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Home , Anjan Chakravartty, Ian Hacking

Studies in History and 43 (2012) 657–665

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Studies in History and Philosophy of Science

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Styles of reasoning: A pluralist view

Otávio Bueno

Department of Philosophy, University of Miami, Coral Gables, FL 33124-4670, USA article info abstract

Article history: Styles of reasoning are important devices to understand scientific practice. As I use the concept, a style of Available online 28 August 2012 reasoning is a pattern of inferential relations that are used to select, interpret, and support evidence for scientific results. In this paper, I defend the view that there is a plurality of styles of reasoning: different Keywords: domains of science often invoke different styles. I argue that this plurality is an important source of dis- Style of reasoning unity in scientific practice, and it provides additional arguments in support of the disunity claim. I also Inference contrast ’s broad characterization of styles of reasoning with a narrow understanding that I Disunity of science favor. Drawing on examples from molecular biology, chemistry and mathematics, I argue that differences Representation in style of reasoning lead to differences in the way the relevant results are obtained and interpreted. The Imaging Hacking result is a pluralist view about styles of reasoning that is sensitive to nuances of inferential relations in scientific activity. Ó 2012 Published by Elsevier Ltd.

When citing this paper, please use the full journal title Studies in History and Philosophy of Science

1. Introduction 2. Styles of reasoning as inferential frameworks

Styles of reasoning play a significant role in shaping our under- Hacking conceives of styles of reasoning as broad frameworks standing of scientific activity (Hacking, 1985, 2002a, 2002b). This that govern a certain way of investigating the world. His original is, in part, due to the role they play in constituting that activity. inspiration emerged from A. C. Crombie’s Styles of Scientific Think- As I use the concept, a style of reasoning is a pattern of inferential ing in the European Tradition (Crombie, 1994), where Crombie relations that are used to select, interpret, and support evidence for develops the idea of certain styles of investigation. In an earlier pa- certain results. If we consider different domains of scientific per in 1981, Crombie described the proposal as follows: research, different styles of reasoning are often involved. The active promotion and diversification of the scientific meth- In this paper, I will illustrate how styles of reasoning shape sci- ods of late medieval and early modern Europe reflected the gen- entific practice, and I will defend the view that there is a plurality eral growth of a research mentality in European society, a of styles of reasoning: different domains of science often invoke mentality conditioned and increasingly committed by its cir- different styles of reasoning. This plurality is an important source cumstances to expect and to look actively for problems to for- of disunity in scientific activity (see Hacking, 1996; Dupré, 1993, mulate and solve, rather than for an accepted consensus & Cartwright, 1999), and it provides additional arguments in sup- without argument. The varieties of scientific method so brought port of the disunity claim. into play may be distinguished as: In order to defend this view, I will examine how different styles of reasoning are employed in different scientific fields. Drawing on examples from molecular biology, chemistry and mathematics, I (a) the simple postulation established in the mathematical will indicate how differences in style of reasoning lead to differ- sciences, ences in the way the relevant results are obtained and interpreted. (b) the experimental exploration and measurement of more The result is a pluralist view about styles of reasoning that is sen- complex observable relations, sitive to nuances of inferential relations in scientific practice. (c) the hypothetical construction of analogical models,

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0039-3681/$ - see front matter Ó 2012 Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.shpsa.2012.07.008 658 O. Bueno / Studies in History and Philosophy of Science 43 (2012) 657–665

(d) the ordering of variety by comparison and taxonomy, main. That is precisely what is accomplished by the production of (e) the statistical analysis of regularities of populations and the phenomena by an apparatus. A class of phenomena is created and calculus of , and such phenomena need to be explained, or accounted for, by suit- (f) the historical derivation of genetic development. able models.1 As will become clear below, with the introduction of what I call narrow styles of reasoning, central to these activities is the activity The first three of these methods concern essentially the science of inferring—different ways of inferring—appropriate conclusions, of individual regularities, and the second three the science of whether they are concerned with phenomena or instruments and the regularities of populations ordered in space and time apparatuses. Some of these inferential practices invoke geometri- (Crombie, 1981, p. 284; quoted in Hacking, 2002a, p. 161). cal considerations; others rely on statistical data, while still others In Hacking’s hands, styles of reasoning remind one of Foucault’s depend on biological or physical information. In contrast, Hacking (see Foucault, 1994), due to their encompassing scope emphasizes that a style of reasoning is concerned with the produc- and their largely uncommitted character with regard to particular tion of the possibility of the relevant truth-conditions rather than theories. In this respect, styles of reasoning are significantly differ- the preservation of truth (see Hacking, 2002a, p. 168). Given the fo- ent from Kuhnian (see Kuhn, 1996) and Lakatos’ re- cus on establishing possible truth-conditions rather than guaran- search programs (see Lakatos, 1978), both of which are teeing truth preservation, one wonders to what extent talk of 2 individuated, in part, by particular theories. In Kuhn’s case, theo- ‘styles of reasoning’ is apt. An alternative, that takes seriously the ries are a central component of a : it is with reference role of reasoning, will be offered below. to a given theory that paradigms are characterized, such as the In his survey and critical examination of Hacking’s conception Newtonian paradigm or the Darwinian paradigm. Similarly, Laka- of styles of reasoning, Martin Kusch charges Hacking’s proposal tos’ research programs are characterized via the key theoretical as being unable to block epistemic relativism (Kusch, 2010). The assumptions in the hard core as well as the series of theories in epistemic relativist insists that there are no non-question begging the protective belt. arguments to favor one conception (or one style of reasoning for Hacking’s of scientific practice tend not to empha- that matter) over another. But it seems to me that Hacking has re- size the role of theories, as his contrast between representing sources to block this form of relativism. He allows for the possibil- and intervening testifies (Hacking, 1983). With this contrast Hack- ity that the same propositions be assessed by different styles of ing was already marking the importance of shifting philosophy of reasoning. Moreover, at least in some cases, there are common science away from a theory-dominated discourse (early philosoph- standards among different styles of reasoning that allow for the ical conceptions focused on various aspects of representation) and assessment of these propositions. This is, in , common practice insisting on the significance of a whole class of activities, which when we use statistical analysis in laboratory sciences (statistical variously exemplify different forms of intervening. Hacking is not reasoning and laboratory reasoning being two different styles of particularly fond of theories as the key ingredient of scientific prac- reasoning). In this instance, statistical analysis provides the rele- tice, and for the most part, theories tend to play a limited role in his vant common standard that can be used to assess the propositions account of scientific activity. It is then not surprising that styles of in question. If needed, one can then adjudicate between the two reasoning are not tied to particular theories. styles of reasoning, without begging the question, by assessing Having said that, it is undeniable that styles of reasoning play a the conclusions that follow from each style given the use of the theoretical role in Hacking’s conceptualization of scientific prac- common standard. Despite the fact that different styles are in- tice. These styles allow him to systematize salient features of sci- volved, relativism need not follow. entific activity and highlight broad patterns and important Hacking explicitly allows for the combination of different styles differences within such practice. But even in this context Hacking of reasoning. The laboratory style can be thought of as a combina- stresses particular activities—rather than theoretical constructs— tion of items (b), (c), and (e) on Crombie’s list. Commenting on Pe- that underlie a style of reasoning. In his discussion of what he calls ter Galison’s trading zones—a zone of communication in which the ‘laboratory style’, Hacking notes that this style is characterized researchers who share very little common background can still ex- by change data and theoretical approximations (Galison, 1997)— Hacking notes: ‘‘The trading-zone idea will be useful in the study the building of apparatus in order to produce phenomena to of styles of reasoning when we begin to describe any that which hypothetical modeling may be true or false, but using employs several styles’’ (Hacking, 2002b, p. 184; italics added). another layer of modeling, namely models of how the apparatus that use multiple styles and common standards provide and instruments themselves work (Hacking, 2002b, p. 184). the precise context in which a non-question-begging choice be- Here we have a number of activities that are crucial to the lab- tween such styles can be made (if needed). One can choose be- oratory style: building an apparatus, as well as hypothetical and tween such styles (if needed) by invoking the relevant common instrumental modeling. The former type of modeling is concerned standards. Epistemic relativism can then be blocked. with accommodating relevant phenomena, whereas the latter fo- The situation here is not unlike the one found in debates about cuses on figuring out how the relevant apparatuses and instru- logical pluralism in which different (say, classical and para- ments work. Note that, within the laboratory style, apparatuses consistent) are at stake. There is enough common ground between produce phenomena that provide empirical constraints for hypo- such logics to allow one to choose one over the other without beg- thetical models. One of the central features of a style of reasoning ging the question (see Bueno & Colyvan, 2004, and Bueno & is to determine the range of what is true or false within a given do- Shalkowski, 2009).

1 has argued that scientific instruments should be thought of as engines of creation—that is, engines that produce phenomena—rather than windows into the invisible world—that is, instruments that provide researchers with access to unobservable objects and their properties (see van Fraassen, 2008; see also Heidelberger, 2003, and Boon, 2004). With his emphasis on instruments as engines of creation, van Fraassen follows Hacking, even though Hacking goes beyond this particular interpretation by favoring a form of entity . According to Hacking, suitable scientific instruments do provide us with access to unobservable entities. So, presumably he would also embrace the conception of instruments as windows into the invisible world. 2 In fact, Hacking himself is not entirely satisfied with the expression ‘styles of reasoning’. When referring to the items on Crombie’s list, he now prefers to use the expression ‘styles of thinking and doing in the European tradition’ (Hacking, 2012). O. Bueno / Studies in History and Philosophy of Science 43 (2012) 657–665 659

3. Styles of reasoning: broad and narrow not undermine the very idea of styles of reasoning nor its useful- ness. It attempts to preserve the generality provided by such styles The discussion above indicates how broad Hacking’s conception with specific information about the domain in question. of styles of reasoning is. Crombie’s original list already formulated An additional reason to introduce narrow styles of reasoning such styles in a general setting: postulational reasoning in mathe- emerges from the role they play in making sense of the laboratory matics, experimental exploration of observable relations and sta- sciences. Given the importance of these sciences, it is worth con- tistical analysis of regularities are indeed very broad categories. sidering Hacking’s own discussion of them, and the role that broad To Crombie’s list Hacking made some equally broad additions, such styles of reasoning play in that discussion. as the laboratory style of reasoning. The result is a very broad con- When Hacking describes the laboratory sciences, and the self- ceptualization of styles of reasoning—henceforth ‘broad styles of vindication mechanisms they employ, he advances a detailed and reasoning’. instructive framework (Hacking, 1992). On his view, a stable labo- But it is worth considering a narrower understanding of style of ratory science emerges from the coherence between three broad reasoning: an understanding that, while still preserving the prac- categories: ideas (roughly, the theoretical components that are in- tice-oriented features that Hacking highlights, is more domain- voked in the experiments conducted in a laboratory), things (the constrained than Hacking’s. The laboratory style of reasoning material features required by a laboratory), and marks and the encompasses a motley of experimental practices, which can only manipulation of marks (the output and interpretation of the exper- be lumped together at the cost of disregarding significant differ- iments conducted in a laboratory). Each of these categories is, in ences among them. In order to make room for the diversity of such turn, divided into five additional subcategories (Hacking, 1992, practices, a more fine-grained conception—a narrow conception— pp. 43–50). The resulting framework is this:3 of styles of reasoning needs to be invoked. Two features are crucial to the narrow conception: (a) Styles of Ideas: (1) questions, (2) background knowledge, (3) systematic reasoning, narrowly understood, are fundamentally inferential in theory, (4) topical hypotheses, and (5) modeling of the : the point of adopting such a style is to be able to infer rel- apparatus. evant information about the domain under investigation. This is a Things: (6) target, (7) source of modification, (8) detectors, (9) feature that, to a certain extent, is also shared by the broad under- tools, and (10) data generators. standing of style of reasoning favored by Hacking. Despite Hack- Marks and the manipulation of marks: (11) data, (12) data assess- ing’s emphasis on the role of styles of reasoning in specifying ment, (13) data reduction, (14) data analysis, and (15) truth-conditions for a certain domain (rather than in preserving interpretation. the truth in that domain), the specification of truth-conditions is ultimately secondary to the determination of the particular This list should not be thought of as a specification of the com- truth-value of the propositions in question. To find out the truth- ponents of the laboratory style of reasoning. Referring to the list value of a given proposition clearly presupposes that such a prop- above, Hacking writes: osition has truth-conditions: that is one reason why styles of rea- I have omitted from my list something that is rather rigid dur- soning are so important. But we should not ignore that the ing the time span of even the most extended experiment—[...] overall goal is to find out—when it can be found out—the relevant ‘‘styles of scientific reasoning’’ (Hacking, 1992, p. 50). truth-value. In many instances, however, the truth-value in ques- tion is constrained: truth with respect to the observable evi- The reason for omitting such styles, Hacking explains (1992, p. dence—that is, empirical adequacy—is often all that can be aimed 50), is that ‘‘experimenters do not literally use them’’. In fact, at (see van Fraassen, 1980 and 1989). ‘‘experimenters do not change their ideal conceptions of the uni- (b) Styles of reasoning, narrowly understood, offer more specific verse in the course of, or at any rate because of, experimental information about particular domains of inquiry, while still provid- work’’ (Hacking, 1992, p. 51). Styles of reasoning are ultimately ing some generality. As understood by Hacking, broadly conceived presupposed by experiments, and thus are not among the list of styles of reasoning operate at a high level of abstraction. Funda- items that compose the laboratory sciences. mentally different inferential practices fall under the description But something is odd with this description. It is not unreason- of postulational reasoning in mathematics. Consider the difference able to claim that experiments presuppose some sort of framework of introducing the set of natural numbers as the smallest set satis- such as a style of reasoning. However, such frameworks cannot be fying certain conditions and constructing these numbers in the way too broad. Otherwise, they would have very little to add regarding that Frege proposed: out of (second-order) plus definitions. If the particular description and implementation of any given exper- we are interested in making sense of postulational reasoning in iment. This is precisely what happens in Hacking’s case. By making mathematics, it is crucial to examine the relevant style of reasoning styles of reasoning extremely broad in scope and nature, Hacking at a substantially lower level of abstraction, so that significant dif- turned them into something largely irrelevant to the understand- ferences within postulational reasoning can be examined and as- ing of details of scientific practice, including the laboratory sci- sessed. In contrast, narrowly understood styles of reasoning— ences. If experimenters do not use styles of reasoning, and if henceforth, ‘narrow styles of reasoning’—operate at a level of such styles are not affected by experimental work, then to make abstraction that allows for the identification and study of these dif- sense of the activity scientists engage with when doing experimen- ferences, while still preserving some generality. After all, despite tal work styles of reasoning are of very limited relevance.4 As a re- the differences between the Fregean and the set-theoretic way of sult, a more fine-grained conception of styles of reasoning—that introducing natural numbers, there is more in common between takes into account specific details of particular scientific domains— them than either has with the experimental exploration of observa- seems to be in order. At this junction narrow styles of reasoning ble relations. So, the introduction of narrow styles of reasoning does become significant.

3 For our purposes, there is no need to describe each of the fifteen components, which are in any case largely self-explanatory. Detailed can be found in Hacking’s (1992) paper. 4 Hacking may grant this point by insisting that the very possibility of experimental work presupposes styles of reasoning. Hence, experimenters do not literally use such styles. What Hacking is ultimately after is a proper understanding of our concepts of . However, an understanding of objectivity that accommodates the specificity of scientific practice is also needed. 660 O. Bueno / Studies in History and Philosophy of Science 43 (2012) 657–665

Narrow styles of reasoning can be characterized in terms of the such transfer procedures may rely on statistical considerations, mechanisms they provide to represent what are perceived as possi- they may be based on data analysis, or invoke visual information bilities in a given domain of inquiry, and to draw inferences from (such as the outputs of various micrographs) about the domain un- these possibilities (together with additional assumptions) about der study. I will consider these components of a narrow style of the domain in question. The representation of possibilities is con- reasoning in turn.6 nected to Hacking’s emphasis on the specification of the range of The specification of the domain is achieved by identifying cer- propositions that are true or false in broad styles of reasoning. tain objects and a family of relations among them, which describe And similarly to Hacking’s proposal, to specify what is possible possible configurations among the objects in question. The ac- (or impossible), given accepted information about a certain do- cepted information need not be complete, and typically it is not, main, requires less than to determine that something is true (or since there are various informational gaps among the objects in- false). Of course, possibility is here understood as a primitive con- volved in scientific research. Researchers often do not know cept, and it is not characterized in terms of truth and possible whether certain relations hold or not among the relevant objects. worlds, as favored by the familiar possible-worlds semantics for In fact, it is precisely because of these gaps that additional research modal discourse (see Lewis, 1986).5 But truth-conditions for modal is needed. Moreover, the accepted information about the domain discourse in terms of possible worlds are unlikely to illuminate sci- need not be true; the only requirement is that it is accepted. It is entific practice, which is concerned with the complexities of the ac- certainly possible to accept certain bits of information without tak- tual world rather than what may be happening in another causally ing them to be true. When researchers use calculations based on isolated world (for additional discussion, see Bueno & Shalkowski, Newtonian theory to send a rocket to the moon, they are clearly 2009). accepting the information provided by the theory, even though Hacking only requires that (broad) styles of reasoning specify they know that the latter is not, strictly speaking, true. Even if the range of what is true or false within the boundaries of that there is a suitable replacement for Newtonian theory that is true, style. He is not defending the assignment of any particular truth-va- the existence of such a replacement is not required for one to ac- lue for the propositions under consideration. There is, of course, a cept the theory and reason from it in a particular domain. All that huge difference between the specification of which propositions is required is the use of the conceptual framework offered by New- are true or false in a given domain and the determination of the tonian physics in the systematization of the relevant phenomena. particular truth-values of these propositions. Only the former is And such use can be implemented independently of any commit- at stake with broad styles of reasoning. ment to the truth of the theory.7 In this way, those who employ a However, there is still a difference between, on the one hand, narrow style of reasoning can invoke the accepted information to specifying which propositions are true or false within a broad style formulate explanations, make predictions, or organize the available and, on the other, formulating possibility conditions for statements data—none of this requires the truth of the information that is in- given accepted assumptions within a narrow style of reasoning. voked. In each case, what matters is the exploration of possibilities. And it is important to mark a salient distinction between broad Similarly, the procedure of inference generation provided by a and narrow styles of reasoning in terms of this difference. A narrow narrow style of reasoning does not assume the truth of the infor- style formulates only what are taken to be possibilities (or impos- mation that one reasons about. None of the two components that sibilities) within a certain domain. And that can be done indepen- characterize a procedure of inference (a logic and other informa- dently of any particular commitment to the truth or the falsity of tion transfer procedures) assumes the truth of the relevant infor- the discourse in question. The exploration of the possible, given ac- mation. A logic need not be thought of as being truth-preserving, cepted features of the domain of investigation, is a central aspect of despite being often presented that way. Rather a logic can be for- a narrow style of reasoning. This is done, in part, by examining var- mulated in terms of a primitive notion of possibility: A follows ious inferential relations among the objects studied in the relevant from B as long as the conjunction of B and the negation of A is domain of investigation. Other possibilities are specified directly impossible. Similarly, information transfer procedures need not by implementing suitable experiments, building machines, or be thought of as being truth-preserving either. In fact, they are devising certain hypotheses in light of the available evidence. not, since in the case of inductive arguments the truth of the pre- Representational and inferential activities are, of course, closely mises fails to guarantee the truth of the conclusion. Moreover, con- connected. In the case of narrow styles of reasoning the connec- siderations based on data analysis need not be truth-preserving tions between them emerges from the key components that char- given that data are often incomplete—and thus not entirely true acterize such styles: one of them deals directly with to begin with. Similar considerations apply to the use of visual representation, the other with the resulting inferential relations. information that, despite being crucial to the research in various In order to represent something—that is, in order to represent a domains of science, is very selective: only those aspects of the sam- certain state as being possible—narrow styles (a) specify a given ple that were intentionally selected for representation and detec- domain of investigation, and (b) determine certain bits of informa- tion by a given instrument, such as an electron microscope, are tion about that domain as being accepted. In order to yield infer- represented on the surface of a micrograph. ences about the domain in question, a narrow style of reasoning There are distinctive narrow styles of reasoning in mathematics, provides a suitable procedure of inference generation. This in- which is guided, of course, by certain principles (typically, compre- volves (i) a (deductive) logic (which may or may not be made hension principles) that characterize a certain class of objects and explicit), and (ii) more broadly, suitable information transfer pro- relations among them. Inferential connections are then established cedures, which are highly context sensitive and rely on additional among the relevant objects with the goal of determining their assumptions about the domain under consideration. For example, properties and additional relations they bear with other objects

5 According to Lewis’ modal realist account: P is possible if and only if there is a world in which P. 6 For further discussion of representation within the context of the current approach, see Bueno & Colyvan (2011), and Bueno & French (2011, 2012). 7 Consider, for instance, the use of literature in the explanation of certain aspects of human psychology. We can say that in The Gambler Dostoyevsky’s portrayal of the psychology of compulsive gamblers provides understanding of the complexities and challenges involved in their behavior—even if as a matter of fact there were no gamblers in the actual world. Thus, the argument to the effect that Dostoyevsky’s insight only emerges because his portrayal was based on the behavior of actual gamblers (even though none of the characters described in the novel in fact exist) misses the point. Dostoyevsky describes a certain behavior that need not exist—and so the description advanced need not be true—for us to gain insight from the account offered. O. Bueno / Studies in History and Philosophy of Science 43 (2012) 657–665 661 in the domain. Among the inferential mechanisms, logic plays a The particular class of accepted information is also important limited role. The role is limited since typically the underlying logic for narrow styles of reasoning given that that class is one compo- is hardly ever made explicit, and informal but rigorous inferences nent in the individuation conditions for such styles. It is, thus, cru- in mathematics typically are only formalized when there is the cial that in order to use a narrow style one invokes the accepted suspicion of a lurking problem.8 information. Changing substantially the accepted information is a In those contexts in which a logic is made explicit, it usually is way of changing a narrow style of reasoning, and thus ultimately classical. This provides a very definite constraint on the styles of invoking some other style in the domain under investigation. If inference involved and the conclusions than can be obtained in the amount of accepted information about the relevant objects in the relevant contexts. Non-constructive, inconsistency-intolerant the domain changes dramatically, the conclusions obtained about inferential procedures are, thus, the norm of mathematical prac- such objects will change as well, and in this way the forms of rea- tice. That does not mean, however, that non-classical logics cannot soning about them will no longer be the same. Similarly, in many be invoked. They are, for instance, in those cases in which con- cases, changing the domain of investigation typically amounts to structive features of mathematical reasoning are at stake (see changing the corresponding narrow style of reasoning, although Bishop & Bridges, 1985), or where certain inconsistent objects are these changes need to be examined on a case-by-case basis. In studied, such as the Russell set in the context of a paraconsistent some instances, an expansion or a contraction of the domain of set theory (see da Costa, Krause, & Bueno, 2007). investigation may not amount to a change in the narrow style, Logic is not the only procedure of inference generation invoked but an improvement on the style’s proper scope. As long as the in mathematics. Diagrams, drawings, pictures, mental images, geo- central features of the accepted information about the domain (re- metrical interpretations, and a variety of other visual devices all vised in accordance with the changed scope) as well as the inferen- play an inferential role in mathematical activity. In the sense that tial components of the style of reasoning remain, the same narrow I am using the concept, inference need not be truth-preserving, style will be in place. as already noted, nor does it provide conclusive justification for Narrow styles of reasoning are meant to provide a focused and the results that are entertained. In many instances, visual devices constrained framework to make sense of significant aspects of sci- play a heuristic role in suggesting why the result in question entific practice. In this respect, narrow styles are introduced to may hold. Usually, the devices alone are not enough to establish achieve a job similar to the one advanced by broad styles of reason- the intended result, but they may suggest a path for a proof; they ing. Hacking’s focus on objectivity is not detracted from the may motivate that the result in question does hold, or they may engagement with narrow styles of reasoning. Given the more con- help the understanding of certain aspects of a given proof. strained features of narrow styles, these styles are better equipped Narrow styles of reasoning are thus invoked in mathematics. to accommodate specific traits of scientific practice than Hacking’s Different styles are embodied in different ways of conceptualizing broad styles of reasoning are. geometry, and the different roles they assign to intuition in under- But why should narrow styles of reasoning be considered styles standing geometrical phenomena. According to one tradition, geo- of reasoning rather than just particular bits of reasoning? Because metrical construction are tied fundamentally to space and depend despite being narrow, they still share common patterns, given that on intuitions of properties of the space in question. According to they are about the same domain of investigation, they invoke the another tradition, geometry is not particularly tied to space any- same logic and the same resources of information transference. more than arithmetic or algebra is. Intuition does not play any spe- These common components bring together the various bits of rea- cial role in geometrical reasoning than in any other area of soning into a common setting, and explain why certain theoretical mathematics. Nothing special about geometry is involved. These devices and inferential patterns are accepted as legitimate and why different styles of reasoning provide different standards of proof others are questioned or rejected altogether. For this reason, they and different proof strategies.9 form a style of reasoning rather than just a hodgepodge of inferen- Consider also the difference between the narrow style of rea- tial mechanisms. soning invoked by a mathematical logician in contrast with the informal but rigorous style adopted by a typical mathematician. 4. Pluralism, visual cultures, and the disunity of science: styles The logician emphasizes the formalization of the relevant proof of reasoning at work procedures invoked, and the process of making explicit the inferen- tial links and the precise assumptions required by the proof in 4.1. Pluralism and visual cultures question. In contrast, the mathematician is perfectly satisfied with the use of an informal language (in fact a natural language aug- Does any form of pluralism emerge from an examination of mented by suitable mathematical symbols), and has no need to styles of reasoning? If so, which kind of pluralism? First, there is make explicit every single inference involved in the derivation of the pluralism regarding different kinds of styles of reasoning, such the relevant theorem. Usually, the proof offers a sketch whose de- as broad and narrow styles. Second, there is the pluralism regard- tails the reader is supposed to fill in. ing particular instances of styles of reasoning, whether they are The difference in style highlights a difference in what is taken to broad or narrow. In this category, we find the multiple examples be a proof. The logician’s conception requires an explicit list of of styles of reasoning provided by Hacking, from geometrical styles inferential steps that leads from the appropriate assumptions to to the laboratory style. There are also examples of narrow styles of the statement of the theorem. The mathematician’s conception re- reasoning in the different uses of images as sources of visual evi- quires something significantly different, since only the central dence in distinct domains of science. As will become clear below, moves in a proof (including the proof structure) are explicitly in some cases, the goal is to establish the existence of a given ob- 10 presented. ject (a new particle, a new kind of structure). In other cases, the goal is to establish certain properties of the relevant objects (a par-

8 Logic plays a far more significant role in computer science. Automatic theorem proving, for instance, cannot be implemented without explicit reference to an underlying logic. A fascinating sociological examination of the connections between formal and informal concepts of proof can be found in MacKenzie (2001); for further discussion, see Bueno & Azzouni (2005), and Azzouni (2006). 9 A fascinating exploration of different styles of reasoning that shaped Frege’s foundational work can be found in Tappenden (2006). 10 For further discussion of and the connections between formal and informal, but rigorous, reasoning in mathematical practice, see Azzouni (2006), Part II. 662 O. Bueno / Studies in History and Philosophy of Science 43 (2012) 657–665 ticular configuration in the sample). But visual evidence is also transmission electron microscope (TEM). The use of TEMs, at this used to establish particular phenomena. A phenomenon, in this point in the 1950s, was already well entrenched in cell biology, context, is a regular pattern that is detected via some form of epi- and it emerged from, and supplemented, the effective use of opti- stemic access, often mediated by suitable scientific instruments cal microscopes in many biological fields. Palade, however, was that produce visual evidence (such as various kinds of micro- very cautious in order to figure out precisely what those ‘small par- scopes). Typically, to establish the existence of a phenomenon, it ticulate components’ were. First, he excluded the possibility that is required that there is good reason to believe in it. This, in turn, they were just artifacts of the method of preparation. After using demands the availability or the construction of evidence for the various such methods, he determined that the small components existence of the phenomenon in question. The phenomenon, visu- were still present. Second, by using an ultra-centrifuge, he estab- ally detected and presented, is made salient by the visual evidence lished that the traits in the sample had different sedimentation available to support it. This is an additional role played by visual times, and their estimated size was consistent with the size of evidence in scientific practice (see Bueno, 2011). the particulate components that were represented on the surface Visual cultures are cultures of creation, manipulation, and dis- of the TEM’s micrographs. These considerations supported the con- semination of images in scientific practice. The issue then arises clusion that the relevant particulate components were indeed as to how visual cultures are shaped by a style of reasoning. Do vi- genuine. sual cultures presuppose a style of reasoning? If so, what kind of In his 1955 paper, Palade remarked that the particulate compo- style (broad or narrow) is presupposed? I argue that visual cultures nents seemed to be mostly composed by ribonucleic acid. How- do presuppose a style of reasoning, and there are advantages in ever, he insisted, further chemical analysis was still required to interpreting such a style as being narrow.11 determine whether this was indeed the case. When the analysis Visual cultures in science are implemented by specifying a do- was finally conducted a few years later, it confirmed Palade’s con- main of investigation and suitable accepted assumptions that are jecture. The particulate components he identified were then called invoked in the study of such domain. The domain determines the ribosomes. objects that are going to be studied, and the accepted assumptions After seeing the TEM images of ribosomes that Palade produced, shape the constraints that are invoked to study the objects in ques- the biological community very quickly accepted the existence of tion. Furthermore, a visual culture also invokes a particular class of this new cellular component. Today ribosome research is an active transfer or inference procedures, which are invoked in order to field within molecular biology, which has uncovered the key role extract information from the relevant images (particularly micro- played by ribosomes in protein synthesis. graphs). Since a visual culture presupposes a domain of investiga- We find here a narrow style of reasoning at work. The style in- tion and accepted assumptions, the examination of objects and volves the study of cell structure and behavior, and it relies heavily relations in the domain is constrained by the conditions expressed on the outputs of imaging instruments (in this case, TEM). The by these assumptions, which shape the understanding of the micrographs that are produced by the research provide visual evi- domain and indirectly suggest ways of exploring and investigating dence for the existence of the relevant structures (in this case, ribo- it. The accepted assumptions include descriptions of the domain somes). The presence of certain marks on the surface of and proper procedures that are invoked in its study. micrographs is interpreted as evidence for the presence of corre- But how exactly are such objects investigated? This is the point sponding objects in the sample. Thus, images are used as inferen- where the specificity of a visual culture is invoked. The investiga- tial devices that allow one to infer, directly from the reliability of tion is implemented in terms of the construction, manipulation, TEMs, the presence of a given phenomenon (the existence of ribo- and interpretation of scientific images, which are produced by var- somes) from suitable traits on TEM’s micrographs. ious kinds of instruments, such as electron and probe microscopes. As a second example, I will consider a different use of visual evi- Scientific images are used, in particular, in inference procedures, dence in scientific practice. This case comes from organic chemis- that is, they are devices that allow researchers to extract informa- try. In 1999, using an atomic force microscope (AFM), which allows tion about the domain represented by the relevant images, and in- researchers to probe the surface of various chemical compounds, a fer, on the basis of such information, that a particular configuration group of chemists at the University of Toledo made an important obtains in the sample under study. discovery (Li, Perozzo, Konnert, Nadarajah, & Pusey, 1999). The In this way, visual cultures exemplify the key components of a group was studying the geometrical configuration of atoms at narrow style of reasoning: they define a domain of objects, rely on the surface of protein crystals. They initially obtained information a class of accepted assumptions about such domain, specify a class about the samples by a series of repeated measurements of their of inference procedures that are used in the investigation of the surfaces using the AFM. The multiple data obtained in this way relevant objects. They form a narrow style of reasoning. In fact, were then statistically combined to produce an idealized imaged they form a class of narrow styles of reasoning, since different do- that offered the average of the various measurements that were mains are investigated with different instruments, which in turn made. This image can be called the experimental image. produce different images about the intended domain. Such images Despite the good resolution of the experimental image, several generate a very diverse, multifaceted basis to establish inferential issues about the geometrical configuration of the atoms at the sur- relations among the objects under investigation. This fact illus- face of the sample are not settled—in particular, the molecular- trates, in turn, the importance of visual cultures in scientific prac- packing arrangement. To address this issue, researchers create a tice. To illustrate the role played by a narrow style of reasoning in theoretical image, in which they introduce (by hand, as it were) such practice, I will consider two examples: one from cell biology, their hypotheses about what they considered to be the particular the other from organic chemistry. atomic configuration at the sample’s surface. The two images In 1955, a paper with the rather cryptic title ‘‘A Small Particu- (the experimental and the theoretical) are then merged together, late Component of the Cytoplasm’’, by George Palade, was pub- so that they can be compared. This produces a third, hybrid image, lished (Palade, 1955). The paper describes a new structure containing both the visual information from the experimental im- identified in the cytoplasm via a careful and thorough use of the age and the hypothetical information from the theoretical image.

11 This does not mean that visual cultures cannot presuppose a broad style of reasoning as well. But as noted above, such a style tends not to illuminate specific details of scientific activity. O. Bueno / Studies in History and Philosophy of Science 43 (2012) 657–665 663

Once the hybrid image was obtained, it became clear that there If there were a method that could be applied to areas as diverse was a huge mismatch between the theoretical and the experimen- as quantum mechanics and pediatrics, it would be unable to pre- tal images: the correlation between the two images was only 62%. serve any specific features of these areas. Such a method would It was not strong enough. not contain any particular traits characteristic from such domains The researchers then returned to the theoretical image, and and would not be particularly relevant to these areas. In order for made a novel hypothesis. The phenomenon of surface reconstruc- a method to identify something general about both quantum tion—the difference between the packing arrangement in the crys- mechanics and pediatrics, it would need to operate at an extremely tal’s surface from the arrangement in the crystal’s interior—was high level of generality. As a result, nothing specific to either domain well known for inorganic crystals. The idea is clear: given that would be maintained, and more importantly, nothing specific about the surface molecules have incomplete bonds, and are in contact science rather than some empirically constrained area of inquiry with the environment, they tend to interact with it, thus changing (such as technology or organized crime) would be characterized. the packing arrangement. However, it was unknown whether that Consider, for instance, the extremely idealized model of scientific phenomenon was also found in organic crystals—the subject of the testing advanced by via modus tollens (Popper, 1959). investigation by the team. The researchers then changed the theo- On this model, in its most general version, to test a scientific theory retical image by incorporating the assumption that surface recon- one needs to draw implications from the theory and compare them struction took place. The result was a new theoretical image, which to experience. The theory is falsified in case the do not was then compared with the original experimental image, thus agree with the theory’s implications; otherwise the theory has not obtaining a second hybrid image. The correlation now between been falsified yet. At this level of generality, however, there is noth- the theoretical and the experimental images was 93%—a far more ing specific about science in such procedure, since technology and significant result. organized crime can both invoke the procedure as well. Here we also have a narrow style of reasoning at work. The do- We thus have a dilemma: either the alleged method is specific main of investigation focuses on properties of organic crystals at about a given scientific field or it is not (i.e. it is general). If the the nanoscale, and similarly to ribosome research, scientific imag- method is specific, then it is unable to unify the variety of areas ing tools play a crucial role. AFM images are invoked as inferential within science (such as quantum mechanics and pediatrics), since devices, but differently from the ribosome case, the inferences are being specific to an area it fails to address other areas. If the meth- not established directly based only on the reliability of the AFM. od is general, it is then unable to provide a unification of science The inferences emerge from the interaction of different versions rather than some other empirically constrained area of investiga- of theoretical images as they are contrasted with the empirical im- tion (such as technology or organized crime), since being general, age. At it is based on the correlation between such images that the the method can be applied beyond the boundaries of science. In intended phenomenon is described. A different style of reasoning, either case, the alleged method fails to provide the required unifi- based on a different way of using scientific images as inferential cation, and a form of methodological disunity emerges. devices, is then involved. (b) Ontological disunity: This is a more radical form of disunity, Note that Hacking’s broad style of reasoning would not be of according to which the world itself lacks unity: there is no overall much use to describe the differences between these two different unity across the various aspects of reality. If particle physics and laboratory sciences. As noted above, the three categories that form cell biology seem to be so different in what they posit, this is be- the laboratory sciences (ideas, things, and marks and their manip- cause the aspects of the world the relevant theories describe are ulation) are not components of the laboratory style of reasoning, fundamentally different. In fact, such aspects are so diverse that since ‘‘experimenters do not literally use’’ such styles of reasoning it should not be surprising why no overall account has managed (Hacking, 1992, p. 50). In contrast, experimenters do use narrow to reduce biology to physics; in fact, not even the reduction of biol- styles of reasoning (although they do not use the expression that ogy to chemistry seems to work. Given the ontological disunity— names such styles!). As a result, narrow styles can be used, as sug- the world itself lacks unity—this outcome is expected (see Dupré, gested above, to identify and illustrate salient differences within 1993, and Cartwright, 1999). experimenters’ practices. (c) Theoretical disunity: The disunity of science emerges from Visual cultures are not the only source of pluralism in which the disunity of the various theories invoked in scientific practice. styles of reasoning are relevant. Styles of reasoning are also signif- There is very little in common between different scientific fields. icant in debates about the disunity of science. I will turn to them As a result, very different theories, with very little in common, now. are advanced in different scientific fields. If we compare pediatrics and quantum mechanics, the kind of scientific theorizing that is in- 4.2. The disunity of science voked in each domain is fundamentally diverse: different concepts, different basic assumptions, and different theoretical components Those who defend disunity views often base their case on par- are invoked in each case. Given how different such fields are, it is ticular aspects of scientific practice. This, in turn, yields different not surprising that very little is shared, conceptually and theoreti- sorts of disunity. cally, between them.12 Moreover, there is no sense in which pediat- (a) Methodological disunity: According to this form of disunity, rics can be reduced to quantum mechanics—even granting that any there is no single method that unifies different scientific fields. such attempted reduction would never be implemented directly, Depending on the domain of science we consider, different meth- but would involve a variety of steps through many sub-disciplines. ods and research strategies are employed. For instance, in many However, it is not even clear exactly what would be gained by such areas of medicine, randomized clinical trials are crucial to provide reduction, given the difference in scale between such fields. For evidence for the relevant results. Such trials, however, are entirely these reasons, keeping them disunified makes sense. (For additional irrelevant to quantum mechanics. And although particle accelera- challenges faced by reductions in science, see Suppes, 1984, pp. 120– tors are central to the production of evidence in particle physics, 125, and Suppes, 2002, pp. 465–469.) they are irrelevant to research in ecology. Not surprisingly, no par- (d) Experimental disunity: There are a variety of experimental ticular method or research strategy unifies all scientific domains. practices across the sciences. Consider, on the one hand, natural

12 Of course, the differences also extend to ontological, methodological, experimental, and axiological features. But I am focusing on the theoretical aspects at this point. 664 O. Bueno / Studies in History and Philosophy of Science 43 (2012) 657–665 experiments in biology. These are naturally occurring events that, dence between theoretical considerations and their ontological im- with some , can be used to test particular biological port. In order to establish that no reduction of molecular biology to hypotheses. The burning of an isolated island may offer an oppor- quantum mechanics or of molecular biology to biochemistry ulti- tunity to test patterns of re-colonization of the island. On the other mately work, one needs to show that the alleged reduction rela- hand, consider extraordinarily complex experiments in particle tions among these domains fail. Careful consideration of the physics, in which every single aspect of the experiment requires proposed inferential connections between the relevant domains, detailed control, adjustment, computer simulations and calcula- as provided by narrow styles of reasoning, is then crucial. In this tions. The contrast between such experimental practices could way, narrow styles are invoked to motivate and support the result- hardly be more striking. It is, thus, not surprising that the resulting ing view. experimental fields are not unified. (For additional discussion, see The outcome of these considerations is indeed a form of plural- Hacking, 1992 and 1996.) ism and a corresponding lack of unity among various scientific (e) Axiological disunity: There are also different goals across sci- fields. Attention to the various narrow styles of reasoning that entific practice. In some cases, the aim is to register and formulate are invoked is central to this task. controlled statistical regularities; in others the aim is to determine At various points in my discussion of narrow styles, anti-realist measured outcomes; in yet others researchers strive to obtain clear moves have been made. Scientific theories have not been taken to images of the relevant phenomena. ’s well-known be true to be good, but empirically adequate only. A conception of distinction between two different traditions in microphysics—a lo- logical consequence that does not presuppose the truth of the gic tradition and an image tradition—clearly illustrates the differ- statements that are assessed has been suggested: it emphasizes ences between the goals of the corresponding researchers. The that the logical consequence relation is a modal notion that is former aims to provide clear statistical patterns among the phe- not spelled out in terms of truth or possible worlds. The plurality nomena under consideration, whereas the latter strives to produce of different styles has also been stressed without assigning a role the right picture that exhibits the relevant phenomena (see Gali- to the truth of the relevant components. These were theoretical son, 1997). The different goals support a lack of unity within the choices on my part, given assumptions I have made elsewhere, corresponding practices. and they yield an anti-realist form of narrow styles of reasoning. The diversity of methodological, theoretical, experimental, axi- Realists, however, need not make the same choices, and they ological, and ontological considerations supports a form of disunity can adjust narrow styles of reasoning to their preferred accounts. of the sciences that go hand in hand with narrow styles of reason- In particular, local forms of realism—about particular domains of ing. Clearly, the different methodological, theoretical, and experi- investigation in which successful instrumental access to an appro- mental considerations each presuppose particular inferential priate class of objects has been established—may mesh well with assumptions, which characterize, in part, a narrow style of reason- narrow styles of reasoning under a realist interpretation. But what- ing. And these assumptions are invoked in a variety of contexts. I ever interpretation is ultimately adopted, distinctive styles may will mention some examples as illustrations. help illuminate various aspects of scientific practice. In this case, Inferential assumptions are used in the implementation of par- realists and anti-realists can pursue together such domains, trying ticular methodological strategies. Consider, for instance, the intro- to understand and come to grips with, in their own terms, the rel- duction of placebo in medical research, and the associated evant inferential devices that are invoked by the narrow styles of inferential strategies to implement controlled trials (see de Craen, reasoning in question.13 Kaptchuk, Tijssen, & Kleijnen, 1999). Inferential assumptions are also employed in the construction 5. Conclusion: the scope of narrow styles of reasoning of theoretical explanations of empirical phenomena. As an example, consider the sort of reasoning invoked by Newton to support his I close with a methodological remark. As formulated here, nar- laws of motion, articulated in the suggestive idea of a deduction row styles of reasoning are clearly different from broad units of from the phenomena (see Smith, 2004, and Harper, 2004). analysis of scientific practice, such as Kuhn’s paradigms, Lakatos’ Inferential assumptions are similarly central to the conception, research programs, and Laudan’s research traditions. All of these execution, and evaluation of experiments. The case, mentioned units are, first, far broader in their scope than narrow styles of rea- above, of the discovery of surface reconstruction in organic crystals soning. Although Kuhn (1996) allows for somewhat more re- illustrates a style of reasoning in experimental research in which stricted paradigms, his unit of analysis tends to cover theoretical inferential assumptions are invoked to extract relevant informa- developments that encompass a very large range of phenomena, tion from the correlation between experimental and theoretical and which unfold over extended periods of time. Moreover, para- images. These assumptions play a key role in the characterization digms tend to have three main components: (a) certain goals and of the relevant experiment. With different assumptions, a different values, (b) a given group of methods, and (c) a determined class kind of experiment would be implemented. The contrast here be- of theories. In contrast, narrow styles of reasoning tend to be more tween the research on organic crystals and Palade’s work on ribo- focused in scope and, at least in same instances, they are not so somes is telling. stretched over time. This allows for considerations that are more Similar points apply to the various axiological considerations directly connected with specific developments in science, coming that are invoked across the sciences. Different goals pursued by dif- to grips with localized advances in particular domains, rather than ferent scientific communities, even within the same field, as illus- with broad traits of scientific change. trated by Galison’s logic and image traditions in microphysics, But perhaps a better candidate from Kuhn’s work in this context suggest that the disunity is widespread. The implementation of would be his use of ‘paradigm’ as referring to exemplars. Since the particular goals is achieved by the use of specific inferential de- exemplars are far more focused than the very broad conception vices in each case. Once again, narrow styles of reasoning are of paradigm just alluded to, they seem to provide precisely what relevant. narrow styles are expected to deliver. There is indeed much in Finally, even the more radical ontological disunity seems to rely common between exemplars and narrow styles. In particular, both on particular inferential devices to articulate the particular depen- provide focused, information-constrained policies of investigation

13 Consider, for instance, the different ways of making sense of instrumental access articulated by a realist (Azzouni, 2004) and an anti-realist (Bueno, 2011). O. Bueno / Studies in History and Philosophy of Science 43 (2012) 657–665 665 for a given domain. Narrow styles of reasoning, however, explicitly Bueno, O., & French, S. (2012). Can mathematics explain physical phenomena? focus on providing information transfer procedures (specific to British Journal for the Philosophy of Science, 63, 85–113. Bueno, O., & Shalkowski, S. (2009). Modalism and logical pluralism. Mind, 118, particular subfields) that allow for inferential relations to be estab- 295–321. lished within the domain of investigation. This is a distinctive fea- Cartwright, N. (1999). The dappled world: A study of the boundaries of science. ture of narrow styles. Cambridge: Cambridge University Press. Crombie, A. C. (1981). 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