Abstract
Our concern is to explain how and why models give us useful knowledge. We argue that if we are to understand how models function in the actual scientific practice the representational approach to models proves either misleading or too minimal—depending on how representation is defined. By ‘representational approach’ we mean one that attributes the epistemic value of models to the representational relationship between a model and some real target system. In contrast we propose turning from the representational approach to the artefactual, which also implies a new unit of analysis: the activity of modelling. Modelling, we suggest, could fruitfully be approached as a scientific practice in which concrete artefacts, i.e., models, are constructed with specific representational means and used in various ways, for example, for the purposes of scientific reasoning, theory construction and design of experiments and other artefacts. Furthermore, we propose that in the activity of modelling the construction of models is intertwined with the construction of new phenomena, concepts, and theoretical principles. We will illustrate these claims by studying the construction of the ideal heat engine by Sadi Carnot.
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Notes
We take it that like scientific models philosophical accounts are also constructed for certain purposes. Accordingly, from our perspective, the conception of models as epistemic tools aims to be a useful tool itself — for the philosophical purpose of finding out how models and modelling give us knowledge.
Representation appears as an activity, too. But then representation is approached differently than from the traditional representational perspective. It does not boil down to a relationship between a model and a target system, but rather refers to a practice that conveys some epistemic content through the use of some external representational means and relevant conventions stipulating their uses. This perspective to representation can be accommodated by some pragmatic approaches to representation; see especially Suárez (2010) and van Fraassen (2008).
Some other pragmatically inclined philosophers of science have tried to overcome this deflationary nature of the pragmatist accounts by adding to their analysis of representation a further stipulation concerning its success. Rather unsurprisingly, then, what was previously presented as an analysis of the representational relationship, i.e., structural relations (van Fraassen 2008) or similarity (Giere 2010), is now suggested as a kind of success criterion. As argued above, morphisms pose too stringent conditions on the success of representation in the light of scientific practice. The case of similarity is trickier. On the one hand, it does not really supply any user-independent success criterion in that it is the users who identify the “relevant respects and sufficient degrees” of similarity. Giere (2010) admits this, arguing that the agent-based approach “legitimates using similarity as the basic relationship between models and the world”.
We actually think that the pragmatic accounts of representation can also accommodate this dimension of model-use, although so far they have not really addressed the dynamics of model building. We thank the anonymous referee for pointing this out for us.
In scientific practice, model-construction and model-use are intertwined because scientific models are typically evolving objects.
In this respect our approach comes close to Mattila’s work on simulation models as “artificial nature”, which is constructed to answer some pertinent scientific questions (Mattila 2006).
An animation that represents the mechanical working of a specific type of heat engine (the Newcomen steam engine) can be found under this link: http://en.wikipedia.org/wiki/Newcomen_steam_engine
Kuhn (1958) argues that Carnot followed Poisson who took from the caloric theory only the hypothesis that the heat content of a gas is a state function (which means that the heat content of an amount of gas is fully determined by the pressure and the temperature of the gas), and further, that at fixed pressure the caloric content is proportional to volume. Accordingly, Poisson developed a formula for the dependence of heat capacity on pressure. These assumptions and formula enabled Carnot to carry out calculations in the empirical part of his Reflexions (starting on ibid., p. 78).
This concept of caloric is enriched with the idea that temperature is the density of caloric. In a further theoretical elaboration, it was postulated that caloric exists in two different states: sensible and latent. In its free state, caloric was conceived of as sensible, being able to affect the thermometer and our senses, whereas in its latent state, caloric is combined with matter and deprived of its characteristic repulsive force, thus being unable to effect the expansion of thermometric substances. This refinement of the caloric theory allowed for explaining e.g., that addition or withdrawal of (latent) heat causes a change of state (e.g., melting, freezing, boiling, condensation, etc.) without a change of temperature (cf. Chang 2003 and 2004).
It must be noted that Carnot’s presupposition of the conservation of heat was in accordance with the caloric theory of heat of his days. Later on, it was replaced by the idea of the conservation of energy (which is the first law of thermodynamics) in the work of his successors such as Thomson (also see Chang 2004).
One should keep in mind that the measurements of several variables crucial to Carnot’s model, such as temperature and (latent) heat, were not at all straightforward. Chang (2004) argues that the measurement and the conception of temperature had not been established in those days. On the contrary, Carnot’s ideal heat engine played an important role in conceptualizing absolute temperature and its operationalization.
This experiential fact describes the so-called adiabatic heating and cooling. This phenomenon could very well have been taken as a counter-example to the theoretical idea that work cannot produce heat—an idea central to the caloric theory of heat. For, the sensible rise of temperature of a gas during compression suggests that heat is produced by expending power. Nevertheless, this phenomenon was (or has been brought) in accordance with the caloric theory by the distinction between sensible and latent caloric (see also former notes). Laplace, for instance, explained adiabatic heating and cooling by assuming that some quantity of latent heat is released when compressing the gas, producing an increased density of free (sensible) caloric that causes an increase of the temperature (see Kuhn 1958; Mendoza 1961; Chang 2003). This refined conception of caloric may also back-up the theoretical principle g.
Clearly, the transfer of heat could not be measured directly. In his actual calculations, Carnot argues: “As for the heat which is used—that is, the heat transferred from A to B—this quantity is clearly that which is required to convert the water into steam…” (ibid., p. 98). Note that the calculation of the efficiency in modern thermodynamics—which has abandoned the caloric theory of heat—uses the consumption of heat (i.e., the difference between the amount of heat entering and leaving the device) rather that the amount of heat that is transferred from body A to B.
This figure presents a well-known modern conception of the Carnot engine, which is based on the conservation of energy rather than heat. It uses representational tools, such as the P-V diagram, that were only developed by Carnot’s successors.
Chang (2004) shows that the modern definition and measurement of temperature had not been settled in Carnot’s days. What is more, establishing the measurement of temperature meets many, often entangled, practical and theoretical challenges with the result that the development of the definition and measurement of temperature has been inextricably intertwined with the development of thermodynamics. Significant to our case is how Thomson initially used Carnot’s conception of the ideal heat engine to define the interval of one degree of temperature (i.e., “absolute temperature”) as the amount that would result in the production of a unit amount of mechanical work in a Carnot engine operating in that temperature interval (Chang 2004, 182). Besides the fact that the ideal heat engine could not easily be operationalized, this idea was abandoned when Carnot’s basic assumption concerning the conservation of the heat was rejected.
Next, Carnot aimed to examine whether the fall of caloric from 1000 to 500 yields more or less motive power than the fall of the same amount of caloric from 500 to 00, i.e., whether motive power is proportional to the difference in temperature.
The difficulty of using these properties of gasses was that it had been shown in measurements that they were not constants, but seemed to be affected by the temperature and the pressure of the gas. It was not theoretically understood whether and how the value of these properties depended on these variables. Carnot’s reasoning in this part of the Reflexions is sometimes obscure and even incoherent. It not only involves empirical data and insights arrived at by the model, but also aspects of the caloric theory of heat that he usually does not spell out. Taking into account the reconstruction of the caloric theory that could back up his reasoning (see former notes) hardly makes it more intelligible. Fox (in Carnot 1986 [1824], 26) argues that Carnot, while working on his Reflexions, seemed to change his conception of heat from a caloric theory to the idea that “Heat is nothing but motive power”. In other words, Carnot’s conception of heat shifted from a caloric theory according to which heat is material (and in which heat is a conserved quantity that cannot be produced or consumed), to a dynamic theory according to which heat is a mode of motion (and where heat is no longer a conserved quantity but can be produced or consumed, e.g., by expending or producing motive power). This may explain the sometimes inimitable manner in which Carnot reasons towards his conclusions in the last part of Reflexions.
We wish to thank anonymous referee for stressing this point.
The notion of ”epistemic motivation” comes from Isabelle Peschard (forthcoming).
The recent developments of the pragmatics of scientific representation are indeed in line with our account of models as epistemic tools. Giere (2006) and van Fraassen (2008) have pointed out the importance of the creation of phenomena as a part of their pragmatic approaches to representation. Suárez (2010, 98), in turn, stresses that “representational force” is always a feature of an “evolving practice”. This seems to fit together with our stress on how the eventual (and evolving) representational properties of a model can be ascribed to its construction process.
One reading of the representational account of models, in line with the semantic version of it, is that the analysis of representation does not even try to explain how models give us knowledge but rather functions as a justificatory account. Thus, on that account, the analysis of representation is supposed to give us a criterion for the success of the model. From our perspective the semantic account does not fare well even in this respect because the justification of a model gets largely built into it in the process of modelling. In this process the model is not just justified by the initial justification its ingredients might have, but also through the new theoretical and conceptual content born in the process of modelling.
References
Ambrosio, C. (2007). Iconicity and network thinking in Picasso’s Guernica: A study of creativity across the boundaries. Unpublished PhD thesis, University College London.
Bailer-Jones, D. M. (1999). Tracing the development of models in the philosophy of science. In L. Magnani, N. J. Nersessian, & P. Thagard (Eds.), Model-based reasoning in scientific discovery (pp. 23–40). New York: Kluwer.
Bailer-Jones, D. M. (2003). When scientific models represent. International Studies in the Philosophy of Science, 17, 59–74.
Bailer-Jones, D. M. (2009). Scientific models in philosophy of science. Pittsburgh: University of Pittsburgh Press.
Bartels, A. (2006). Defending the structural concept of representation. Theoria, 55, 7–19.
Boon, M. (2006). How science is applied in technology. International Studies in the Philosophy of Science, 20(1), 27–47.
Boon, M. (2011). In Defence of the engineering sciences: On the epistemological relations between science and technology. Techné: Research in Philosophy and Technology., 15(1), 49–71.
Boon, M., & Knuuttila, T. (2009). Models as epistemic tools in engineering sciences: A pragmatic approach. In A. Meijers (Ed.), Handbook of the philosophy of technological sciences (pp. 687–719). Amsterdam: Elsevier Science.
Boumans, M. (1999). Built-in justification. In M. S. Morgan & M. Morrison (Eds.), Models as mediators. Perspectives on natural and social science (pp. 66–96). Cambridge: Cambridge University Press.
Carnot, S. (1986 [1824]). Reflexions on the motive power of fire, translated and edited by Robert Fox. New York: Manchester University Press.
Chang, H. (2003). Preservative realism and its discontents: Revisiting caloric. Philosophy of Science, 70, 902–912.
Chang, H. (2004). Inventing temperature: Measurement and scientific progress. Oxford University Press.
Clark, A. (1997). Being there: Putting the brain, body, and world together again. Cambridge, MA: MIT Press.
Clausius, R. (1865). The mechanical theory of heat—with its applications to the steam engine and to physical properties of bodies. London: John van Voorst, 1 Paternoster Row. MDCCCLXVII.
Clausius, R. (1899 [1850]). On the motive power of heat, and on the laws which can be deduced from it for the theory of heat. In The second law of thermodynamic. Memoirs by Carnot, Clausius and Thomson. New York and London: Harper & Brothers Publishers.
Contessa, G. (2007). Representation, interpretation, and surrogative reasoning. Philosophy of Science, 71, 48–68.
da Costa, N. C. A., & French, S. (2000). Models, theories and structures: Thirty years on. Philosophy of Science, 67, S116–127.
Dalton, J. (1842). A new system of chemical philosophy, Part 1 (2nd ed.). London: John Weale, Architectural Library, High Holborn.
French, S. (2003). A model-theoretic account of representation (or, i don’t know much about art…but i know it involves isomorphism). Philosophy of Science, 70, 1472–1483.
French, S., & Ladyman, J. (1999). Reinflating the semantic approach. International Studies in the Philosophy of Science, 13, 103–121.
Frigg, R. (2002). Models and representation: Why structures are not enough. Measurement in Physics and Economics Project Discussion Paper Series, DP MEAS 25/02. London: London School of Economics.
Frigg, R. (2006). Scientific representation and the semantic view of theories. Theoria, 55, 49–65.
Giere, R. N. (1988). Explaining science: A cognitive approach. Chicago and London: The University of Chicago Press.
Giere, R. N. (2004). How models are used to represent reality. Philosophy of Science, 71, 742–752.
Giere, R. N. (2006). Scientific perspectivism. Chicago: The University of Chicago Press.
Giere, R. N. (2010). An agent-based conception of models and scientific representation. Synthese, 172, 269–281.
Godfrey-Smith, P. (2006). The strategy of model-based science. Biology and Philosophy, 21, 725–740.
Hughes, R. I. G. (1997). Models and representation. Philosophy of Science, 64, S325–S336.
Knuuttila, T. (2005). Models, representation, and mediation. Philosophy of Science, 72, 1260–1271.
Knuuttila, T. (2011). Modelling and representing: An artefactual approach to model-based representation. Studies in the History and Philosophy of Science, 42(2), 262–271.
Knuuttila, T., & Merz, M. (2009). An objectual approach to scientific understanding: The case of models. In H. W. de Regt, S. Leonelli, & K. Eigner (Eds.), Scientific understanding: Philosophical perspectives (pp. 146–168). Pittsburgh: University of Pittsburgh Press.
Knuuttila, T., & Voutilainen, A. (2003). A parser as an epistemic artefact: A material view on models. Philosophy of Science, 70, 1484–1495.
Kress, G., & van Leeuwen, T. (2001). Multimodal discourse: The modes and media of contemporary communication. London: Arnold.
Kuhn, T. S. (1958). The caloric theory of adiabatic compression. Isis, 49(2), 132–140.
Larkin, J. H., & Simon, H. A. (1987). Why a diagram is (sometimes) worth 10,000 words. Cognitive Science, 11, 65–99.
Mäki, U. (2009). Missing the world: Models as isolations and credible surrogate systems. Erkenntnis, 70, 29–43.
Massimi, M. (2008). Why there are no ready-made phenomena: What philosophers of science should learn from Kant. Royal Institute of Philosophy Supplement, 83(63), 1–35.
Mattila, E. (2006). Questions to artificial nature: A philosophical study of interdisciplinary models and their functions in scientific practice. Philosophical studies from the University of Helsinki, 14. Helsinki: University of Helsinki.
Mendoza, E. (1961). A sketch for a history of early thermodynamics. Physics Today, 14(2), 32–42.
Morrison, M., & Morgan, M. S. (1999). Models as mediating instruments. In M. S. Morgan & M. Morrison (Eds.), Models as mediators. Perspectives on natural and social science (pp. 10–37). Cambridge: Cambridge University Press.
Peschard, I. (2011). Making sense of modeling: Beyond representation. European Journal for Philosophy of Science.
Peschard, I. (forthcoming).In S. Vaienti (Ed.) Is simulation an epistemic substitute for experimentation? To appear in Simulations and Networks. Paris: Hermann.
Sterelny, K. (2004). Externalism, epistemic artefacts and the extended mind. In ed. R. Schantz (Ed.), The externalist challenge. New studies on cognition and intentionality (pp. 239–254). Berlin & New York: de Gruyter.
Suárez, M. (1999). Theories, models, and representations. In L. Magnani, N. J. Nersessian, & P. Thagard (Eds.), Model-based reasoning in scientific discovery (pp. 75–83). New York: Kluwer.
Suárez, M. (2003). Scientific representation: Against similarity and isomorphism. International Studies in the Philosophy of Science, 17, 225–244.
Suárez, M. (2004). An inferential conception of scientific representation. Philosophy of Science, 71, 767–779.
Suárez, M. (2008). Scientific fictions as rules of inference. In M. Suárez (Ed.), Fictions in science: Philosophical essays on modeling and idealization (pp. 158–178). London & New York: Routledge.
Suárez, M. (2010). Scientific representation. Blackwell’s Philosophy Compass, 5, 91–101.
Suppe, F. (1974). The structure of scientific theories. Urbana: University of Illinois Press.
Suppe, F. (1989). The semantic conception of theories and scientific realism. Urbana and Chicago: University of Illinois Press.
Van Fraassen, Bas. (1980). The scientific image. Oxford: Oxford University Press.
Van Fraassen, Bas. (2008). Scientific representation: Paradoxes of perspective. Oxford: Oxford University Press.
Vorms, M. (2011). In P. Humphreys, & Imbert C. (Eds.), Formats of representation in scientific theorising. To appear in representations, models, and simulations. Routledge.
Weisberg, M. (2007). Who is a modeler. British Journal for the Philosophy of Science, 58, 207–233.
Zhang, J. (1997). The nature of external representations in problem solving. Cognitive Science, 21, 179–217.
Acknowledgements
We wish to thank Marcel Boumans, Hasok Chang and two anonymous referees for their constructive comments on the earlier drafts of this paper. This research was supported by the Academy of Finland and the Dutch National Science Foundation (NWO).
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Knuuttila, T., Boon, M. How do models give us knowledge? The case of Carnot’s ideal heat engine. Euro Jnl Phil Sci 1, 309 (2011). https://doi.org/10.1007/s13194-011-0029-3
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DOI: https://doi.org/10.1007/s13194-011-0029-3