Abstract
It is often claimed that scientists can obtain new knowledge about nature by running computer simulations. How is this possible? I answer this question by arguing that computer simulations are arguments. This view parallels Norton’s argument view about thought experiments. I show that computer simulations can be reconstructed as arguments that fully capture the epistemic power of the simulations. Assuming the extended mind hypothesis, I furthermore argue that running the computer simulation is to execute the reconstructing argument. I discuss some objections and reject the view that computer simulations produce knowledge because they are experiments. I conclude by comparing thought experiments and computer simulations, assuming that both are arguments.
Similar content being viewed by others
Notes
That thought experiments can produce new knowledge is the majority view in the philosophical literature; see e.g. Gendler (2004), p. 1153 and Cooper (2005), p. 328. A dissenting voice is Atkinson and Peijnenburg (2004). Moue et al. (2006) and Brown and Fehige (2010) review the current philosophical research literature about scientific thought experiments, see also Kühne (2005).
Cf. Frigg and Reiss (2009), p. 596 for a similar distinction.
For instance, Humphreys (2004), p. 71 draws a comparison between argument schemes and what he calls computational templates.
Galileo’s TE can be found in Galilei (1933), Vol. VIII, 107–109 (see Galilei 1974 for a translation into English); see Brown (1991), p. 43, Norton (1996), pp. 340–345, Gendler (1998), Atkinson and Peijnenburg (2004), McAllister (2004) and Kühne (2005), pp. 41–57 for the philosophical discussion about Galileo’s TE. See Brown (1991), pp. 3–6 and Norton (1996), pp. 349–351 for Stevin’s TE. For philosophical thought experiments see e.g. Cohnitz (2006).
Here the “context of discovery” has to be taken with some grain of salt. The context of discovery concerns what is done when a TE is run. It is not about the construction and first discovery of a TE. Norton’s argument does not say much about the construction of TEs. In this paper, I understand “context of discovery” in the sense in which Norton uses the term.
But can we really gain new knowledge by running through an argument? Some might want to deny this because the conclusion of the argument was already entailed or supported by prior knowledge. If knowledge is closed under deduction and under sound inductive argument, we cannot obtain new knowledge by going through an argument. But the assumption that knowledge is closed in this way is not very plausible to begin with, and when we run through a sound argument, the conclusion can at least be new in the sense that we did not believe it before. If this psychological sense of novelty is not sufficient at this point, it should be pointed out what the stronger sense of novelty is and why thought experiments provide new knowledge in this stronger sense (cf. Norton 1996, p. 346).
Such TEs include Newton’s bucket experiment, Stevin’s thought experiment (ibid., pp. 347–351) and an argument concerning the continuum hypothesis (see Norton 2004a, pp. 1147–1148).
Very briefly, my own view is as follows: I agree with Norton that TEs can be reconstructed as arguments in some way. But it is naïve to think that we reason from the premises to the conclusion of this argument when we conduct a thought experiment on our own (i.e., if we think what may happen in a certain counterfactual scenario as pictured by a TE). At least in some kinds of TEs, we “know” more intuitively what will happen. This point has implications for both the context of justification and the context of discovery.
Cf. Weisberg (2007)
Checked 12/2011
Balzer (2009), p. 324 assumes likewise that the inputs to, and the outputs of, simulations can be represented as sentences. –Since my example is from physics, I am speaking of physical characteristics such as mass etc. But nothing hinges on the characteristics being from physics, and in other examples we would be concerned with chemical characteristics etc.
By stressing the empirical significance of the premises I do not mean to exclude statements about unobservables and their characteristics (provided we can refer to unobservables). Rather, what I call “empirical meaning” has to extend beyond purely mathematical significance and to refer to concrete systems in some however indirect way.
I take the notion of an argument scheme from Kitcher (1981), Section 5.
Note that we cannot generalize our initial reconstructing argument by quantifying over p and C in each premise. It is important that we first fix one system and coordinates and then go through the whole argument.
See Press et al. (2007), Section 1.1 for an introduction.
See e.g. Press et al. (2007), Section 1.1 again.
See Press et al. (2007), p. 10 for an estimate.
She will not even think that the original differential equations are literally true of the target because they rest upon idealizations. For the time being, I will bracket this fact, and return to it later on page 24.
Approximation errors quantify the differences between the solutions to the difference equations and to the exact differential equations.
See Press et al. (2007), p. 11 for this interaction.
See e.g. Kronsjö (1979), pp. 1–2 for a definition of algorithms.
As every utterance, the statement of results from simulations is subject to rules of pragmatics; see e.g. Grice (1989) for such rules.
D does not imply that the reconstructing argument itself is dispensable. Also, the use of the computer is only dispensable in principle, but not in practice: Many epistemic tasks cannot be completed without computers in practice. As Humphreys (2004, Section 5.5; 2009, pp. 623–624) and Winsberg (2010), p. 5 point out, the perspective of what is possible in principle is often not relevant in the philosophy of science; and to the extent to which the perspective is irrelevant, D is not applicable.
If we executed the reconstructed argument accurately, we would not obtain the values that the computer outputs, but values that do not suffer from any roundoff errors. That our values differ from the output by the computer does not pose any problem; for epistemological purposes, the simulation becomes certainly dispensable.
Some simulation scientists, e.g. Oberkampf and Roy (2010), Chs. 10–11 recommend that validation include certain experiments, which they call validation experiments. Clearly, such experiments are not merely inferences. But if such experiments are run, it is not very plausible to take them to be literal part of a computer simulation study.
This is a term that is introduced in CSs based upon the Navier-Stokes equations to smooth out shocks. Without eddy viscosity, the simulations can be caught in numerical problems. See e.g. Winsberg (2010), pp. 13–15.
See page 13 above.
An argument with false premises and conclusions can of course generate new knowledge if the conclusion is known to be false and used to reject the premises. But we are here concerned with a different case; we refer to arguments the premises and conclusions of which are obviously wrong, e.g. because they assume the wrong type of ontology. Also, the focus of this paper is on simulations the results or conclusions of which produce new knowledge.
According to Weisberg (2007), the analysis of a model is a crucial step in modeling.
For other very interesting reflections about reasoning see Grice (2001).
Reasoning can also lead one to abandon a mental state, but we can safely bracket this case for our purposes.
Wedgwood only introduces basic steps of reasoning to exclude external deviant causal chains (ibid., pp. 660–665). I do not think it to be absolutely necessary that the steps are “atomic” in that no analysis into other steps of reasoning is possible. We have only to guarantee that the basic steps entirely belong to the cognitive system. If this is right, it is immaterial whether the basic steps are “atomic” or not.
In this way, we obtain an argument in which the algorithm corresponds to many premises. I have suggested on p. 20 that we can always unpack the algorithm into a larger number of assumptions or premises.
One may object that Wedgwood (2006) take pains to isolate the reasoner from her environment in order to rule out external deviant causal chains (ibid., pp. 665–666). This may suggest that Wedgwood’s account is only applicable to human reasoners. I do not agree with this objection. What Wedgwood has to achieve if the account is to work, is to isolate the cognitive system that is the bearer of some chain of reasoning. If the extended mind thesis is true, then cognitive systems may extend beyond a human being.
Recall page 19.
See the quotation on my page 8 above.
E.g. Gendler (2004), p. 1154.
Recall Humphreys’s point that CSs are the modern successors of TEs (see my page 2 above and Humphreys 2004, p. 115).
Cf. the discussion about Galileo’s TE with the falling bodies; see e.g. Atkinson and Peijnenburg (2004).
See Fine (2009) and references therein for philosophical discussion about the EPR argument.
Cf. Lenhard and Winsberg (2010).
Explanations are arguments according to the DN-model of explanation (Hempel and Oppenheim 1948). Even though many objections have been levelled against the DN-model (see Salmon 1989, particularly pp. 46–50, for an overview), most of them do not cast doubts on the idea that explanations are arguments. That explanations provide arguments is also important for e.g. the unificationist view of explanation (see Friedman 1974 and Kitcher 1981 for classic references).
See Friedman (1974) for the connection between explanation and understanding.
Cf. Suárez (2004)
The paper by Barberousse et al. (2009) has a lot to say about the process of running simulations, but it does not end up with a clear statement about how this process produces knowledge.
References
Atkinson, D., & Peijnenburg, J. (2004). Galileo and prior philosophy. Studies in History and Philosophy of Science, 35, 115–136.
Bailer-Jones, D. M. (2003). When scientic models represent. International Studies in the Philosophy of Science, 17, 59–75.
Balzer, W. (2009). Die Wissenschaft und ihre M ethoden (2nd ed.). Karl Alber, Freiburg und München.
Barberousse, A., Franceschelli, S., & Imbert, C. (2009). Computer simulations as experiments. Synthese, 169, 557–574.
Bartuccelli, M. V., Gentile, G., & Georgiou, K. (2001). On the dynamics of a vertically-driven damped planar pendulum. Proceedings of the Royal Society of London, Series A, 457, 1–16.
Bertschinger, E. (1998). Simulations of structure formation in the universe. Annual Review of Astronomy and Astrophysics, 36, 599–654.
Bishop, M. A. (1999). Why thought experiments are not arguments. Philosophy of Science, 66, 543–541.
Brown, J. R., & Fehige, Y. (2010). Thought experiments. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (winter 2010 ed.).
Brown, J. R. (1991). The laboratory of the mind: Thought experiments in the natural sciences. Routledge, London.
Brown, J. R. (2004). Peeking into Plato’s haeven. Philosophy of Science, 71, 1126–1138.
Clark, A. (2007). Curing cognitive hiccups: A defense of the extended mind. Journal of Philosophy, 104, 163–192.
Clark, A., & Chalmers, D. J. (1998). The extended mind. Analysis, 58(1), 7–19.
Cohnitz, D. (2006). Gedankenexperimente in der Philosophie. Mentis, Paderborn.
Cooper, R. (2005). Thought experiments. Metaphilosophy, 3, 328–347.
Dolag, K., Borgani, S., Schindler, S., Diaferio, A., & Bykov, A. M. (2008). Simulation techniques for cosmological simulations. Space Science Reviews, 134, 229–268. Preprint under 0801.1023v1.
Efstathiou, G., Davis, M., White, S. D. M., & Frenk, C. S. (1985). Numerical techniques for large cosmological N-body simulations. Astrophysical Journal Supplement Series, 57, 241–260.
Einstein, A., Podolsky, B., & Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete? Physical Review, 47, 777–780.
Einstein, A. (1961). Relativity, the special and the g eneral theory. A popular e xposition. Methuen, London, 1920, here quoted after edition published by Crown, New York.
Fine, A. (2009). The Einstein-Podolsky-Rosen argument in quantum theory. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Fall 2009 ed.). http://plato.stanford.edu/archives/fall2009/entries/qt-epr/.
Frankfurt, H. G. (1978). The problem of action. American Philosophical Quarterly, 15, 157–62.
Friedman, M. (1974). Explanation and scientific understanding. Journal of Philosophy, 71, 5–19.
Frigg, R. P., & Reiss, J. (2009). The philosophy of simulation: Hot new issues or same old stew? Synthese, 169, 593–613.
Frigg, R. P., Hartmann, S., & Imbert, C. (Eds.) (2009). Models and simulations. Special Issue. Synthese (Vol. 169, pp. 425–626).
Frigg, R. P., Hartmann, S., & Imbert, C. (Eds.) (2011). Models and simulations 2. Special Issue. Synthese (Vol. 180, pp. 1–77).
Galilei, G. (1933). Le Opere di G alileo Galilei. Florence: G. Barbèra.
Galilei, G. (1974). Two new sciences. Translation by S. Drake. Madison (WI): University of Wisconsin Press.
Galison, P. (1996). Computer simulations and the trading zone. In P. Galison & D. J. Stump (Eds.), The disunity of science. Boundaries, contexts, and power (pp. 118–157). Stanford: Stanford University Press.
Galison, P. (1997). Image and logic. A materical culture of microphysics. Chicago: University of Chicago Press.
Gendler, T. S. (1998). Galileo and the indispensability of scientific thought experiment. British Journal for the Philosophy of Science, 49, 397–424.
Gendler, T. S. (2000). Thought experiment. O n the powers and l imits of imaginary c ases. New York: Garland Publishing.
Gendler, T. S. (2004). Thought experiments rethought and reperceived. Philosophy of Science, 71, 1152–1163.
Giere, R. N. (2004). How models are used to represent. Philosophy of Science, 71, 742–752.
Giere, R. N. (2009). Is computer simulation changing the face of experimentation? Philosophical Studies, 143(1), 59–62.
Gillespie, D. T. (1976). A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. Journal of Computational Physics, 22, 403–434.
Gillespie, D. T. (1977). Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry, 81, 2340–2361.
Gramelsberger, G. (2010). Computerexperimente. Zum W andel der Wissenschaft im Z eitalter des Computers. Transcript, Bielefeld.
Gramelsberger, G. (2011a). Generation of evidence in simulation runs: Interlinking with models for predicting weather and climate change. Simulation & Gaming, 42(2), 212–224.
Gramelsberger, G. (2011b). What do numerical (climate) models really represent?. Studies in History and Philosophy of Science, Part A 42, 296–302. Model-Based Representation in Scientific Practice.
Grice, P. (1989). Logic and conversation. In H. P. Grice (Ed.), Studies in the ways of w ords (pp. 1–143). Cambridge, MA: Harvard University Press.
Grice, P. (2001). Aspects of reason. Oxford: Oxford University Press.
Grüne-Yanoff, T. (2009). The explanatory potential of artificial societies. Synthese, 169, 539–555.
Hartmann, S. (1996). The world as a process: Simulations in the natural and social sciences. In R. Hegselmann, K. G. Troitzsch, & U. Mueller (Eds.), Modelling and simulation in the social sciences from the philosophy of science point of view (pp. 77–100). Dordrecht: Kluwer. Quoted from the revised version at http://philsci-archive.pitt.edu/archive/00002412/.
Hempel, C. G., & Oppenheim, P. (1948). Studies in the logic of explanation. Philosophy of Science, 15, 135–175.
Hockney, R. W., & Eastwood, J. W. (1988). Computer simulation using particles (special student ed.). ed., Adam Hilger, Bristol etc.
Humphreys, P. (1990). Computer simulations. In PSA: Proceedings of the biennial meeting of the philosophy of science association 1990 (pp. 497–506) (English).
Humphreys, P. (2004). Extending ourselves: C omputational science, e mpiricism, and scientific m ethod. New York: Oxford University Press.
Humphreys, P. (2009). The philosophical novelty of computer simulation methods, Synthese, 169, 615–626.
Irvine, A. D. (1991). Thought experiments in scientific reasoning. In: T. Horowitz & G. J. Massey (Eds.), Thought experiments in science and philosophy (pp. 149–165). Savage, MD: Rowman and Littlefield.
Kitcher, P. (1981). Explanatory unification. Philosophy of Science, 48, 507–531.
Klypin, A. (2000). Numerical simulations in cosmology I: Methods. astro-ph/0005502.
Kronsjö, L. (1979). Algorithms: Their c omplexity and efficiency. Chichester: Wiley.
Kuhn, T. S. (1964). A function for thought experiments. In L’Aventure de la S cience, Mé langes Alexandre K oyré, Hermann, Paris (Vol. 2). (Reprinted in Kuhn, T. S., The Essential Tension: Selected Studies in Scientific Tradition and Change. Chicago: University of Chicago Press, 1977, pp. 240–265, 307–334).
Kühne, U. (2005). Die Methode des G edankenexperiments. Suhrkamp, Frankfurt am Main.
Küppers, G., & Lenhard, J. (2005a). Computersimulationen: Modellierungen 2. Ordnung. Journal for General Philosophy of Science, 36(2), 305–329.
Küppers, G., & Lenhard, J. (2005b). Validation of simulation: Patterns in the social and natural sciences. Journal of Artificial Societies and Social Simulation, 8(4), 3.
Lenhard, J. (2007). Computer simulation: The cooperation between experimenting and modeling. Philosophy of Science, 74, 176–194.
Lenhard, J., & Winsberg, E. (2010). Holism, entrenchment, and the future of climate model pluralism. Studies in History and Philosophy of Science Part B, 41(3), 253–262.
Mach, E. (1926). Erkenntnis und Irrtum. S kizzen zur Psychologie der F orschung (5th ed.). Johann Ambrosius Barth, Leipzig (coincides with the 4th ed.).
McAllister, J. (2004). Thought experiments and the belief in phenomena. Philosophy of Science, 71, 1164–1175.
Menary, R. (Ed.) (2010). The extended m ind. Cambridge, MA: MIT Press.
Morrison, M. (2009). Models, measurement and computer simulation: The changing face of experimentation. Philosophical Studies, 143, 33–57.
Moue, A., Masavetas, K. A., & Karyianni, H. (2006). Tracing the development of thought experiments in the philosophy of natural sciences. Journal for General Philosophy of Science, 37, 61–75.
Norton, S. D., & Suppe, F. (2001). Why atmospheric modeling is good science. In P. Edwards & C. Miller (Eds.), Changing the atmosphere (pp. 67–106). Cambridge, MA: MIT Press.
Norton, J. D. (1991). Thought experiments in Einstein’s work. In T. Horowitz & G. J. Massey (Eds.), Thought experiments in science and philosophy (pp. 129–144). Savage, MD: Rowman and Littlefield.
Norton, J. D. (1996). Are thought experiments just what you thought? Canadian Journal of Philosophy, 26, 333–366.
Norton, J. D. (2004a). On thought experiments: Is there more to the argument? Proceedings of the 2002 Biennial Meeting of the Philosophy of Science Association, Philosophy of Science, 71, 1139–1151.
Norton, J. D. (2004b). Why thought experiments do not transcend empiricism. In C. Hitchcock (Ed.), Contemporary debates in the philosophy of science (pp. 44–66). Oxford: Blackwell.
Oberkampf, W. L., & Roy, C. J. (2010). Verification and validation in scientific computing. Cambridge: Cambridge University Press.
Pang, T. (2006). An introduction to computational physics (2nd ed.). Cambridge, MA: Cambridge University Press.
Parker, W. S. (2009). Does matter really matter? Computer simulations, experiments, and materiality. Synthese, 169(3), 483–496.
Peebles, P. J. E. (1980). The large scale structure of the universe. Princeton, NJ: Princeton University Press.
Perret-Gallix, D. (2002). Simulation and event generation in high-energy physics. Computer Physics Communications, 147(1–2), 488–493.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (2007). Numerical recipes. T he art of s cientific computing (3rd ed.), New York: Cambridge University Press.
Russell, B. (1905). On denoting. Mind, 14, 479–493. (Reprinted in Russell, Bertrand, Essays in Analysis, London: Allen & Unwin, pp. 103–119 (1973))
Salmon, W. (1989). Four decades of s cientific explanation. Minneapolis: University of Minnesota Press.
Soter, S. (2007). Are planetary systems filled to capacity? Scientific American, 95(5), 424.
Stöckler, M. (2000). On modeling and simulations as instruments for the study of complex systems. In M. Carrier, G. J. Massey, & L. Ruetsche (Eds.), Science at the century’s end: Philosophical questions on the progress and limits of science (pp. 355–373). Pittsburgh, PA: University of Pittsburgh Press.
Strawson, P. F. (1950). On referring. Mind, 59, 320–344.
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.
Tymoczko, T. (1979). The four-color problem and its philosophical significance. Journal of Philosophy, 76, 57–83.
Weber, K. (1999). Simulation und Erklärung. Waxmann, Münster.
Wedgwood, R. (2006). The normative force of reasoning. Noũs, 40, 660–686.
Weisberg, M. (2007). Who is a modeler? British Journal for Philosophy of Science, 58, 207–233.
Winsberg, E. (1999). Sanctioning models. The Epistemology of Simulation. Science in Context, 12, 275–292.
Winsberg, E. (2001). Simulations, models, and theories: Complex physical systems and their representations. Philosophy of Science (Proceedings), 68, 442–454.
Winsberg, E. (2010). Science in the age of computer simulations. Chicago: University of Chicago Press.
Acknowledgements
An earlier version of this paper was presented at the workshop “Thought experiments and Computer Simulations” at the IHPST, Paris in March 2010. I’m grateful to the organizers and the other participants. Special thanks to John Norton for discussion and encouragement.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Beisbart, C. How can computer simulations produce new knowledge?. Euro Jnl Phil Sci 2, 395–434 (2012). https://doi.org/10.1007/s13194-012-0049-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13194-012-0049-7