a more general perspective-namely, from the kind of question with which Kuhn has traditionally introduced his thesis of incommensurability. Then I shall discuss the intuitive idea of the higher level incommensurability via some historical examples, especially the famous debates between Boyle and Hobbes concerning the former’s air-pump experiments. I will return to the question of ‘kinds’ discussed by Hacking and Buchwald at the end. ‘Hacking worried whether Mill’s idea of ‘real kinds’ could capture Kuhn’s idea of natural kinds. Thus, Kuhn says that the set of planets is a natural kind. But is it a real kind? Is there an endless number of things to find out about planets, qua planets? %ee Jed Buchwald, ‘Kinds and The Wave Theory of Light’, Studies in HistoryandPhilosophy of Science 23 (1992), 39-74. It is an excellent paper in bringing Buchwald’s studies of the wave theory of light to illustrate Kuhn’s recent ideas of taxonomic structures and to make them more precise and interesting. Specifically, Buchwald stressed an ‘instrument-grounded’ taxonomy in many scientific disciplines, where im ortant or new instruments sit as the ‘sorters’ on almost all branching nodes of the taxonomic tree. P Ibid., p. 41, footnote 7. ‘Since his paper in the 1982 PSA, ‘Commensurability, Comparability, Communicability’, Kuhn’s thesis of incommensurability has been derived naturally from his numerous discussions of lexicon structure. His notion of incommensurability now comes closer to that of untranslatability. Both Hacking (see op cit., note 2) and Buchwald (ibid.) gave good reviews of how to understand the thesis of incommensurability from the ideas of the lexicon structure. By using the notion of the ‘general taxonomy of knowledge’, I have alluded to a higher-level incommensurability in an earlier paper: D. Fu, ‘Problem Domain, Taxonomy and Comparativity in Histories of Science-with a Case Study in the Comparative History of “Optics” ‘, in Cheng-hung Lin and D. Fu (eds) Philosophy and Conceptual History of Science in Taiwan, Boston Studies in the Philosophy of Science (Dordrecht: Reidel, 1992). vol. 141, pp. 123-148.

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Kuhn’s starting point in introducing

his thesis of incommensurability

is typically

‘passages or sentences that don’t make sense for an historian of science who is reading an ancient text of science’. Kuhn also appeals to such passages in urging the historian to ‘learn a foreign language or a lexicon of taxonomic kinds’. The initial response of ‘couldn’t make sense of some passages or sentences’ is of course a moment of ‘misreading’. However, what I wish to suggest in this paper is that usually there are several levels of misreading.

The level of misreading

to which Kuhn has paid full

attention is often the level where the lexicon structure of a scientific discipline has changed considerably after some form of revolution or the ‘speciation’ of a new discipline. Kuhn’s recent thesis of structural changes in the lexicon of kind terms, I believe, accurately describes and explains ‘misreading’ on this level. However, I believe that there is a different, or higher, level of misreading as well. The phenomenon of ‘being unable to make sense of some passages’ also occurs on this higher level, but the nature of the misreading is usually quite different. Kuhn has usually focused on lexicon changes within a scientific discipline, be it theories of motion, optics, or heavenly bodies. The network relationships or ‘distance’ between the discipline in question and other scientific disciplines, however, has not been adequately discussed.’ Misreading on this higher level often results from a phenomenon that is quite familar to historians of science, that of mislocating

the ancient text in question

by placing it in the wrong category of science. Instead of reading ancient text X as a study of science A, one misreads X as a study of science B. Systematic misreading hence follows from this ‘ahistorical categorization’ of the ancient text. To put the matter in a different way, the cause of misreading on this level often lies in the problem of how historians of science can correctly place an ancient text in a specific position in relation to other kinds of disciplines. In short, the cause of misreading here is a mistake concerning the inter-disciplinary relationships in a network of ancient or foreign disciplines.”

Regarding misreading

on this level, Kuhn’s strategy of learning

a new lexicon of kind terms is inadequate and cannot even cope with this new set of problems. Instead, we have to learn a new interdisciplinary network relationship.”

‘To be sure, Kuhn has written quite a bit on the topic of cross-disciplinary fertilization, most recently in his comments in J. L. Heilbron, ‘A Mathematician’s Mutiny, with Morals’, in P. Horwich (ed.), World Change: Thomas Kuhn and the Nature of Science (Cambridge, MA: MIT Press, 1993) pp. 81-129, especially p. 321. ‘%-isrea d’mgs of this kind by historians of science or by scientists of later times have stemmed from the diachronic higher-level incommensurability. But the ‘higher’ incommensurability discussed in this paper also covers the synchronichigher-level incommensurability, as shown in my discussion of the Boyle-Hobbes debate in Section III. Diachronic higher-level incommensurabilitv need not to be oreceded by synchronic higher-level incommensurability. “Both Heilbron (ibid.) and Kuhn (‘Afterwords’, in P. Horwich, ibid.) have some interesting and optimistic remarks concerning this new language-learning. Thus Heilbron remarked (p. 107): ‘[Kuhn’s] argument that theories on either side of a revolution are incommensurable because the meanings of terms change so radically applies also, and perhaps more plausibly, to the names of disciplines ’ and Kuhn also commented (p. 321): ‘Like “force” and “element”, “physics” and “astronomy” are kind terms, and

Higher Taxonomy and Higher Incommensurability

Sometimes

this may lead to a new grand taxonomy

277

of knowledge

covering

many

disciplines. Therefore, it is useful here to distinguish of taxonomy

two kinds of ‘taxonomy’. One is the kind

already discussed in detail by Kuhn, Hacking and Buchwald. We may

call it an ‘I-taxonomy’ (instrument-grounded taxonomy) in order to emphasize its connection to instrumentalities, a point beautifully argued by Buchwald in a paper already mentioned. l2 However, in order to cover many more kinds of disciplinary taxonomy ranging from Greek, Medieval, or Chinese ‘sciences’, where instruments may not be involved at all, I prefer ‘d-taxonomy’ (disciplinary taxonomy) to convey this wider sense of taxonomy, which of course includes the I-taxonomy. Now, as many d-taxonomies connect laterally and upwards to higher-order relations, we may call this ‘higher’-order tree a ‘K(nowledge)-taxonomy’ by treating every d-taxonomy as a node in the grand K-taxonomy tree. Viewed from this distinction, perhaps we would better understand why, in addition to d-taxonomies, it is important to push to a higher level: the d-taxonomic structure seems to: (a) not easily address lateral relations among d-taxonomies, like the Hacking-Buchwald problem discussed in the previous section; and (b) not subsume morally hierarchic relations among kinds of knowledge that nevertheless have powerful historical efficacy in structuring the d-taxonomies themselves. A K-taxonomy often embodies, as it were, a number of moral hierarchies of knowledge. A moral hierarchy consists of an ordered set of d-taxonomies sitting on the same branching level of a K-taxonomy, ordered in terms of the superiority of some historically conditioned values. On the other hand a d-taxonomy does not embody any moral hierarchy at a11.13In this picture, Kuhnian

incommensurability (or ‘d-incommensurability’) is best applied to terms in localized d-taxonomies that sit together at comparable places within an otherwise-unaltered K-taxonomy. Before I am prepared to make some more precise suggestions concerning the higher-order incommensurability, I would like to introduce the intuitive idea of it by

“continued they carry behavioral expectations with them. These and other names of individual sciences are acquired together in a contrast set.. . Interjection of a name not current at the time thus usually results in a violation of the no-overlap principle and generates conflicting expectations about behavior.’ But is it not the case that scientific disciplines typically ‘overlap’ easily with each other in various ways? I tend to believe that a strict no-overlap principle could only be established within a disciplinary taxonomy. I shall return to this issue in the final sections of this paper. ‘*Jed Buchwald, ‘Kinds and The Wave Theory of Light’, Studies in History and Philosophy ofscience 23 (1992), 39-74. ‘3Probably not every K-taxonomy embodies moral hierarchies of knowledge. It is also not clear what kind of moral hierarchies are embodied in many Chinese grand taxonomies of knowledge, although frequently there are some ‘orders’ embedded in them. But I do think that this notion of ‘moral hierarchy’ in K-taxonomy is a very important one, especially for the historical example of The Boyle-Hobbes debate and others to be discussed in the next two sections. Thus, for a detailed explication of ‘moral hierarchies’ in a K-taxonomy in terms of historical examples, see Section III of this paper and, in particular, Fig. I. For the suggestive notions like ‘moral hierarchy’ and some others, I am especially indebted to a wonderful referee who raised many extremely important issues with me.

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some historical examples. Let me begin from the higher level ‘misreading’

already

sketched above. II Historical examples of the higher-level short examples concerning Making Sex-Body

‘misreading’

this type of miscategorization

are many. Let me give three and re-categorization.

In his

and Gender from the Greeks to Freud’4 Thomas Laqueur shows

that the network position of the discipline ‘biology’ shifted drastically from the eighteenth to the nineteenth centuries. This shift of network position was accompanied by a fundamental shift in the meaning of the human ‘body’ and the shift from the ancient and medieval ‘one-sex’ model to the ‘two-sexes’ model in human biology in the nineteenth century. To the ancient Greeks, Laqueur argued, biology did not play a determining role in other social and cultural sciences, as it did in the nineteenth century. Rather, the human body and biology served as an illustrative locus for what was considered ‘natural’ in the social and political realms. Biological sex was just a further illustration of what were the natural gender relationships in the society. At most, the taxonomic tree (d-taxonomy) of biology was homologous to other taxonomic trees in the social and political sciences: ‘microcosmic creation mirrored the macrocosmic’. l5 In ancient Greece, therefore, gender relations historically preceded sex relations. In nineteenth-century Europe, disciplines

the relationship

between

biology

and

other

was turned on its head. The human body, anatomy and biology were now

fundamental in determining what should be considered normal/pathological and normative/perversive in the social, gender and even political domains. The assertions and claims of doctors and physicians had enormous social implications. In short, although the lexicon of kind terms in the Kuhnian sense changed drastically between the time of the ancient discipline

of human

Greeks and the end of the nineteenth

biology,

there were also many changes

century

concerning the position of human biology in relation to other disciplines. hierarchy was then established among these disciplines. A similar drastic re-categorization

within the

on a higher level A moral

of a science between the time of ancient Greece

and modem Europe can also be seen for the discipline of optics. A dominant idea in optics in ancient Greece was the visual ray theory. Because of the characteristics of the theory-a geometrical extromission theory of vision-the discipline itself was located within the field of geometrical and mathematical science. Though a theory of vision, it had no connection with the anatomy of the eye; because it was based on extromission rays, it was a science of the ‘soul’. As Gerard Simon has shown, this is a far cry from the seventeenth-century ‘geometrical optics’ of Kepler and his 14Thomas Laqueur, Making Sex-Body and Genderfromthe Greeks to Freud (Cambridge, University Press, 1990). “Ibid., p. 49.

MA: Harvard

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successors, despite its apparent similarity to it. l6 In the ancient Euclidean tradition, although reflection and refraction were studied by Heron and Ptolemy and hence were included in the problem domain of optics, they had an epistemological status lower than that of direct vision; i.e. for them, reflection and refraction were concerned with the knowledge of falsity and distortion. Precisely because of this tradition, the medievals heaped up all kinds of compounded mirrors owing to their fascination with the realm of the imaginary. In contrast, for modems this use of mirror is only an application of the law of reflection. In short, ancient optics, though having a domain space seemingly close to that of modem optics, was more a science of the ‘visible’ than a science of light. This mathematical science was therefore closer to ancient psychology than to physics. The phenomena of ‘misreading’ the place of an ancient or foreign discipline perhaps manifests itself most strongly in studies of the history of ‘sciences’ in non-western cultures, e.g. the history of Chinese science. In the past, many Chinese historians of Chinese science, without due methodological caution, simply imposed the contemporary (Western) taxonomy of general knowledge upon the history of various knowledge traditions in China. Numerous articles discussed the history of Chinese ‘physics’, ‘optics’, ‘electricity and magnetism’, ‘geology’, ‘biology’, ‘social sciences’ and so on, without being able to identify in historical records either the existence of the corresponding scientific communities or their d-taxonomic unity among texts in the general K-taxonomy of Chinese knowledge. It seems to me, for example, that crude comparisons between Western optics and Chinese ‘optics’ designed to show the precedence of the Chinese in discovering various isolated elements of contemporary knowledge of optics serve only to hide the important incommensurabilities on a higher level between radically different contemporary (Western) and historical Chinese general K-taxonomies.‘7 I have just finished a study on the categories of ‘divine marvels’ and ‘strange occurrences’ in an eleventh-century Chinese book of ‘jottings’, which recorded natural phenomena on a comprehensive scale. This text was especially famous in the past for the supposedly ‘scientific’ characteristics of most of its content. However, many of the alleged scientific elements in the text are really the results of (mis-)reading the jottings (Mengxi Bitan) by imposing on them the general K-taxonomy of twentieth-century Western science and technology. Only by carefully following the general taxonomy of knowledge in eleventh-century China can we begin to appreciate both the fascinating pecularities

‘kerard Simon, ‘Behind the Mirror’, Graduate Faculty Philosophy Journal 12 (1987), 311-350; (originally translated from Simon’s L.e Temps de la refexion (1981), pp. 298-332; L-e Regard, l’etre et I’ufTarence a&s l’optique de l’antiquitk (Paris: Editions du Seuil, 1988). For a short discussion of the changing disciplinary ‘position’ of optics in the Western history of science, and its comparative situation with the Chinese history of the so-called ‘optics’, see D. Fu (op. cit., note 8). It is quite a common practice for early historians of Chinese science to bluntly impose the contemporary general taxonomy of knowledge onto some ancient Chinese texts, and thus to create imaginary communities of learning. The ‘discipline’ of the so-called Chinese ancient optics is only one example.

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Studies in History and Philosophy of Science

and the surprising ingenuity in the ways of understanding written in that specific historical context.‘*

nature manifested

in a text

III Consider, as a more detailed example, the position of Leviathan in the network of knowledge disciplines of the seventeenth-century England. Steven Shapin and Simon Schaffer give an impressive account of it in their Leviathan and the Air-pump. Instead of reading kviathan as the beginning of modem political philosophy ‘as usual’, Shapin and Schaffer read it as natural philosophy and epistemology.” Adopting the sympathetic view of an historian of science, Shapin and Schaffer consider the relationship of Leviathan to other Hobbesian doctrines and the end of natural philosophy. They show that, philosophy, and natural philosophy are closely related, occupy a morally higher position (being ‘science’) in of ‘knowledge of fact’, i.e. memory, history, sensation Hobbes stated?

such as logic, motion, body for Hobbes, geometry, civil and that together these fields respect to the lower position and experimentations.

Thus

There are of KNOWLEDGE two kinds; whereof one is ‘knowledge of fact’: the other ‘knowledge of the consequence of one affirmation to another’. The former is nothing else, but sense and memory, and is ‘absolute knowledge’; as when we see a fact doing, or remember it done: and this is the knowledge required in a witness. The latter is called ‘science’; and is ‘conditional’; as when we know, that, ‘if the figure shown be a circle, then any straight line through the centre shall divide it into two equal parts’. And this is the knowledge required in a philosopher; that is to say, of him that pretends to reasoning.

For people such as Boyle and many other members of the Royal Society, on the other hand, a very different network of relationships between various disciplines should be constructed. For them, experimental sciences dealing with matters of fact had the morally higher position and these sciences alone could secure assent to all parties to a discussion. In contrast, politics or philosophical speculations concerning ‘causes’ were powerful

in generating

differences

among

people.

The Christian

religion, however, could be properly included in natural philosophy by Boyle and later on by Newton. From the perspective of these two different networks of disciplines, “For acontextual and taxonomical study of the famous eleventh-century Chinese jottings, MengXi-Bitan (‘Brush Talks from the Dream Brook’), conducted strictly from the viewpoint of the dominant general taxonomy of knowledge in eleventh-century China, see D. Fu, ‘A Contextual and Taxonomic Study on the “Divine Marvels” and “Strange Occurrences” in MengXi-Biran (“Brush Talks from the Dream Brook”)‘, Chinese Science 11 (1993-4), 3-35. “Steven Shapin and Simon Schaffer, Leviathan and the Air-pump: Hobbes, Boyle and the Experimental Life (Princeton, NJ: Princeton University Press, 1985). “See Hobbes’s Leviathan, the first part, ch. 9, ‘Of the several Subjects of Knowledge’. After this introduction, Hobbes set natural history and civil history together, as the ‘history’ which is the register of ‘knowledge of fact’. The registers of science, on the other hand, are such ‘books’ as contain the ‘demonstrations’ of consequences of one affirmation to another; and are commonly called ‘books of philosophy’.

Higfier

Taxonomy and Higher Incommensurability

Leviathan’s

281

truth and the truth of the air-pump,

argue Shapin and Schaffer,

‘are

products of different forms of social life’ .*l Figure 1 contrasts these two knowledge trees, or two K-taxonomies.** In Fig. structures by vertical occurs in

1 we see that Hobbes’ philosophy-science-knowledge of consequence are morally superior to knowledge-of-fact structures. This is represented displacement: a simple, two-placed moral hierarchy. A similar situation Boyle’s table, where the ‘certainty’ structure is morally superior to the

‘uncertainty’

structure.

However,

this certainly

does not mean

that, for every

branching, what sits higher is superior. It is not the case that, for Hobbes, natural philosophy is superior to civil philosophy and we have no reasons to suppose that meteorology is superior to astrology, nor music to ethics. One thing is relatively certain though: if a K-tree does contain I-taxonomies (and this certainly need not be the case), then the categories within any given I-taxonomy do not form what one might call a ‘morally-hierarchic’ set. On the other hand, there is indeed a kind of subtle moral hierarchy on the branching level where ‘elaborate’ or ‘unobvious’ experimentation sits-a very important branching level for our subject in this section (indicated by triangle symbols). For Hobbes, ‘experiments that every man maketh to himself were ‘experience’ and they were but ‘sense and memory’. They generated certainty in him who has the experience; they could not, however, produce the collective certainty which was the prerogative

of philosophy.23 Hobbes does allow experimentations

to

‘enrich the natural histories’, and he often uses natural history as a close analogy to talk about experimentations; both of them need witness. However, the kind of ‘unobvious’

(‘elaborate’)

experimentations

performed by Boyle were considered

Hobbes morally inferior to obvious experiments stated: ‘As for mean and common experiments,

or natural observation.

by

Thus Hobbes

I think them a great deal better witness

of nature, than those that are forced by fire, and known but to a very few’. All of these again are directly concerning

or indirectly

linked

to the two different

what is a ‘noble philosopher’.

For Hobbes,

‘banausic’ and ‘If the science were said to be experiments best of all physicists

forms of social life

the philosopher

was not

of natural things, then the

are quacks’.“4

I certainly do not wish to deny that within the realm of pneumatics, air-pump, and the more general experimental sciences, there are many important Kuhnian

“Ibid., p. 154. 221bid. In the same chapter, Hobbes drew a very complicated but logical table of classification of ‘science’; the first two immediate grand sub-divisions are: consequences from the accidents of bodies natural; which is called naturalphilosophy, and consequences from the accidents of ‘politic’ bodies; which is called politics and civil philosophy. See an analytical and slightly expanded picture of Hobbes’ table in art one of Fig. 1. Note here that for Hobbes, civil history is radically different from civil philosophy. %Hobbes was excluded from being a Fellow of the Royal Society. In the beginning of his ‘Dialogus Physicus’, Hobbes asked why there are just ‘fifty men’ to meet each week at Gresham College: ‘Cannot anyone who wishes come, since, as I suppose, they meet in a public place, and give his opinion on the experiments which are seen, as well as they?’ Interlocutoranswered: ‘Not at all’. In here and in other places, Hobbes explicitly challenged whether the ‘experimental spaces’ are public. See op. cit., note 19, ch. 4. 240p. cit., note 19, pp. 125-131.

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Higher Taxonomy and Higher Incommensurability incommensurable

elements. To see that, it suffices simply to look at the cross-purpose

‘debates’ between emphasize

283

Hobbes and Boyle, although

the obvious

incommensurability

Kuhnian

Shapin and Schaffer do not fully

incommensurability

in the Kuhnian

occurring

there. However,

sense does not exhaust the differences

between

‘Leviathan’s truth’ and the ‘truth of air-pump’. What Shapin and Schaffer describe in terms of a Wittgensteinian ‘form of life’ could at least partly be re-described in more precise language as different, conflicting network relationships linking various doctrines or disciplines. The differences between two kinds of network relationships constitute therefore a higher level of incommensurability.

As can easily be seen from

Fig. 1, the ‘positionings’ of experimental sciences and that of knowledge of causes are quite different and even conflict with each other in Hobbes’ and Boyle’s respective ‘forms of life.’ I find it difficult not to take this type of different ‘positioning’ as an important element in explaining the persistent incommensurability in the debates between Hobbes’ and Boyle’s supporters. The debate between Hobbes and Boyle about how to describe and interpret the numerous ‘unobvious and elaborate’ experiments done in Boyle’s air-pump is a good example of how a transgressing incommensurability between K-taxonomies strongly influences

the instrumental

incommensurability

between I-taxonomies

of Boyle and

Hobbes in pneumatics. In Fig. 2(a) and (b), I sketch two partial I-taxonomies of ‘air’ in pneumatics, attributed to Boyle and Hobbes, respectively. In Boyle’s I-taxonomy of ‘air’, we see Boyle’s air-pump machines and various related experiments serve as instrument-nodes to branch ‘common air’ into a series ‘kinds’ of subtle air with ever lower spring. The hypothetical ‘aether’ could be a special kind on the bottom, but actually was ruled out because of the failure in detecting any ‘aether-wind’ in Boyle’s elaborate experiments

discussed

in his Continuation

Mechanical.25 The root of Boyle’s I-taxonomy, which contains

of New Experiments

Physico-

‘air’, is a fully independent

category

many ‘matters of fact’, no-overlap

sub-kinds.

The epistemological

status of this I-taxonomy is guaranteed by its position in Boyle’s general K-taxonomy in Fig. 1 (in the ‘certainty’ sub-structure). As a contrast, Hobbes’ smaller ‘I-taxonomy’ of air is quite different in Fig. 2(b). According to Hobbes, it was impossible to understand the air-pump experiments ‘unless the nature of the air is known first’. Thus supported by doctrines in other parts of his Nature Philosophy, Hobbes ‘stipulated’ the constitution

of air in advance before

letting the air to be tried out in Boyle’s ‘always leaking’ air-pump.26 Hobbes’ category of air is then not ‘independent’

in the sense of Boyle’s. Under the morally superior

“See op. cit., note 19, Shapin and Schaffer’s discussion in pp. 182-185. 26Hobbes’ attitude here actually is not so ‘dogmatic’ as it might sound. According to Shapin and Schaffer, a kind of ‘Duhem-Quine’ thesis was embedded in Hobbes’ attitudes towards Boyle’s experiments. Hobbes contended that all experiments carry with them a set of theoretical assumptions embedded in the actual construction and functioning of the apparatus and that, both in principle and in practice, those assumptions could always be challenged. Thus, in particular, Hobbes wanted to show that Boyle’s explanations invoked vacuism, whereas his own alternatives proceeded from plenism. See op. cit., note 19, pp. 11 l-l 12; 185-187.

Studies in History and Philosophy of Science

284 AIR ( Boyle’s

l-taxonomy

)

air-pump .‘resid?c (low

common air sucked out

air”

spring)

(high spring ) Marbles cohesion. experiment 31

7

7

failure “spring still too strong”

I I SUCCtZSS?

marbles-separate “very weak” new

I I

of expanded

air

air-pump

muFrn;r;;d

I I I I

spring

I “very

success weakened” spring

calibration of receiver’s by separation

fHilure?

more

contents

sucks e void-in-void experiment

I

I success no common

“practically

r

failure air”

(later the problem of ” anomalous suspension” from Huygens)

I aether-wind

8 I I t I I 0 I I

experiment

failure “operational vacuum” finally established Fig. 2(a).

success? “aether”

guidance of Natural philosophy, Hobbes was convinced that Boyle’s air-pump, no matter how effective, could not hope to suck the aether out of the receiver. The all-permeable aether thus figures prominently from the root down to the nodes in Hobbes’ I-taxonomy. The failure of separating marbles in the air-pump, the famous ‘cohesion experiments’ reported in experiment 3 1 of Boyle’s New Experiments, was indeed a ‘success’ for Hobbes and thereby confirmed Hobbes’s aether and its physical efficacy. Boyle’s final success in separating marbles in the air-pump and his

Higher Taxonomy and Higher Incommensurability

285

Stipulated & Supported by doctrines from Hobbes’ Natural Philosophy

AIR ( Hobbes’ ” I-taxonomy” )

acthcr

grosser, aqueous, effluvia

earthy,

Iair-p;mp 1

grosser earthy

effluvia

purer air and aether, through leaks,

I marbles

Boyle’s

exp.31

;

Icohesion,

I I I I I I I

success! “marbles not separated” purer air & aether

failure? f--

“vehement circulation

more

sucks

of air &

aether”

explaining some of Boyle’s experiments. and ingoring some others, all guided by Hobbes’ Natural Philosophy. Fig. Z(b).

experimental results in not detecting any aether-wind were, understandably, ignored by Hobbes, most likely due to the morally low status of ‘unobvious experiments’ in Hobbes’ K-taxonomy. Finally, the superior position of Natural Philosophy in Hobbes’ K-taxonomy (and hence its influence in his discussion of natural phenomena) demands from Boyle’s I-taxonomy something which is inferior in Boyle’s K-taxonomy and which is deliberately ignored by Boyle: the ‘causes’ of the air spring.

Studies in History and Philosophy of Science

286

Boyle’s strategy of appealing to ‘nescience’ with respect to the causes of spring is far from satisfactory to Hobbes since, from the standpoint of mechanical philosophy, the very hypothesis

of the spring of the air was absurd ‘unless perhaps we concede

what is not to be conceded, Shapin and Schaffer’s

that something

analysis

can be moved by itself’.27

of the ‘mechanics

of fact-making

and its three

technologies’ in shaping the experimental life of Boyle’s men and the immediate tradition of the Royal Society has some further implications. Their analysis of the debates between Hobbes and Boyle calls to mind the debates between Newton and his adversaries, such as Hooke, Huygens and Leibniz, in issues like optics and celestial mechanics. Newton’s dictum of ‘Hypotheses non fingo’ drew a sharp distinction in terms of certainty, just like Boyle’s distinction between knowledge of causes and ‘matters of fact’. On the other hand, Newton’s adversaries could not accept Newton’s ‘new theory of light and colours’ and ‘universal attraction’ as having a higher epistemological status than other competing ‘hypotheses’. That is, Newton claimed that his own ‘theory’ (matters of fact for Boyle) was certain, ‘deduced directly from experiments’, whereas his adversaries offered only hypotheses, ‘the kind of thing of which philosophers could easily invent many’. All of this has long been well documented by Newton scholars. However, what I wish to emphasize here in connection with the debates between Hobbes’ and Boyle’s men is this: although the ideal structure of a K-taxonomy of knowledge may not be quite the same among Hobbes, Hooke, Huygens and Leibniz, their similar ‘positionings’ of knowledge of causes and experimental matters of fact (Hobbes being the most radical) contribute significantly to their ‘incommensurable debates’ with Boyle, Newton and later Newtonians. 28We can see pe rsistent structural differences between the K-taxonomical traditions (see Fig. 1) of Descartes-Hobbes-Huygens-Leibniz and Boyle-Newton, which then result in a higher level of incommensurability. In an interesting contribution to the literature on ‘incommensurable Biagioli29 has recently historical

context:

given an account of competition

the social competition

between

debates’,

between paradigms

different

in an

social-professional

“Hobbes, ‘Dialogus Physicus’, translated by S. Schaffer, in op. cit., note 19, pp. 254-255. Also op. cit., note 19, chs 4-5. In defense, Boyle’s tactics were to ‘hoist Hobbes on his own petard’. Whose natural philosophy was it, Boyle inquired, that was truly mechanical? Boyle pointed out that although Hobbes used the ‘simple circular motion’ of earthy particles to explain gravity, he has not produced a satisfactory mechanical ‘causal account’ of that motion either. This again, for Boyle, shows the situation of ‘uncertainty’ concerning the knowledge of causes in Boyle’s K-taxonomy. See pp. 203-205. *%iven the grand differences between two general K-taxonomies, how do scientists rationally consider the competitions between them, or, in a more Lakatosian language, between the two scientific programs proceeding in different historical contexts? D. Fu, ‘Problem Domain and Developmental Strategies: a Study on the Logic of Competition and Development of Scientific Programs’, Ph.D. Dissertation (Columbia University, New York: University Microfilms, 86-10760) gave an account concerning the ‘logic’ of competition and development of scientific programs without explicitly conceptualizing this higher-order incommensurability. I used precisely the debate and competition between Newtonian optics and Huygensian optics as a case study for my philosophical argument. %ario Biagioli, ‘The Anthropology of Incommensurability’, Studiesin History and Philosophy of Science 21 (1990), 183-209.

Higher Taxonomy and Higher Incommensurability

287

identities-Aristotelian philosophers and Galilean mathematicians. Biagioli, however, suggests that Kuhn’s treatment of incommensurability is too restricted, being limited only to a linguistic approach. The narrowness of his approach prevents Kuhn from fully appreciating the significance of social-professional identities (or ‘interests’) in the social genesis of incommensurability. Therefore, he overestimates the possibilities for dialogue and theory evaluation offered by bilingualism.30 I think that Kuhn’s linguistic approach is indeed not broad enough to cover some higher historical constructions, namely the ‘general K-taxonomy’ in which Kuhn’s specific analysis of the d-taxonomy of a certain branch of science is located. Once a ‘broader’ linguistic approach (in the sense of admitting levels of incommensurability stressed in this essay) is adopted, the previously ignored social relationships among different social-professional identities emphasized by Biagioli could be much better ‘reflected’ in the positions of the disciplines in question in a general taxonomy of knowledge. Thus, the debate between Aristotelian philosophers and Galilean mathematicians could also be construed as a difference in positioning philosophy and mathematics in competing K-taxonomies. This broader linguistic approach has a further advantage in that the depth of incommensurability and the difficulties of bilingualism are still clearly visible even when the social-professional differences are not so drastic as in the case of the Aristotelians and Galileo.3’

IV

Having introduced the intuitive idea of a higher level of incommensurability by means of illustrative historical examples, I shall now make some more precise suggestions concerning these higher-level ‘network relationships’ using the taxonomic ‘tree language’ suggested by Kuhn, Hacking and Buchwald. A scientific discipline can be considered as consisting of a tree of kind terms (or, in more complicated cases, a small ‘forest’ of a number of interconnected trees). The tree-trunk constitutes the major, all-encompassing category that distinguishes the tree. Distinct branches emerge from the trunk, defining its immediate sub-kinds. Each branch may have its own sub-kinds, and these must eventually bottom-out, which is to say that they end up in classes with no sub-kinds. The network relationship of disciplines discussed above (in Section I) is the relationship between various trees (d-taxonomies). I will consider several typical relationships here: (i) from ancient Greece to the Renaissance, analogous or 3or6id., pp. 201-203. 3’In terms of Biagioli’s account of the social-professional identities, it is much more difficult to explain the persistent structural differences between the Descartes-Hobbes-Huygens-leibniz and Boyle-Newton taxonomical traditions. All of them are ‘new’ natural philosophers who were proposing various new sciences in seventeenth-century Europe. They have almost the same identity in Biagioli’s scale. One more word about the ‘linguistic approach’. Although Kuhnian incommensurability follows from the genesis proposed by Biagioli, linguistically speaking that genesis actually happened on higher-level network relationships among disciplines discussed in this paper.

Studies in History and Philosophy of Science

288 homologous

relationships

between macro- and micro-worlds

more or less horizontal-homologous various disciplines.

relations

There is essentially

between

a graphical

d-taxonomies:

they have the same connectivity

not together

form hierarchical

relationships

could be considered

d-taxonomies

representing

equivalence-relation

between

structure. But these d-taxonomies and the usual

as

image

do

of a grand

K-taxonomy with a major trunk and many sub-branchings does not apply here; (ii) the hierarchical-level relationships, perhaps more ‘modern’ in Western history, between various trees (d-taxonomies) could in turn be considered as follows: the root of a K-taxonomy

occupies the highest level of the hierarchy, and the infimae species

of that K-tree are naturally on the lowest floor. If tree A is in a hierarchical order (a K-taxonomy) one level higher than tree B and B stems from A, then at least some nodes in the higher levels of tree B can be connected to some nodes in the lower levels of tree A. I am thinking, for example, of the special distinction that all chemical reactions are interactions among electrons of atoms or molecules only and do not affect the atomic nucleus of the interacting atoms or molecules. This distinction may be viewed as a connectable link between the tree of chemical reactions and that of atomic science in physics. The crucial point here is that, once a connection is made between A and B, then the growth of the hierarchically lower tree B must be ‘confined’ or ‘restrained’ by the structure of tree A and the position of the connection point between trees A and B. All B-kinds are together distinguished from other kinds by the distinguishing properties of A-kinds at the lowest, all-embracing level of A-tree, as required by the no-overlap condition of A-tree. The extension of kind terms in tree B might be shifted, not necessarily only because of changes in the internal structure of tree B as in a Kuhnian incommensurability, but also because of changes in the general hierarchy itself, or changes in the internal structure of tree A, or even changes in the connection

point

between

trees A and B;32 (iii) the moral

relationships, already discussed in the Hobbes-Boyle the d-taxonomies sitting on the same branching K-taxonomy.

However, not every hierarchical

hierarchy

debates example, are between of a hierarchical level in a

branching,

with the d-taxonomies

on

it, would constitute a moral hierarchy. Many d-taxonomies on the same branching are just morally ‘neutral’ to each other. Although these two kinds of ‘hierarchies’ [i.e. relationships

(ii) and (iii)] are related, it is important not to confuse a moral hierarchy

with the hierarchical floor level of a K-taxonomy; (iv) d-taxonomic trees or even forests that are remote from each other, may or may not have some ‘common’ lower and lowest sub-kinds (infimae species). Now, if tree A and tree B do have some “The questions raised by reductionism between d-taxonomic trees sitting on different but neighboring hierarchical levels could be considered in this context. Disciplines usually overlap each other in various ways, either by ‘remote contacts’ or by ‘continuation kinds’ between d-trees on neighboring levels. By the latter I mean that, since a discipline on a lower level usually could grow in new areas with new kinds that cannot be directly explained by the taxonomic kinds in its parent discipline, we may call the remaining kinds the ‘continuation kinds’ that can be explained by its parent-hence a special situation of ‘overlap’ between neighboring levels. It might be possible, then, to say that one necessary condition for reduction is that a new no-overlap condition ‘between d-trees on neighboring levels’ could be strictly established.

Higher Taxonomy and Higher Incommensurability

289

common lower sub-kinds, I shall refer to A and B as having a ‘remote contact’. I will discuss this fourth kind of relationship in the next section. We can now explain higher-order incommensurability or ‘misreading’ as a matter of locating an ancient text in the wrong position with respect to homologous, hierarchical-level, or moral hierarchy relationships. Thus, even if a scientific discipline does not undergo a transformation in its own tree structure X from time one (tl) to time two (t2) (and hence presumably remains ‘translatable’ in the Kuhnian sense), incommensurability could still occur if the network position of X itself changes between tl and t2. Translations (at t2) of sentences (uttered at tl) concerning the structure of tree X or the relationships between tree X and its neighboring trees could be ‘strange or make no sense at a11’.33The extension of kind terms in X may also shift due to changes in the confining or restraining effects of the higher trees over and above tree X in the K-taxonomy. Appraisals and evaluations (at t2) of the objectivity or implications of tree X (as it was organized at tl), which inevitably bear on the ‘network position’ of tree X within the forest, could be misleading and ahistorical. Incidentally, what gets explained above is described in diachronical terms, but it could also be described in synchronical terms. However, one might ask whether the violations in hierarchical-level, or moral hierarchy, relationships are instrumentally efficacious at all. For example, one can imagine partisans A holding scheme x, and partisans B holding scheme y, where the x scheme sits in the K-taxonomy somewhere very different from the y scheme-and yet x and y, considered in themselves, might have exactly the same connectivity structure (the same d-taxonomy), i.e. I-incommensurability might conceivably not arise for these two schemes at all. There may be some ‘strange or make-no-sense’ sentences involved in the communications between A and B in this example, as briefly discussed diachronically in the previous paragraph, but this may or may not be efficacious in practice. Nevertheless, as I have already shown in the Boyle-Hobbes debates example in Section III, violations in higher-order K-taxonomy relationships (specifically ‘moral hierarchy’ in that case) exert strong influences on the instrumental incommensurability between Boyle’s and Hobbes’ I-taxonomies of ‘Air.’ In a sense, the incommensurable I-taxonomies of ‘Air’ between Boyle and Hobbes are structured by the incommensurable K-taxonomies between Boyle and Hobbes, as Figs 1 and 2 have amply shown.34 33Different feelings could be evoked during ‘saying something strange or make no sense’, especially with respect to the distinction between a moral and an I-taxonomic violation. One might ask: if A makes an assertion X, would B say that x is (one of): repugnant, nonsensical, irrelevant, stupid, utterly wrong, possibly mistaken (or some combination of these adjectives)? One referee suggested to me that the move from ‘repugnant’ to ‘possibly mistaken’ is a move from a deep violation of moral hierarchy to an emerging instability within an I-taxonomy. As for violations concerning ‘homologous’ or ‘hierarchical-levels’ relationships, I suspect that probably there are no such clear differences there. 341 do not wish to give the impression in this paper that although higher-level incommensurability is something important which Kuhn more or less ignored, it is also something we can simply add on to his account. The Kuhnian incommensurability itself may be strongly influenced by incommensurable K-taxonomies-they are instrumentally efficacious in d-taxonomies for some cases at least. On the other

290

Studies in History and Philosophy of Science

If the term ‘mat’ in ‘the cat sat on the mat’ is a simple case of Kuhnian untranslatability from English to French,35 then terms like ‘orgasm’ or ‘sperm’ perhaps could be viewed as incommensurable terms in a higher order. These terms are not primarily theoretical terms linked to specific theories; rather, in ancient Greece they were positioned at the intersection between biology, culture, power, legitimacy and fatherhood. However, the complicated transformations of eighteenth- and nineteenth-century Europe, as ably argued by Laqueur, made the old relationship of intersection between trees untenable. As a result of this higher-order incommensurability, the extension of the term ‘sperm’ shifted as we11.36 Let me consider this higher-order incommensurability as it relates to Kuhn’s recent argument that ‘water’ did not always refer to HzO,~~ which Kuhn introduced specifically to counter causal theories of reference.38 Kuhn points out:39 In 1750 the primary differences between chemical species were the states of aggregation or modelled upon them. Water, in particular, was an elementary body of which liquidity was an essential property . . . Not until the 178Os, in an episode long known as ‘The Chemical Revolution’, was the taxonomy of chemistry transformed so that a chemical species might exist in all three states of aggregation. Thereafter, the distinction between solids, liquids and gases became physical, not chemical.. . . [The stuff] that people in 1750 label ‘water’ [refers] to liquid HzO. It should be described not simply as Hz0 but as close-packed Hz0 particles in rapid relative motion.

However, it seems to me that the transformation in the 1780s and thereafter could not have been simply a change of taxonomy internal to chemistry alone. For water and other stuffs, in order to precisely say ‘the distinction between solids, liquids and gases became physical, not chemical’, we must have proper support from the development of physical sciences (thermodynamics, gas dynamics, etc.) as well.

hand, I am not sure whether higher-level incommensurability fits easily with Kuhn’s emphasis on the role of ‘internal’ exemplars and (intra-disciplinary) similarity relations in providing semantic content. I suspect, however, that the ‘fits’ would not be very easy and that there might be problems there. However, the problems involved there are certainly outside the scope of the present paper. ‘%e T. Kuhn, ‘The Road Since Structure’, Presidential Address to the PSA, in A. Fine, M. Forbes and L. Wessels (eds) PSA 1990 (East Lansing, MI: PSA, 1990). vol. 2, p. 5. Kuhn wrote: ‘[Because of the incommensurability between the French and English taxonomies for floor coverings], in each particular case for which the English statement is true, one can find a co-referential French statement, some using “tapis”, others “paillasson”, still others “carpette” and so on. But there is no single French statement which refers to all and only the situations in which the English statement is true. In that sense, the English statement cannot be made in French’. 360p. cit., note 14, pp. 55-58. “Thomas Kuhn, ‘Possible Worlds in History of Science’, in S. Allen (ed.) Proceedings of Nobel Symposium 65 (Berlin: de Gmyter, 1989), pp. 9-32; Thomas Kuhn, ‘Dubbing and Redubbing: the Vulnerability of Rigid Designation’, in C. W. Savage (ed.) Scientific Theories, Minnesota Studies in the Philosophy of Science, XIV (Minneapolis: University of Minnesota Press, 1990). pp. 298-3 18. (This paper is a somewhat revised version of Kuhn 1989, with reductions in p. 301, pp. 308-309 and with additions in psp.,314-315.) Htlary Putnam, ‘The Meaning of “Meaning” ,’ Mind, Language and Reality (Cambridge: Cambridge University Press, 1975). pp. 215-271. 390p. cit., note 37, first reference, p. 28.

Higher Taxonomy and Higher Incommensurability

291

Various points of connection between the transformed chemical forest and other forests of physical sciences (which were growing and transforming as well) in the grand network of relationships should have been rearranged too. Similarly, when Kuhn asks ‘Is heavy water really water? And what may one say about a sample of close-packed particles of Hz0 in rapid relative motion at the critical point, under the conditions of temperature and pressure, that is, at which the liquid, solid and gaseous states are indistinguishable. Is it really water?‘,40 he shifts the ground of discussion concerning the ‘extension of water’ from elementary chemistry to physical chemistry and even to atomic science. In short, the question concerning the extension of water is related to a number of scientific disciplines and their respective taxonomies.

V

Let us now consider the relation of ‘remote contact’ (by sharing some common lower sub-kinds or infimae species), the fourth kind of relationship between d-taxonomic trees introduced in the last section. This special relationship actually brings us back to the anomalous case of the ‘non-overlapping’ condition discussed by Hacking and Buchwald and mentioned at the beginning of this paper. Buchwald hints that he would tolerate this special overlap situation as long as the two fields of inquiry were distant from each other. However, judging the issue from the perspective of ‘network relationships between disciplines’, we can find some new implications of this tolerance. Note that the condition that d-taxonomic trees do not overlap urged by Kuhn and Buchwald is primarily concerned with the graphic connectivity within a d-tree structure. As to multiple d-trees (corresponding to various fields of inquiry) grouped together most likely in a grand K-taxonomy, I suspect that such overlap occurs more often than we might expect. After all, it is not surprising that, from time to time, human beings inquire about the ‘same kind’ of stuff from very different d-taxonomic perspectives. Furthermore, it is often the case that different or even remote disciplines pay some attention to what other disciplines are doing, in the hope of learning from or taking advantage of the results of others. When such ‘learning’ or ‘communication’ takes place, instead of being avoided, various remote contacts would be actively searched for. The various learning and communication processes between chemistry and biology during different stages in the development of these two disciplines is one good example. As biochemistry grew and separated from chemistry, chemists in the beginning avoided paying too much attention to what biochemists were doing. 4oOp. cit., note 37, first reference, p. 29. Strictly speaking, Kuhn’s example here is not exactly right. and From a simple discussion on ‘critical point’, ‘triple line’ and ‘super-heating’ in thermodynamics phase-transitions, we could easily see that the phenomenon of super-heating is much more suitable for Kuhn to criticize the example of ‘water’ discussed in causal theory of reference. See F. W. Sears and G. L. Salinger, Thermodynamics, Kinetic Theon: and Statistical Thermodynamics (3rd edn) (Reading, MA: Addison Wesley, 1975), pp. 30-40, the section on ‘surfaces for real substances’.

Studies in History and Philosophy of Science

292 However, as biochemistry

expanded the space of its disciplinary

showing interest in areas of remote contact. As the production

trees, chemists began of highly complex

molecules became too difficult or costly for chemists, research into the ‘self-organization’ of complex molecules learning

in the bio-sciences

and research in chemistry.4’

became a new (borrowed) area of

In this way, ‘highly complex

molecules’

in

self-organization research may create new remote contact points for the disciplinary trees of chemistry and biology. Perhaps learning and communication between d-taxonomic trees through remote contacts are all right among d-trees that sit at the same morally hierarchic level of a K-taxonomy (‘equally good sciences’). But what would be the situations for d-trees that sit at distinct moral levels? Learning from and communication to a d-taxonomy that sits on a higher moral level should be no problem for ‘lower’ disciplines,42 and history of the sciences provides plenty of examples of these. Problems may occur the other way around. But that does not have to be the case, as long as the results of making remote contacts with d-trees on lower moral levels prove fruitful for higher d-trees themsleves. I am thinking of the results of making contacts with ‘domestic pigeons’ for Charles Darwin’s grand project concerning the origin of species. What we have discussed above is an epistemological viewpoint. Remote contacts in the sense of learning and communication may in fact help to foster the growth of various sciences. But, reasoned Hacking, there is this metaphysical claim about the empirical world: perhaps ultimately there are only taxonomic kinds in nature. Hence presumably there should be no overlap or remote contact at all. Hacking even suggests that ‘[although] there might turn out to be no real kinds or taxonomic kinds in nature, yet it still be the case that nature is such that it is a good strategy to speculate about the nature as if there were such kinds’.43 What Hacking is suggesting, I think, is an epistemological principle. What I wish to propose here, however, is a somewhat different epistemological principle. I wish to remain neutral concerning

whether there are only taxonomic

kinds in nature. But

there are good epistemological reasons to avoid ‘overlap’ within a d-taxonomic tree. What makes overlap within a d-taxonomic tree undesirable is that it constitutes a ‘loop’ within a d-tree. An overlap in a tree happens only if there is a branching on the higher levels of the tree, and then on the lower levels of that same tree some branches meet again. The fact that the branches meet on the lower levels voids or invalidates the sorting function of some branching nodes on the higher levels of the same tree. It invalidates scientific instruments served as ‘sorters’ on branching nodes

4’For the point about ‘self-organization’, I am indebted to professor MO Zhong-yuan, Department of Chemistry, Taiwan University. “This happens for ‘young disciplines’ as well. Thus we may want to consider the emergence of d-taxonomies that initially cross moral hierarchies but that segregate out over time with increasing specialization. 43Hacking, op. cit., note 3.

Higher Taxonomy and Higher Incommensurability

in I-taxonomies on a higher distinctions

293

as discussed by Buchwald. 44 In other words, the ‘distinction’ level becomes

void,

since lower-level

branches

based

made

on higher

meet again. Expressed graphically, these branches constitute a loop. From

this perspective,

what makes the ‘remote contact’ cases tolerable is precisely that no

loops occur in inter-disciplinary contexts. Of course, as sciences grow, there is always the possibility of a new ‘overarching’ d-tree trunk being constructed that links two d-trees that were previously unconnected except for remote contacts. Suppose this indeed happens; then this new over-arching tree trunk and the previous remote contacts constitute new loops and these new loops would naturally generate pressure to reconstruct the topologies of the two smaller trees in order to avoid overlap internal to the single new tree.45 Of course, I do not believe over-arching d-taxonomic of all areas of knowledge,

that scientists

will ever develop

an ‘ultimate’

tree trunk in the sense of one that connects all the forests e.g. something with an ultimate root like the Aristotelian

‘substance’. If that were really possible in some hyper-unified vision of science, the ultimate root, ‘substance’, would render any remote contact between sub-disciplines a ‘bad loop’.& The course of the history of science does not seem to lead in that direction, however, and the failure of various radical theses of reductionism does not seem to support that possibility either, not to mention that the Kuhnian thesis of incommensurability itself blocks any simple reductionism or unification. I also wish to add here that, from the viewpoint of ‘learning and communication through remote contacts’ developed in this section, a single, rigid and ‘total’ d-taxonomic tree of things may be in principle an obstacle for the development and growth of science. Depending on how the network of relationships between scientific disciplines changes throughout history, scientists will themselves decide which overlaps are only remote contacts and which are bad loops. This is a higher-order phenomenon. Considerations discussed above again show the problems that arise from limiting discussions of ‘taxonomy’ to issues within the structure of a single d-taxonomic tree. “Note here that the ‘loop’ in question can only occur in a d-taxonomic tree. It will not occur in a K-taxonomy. As already defined, remote contacts do not mean sharing ‘common disciplines’, but sharing common lower sub-kinds or infimae species within two d-taxonomic trees. One referee suggested that the problem of ‘loop’ could be rephrased and further developed along the following line: that the no-overlap condition ties immediately to the possibility of there being determinate infimae species below a branch-point that connects across to other kinds; if overlap were possible, then looping could prevent unambiguous access to these species. 451 am not sure what to say if someone responds by saying that what if ‘the loop in question is big enough?’ From an historical and developmental viewpoint, that is not so bad as what might be sounded from a logical viewpoint. 461 am indebted to Professor John Haugeland for raising this interesting question in the Mind and Cognition Conference. One more word about ‘unified science’. Although Hacking mentioned ‘meshing’ in his (1993) revised version (op. cit., note 2, pp. 298-299). the idea is very vague, as is Quine’s short discussion of it (W. V. Quine, ‘Natural Kinds’, in OntologicalRelativity and OtherEssays(New York: Columbia University Press, 1969), pp. 135-138). Surely there are ‘kinds’ in the so-called mature sciences, as Hacking rightly asserted. The major point discussed in this paper, however, is not so much about the ‘mature sciences’ as about the histories of sciences. Moreover, as Quine (ibid.) discussed the ‘branches’ of sciences there, he did not pay attention to the general classification of knowledge, which also has a close relationship with the Kuhnian taxonomy, kinds, etc.

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Acknowledgements-The first draft of this paper was read on 17 May 1993 to The International Conference on Mind and Cognition at the Institute of European and American Studies, Academia Sinica, Taiwan. I appreciate the many valuable comments from Professors John Haugeland, Paul Churchland and MO Zhong-yuan at the conference. I am very grateful for the extremely valuable criticisms and suggestions from two referees of Studies in History and Philosophy of Science.