2000 character limit reached
Mathematical Explanations (2402.09413v1)
Published 31 Dec 2023 in cs.AI
Abstract: A definition of what counts as an explanation of mathematical statement, and when one explanation is better than another, is given. Since all mathematical facts must be true in all causal models, and hence known by an agent, mathematical facts cannot be part of an explanation (under the standard notion of explanation). This problem is solved using impossible possible worlds.
- Beckers, S. (2021). Causal sufficiency and actual causation. Journal of Philosophical Logic 50, 1341–1374.
- Cresswell, M. J. (1970). Classical intensional logics. Theoria 36, 347–372.
- Cresswell, M. J. (1972). Intensional logics and logical truth. Journal of Philosophical Logic 1, 2–15.
- Cresswell, M. J. (1973). Logics and Languages. London: Methuen and Co.
- Gärdenfors, P. (1988). Knowledge in Flux. Cambridge, MA: MIT Press.
- Actual causes and thought experiments. In J. Campbell, M. O’Rourke, and H. Silverstein (Eds.), Causation and Explanation, pp. 43–67. Cambridge, MA: MIT Press.
- Hall, N. (2007). Structural equations and causation. Philosophical Studies 132, 109–136.
- Halpern, J. Y. (2015). A modification of the Halpern-Pearl definition of causality. In Proc. 24th International Joint Conference on Artificial Intelligence (IJCAI 2015), pp. 3022–3033.
- Halpern, J. Y. (2016). Actual Causality. Cambridge, MA: MIT Press.
- Causes and explanations: a structural-model approach. Part I: Causes. British Journal for Philosophy of Science 56(4), 843–887.
- Causes and explanations: a structural-model approach. Part II: Explanations. British Journal for Philosophy of Science 56(4), 889–911.
- Hempel, C. G. (1965). Aspects of Scientific Explanation. New York: Free Press.
- Hintikka, J. (1962). Knowledge and Belief. Ithaca, N.Y.: Cornell University Press.
- Hintikka, J. (1975). Impossible possible worlds vindicated. Journal of Philosophical Logic 4, 475–484.
- Hitchcock, C. (2001). The intransitivity of causation revealed in equations and graphs. Journal of Philosophy XCVIII(6), 273–299.
- Hitchcock, C. (2007). Prevention, preemption, and the principle of sufficient reason. Philosophical Review 116, 495–532.
- Kripke, S. (1965). A semantical analysis of modal logic II: non-normal propositional calculi. In L. Henkin and A. Tarski (Eds.), The Theory of Models, pp. 206–220. Amsterdam: North-Holland.
- Causation: A User’s Guide. Oxford, U.K.: Oxford University Press.
- Rantala, V. (1982). Impossible worlds semantics and logical omniscience. Acta Philosophica Fennica 35, 18–24.
- Salmon, W. C. (1984). Scientific Explanation and the Causal Structure of the World. Princeton, N.J.: Princeton University Press.
- Weslake, B. (2015). A partial theory of actual causation. British Journal for the Philosophy of Science. To appear.
- Woodward, J. (2003). Making Things Happen: A Theory of Causal Explanation. Oxford, U.K.: Oxford University Press.
Sponsored by Paperpile, the PDF & BibTeX manager trusted by top AI labs.
Get 30 days freePaper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.