Abstract
Counterfactuals have become an important area of interdisciplinary interest, especially in logic, philosophy of language, epistemology, metaphysics, psychology, decision theory, and even artificial intelligence. In this study, we propose a new form of analysis for counterfactuals: analysis by algorithmic complexity. Inspired by Lewis-Stalnaker's Possible Worlds Semantics, the proposed method allows for a new interpretation of the debate between David Lewis and Robert Stalnaker regarding the Limit and Singularity assumptions. Besides other results, we offer a new way to answer the problems raised by Goodman and Quine regarding vagueness, context-dependence, and the non- monotonicity of counterfactuals. Engaging in a dialogue with literature, this study will seek to bring new insights and tools to this debate. We hope our method of analysis can make counterfactuals more understandable in an intuitively plausible way, and a philosophically justifiable manner, aligned with the way we usually think about counterfactual propositions and our imaginative reasoning.
References
Aaronson, S. 2013. Why philosophers should care about computational complexity, in Computability: Turing, Gödel, Church, and Beyond, ed. B. Jack Copeland, Carl J. Posy and Oron Shagrir, Cambridge, MA: The MIT press: 261-328.
Adams, E. W. 1976. Prior Probabilities and Counterfactual Conditionals, in Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science 6ª, ed. William L. Harper and Clifford Alan Hooker, Springer Netherlands: 1-21. doi:10.1007/978-94-010- 1853-1_1
Bell, E. T. 2000.The queen of mathemathics, in The World of Mathematics, ed. James R. Newman, Courier Corporation.
Bennett, J. 2003. Conditionals, Oxford: Oxford University Press.
Bottou, L., Peters, J., Quiñonero-Candela, J., Denis, X., Charles, D., Chickering, M., Portugaly, E., Dipankar, R., Simard, P., and Snelson, E. 2013. Counterfactual reasoning and learning systems: The example of computational advertising, The Journal of Machine Learning Research, 14/65: 3207-60.
Bradley, R. 2002. Indicative conditionals, Erkenntnis, 56/3: 345- 78.
Byrne, R. 2008. The Rational Imagination: How People Create Alternatives to Reality, The Behavioral and brain sciences, 30: 439-53. doi:10.1017/S0140525X07002579.
Byrne, R. 2016. Counterfactual Thought, Annual Review of Psychology, 67/1: 135-57. doi:10.1146/annurev-psych- 122414-033249
Chaitin, G. J. 1991. Algorithmic information and evolution, in Perspectives on Biological Complexity, IUBS Press: 51- 60.
Chaitin, G. J. 2006. Speculations on Biology, Information and Complexity, CDMTCS - Centre for Discrete Mathematics and Theoretical Computer Science Research Report Series, IBM Research, Yorktown Heights, USA.
Chaitin, G. J. 2007. Thinking about Godel and Turing: Essays on Complexity, 1970-2007, ed. Gregory J Chaitin, World Scientific Publishing Company.
Costello, T., and McCarthy, J. 1999. Useful Counterfactuals, Linköping Electronic Articles in Computer and Information Science, 4/12: 1-24.
Edgington, D. 2003. What If? Questions About Conditionals , Mind & Language, 18/4: 380-401. doi:10.1111/1468-0017.00233
Edgington, D. 2014. Estimating Conditional Chances and Evaluating Counterfactuals, Studia Logica: An International Journal for Symbolic Logic, 102/4: 691-707.
Epstude, K., and Roese, N. J. 2008. The functional theory of counterfactual thinking, Personality and Social Psychology Review, 12/2: 168-192. doi:10.1177/1088868308316091.
Fredkin, E. 2003. An Introduction to Digital Philosophy, International Journal of Theoretical Physics, 42/2.
Gillies, A. 2007. Counterfactual Scorekeeping, Linguistics and Philosophy, 30/3: 329-360. doi:10.1007/s10988-007- 9018-6
Goodman, N. 1947. The Problem of Counterfactual Conditionals , The Journal of Philosophy, 44/5: 113-28. xxx
Griffin, M. 1999. Leibniz on God's Knowledge of Counterfactuals, The Philosophical Review, 108/3: 317-43. doi:10.2307/2998464
Hájek, A. 2014. Probabilities of counterfactuals and counterfactual probabilities, Journal of Applied Logic, 12/3: 235-51. doi:10.1016/j.jal.2013.11.001
Kaufmann, S. 2005. Conditional predictions, Linguistics and Philosophy , 28/2: 183-84. doi:10.1007/s10988-005- 3731-9
Kolmogorov, A.N. 1998. On Tables of Random Numbers, Theoretical Computer Science, 207/2: 387-395. doi:10.1016/S0304-3975(98)00075-9
Kripke, S.A. 1963. Semantical Analysis of Modal Logic I: Normal Modal Propositional Calculi, Zeitschrift Für Mathematische Logik Und Grundlagen Der Mathematik, 9/5-6: 67-96. doi:10.1002/malq.19630090502
Kvart, I. 1986. A Theory of Counterfactuals, Indianapolis: Hackett.
Kvart, I. 1992. Counterfactuals, Erkenntnis, 36/2: 139-79. doi:10.1007/BF00217472.
Leitgeb, H. 2012a. A probabilistic semanticsfor counterfactuals, Part A, Rev. Symb. Log, 5/1: 16-84.
Leitgeb, H. 2012b. A probabilistic semantics for counterfactuals, Part B, Rev. Symb. Log, 5/1: 85-121.
Lewis, D. 1973a. Counterfactuals and Comparative Possibility, Journal of Philosophical Logic, 2/4. doi:10.2307/2215339
Lewis, D. 1973b. Counterfactuals, Cambridge, MA: Harvard University Press.
Lewis, D. 1979. Counterfactual Dependence and Time’s Arrow, Noûs, 13/4: 455-76. doi:10.2307/2215339
McGee, V. 1989. Conditional probabilities and compounds of conditionals, Philos. Rev, 98/4: 485-541.
McQuail, D. 2000. McQuail's Mass Communication Theory (4th edition), London: Sage: 16-34.
Morreau, M. 2010. It Simply Does Not Add Up: Trouble with Overall Similarity, The Journal of Philosophy, 107/9: 469-90. doi:10.5840/jphil2010107931
Pearl, J. 1995. Causation, Action, and Counterfactuals , in Computational Learning and Probabilistic Reasoning, ed. A. Gammerman, New York: John Wiley and Sons: 235- 55.
Pearl, J. 2013. Structural Counterfactuals: A Brief Introduction, Cognitive Science, 37/6: 977-85. doi:10.1111/cogs.12065
Quine, W. V. O. 1960. Word and Object, Cambridge, MA: The MIT press .
Quine, W. V. O. 1982. Methods of Logic, 4º edition, Cambridge, MA: Harvard University Press.
Roese, N. 1999. Counterfactual thinking and decision making, Psychonomic Bulletin & Review, 6: 570-78. doi:10.3758/BF03212965.
Schulz, K. 2007. Minimal Models in Semantics and Pragmatics: Free Choice, Exhaustivity, and Conditionals . PhD Thesis, Amsterdam: University of Amsterdam: Institute for Logic, Language and Computation, URL = http://www.illc.uva.nl/Research/Publications/Dissertations/DS-2007-04.text.pdf
Shane, L., and Hutter, M. 2007. Universal Intelligence: A Definition of Machine Intelligence, Minds and Machines, 17/4: 391-444. doi:10.1007/s11023-007- 9079-x.
Solomonoff, R. J. 1964. A formal theory of inductive inference. Information and Control, 7/1: 1-22. doi:10.1016/S0019-9958(64)90223-2
Stalnaker, R. C. 1968. A Theory ofConditionals , in Studies in Logical Theory, ed. Nicholas Rescher, Oxford: Basil Blackwell: 98-112.
Stalnaker, R. C. 1980. A Defense of Conditional Excluded Middle, in IFS, ed. William L. Harper, Robert Stalnaker, Glenn Pearce, Springer: 87-104. doi:10.1007/978-94-009- 9117-0_4
Steinhart, E. 1998. Digital metaphysics, in The Digital Phoenix, ed. T. Bynum and J. Moor. New York: Basil Blackwell, URL= http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.469.661&rep=rep1&type=pdf
Todd, W. 1964. Counterfactual Conditionals and the Presuppositions of Induction, Philosophy of Science, 31/2: 101-10. doi:10.1086/287987
Turing, A. M. 1936. On computable numbers, with an application to the Entscheidungsproblem, Proceedings of the London Mathematical Society, 42/2: 230-65.
Warmbrōd, K. 1981a. Counterfactuals and Substitution of Equivalent Antecedents, Journal of Philosophical Logic , 10/2: 267-89. doi:10.1007/BF00248853
Warmbrōd, K. 1981b. An Indexical Theory of Conditionals , Dialogue, Canadian Philosophical Review, 20/4: 644-64. doi:10.1017/S0012217300021399
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