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Thought Experiments in Model-Based Reasoning

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Springer Handbook of Model-Based Science

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Abstract

Thought experimentation is at least as old as Western philosophy. Scholars have made much use of it in many disciplines. For instance, philosophical discussions on ethics, morality, knowledge, and language abound with thought experiments. Likewise, great scientific developments, such as in physics and mathematics, have been achieved via thought experimentation. This is true even long before the introduction of the term, between the late seventeenth and nineteenth centuries. But what is a thought experiment? Although giving a clear answer to this question is a very complicated task, it is quite common to consider thought experiments as pieces of reasoning about imaginary cases mainly performed with the aim of increasing our knowledge or understanding of the world. In this chapter, I review the lively debate on thought experiments. First, I introduce some famous examples and detail six of them (Sect. 21.1). Second, I give some historical background (Sect. 21.2). Then, I focus on three of the main questions asked in the literature, namely: What is a thought experiment? (Sect. 21.3), What is the function of thought experiments? (Sect. 21.4), How do thought experiments achieve their function? (Sect. 21.5). These issues will lead to tackle other important points, such as the relationship between real and thought experimentation, the differences between philosophical and scientific thought experimentation, the role played by intuitions and imagination in thought experimentation.

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Abbreviations

EPR:

Einstein–Podolsky–Rosen

QM:

quantum mechanics

RE:

real experiment

TE:

thought experiment

References

  1. Plato: The Republic (Cosimo, New York 2008), translated by Benjamin Jowett

    Google Scholar 

  2. H. Putnam: Reason, Truth and History (Cambridge University Press, Cambridge 1981)

    Book  Google Scholar 

  3. J. Locke: An Essay Concerning Human Understanding (Thomas Dring Samuel Manship, London 1690/ 1694)

    Google Scholar 

  4. G. Galilei: Discorsi e Dimostrazioni Matematiche Intorno a Due Nuove Scienze (Louis Elsevier, Leida 1638)

    Google Scholar 

  5. E. Condillac: Traité des Sensations (Chez de Bure, London/Paris 1754)

    Google Scholar 

  6. I. Kant: Von dem ersten Grunde des Unterschieds der Gegenden im Raume. In: Vorkritische Schriften, ed. by A. Buchenau (Bruno Cassirer, Berlin 1768) pp. 375–383

    Google Scholar 

  7. C. Darwin: The Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life (John Murray, London 1859)

    Book  Google Scholar 

  8. H. Poincaré: La Science et l’hypothèse (E. Flammarion, Paris 1908)

    MATH  Google Scholar 

  9. A. Einstein, L. Infeld: The Evolution of Physics. The Growth of Ideas from Early Concepts to Relativity and Quanta (Simon Schuster, New York 1938)

    MATH  Google Scholar 

  10. W. Heisenberg: Physikalische Prinzipien der Quantentheorie (Hirzel, Leipzig 1930)

    MATH  Google Scholar 

  11. T. Burge: Individualism and the mental, Midwest Stud. Philos. 4, 73–121 (1979)

    Article  Google Scholar 

  12. J. Searle: Minds, brains, and programs, Behav. Brain Sci. 3, 417–457 (1980)

    Article  Google Scholar 

  13. T. Horowitz, G. Massey (Eds.): Thought Experiments in Science and Philosophy (Rowman Littlefield, Lanham 1991)

    Google Scholar 

  14. R. Casati, A. Jacomuzzi, P. Kobau (Eds.): Esperimenti Mentali (Rosenberg Sellier, Turin 2009)

    Google Scholar 

  15. K. Ierodiakonou, S. Roux (Eds.): Thought Experiments in Methodological and Historical Contexts (Brill, Leiden-Boston 2011)

    Google Scholar 

  16. M. Frappier, L. Meynell, J.R. Brown (Eds.): Thought Experiments in Philosophy, Science, and the Arts (Routledge, London, New York 2013)

    Google Scholar 

  17. M.G. Tarallo, T. Mazzoni, N. Poli, D.V. Sutyrin, X. Zhang, G.M. Tino: Test of Einstein Equivalence Principle for 0-spin and half-integer-spin atoms: Search for spin-gravity coupling effects, Phys. Rev. Lett. 113, 023005-1–023005-5 (2014)

    Article  Google Scholar 

  18. Stevinus: De Staticae Elementis (Ioannis Patii, Leiden 1605/ 1608)

    Google Scholar 

  19. I. Newton: Philosophiae Naturalis Principia Mathematica (Joseph Streater, London 1687)

    Google Scholar 

  20. E. Gettier: Is justified true belief knowledge?, Analysis 23, 121–123 (1963)

    Article  Google Scholar 

  21. B. Russell: Human Knowledge: Its Scope and Its Limits (Allen Unwin, London 1948)

    Google Scholar 

  22. M. Cohen: 101 Philosophy Problems (Routledge, London, New York 1999)

    Book  Google Scholar 

  23. H. Putnam: Meaning and Reference, J. Philos. 70, 699–711 (1973)

    Article  Google Scholar 

  24. H. Putnam: Meaning of ‘‘Meaning, Minnesota Stud. Philos. Sci. 7, 131–193 (1975)

    Google Scholar 

  25. F. Jackson: Epiphenomenal qualia, Philos. Q. 32, 27–36 (1982)

    Article  Google Scholar 

  26. P. Ludlow, Y. Nagasawa, D. Stoljar (Eds.): There’s Something About Mary. Essays on Phenomenal Consciousness and Franck Jackson’s Knowledge Argument (MIT Press, Cambridge, London 2004)

    Google Scholar 

  27. J.R. Brown, Y. Fehige: Thought experiments. In: The Stanford Encyclopedia of Philosophy, ed. by E.N. Zalta, http://plato.stanford.edu/archives/fall2011/entries/thought-experiment/ (2014)

  28. E. Mach: Über Gedankenexperimente, Z. Phys. Chem. Unterr. 10, 1–5 (1896), Translated by W.O. Price, S. Krimsky: On thought experiments, Philosophical Forum 4(3), 446–457 (1973)

    Google Scholar 

  29. H.C. Ørsted: Förste Indledning til den Almindelige Naturlære (J.S. Schultz, Copenhagen 1811)

    Google Scholar 

  30. C. Schildknecht: Philosophische Masken: Literarische Formen der Philosophie bei Platon, Descartes, Wolff und Lichtenberg (Metzler, Stuttgart 1990)

    Book  Google Scholar 

  31. U. Kühne: Die Methode des Gedankenexperiments (Suhrkamp, Frankfurt 2005)

    Google Scholar 

  32. J. Witt-Hansen: H.C. Ørsted, Immanuel Kant, and the thought experiment, Danish Yearb. Philos. 13, 48–65 (1976)

    Google Scholar 

  33. Y. Fehige, M.T. Stuart: On the origins of the philosophy of thought experiments: The forerun, Perspect. Sci. 22, 179–220 (2014)

    Article  Google Scholar 

  34. A.S. Moue, K.A. Masavetas, H. Karayianni: Tracing the development of thought experiments in the philosophy of natural sciences, J. Gen. Philos. Sci. 37, 61–75 (2006)

    Article  Google Scholar 

  35. D. Cohnitz: Ørsteds Gedankenexperiment: Eine Kantianische Fundierung der Infinitesmalrechnung? Ein Beitrag zur Begriffsgeschichte von ‘‘Gedankenexperiment’’ und zur Mathematikgeschichte des frühen 19. Jarhunderts, Kant-Studien 99, 407–433 (2008)

    Article  Google Scholar 

  36. M. Buzzoni: Thought Experiment in the Natural Sciences: An Operational and Reflexive-Transcendental Conception (Königshausen Neumann, Würzburg 2008)

    Google Scholar 

  37. S. Roux: Introduction: The emergence of the notion of thought experiments. In: Thought Experiments in Methodological and Historical Contexts, ed. by K. Ierodiakonou, S. Roux (Brill, Leiden-Boston 2011) pp. 1–33

    Chapter  Google Scholar 

  38. N. Rescher: Thought experimentation in presocratic philosophy. In: Thought Experiments in Science and Philosophy, ed. by T. Horowitz, G. Massey (Rowman Littlefield, Lanham 1991) pp. 31–42

    Google Scholar 

  39. N. Rescher: What If?: Thought Experimentation in Philosophy (Transaction Publishers, New Brunswick 2005)

    Google Scholar 

  40. A. Irvine: Thought experiments in scientific reasoning. In: Thought Experiments in Science and Philosophy, ed. by T. Horowitz, G. Massey (Rowman Littlefield, Lanham 1991) pp. 149–166

    Google Scholar 

  41. K. Ierodiakonou: Ancient thought experiments: A first approach, Ancient Philos. 25, 125–140 (2005)

    Article  Google Scholar 

  42. I. Lakatos: Proofs and Refutations. The Logic of Mathematical Discovery (Cambridge University Press, Cambridge 1976)

    Book  MATH  Google Scholar 

  43. M. Stöltzner: The dynamics of thought experiments – Comment to Atkinson. In: Observation and Experiment in the Natural and Social Sciences, ed. by M. Galavotti (Kluwer Academic Publishers, Dordrecht 2003) pp. 243–258

    Google Scholar 

  44. P. King: Mediaeval thought-experiments: The metamethodology of mediaeval science. In: Thought Experiments in Science and Philosophy, ed. by T. Horowitz, G. Massey (Rowman Littlefield, Lanham 1991) pp. 43–64

    Google Scholar 

  45. D. Perler: Thought experiments: The methodological function of angels in late medieval epistemology. In: Angels in Medieval Philosophical Inquiry, ed. by I. Iribarren, M. Lenz (Ashgate, Aldershot 2008) pp. 143–153

    Google Scholar 

  46. C. Grellard: Thought experiments in late medieval debates on atomism. In: Thought Experiments in Methodological and Historical Contexts, ed. by K. Ierodiakonou, S. Roux (Brill, Leiden-Boston 2011) pp. 65–82

    Chapter  Google Scholar 

  47. G. Prudovsky: The confirmation of the superposition principle: The role of a constructive thought experiment in Galileo’s Discorsi, Stud. Hist. Philos. Sci. 20, 453–468 (1989)

    Article  MathSciNet  Google Scholar 

  48. D. Atkinson, J. Peijnenburg: Galileo and prior philosophy, Stud. Hist. Philos. Sci. 35, 115–136 (2004)

    Article  MathSciNet  Google Scholar 

  49. P. Palmieri: ‘‘Spuntur lo scoglio più duro’’: Did Galileo ever think the most beautiful thought experiment in the history of science?, Stud. Hist. Philos. Sci. 36, 305–322 (2005)

    Article  Google Scholar 

  50. J. Daiber: Experimentalphysik des Geistes: Novalis und das Romantische Experiment (Vadenhoeck Ruprecht, Göttingen 2001)

    Google Scholar 

  51. Y. Fehige: Poems of productive imagination: Thought experiments, theology, and science in Novalis, Neue Z. Syst. Theol. Religionsphilos. 55, 54–83 (2013)

    Google Scholar 

  52. R. Sorensen: Thought Experiments (Oxford University Press, Oxford 1992)

    Google Scholar 

  53. A. Meinong: Über die Stellung der Gegenstandstheorie im System der Wissenschaften (Voigtländer, Leipzig 1907)

    Google Scholar 

  54. P. Duhem: La Théorie Physique: Son Objet, sa Structure (Vrin, Paris 1914)

    Google Scholar 

  55. J.R. Brown: The Laboratory of the Mind: Thought Experiments in the Natural Sciences (Routledge, London 1991)

    Google Scholar 

  56. A. Bokulich: Rethinking thought experiments, Perspect. Sci. 9, 285–307 (2001)

    Article  Google Scholar 

  57. M. Buzzoni: Esperimento ed Esperimento Mentale (FrancoAngeli, Milano 2004)

    Google Scholar 

  58. K. Popper: On the use and misuse of imaginary experiments, especially in quantum theory. In: The Logic of Scientific Discovery (Hutchinson, London 1959) pp. 442–456

    Google Scholar 

  59. C. Hempel: Typological methods in the natural and the social sciences. In: Aspects of Scientific Explanation and Other Essays in the Philosophy of Science (Free Press, New York 1965) pp. 155–171

    Google Scholar 

  60. A. Koyré: Galileo’s treatise de motu gravium: The use and the abuse of imaginary experiment, Rev. Hist. Sci. Paris. 13, 197–245 (1960)

    Google Scholar 

  61. T.S. Kuhn: A function for thought experiments. In: L’aventure de la Science, Mélanges Alexandre Koyré, ed. by I.B. Cohen, R. Taton (Hermann, Paris 1964) pp. 307–343

    Google Scholar 

  62. J.J. Thomson: A defense of abortion, Philos. Public Aff. 1, 47–66 (1971)

    Google Scholar 

  63. D. Parfit: Reasons and persons (Clarendon Press, Oxford 1984)

    Google Scholar 

  64. M. Cohen: Wittgenstein’s Beetle and Other Classic Thought Experiments (Blackwell, Oxford 2005)

    Book  Google Scholar 

  65. R. Cooper: Thought Experiments, Metaphilosophy 36, 328–347 (2005)

    Article  Google Scholar 

  66. G. Boniolo: On a unified theory of models and thought experiments in natural sciences, Int. Stud. Philos. Sci. 11, 121–142 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  67. U. Gähde: Gedankenexperimente in Erkenntnistheorie und Physik: Strukturelle Parallelen. In: Rationalität, Realismus, Revision, ed. by J. Nida-Rümlin (de Gruyter, Berlin 2000) pp. 457–464

    Google Scholar 

  68. J. Norton: Thought experiments in Einstein’s work. In: Thought Experiments in Science and Philosophy, ed. by T. Horowitz, G. Massey (Rowman Littlefield, Lanham 1991) pp. 129–148

    Google Scholar 

  69. R. Laymon: Thought experiments by Stevin, Mach and Gouy: Thought experiments as ideal limits and as semantic domains. In: Thought Experiments in Science and Philosophy, ed. by T. Horowitz, G. Massey (Rowman Littlefield, Lanham 1991) pp. 167–192

    Google Scholar 

  70. J.R. Brown: Thought experiments: A Platonic account. In: Thought Experiments in Science and Philosophy, ed. by T. Horowitz, G. Massey (Rowman Littlefield, Lanham 1991) pp. 119–128

    Google Scholar 

  71. J.R. Brown: Why thought experiments transcend experience. In: Contemporary Debates in the Philosophy of Science, ed. by C. Hitchcock (Blackwell, Oxford 2004) pp. 23–43

    Google Scholar 

  72. J.R. Brown: Peeking into Plato’s Heaven, Philos. Sci. 71, 1126–1138 (2004)

    Article  Google Scholar 

  73. N.J. Nersessian: In the theoretician’s laboratory: Thought experimenting as mental modelling. In: PSA 1992, ed. by D. Hull, M. Forbes, K. Okruhlik (Philosophy of Science Association, East Lansing 1993) pp. 291–301

    Google Scholar 

  74. I. Hacking: Do thought experiments have a life of their own? Comments on James Brown, Nancy Nersessian and David Gooding. In: PSA 1992, ed. by D. Hull, M. Forbes, K. Okruhlik (Philosophy of Science Association, East Lansing 1993) pp. 302–308

    Google Scholar 

  75. P. Humphreys: Seven theses on thought experiments. In: Philosophical Problems of the Internal and External World: Essays on the Philosophy of Adolf Grunbaum, ed. by J. Earman, A. Janis, J. Massey, N. Rescher (University of Pittsburgh Press/Universitätsverlag Konstanz, Pittsburgh/Konstanz 1993) pp. 205–227

    Google Scholar 

  76. T. Gendler Szabó: Galileo and the indispensability of scientific thought experiment, Br. J. Philos. Sci. 49, 397–424 (1998)

    Article  Google Scholar 

  77. E. Weber, T. De Mey: Explanation and thought experiments in history, Hist. Theory 42, 28–38 (2003)

    Article  Google Scholar 

  78. R. Snooks: Another scientific practice separating chemistry from physics: Thought experiments, Found. Chem. 8, 255–270 (2006)

    Article  Google Scholar 

  79. J. Peijnenburg, D. Atkinson: When are Thought Experiments Poor Ones?, J. Gen. Philos. Sci. 34, 305–322 (2003)

    Article  Google Scholar 

  80. G. McComb: Thought experiment, definition, and literary fiction. In: Thought Experiments in Philosophy, Science, and the Arts, ed. by M. Frappier, L. Meynell, J.R. Brown (Routledge, London, New York 2013) pp. 207–222

    Google Scholar 

  81. T. Gendler Szabó: Thought experiment. In: Encyclopedia of Cognitive Science, ed. by L. Nadel (New York/London, Nature/Routledge 2002) pp. 388–394

    Google Scholar 

  82. E. Brendel: Intuition pumps and the proper use of thought experiments, Dialectica 58, 88–108 (2004)

    Google Scholar 

  83. E. Mach: Erkenntnis und Irrtum (Barili, Leipzig 1905)

    MATH  Google Scholar 

  84. N.J. Nersessian: How do scientists think? Capturing the dynamics of conceptual change in science. In: Cognitive Models of Science, ed. by R.N. Giere (University of Minnesota Press, Minneapolis 1992) pp. 3–44

    Google Scholar 

  85. D. Gooding: What is experimental about thought experiments? In: PSA 1992, ed. by D. Hull, M. Forbes, K. Okruhlik (Philosophy of Science Association, East Lansing 1993) pp. 280–290

    Google Scholar 

  86. S. Häggqvist: Thought Experiments in Philosophy (Almqvist Wiksel, Stockholm 1996)

    Google Scholar 

  87. K. Wilkes: Real People: Personal Identity Without Thought Experiments (Clarendon Press, Oxford 1988)

    Google Scholar 

  88. M. Bishop: Why thought experiments are not arguments, Philos. Sci. 66, 534–541 (1999)

    Article  Google Scholar 

  89. D. Hull: A Function for actual examples in philosophy of science. In: What the Philosophy of Biology is: Essays Dedicated to David Hull, ed. by M. Ruse (Kluwer Academic Publishers, Dordrecht 1989) pp. 309–321

    Chapter  Google Scholar 

  90. D. Hull: That just don’t sound right: A plea for real examples. In: The Cosmos of Science: Essays of Exploration, ed. by J. Earman, J.D. Norton (University of Pittsburgh Press, Pittsburgh 1997) pp. 430–457

    Google Scholar 

  91. S. Krimsky: The Nature and Function of ‘‘Gedankenexperimente’’ in Physics, Ph.D. Thesis (University of Michigan, Ann Arbor 1970)

    Google Scholar 

  92. H. Reichenbach: Experience and Prediction. An Analysis of the Foundations and the Structure of Knowledge (University of Chicago Press, Chicago 1938)

    Book  Google Scholar 

  93. C. Daly: An Introduction to Philosophical Methods (Broadview Press, Peterborough 2010)

    Google Scholar 

  94. R. Arthur: Can thought experiments be resolved by experiment? The case of Aristotle’s wheel. In: Thought Experiments in Philosophy, Science, and the Arts, ed. by M. Frappier, L. Meynell, J.R. Brown (Routledge, London, New York 2013) pp. 107–122

    Google Scholar 

  95. J. Fodor: On knowing what we would say, Philos. Rev. 73, 198–212 (1964)

    Article  Google Scholar 

  96. P. Feyerabend: Against Method (Verso, London 1978)

    Google Scholar 

  97. W.V. Quine: Review of identity and individuation, J. Philos. 69, 488–497 (1972)

    Article  Google Scholar 

  98. P. Thagard: The Brain and the Meaning of Life (Princeton University Press, Princeton 2010)

    Book  Google Scholar 

  99. P. Thagard: Thought experiments considered harmful, Persp. Sci. 22, 288–305 (2014)

    Article  Google Scholar 

  100. M. Arcangeli: Il posto delle favole. In: Rivista di Estetica, s.i. Esperimenti mentali, Vol. 42, ed. by R. Casati, A. Jacomuzzi, P. Kobau (Rosenberg Sellier, Turin 2009) pp. 3–19

    Google Scholar 

  101. J. Lennox: Darwinian thought experiments: A function for just-so stories. In: Thought Experiments in Science and Philosophy, ed. by T. Horowitz, G. Massey (Rowman and Littlefield 1991) pp. 223–245

    Google Scholar 

  102. J. Lennox: Darwin’s methodological evolution, J. Hist. Biol. 38, 85–99 (2005)

    Article  Google Scholar 

  103. L.S. Swan: Synthesizing insight: Artificial life as thought experimentation in biology, Biol. Philos. 24, 687–701 (2009)

    Article  Google Scholar 

  104. F. Doolittle: Craig venter’s new life. The realization of some thought experiments in biological ontology. In: Thought Experiments in Philosophy, Science, and the Arts, ed. by M. Frappier, L. Meynell, J.R. Brown (Routledge, London, New York 2013) pp. 160–176

    Google Scholar 

  105. J. McAllister: Thought experiments and the belief in phenomena, PSA 2002, Philos. Sci. 71, 1164–1175 (2004)

    Article  Google Scholar 

  106. J. Maffie: ‘‘Just-so’’ stories about ‘‘inner cognitive Africa’’: Some doubts about Sorensen’s evolutionary epistemology of thought experiments, Biol. Philos. 12, 207–224 (1997)

    Article  Google Scholar 

  107. R. Sorensen: Precis of thought experiments, Informal Log. 17(3), 385–387 (1995)

    Google Scholar 

  108. M. Bunzl: Bunzl on Sorensen’s thought experiments, Informal Log. 17(3), 389–393 (1995)

    Google Scholar 

  109. R. Feldman: Feldman on Sorensen’s thought experiments, Informal Log. 17(3), 394–398 (1995)

    Google Scholar 

  110. R. Sorensen: Sorensen’s reply to Bunzl and Feldman, Informal Log. 17(3), 399–405 (1995)

    Google Scholar 

  111. M. Buzzoni: Thought experiments from a Kantian point of view. In: Thought Experiments in Philosophy, Science and the Arts, ed. by M. Frappier, L. Meynell, J.R. Brown (Routledge, London, New York 2013) pp. 90–106

    Google Scholar 

  112. Y. Fehige: Experiments of pure reason. Kantianism and thought experiments in science, Epistemologia Ital. J. Philos. Sci. 35, 141–160 (2012)

    Google Scholar 

  113. Y. Fehige: The relativized a priori and the laboratory of the mind: Towards a neo-kantian account of thought experiments in science, Epistemologia Ital. J. Philos. Sci. 36, 55–63 (2013)

    Google Scholar 

  114. M. Buzzoni: On thought experiments and the Kantian a priori in the natural sciences: A reply to Yiftach J. H. Fehige, Epistemologia Ital. J. Philos. Sci. 36, 277–293 (2013)

    Google Scholar 

  115. J. Norton: Why thought experiments do not transcend empiricism. In: Contemporary Debates in the Philosophy of Science, ed. by C. Hitchcock (Blackwell, Oxford 2004) pp. 44–66

    Google Scholar 

  116. J. Norton: Are thought experiments just what you thought?, Canad. J. Philos. 26, 333–366 (1996)

    Article  Google Scholar 

  117. J. Norton: On thought experiments: Is there more to the argument?, PSA 2002, Philos. Sci. 71, 1139–1151 (2004)

    Article  Google Scholar 

  118. T. Gendler Szabó: Thought Experiment: On the Powers and Limits of Imaginary Cases (Garland Press, New York 2000)

    Google Scholar 

  119. T. Williamson: The Philosophy of Philosophy (Blackwell, Malden 2007)

    Book  Google Scholar 

  120. N. Gilbert, K. Troitzsch: Simulation for the Social Scientist (Open University Press, Philadelphia 1999)

    Google Scholar 

  121. C. Beisbart, J. Norton: Why Monte Carlo simulations are inferences and not experiments, Int. Stud. Philos. Sci. 26, 403–422 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  122. D. Dowling: Experimenting on theories, Sci. Context 12(2), 261–273 (1999)

    Article  Google Scholar 

  123. A. Barberousse, S. Franceschelli, C. Imbert: Computer simulations as experiments, Synthese 169(3), 557–574 (2009)

    Article  MathSciNet  Google Scholar 

  124. E. Winsberg: A tale of two methods, Synthese 169(3), 575–592 (2009)

    Article  Google Scholar 

  125. W. Parker: Does matter really matter? Computer simulations, experiments and materiality, Synthese 169(3), 483–496 (2009)

    Article  Google Scholar 

  126. E.A. Di Paolo, J. Noble, S. Bullock: Simulation models as opaque thought experiments. In: Proceedings of the Seventh International Conference on Artificial Life, ed. by M.A. Bedau, J.S. McCaskill, N.H. Packard, S. Rasmussen (MIT Press, Cambridge 2000) pp. 497–506

    Google Scholar 

  127. S. Chandrasekharan, N.J. Nersessian, V. Subramanian: Computational modeling: Is this the end of thought experiments in science? In: Thought Experiments in Philosophy, Science, and the Arts, ed. by M. Frappier, L. Meynell, J.R. Brown (Routledge, London, New York 2013) pp. 239–260

    Google Scholar 

  128. F. Staudner: Virtuelle Erfahrung. Eine Untersuchung über den Erkenntniswert von Gedankenexperimenten und Computersimulationen in den Naturwissenschaften, Ph.D. Thesis (Friedrich Schiller Universität, Jena 1998)

    Google Scholar 

  129. M. Velasco: Experimentación y técnicas computacionales, Theoria 17, 317–331 (2002)

    Google Scholar 

  130. J. Lenhard: Epistemologie der Iteration: Gedankenexperimente und Simulationsexperimente, Dtsch. Z. Philos. 59, 131–154 (2011)

    Google Scholar 

  131. R. El Skaf, C. Imbert: Unfolding in the empirical sciences: Experiments, thought experiments and computer simulations, Synthese 190, 3451–3474 (2013)

    Article  Google Scholar 

  132. M. Bishop: An epistemological role for thought experiments. In: Idealization in Contemporary Physics, ed. by N. Shanks (Rodopi, Amsterdam, Atlanta 1998) pp. 19–33

    Google Scholar 

  133. M. Schulzke: Simulating philosophy: Interpreting video games as executable thought experiments, Philos. Technol. 27, 251–265 (2014)

    Article  Google Scholar 

  134. M. Bunzl: The logic of thought experiments, Synthese 106, 227–240 (1996)

    Article  Google Scholar 

  135. N.J. Nersessian: Thought experiments as mental modelling: Empiricism without logic, Croat. J. Philos. 7(20), 125–161 (2007)

    Google Scholar 

  136. R. Arthur: On thought experiments as a priori science, Int. Stud. Philos. Sci. 13, 215–229 (1999)

    Article  Google Scholar 

  137. N. Miščević: Modelling intuitions and thought experiments, Croat. J. Philos. 20, 181–214 (2007)

    Google Scholar 

  138. W. Hopp: Experiments in thought, Perspect. Sci. 22, 242–263 (2014)

    Article  Google Scholar 

  139. J.R. Brown: Why empiricism won’t work. In: PSA 1992, ed. by D. Hull, M. Forbes, K. Okruhlik (Philosophy of Science Association, East Lansing 1993) pp. 271–279

    Google Scholar 

  140. R. Urbaniak: ‘‘Platonic’’ thought experiments: How on Earth?, Synthese 187, 731–752 (2012)

    Article  MATH  Google Scholar 

  141. S. Häggqvist: A model for thought experiments, Canad. J. Philos. 39, 56–76 (2009)

    Google Scholar 

  142. P.A. Schilpp (Ed.): Albert Einstein: Philosopher-Scientist (Open Court, La Salle 1949)

    MATH  Google Scholar 

  143. T. De Mey: The dual nature view of thought experiments, Philosophica 72, 61–78 (2003)

    Google Scholar 

  144. J.Y. Goffi, S. Roux: On the very idea of a thought experiment. In: Thought Experiments in Methodological and Historical Contexts, ed. by K. Ierodiakonou, S. Roux (Brill, Leiden-Boston 2011) pp. 165–192

    Chapter  Google Scholar 

  145. T. Gendler Szabó: Thought experiments rethought – And reperceived, Philos. Sci. 71, 1152–1164 (2004)

    Article  Google Scholar 

  146. D. Gooding: Experiment and the Making of Meaning: Human Agency in Scientific Observation and Experiment (Kluwer Academic Publishers, Dordrecht, Boston 1990)

    Book  Google Scholar 

  147. D. Gooding: The procedural turn; or, why do thought experiments work? In: Cognitive Models of Science, ed. by R.N. Giere (University of Minnesota Press, Minneapolis 1992) pp. 45–76

    Google Scholar 

  148. M. Reiner, J. Gilbert: Epistemological resources for thought experimentation in science learning, Int. J. Sci. Educ. 22(5), 489–506 (2000)

    Article  Google Scholar 

  149. N. Miščević: Mental Models and Tought Experiments, Int. Stud. Philos. Sci. 6, 215–226 (1992)

    Article  Google Scholar 

  150. J.R. Brown: What Do we see in a thought experiment? In: Thought Experiments in Philosophy, Science, and the Arts, ed. by M. Frappier, L. Meynell, J.R. Brown (Routledge, London, New York 2013) pp. 53–68

    Google Scholar 

  151. A. Janis: Can thought experiments fail? In: Thought Experiments in Science and Philosophy, ed. by T. Horowitz, G. Massey (Rowman Littlefield, Lanham 1991) pp. 113–118

    Google Scholar 

  152. M. Arcangeli: Poveri esperimenti mentali. In: Analisi. Annuario e Bollettino della Società Italiana di Filosofia Analitica (SIFA, ed. by R. Davies (Mimesis, Milano/Udine 2011) pp. 277–290

    Google Scholar 

  153. D. Rowbottom: Intuitions in science: Thought experiments as argument pumps. In: Intuitions, ed. by A. Booth, D. Rowbottom (Oxford Univ. Press, Oxford 2014) pp. 119–134

    Chapter  Google Scholar 

  154. A. Einstein, B. Podolsky, N. Rosen: Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev. 47, 777–780 (1935)

    Article  MATH  Google Scholar 

  155. D. Atkinson: Experiments and thought experiments in natural science. In: Observation and Experiment in the Natural and Social Sciences, ed. by M.C. Galavotti (Kluwer Academic Publishers, Dordrecht 2003) pp. 209–225

    Google Scholar 

  156. A. Pessin, S. Goldberg (Eds.): The Twin Earth Chronicles: Twenty Years of Reflection on Hilary Putnam’s ‘‘The Meaning of Meaning’’ (M. E. Sharpe, New York 1996)

    Google Scholar 

  157. G.N. Schlesinger: The power of thought experiments, Found. Phys. 26(4), 467–482 (1996)

    Article  MathSciNet  Google Scholar 

  158. G. Boniolo: On Scientific Representations From Kant to a New Philosophy of Science (Palgrave Macmillan, New York 2008)

    Google Scholar 

  159. A. Aspect, P. Grangier, G. Roger: Experimental realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A new violation of Bell’s inequalities, Phys. Rev. Lett. 49(2), 91–94 (1982)

    Article  Google Scholar 

  160. M. Rédei: Thinking about thought experiments in physics. Comment on 'Experiments and thought experiments by David Atkinson'. In: Observation and Experiment in the Natural and Social Sciences, ed. by M. Galavotti (Kluwer Academic, Dordrecht 2003) pp. 237–241

    Google Scholar 

  161. D. Cohnitz: Poor thought experiments? A comment on Peijnenburg and Atkinson, J. Gen. Philos. Sci. 37, 373–392 (2006)

    Article  Google Scholar 

  162. M. Dorato: Dalla freccia di Lucrezio all’ascensore di Einstein: Alcune considerazioni sul ruolo degli esperimenti mentali nella scienza. In: Rivista di Estetica, s.i. Esperimenti mentali, Vol. 42, ed. by R. Casati, A. Jacomuzzi, P. Kobau (Rosenberg Sellier, Turin 2009) pp. 21–37

    Google Scholar 

  163. J. McAllister: The evidential significance of thought experiment in science, Stud. Hist. Philos. Sci. Part A 27, 233–250 (1996)

    Article  MathSciNet  Google Scholar 

  164. J. Norton: Chasing the light: Einstein’s most famous tought experiment. In: Thought Experiments in Philosophy, Science, and the Arts, ed. by M. Frappier, L. Meynell, J.R. Brown (Routledge, London, New York 2013) pp. 123–140

    Google Scholar 

  165. J. Norton: Seeing the laws of nature, Metascience 3, 33–38 (1993)

    Google Scholar 

  166. J.R. Brown: Counter thought experiments, R. Inst. Philos. Suppl. 61(82), 155–177 (2007)

    Article  Google Scholar 

  167. K. Ierodiakonou: Remarks on the history of an ancient thought experiment. In: Thought Experiments in Methodological and Historical Contexts ed by K. Ierodiakonou, S. Roux (Brill, Leiden-Boston 2011) pp. 37–50

    Google Scholar 

  168. E. Mach: Die Mechanik in ihrer Entwicklung historisch-kritisch dargestellt (Brockhaus, Leipzig 1883)

    MATH  Google Scholar 

  169. S. Krimsky: The multiple-world thought experiment and absolute space, Noûs 6(3), 266–273 (1972)

    Article  Google Scholar 

  170. S. Krimsky: The use and misuse of critical Gedankenexperimente, Z. Allg. Wissenschaftstheor. 4, 323–334 (1973)

    Article  Google Scholar 

  171. H. Helm, J. Gilbert: Thought experiments and physics education – Part 1, Phys. Educ. 20, 124–131 (1985)

    Article  Google Scholar 

  172. H. Helm, J. Gilbert, M.D. Watts: Thought experiments and physics education – Part 2, Phys. Educ. 20, 211–217 (1985)

    Article  Google Scholar 

  173. S. Klassen: The science thought experiment: How might it be used profitably in the classroom?, Interchange 37, 77–96 (2006)

    Article  Google Scholar 

  174. A. Velentzas, K. Halkia, C. Skordoulis: Thought experiments in the theory of relativity and in quantum mechanics: Their presence in textbooks and in popular science books, Sci. Educ. 16, 353–370 (2007)

    Article  Google Scholar 

  175. M. Toscano: Thought experimentation and modelling in the science classroom, AARE Conf. Proc. (2007), TOS07411

    Google Scholar 

  176. R. Casati: Dov’è il Sole di notte? (Raffaello Cortina Editore, Milano 2013)

    Google Scholar 

  177. J.C. Maxwell: Theory of Heat (Longman, London 1871)

    Google Scholar 

  178. M. Johnston: Human beings, J. Philos. 84, 59–83 (1987)

    Article  Google Scholar 

  179. R. Casati, J. Dokic: La Philosophie du Son (Chambon, Nîmes 1994)

    Google Scholar 

  180. D. Borsboom, G.J. Mellenbergh, J. Van Heerden: Functional thought experiments, Synthese 130, 379–387 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  181. J. Reiss: Genealogical thought experiments in economics. In: Thought Experiments in Philosophy, Science, and the Arts, ed. by M. Frappier, L. Meynell, J.R. Brown (Routledge, London, New York 2013) pp. 177–190

    Google Scholar 

  182. N. Miščević: Political thougt experiments from Plato to Rawls. In: Thought Experiments in Philosophy, Science, and the Arts, ed. by M. Frappier, L. Meynell, J.R. Brown (Routledge, London, New York 2013) pp. 191–206

    Google Scholar 

  183. M.W. Jackson: The government of reason, J. Value Inq. 26(2), 163–174 (1992)

    Article  Google Scholar 

  184. M. Shumelda: At the limits of possibility: Thought experiment in quantum gravity. In: Thought Experiments in Philosophy, Science, and the Arts, ed. by M. Frappier, L. Meynell, J.R. Brown (Routledge, London, New York 2013) pp. 141–159

    Google Scholar 

  185. C. Myers: Analytical thought experiments, Metaphilosophy 17, 109–118 (1986)

    Article  Google Scholar 

  186. J. Ichikawa, B. Jarvis: Thought-experiment intuitions and truth in fiction, Philos. Stud. 142, 221–246 (2009)

    Article  Google Scholar 

  187. P. Engel: Philosophical thought experiments: In or out of the armchair? In: Thought Experiments in Methodological and Historical Contexts, ed. by K. Ierodiakonou, S. Roux (Brill, Leiden-Boston 2011) pp. 145–163

    Google Scholar 

  188. R. Sorensen: Veridical idealizations. In: Thought Experiments in Philosophy, Science, and the Arts, ed. by M. Frappier, L. Meynell, J.R. Brown (Routledge, London, New York 2013) pp. 30–52

    Google Scholar 

  189. T.S. Kuhn: Objectivity, value judgement, and theory choice. In: The Essential Tension, (University of Chicago Press, Chicago 1973) pp. 320–339

    Google Scholar 

  190. P.M. Churchland: The ontological status of observables: In praise of the superempirical virtues. In: Images of Science: Essays on Realism and Empiricism, ed. by P.M. Churchland, C.A. Hooker (University of Chicago Press, Chicago 1985) pp. 35–47

    Google Scholar 

  191. J.R. Griesemer, W.C. Wimsatt: Picturing weismannism: A case study of conceptual evolution. In: What the Philosophy of Biology Is: Essays Dedicated to David Hull, ed. by M. Ruse (Kluwer Academic Publishers, Dordrecht 1989) pp. 75–137

    Chapter  Google Scholar 

  192. G. Bealer: Intuition and the autonomy of philosophy. In: Rethinking Intuition. The Psychology of Intuition and Its Role in Philosophical Inquiry, ed. by M. DePaul, W. Ramsey (Rowman Littlefield, Lanham 1998) pp. 201–239

    Google Scholar 

  193. K. Shrader-Frechette: Using a thought experiment to clarify a radiobiological controversy, Synthese 128, 319–342 (2001)

    Article  Google Scholar 

  194. V. Giardino: Sperimentare con i Triangoli. In: Rivista di Estetica, s.i. Esperimenti mentali, Vol. 42, ed. by R. Casati, A. Jacomuzzi, P. Kobau (Rosenberg, Sellier, Turin 2009) pp. 39–54

    Google Scholar 

  195. M. Buzzoni: On mathematical thought experiments, Epistemol. Ital. J. Philos. Sci. 34, 61–88 (2011)

    MATH  Google Scholar 

  196. J. McAllister: Thought experiment and the excercise of imagination in science. In: Thought Experiments in Philosophy, Science, and the Arts, ed. by M. Frappier, L. Meynell, J.R. Brown (Routledge, London, New York 2013) pp. 11–29

    Google Scholar 

  197. T. Gendler Szabó, J. Hawthorne (Eds.): Conceivability and Possibility (Clarendon/OUP, New York/Oxford 2002)

    Google Scholar 

  198. D.H.M. Brooks: The method of thought experiment, Metaphilosophy 25(1), 71–83 (1994)

    Article  Google Scholar 

  199. M. DePaul, W. Ramsey (Eds.): Rethinking Intuition. The Psychology of Intuition and Its Role in Philosophical Inquiry (Rowman Littlefield, Lanham 1998)

    Google Scholar 

  200. H. Cappelen: Philosophy Without Intuitions (Oxford Univ. Press, Oxford 2012)

    Book  Google Scholar 

  201. E. Chudnoff: Intuition (Oxford Univ. Press, Oxford 2013)

    Book  Google Scholar 

  202. A. Booth, D. Rowbottom: Intuition (Oxford Univ. Press, Oxford 2013)

    Google Scholar 

  203. A. Tversky, D. Kahneman: The framing of decisions and the psychology of choice, Science 211, 453–463 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  204. T. Horowitz: Philosophical intuitions and psychological theory, Ethics 108, 367–385 (1998)

    Article  Google Scholar 

  205. S. Black, J. Tweedale: Responsibility and alternative possibilities: The use and abuse of examples, J. Ethics 6, 281–303 (2002)

    Article  Google Scholar 

  206. J.M. Doris, S.P. Stich: As a matter of fact: Empirical perspectives on ethics. In: The Oxford Handbook of Contemporary Philosophy, ed. by F. Jackson, M. Smith (OUP, Oxford 2005) pp. 114–152

    Google Scholar 

  207. J. Alexander, J. Weinberg: Analytic epistemology and experimental philosophy, Phil. Compass 2, 56–80 (2007)

    Article  Google Scholar 

  208. J. Knobe, S. Nichols (Eds.): Experimental Philosophy (OUP, Oxford 2008)

    Google Scholar 

  209. K. Ludwig: The epistemology of thought experiments: First person versus third person approaches, Midwest Stud. Philos. 31, 128–159 (2007)

    Article  Google Scholar 

  210. T. Williamson: Replies to Ichikawa, Martin and Weinberg, Philos. Stud. 145, 465–476 (2009)

    Article  Google Scholar 

  211. T. Williamson: Philosophical ‘intuitions’ and scepticism about judgement, Dialectica 58, 109–153 (2004)

    Article  Google Scholar 

  212. T. Williamson: Armchair philosophy, metaphysical modality and counterfactual thinking, Proc. Aristot. Soc. 105, 1–23 (2005)

    Google Scholar 

  213. E. Machery: Thought experiments and philosophical knowledge, Metaphilosophy 42(3), 191–214 (2011)

    Article  Google Scholar 

  214. K. Lehrer: Theory of Knowledge (Westview Press, Boulder 1990)

    MATH  Google Scholar 

  215. S. Kripke: Naming and Necessity (Blackwell, Oxford 1980)

    Google Scholar 

  216. J. Weinberg, S. Nichols, S. Stich: Normativity and epistemic intuitions, Phil. Topic 29, 429–460 (2001)

    Article  Google Scholar 

  217. E. Machery, R. Mallon, S. Nichols, S. Stich: Semantics, cross-cultural style, Cognition 92, B1–B12 (2004)

    Article  Google Scholar 

  218. D. Dennett: Elbow Room: The Varieties of Free Will Worth Wanting (MIT Press, Cambridge 1984)

    Google Scholar 

  219. P. Swirski: Of Literature and Knowledge: Explorations in Narrative Thought Experiments, Evolution and Game Theory (Routledge, London, New York 2007)

    Google Scholar 

  220. M.T. Stuart: Philosophical conceptual analysis as an experimental method. In: Meaning, Frames and Conceptual Representation, ed. by T. Gamerschlag, D. Gerland, R. Osswald, W. Petersen (Düsseldorf University Press, Düsseldorf 2015) pp. 161–186

    Google Scholar 

  221. T. Gendler Szabó: Philosophical thought experiments, intuitions and cognitive equilibrium, Midwest Stud. Philos. 31, 68–89 (2007)

    Article  Google Scholar 

  222. M.T. Stuart: Cognitive science and thought experiments: A refutation of Paul Thagard’s skepticism, Perspect. Sci. 22, 264–287 (2014)

    Article  Google Scholar 

  223. M. Arcangeli: Imagination in thought experimentation: Sketching a cognitive approach to thought experiments. In: Model-Based Reasoning in Science and Technology, ed. by L. Magnani, W. Carnielli, C. Pizzi (Springer, Dordrecht 2010) pp. 571–587

    Chapter  Google Scholar 

  224. T. De Mey: Imagination’s grip on science, Metaphilosophy 37, 222–239 (2006)

    Article  Google Scholar 

  225. E. McMullin: Galilean Idealization, Stud. Hist. Philos. Sci. 16, 247–273 (1985)

    Article  MathSciNet  Google Scholar 

  226. P. Palmieri: Mental models in Galileo’s early mathematization of nature, Stud. Hist. Philos. Sci. 34, 229–264 (2003)

    Article  MathSciNet  Google Scholar 

  227. N.J. Nersessian: Creating Scientific Concepts (MIT Press, Cambridge 2008)

    Google Scholar 

  228. P.N. Johnson-Laird: Mental Models: Toward a Cognitive Science of Language, Inference and Consciousness (Harvard Univ. Press, Cambridge 1983)

    Google Scholar 

  229. P.N. Johnson-Laird: The history of mental models. In: Psychology of Reasoning: Theoretical and Historical Perspectives, ed. by K. Manktelow, M.C. Chung (Psychology Press, New York 2004) pp. 179–212

    Google Scholar 

  230. Y. Fehige, H. Wiltsche: The body, thought experiments, and phenomenology. In: Thought Experiments in Philosophy, Science, and the Arts, ed. by M. Frappier, L. Meynell, J.R. Brown (Routledge, London, New York 2013) pp. 69–89

    Google Scholar 

  231. J. Zeimbekis: Thought experiments and mental simulations. In: Thought Experiments in Methodological and Historical Contexts, ed. by K. Ierodiakonou, S. Roux (Brill, Leiden-Boston 2011) pp. 193–215

    Chapter  Google Scholar 

  232. A. Goldman: Simulating Minds: The Philosophy, Psychology, and Neuroscience of Mindreading (OUP, Oxford 2006)

    Book  Google Scholar 

  233. A. Goldman: Mirroring, mindreading, and simulation. In: Mirror Neuron Systems: The Role of Mirroring Processes in Social Cognition, ed. by J.A. Pineda (Humana Press, New York 2009) pp. 311–330

    Google Scholar 

  234. L. Meynell: Imagination and insight: A new account of the content of thought experiments, Synthese 191(17), 4149–4168 (2014)

    Article  Google Scholar 

  235. M.T. Stuart: Imagination: A ‘Sine Qua Non’ of scientific understanding, Croat. J. Philos. (2015), forthcoming

    Google Scholar 

  236. K. Mulligan: La varietà e l’unità dell’immaginazione, Riv. Estet. 11, 53–67 (1999)

    Google Scholar 

  237. M. Balcerack Jackson: On the epistemic value of imagining, supposing, and conceiving. In: Knowledge through Imagination, ed. by A. Kind, P. Kung (Oxford Univ. Press, Oxford 2016) pp. 41–60

    Chapter  Google Scholar 

  238. L. Souder: What are we to think about thought experiments?, Argumentation 17, 203–217 (2003)

    Article  Google Scholar 

  239. J. Weinberg: Configuring the cognitive imagination. In: New Waves in Aesthetics, ed. by K. Stock, K. Thomson-Jones (Palgrave Macmillan, Houndmills, Basingstoke 2008) pp. 203–223

    Chapter  Google Scholar 

  240. D. Davies: Thought experiments and fictional narratives, Croat. J. Philos. 7, 29–45 (2007)

    Google Scholar 

  241. D. Davies: Learning through fictional narratives in art and science. In: Beyond Mimesis and Convention, ed. by R. Frigg, M.C. Hunter (Kluwer Academic Publishers, Dordrecht 2010) pp. 51–70

    Chapter  Google Scholar 

  242. K. Walton: Mimesis as Make-Believe: On the Foundations of the Representational Arts (Harvard University Press, Harvard 1990)

    Google Scholar 

  243. E.A. Davenport: Literature as thought experiment (On aiding and abetting the muse, Philos. Soc. Sci. 13(3), 279–306 (1983)

    Article  Google Scholar 

  244. N. Carroll: The wheel of virtue: art, literature, and moral knowledge, J. Aesthet. Art Crit. 60(1), 3–26 (2002)

    Article  Google Scholar 

  245. C.Z. Elgin: The laboratory of the mind. In: A Sense of the World: Essays on Fiction, Narrative, and Knowledge, ed. by W. Huerner, J. Gibson, L. Pocci (Routledge, London 2007) pp. 43–54

    Google Scholar 

  246. C.Z. Elgin: Fiction as thought experiment, Perspect. Sci. 22, 221–241 (2014)

    Article  Google Scholar 

  247. D. Davies: Can philosophical thought experiment be ‘‘screened’’? In: Thought Experiments in Philosophy, Science, and the Arts, ed. by M. Frappier, L. Meynell, J.R. Brown (Routledge, London, New York 2013) pp. 223–238

    Google Scholar 

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Acknowledgements

I am very grateful to Marco Buzzoni, Jérôme Dokic, Yiftach Fehige, and Michael Stuart for helpful comments on earlier versions of this chapter. I would also like to thank the editor in charge of the part D, Nora Schwartz, for her support.

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Arcangeli, M. (2017). Thought Experiments in Model-Based Reasoning. In: Magnani, L., Bertolotti, T. (eds) Springer Handbook of Model-Based Science. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-319-30526-4_21

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