Two Styles of Reasoning in Scientific Practices: Experimental and Mathematical Traditions

Abstract

This article outlines a philosophy of science in practice that focuses on the engineering sciences. A methodological issue is that these practices seem to be divided by two different styles of scientific reasoning, namely, causal-mechanistic and mathematical reasoning. These styles are philosophically characterized by what Kuhn called ‘disciplinary matrices’. Due to distinct metaphysical background pictures and/or distinct ideas of what counts as intelligible, they entail distinct ideas of the character of phenomena and what counts as a scientific explanation. It is argued that the two styles cannot be reduced to each other. At the same time, although they are incompatible, they must not be regarded as competing. Instead, they produce different kinds of epistemic results, which serve different kinds of epistemic functions. Moreover, some scientific breakthroughs essentially result from relating them. This view of complementary styles of scientific reasoning is supported by pluralism about metaphysical background pictures.

Acknowledgements

This research was supported by a grant from the Netherlands Organisation for Scientific Research (NWO Vidi grant). I would like to thank Henk Procee, Fokko-Jan Dijksterhuis, and James McAllister for their constructive contributions and critical comments. I would also like to thank the organization of the first biennial conference of the Society for the Philosophy of Science in Practice, SPSP2007, where this paper was presented.

Notes

The difference between Lynch's (1998) and Cartwright's (1999) metaphysical pluralism is that Lynch's pluralism is about our ways of conceptualizing, whereas Cartwright assumes that this plurality exists in the world, independent of us. Lynch's position is highly influenced by Kant's transcendental idealism (which is why he refers to his position as a relativistic Kantianism) and Putnam's (1981) internal realism.

Elsewhere, I follow Kant ([1787] 1998) in arguing that metaphysical background ideas are indispensable in doing science, but must be understood as regulative ideas that guide our epistemic activities, rather than claims about how the world really is independent of us (Boon forthcoming-b; also see Neiman 1994 and Chang 2009).

My view of phenomena differs from that of Bogen and Woodward (1988). With regard to the relation between phenomena and patterns of measured data, they propose that data play the role of evidence for the existence of phenomena. Moreover, data for the most part can be straightforwardly observed, whereas phenomena cannot. They defend the view that theories predict phenomena, whereas data typically cannot be predicted or systematically explained by theory. I agree that data can function as evidence for phenomena (although I disagree with their ontological interpretation of phenomena as pre-given independent entities ‘out there’). I also agree that theories (or scientific models) predict phenomena rather than data, as the latter are idiosyncratic to an experimental set-up. However, I dispute the claim that patterns of measured variables cannot be predicted or explained by scientific models. Moreover, although data are ‘straightforwardly observed’, patterns of measured variables are not. Finally, patterns of measured variables do not somehow coincide with, or represent, the physical phenomenon. For these reasons, I will also call the data pattern a phenomenon.

My position deviates from Giere's (2006) scientific perspectivism in the following sense. Giere assumes that different (instrumental and theoretical) perspectives coincide when it comes to the structure of the real objects. In contrast, my position is that we are intellectually capable of different ways of conceptually interpreting and structuring what we observe or measure (Boon 2009); distinct epistemic outcomes (such as laws and models) are held together by the real target system, which explains how it is possible that we are capable of relating them in our further epistemic activities.

Salmon's two examples and their scientific explanations are summarized as follows: (1) A balloon filled with helium will move forward in an airplane that accelerates rapidly for take-off because: (a) the sum of forces exerted on it will push it to the front, which is a causal explanation, or (b) according to Einstein's principle, acceleration is physically equivalent to a gravitational field, which is a fundamental or unification-type explanation. (2) The carriage with no brakes on the wheels, and which holds an actively pushing, pulling, rocking and bouncing baby, will not move away from its horizontal position on the floor because: (a) all of the forces exerted by the baby on the carriage, and the carriage on the baby, are cancelled out, which is a causal explanation, or (b) according to the law of conservation of linear momentum the system of the baby and the carriage is essentially isolated when the brake is off, which is an explanation in the unification sense, for it appeals directly to a fundamental law of nature.

Hacking (1983) articulated this distinction by distinguishing between realism about entities versus realism about laws. By arguing in favour of entity realism, and rejecting realism about laws, he exemplifies the point of view that adopting both is philosophically problematic. In current debate, the difficulty of accepting incompatible metaphysical ideas is illustrated in the controversy between realism about theoretical entities (Hacking 1983) and their capacities (Cartwright 1989) versus realism about abstract structures in the world, such as Worrall's (1989) structural realism. These competing versions of scientific realism seem to reflect the distinct metaphysical ideas of the two kinds of scientific approaches (experimental and mathematical) and the character of their typical epistemic results (e.g., causal-mechanistic and mathematical models) in current scientific practices. According to Worrall (1989), we should not accept standard scientific realism, which asserts that the nature of the unobservable objects that cause the phenomena we observe is correctly described by our best theories. However, neither should we be anti-realists about science. Rather, we should adopt structural realism and epistemically commit ourselves only to the mathematical or structural content of our theories. Surveys clarifying the debate on structural realism have been presented by Psillos (2000) and Ladyman (2008).

Hacking (1992, 56–57) defends the idea that coherence of elements that together constitute a laboratory science (namely, ‘ideas’, ‘things’, and ‘marks’) explains its stability. This idea can be understood as adding materiality to Kuhn's idea of disciplinary matrix, thus expanding on Kuhn's notion of ‘coherency within a disciplinary matrix’. I fully agree that instruments and experiments also must be ‘matched-in’. However, I disagree with the suggestion that a laboratory science is one self-vindicated whole. Conversely, I defend the view that a scientific practice may incorporate incompatible descriptions of phenomena, laws, models and theories, which are coherently constructed within the confines of a specific disciplinary matrix (or style of reasoning and conceptual scheme), and which may function in complementary ways within one practice. This account explains better than Hacking's, how it is possible that practices evolve due to vivid exchange with other practices, as in the case of biotechnology and nanotechnology.

In this article, I utilize two accounts of causal interaction: (1) Woodward's (2003a) manipulationist theory of causal interaction which accounts for the cause-effect relationship that (may) result from interventions (e.g. in experiments); and (2) Cartwright's (1989) notion of capacities and tendencies, which are properties—however, not the ‘essential’ or ‘primary’ properties that characterize a specific type of object, but properties that (only) exert themselves under specific physical conditions. An example is oxygen, which has the capacity of oxidizing iron. This capacity only manifests itself at a sufficiently high temperature, etc. Another example is gold, which has the capacity of being red. This capacity only manifests itself in nano-sized gold particles, etc.

The debate about phenomena and data between Bogen and Woodward (1988), McAllister (1997) and Glymour (2000) considers whether the distinction between phenomena and patterns of data proposed by Bogen and Woodward can be maintained while it is held that descriptions of phenomena do not involve theoretical interpretation (phenomena as mini-theories). McAllister denies that this view can be coherently defended, while Glymour denies that phenomena add anything to data. I agree with Bogen and Woodward that a distinction between (in my terms) patterns of measured variables and phenomena is important. At the same time, I deny their ontological interpretation and argue that phenomenological descriptions of physical and mathematical phenomena involve ‘non-trivial’ theoretical interpretations (see also note 3 above).

This so-called positivistic interpretation of Newton, according to which Newton's introduction of the notion of force was primarily a mathematically defined concept rather than a physical concept, has been abandoned by most historians of science (personal communication from Steffen Ducheyne; see also Ducheyne 2007; Janiak 2007). Nevertheless, my understanding of Newton's abstract fundamental theory as a mathematical framework within which mathematically constructed phenomena of specific types of target systems (e.g. Newtonian systems; also see Giere 1988, 2006) can be interpreted, is a philosophical view rather than a historical claim about what Newton actually believed. In other words, my philosophical point (which will be explained in more depth elsewhere) is that Newton's theory of motion can be understood as an abstract mathematical theory that enables us to account for mathematical patterns of observed or measured data produced by target systems of a specific type, similar to how Euclidean geometry is employed in discerning and accounting for geometrically constructed phenomena. Subsequently, a physical interpretation of ‘force’ enables us to relate this mathematical approach to physical, causal-mechanistic approaches.

Again, this is not a historical claim. The philosophical crux is that mathematical ways of thinking about a target system can in principle occur independently from physical ways of thinking about it. In that case, thinking about the target system abstracts from physical interpretations; it is conceptually understood as a mathematical system.

Additional information

Notes on contributors

Mieke Boon

Mieke Boon is at the Department of Philosophy, University of Twente.