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Series:   Elements in Philosophy and Logic

The Many Faces of Impossibility

Published online by Cambridge University Press:  28 February 2024

Koji Tanaka  and
Alexander Sandgren
Koji Tanaka
Affiliation:
Australian National University
Alexander Sandgren
Affiliation:
Umeå Universitet, Sweden

Summary

Possible worlds have revolutionised philosophy and some related fields. But, in recent years, tools based on possible worlds have been found to be limited in many respects. Impossible worlds have been introduced to overcome these limitations. This Element aims to raise and answer the neglected question of what is characteristically impossible about impossible worlds. The Element sheds new light on the nature of impossible worlds. It also aims to analyse the main features and utility of impossible worlds and examine how impossible worlds can capture distinctions which are unavailable if we limit ourselves to possible world-based tools.
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Keywords

impossible worldslogical impossibilitynon-normal worldsnon-classical logichyperintentionalitycounterpossibles
Type
Element
Information
Series: Elements in Philosophy and Logic
Online ISBN: 9781009180573
Publisher: Cambridge University Press
Print publication: 28 March 2024

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References

Badura, C., & Berto, F. (2018). ‘Truth in Fiction, Impossible Worlds, and Belief Revision’. Australasian Journal of Philosophy, 97(1), 178–193.CrossRefGoogle Scholar
Baker, A. (2005). ‘Are There Genuine Mathematical Explanations of Physical Phenomena?’. Mind, 114(454), 223–238.CrossRefGoogle Scholar
Baker, A. (2009). ‘Mathematical Explanation in Science’. British Journal for the Philosophy of Science, 60(3), 611–633.CrossRefGoogle Scholar
Baker, A. (2017a). ‘Mathematical Spandrels’. Australasian Journal of Philosophy, 95(4), 779–793.CrossRefGoogle Scholar
Baker, A. (2017b). ‘Mathematics and Explanatory Generality’. Philosophia Mathematica, 25(2), 194–209.Google Scholar
Baker, A., & Colyvan, M. (2011). ‘Indexing and Mathematical Explanation’. Philosophia Mathematica, 19, 323–334.CrossRefGoogle Scholar
Baron, S. (2020). ‘Counterfactual Scheming’. Mind, 129(514), 535–562.CrossRefGoogle Scholar
Baron, S., Colyvan, M., & Ripley, D. (2017). ‘How Mathematics Can Make a Difference?’. Philosophers’ Imprint, 17(3).Google Scholar
Baron, S., Colyvan, M., & Ripley, D. (2020). ‘A Counterfactual Approach to Explanation in Mathematics’. Philosophia Mathematica, 28(1), 1–34.CrossRefGoogle Scholar
Barwise, J. (1989). The Situation in Logic. Stanford: CSLI.Google Scholar
Barwise, J., & Perry, J. (1983). Situations and Attitudes. Cambridge, MA: MIT Press.Google Scholar
Beall, J., & Restall, G. (2006). Logical Pluralism. Oxford: Oxford University Press.Google Scholar
Bernstein, S. (2016). ‘Omission Impossible’. Philosophical Studies, 173, 2575–2589.CrossRefGoogle Scholar
Berto, F. (2021). ‘Equivalence in Imagination’. In Badura, C., & Kind, E. (Eds.), Epistemic Uses of Imagination (pp. 122–140). New York: Routledge.CrossRefGoogle Scholar
Berto, F. (2022). Topics of Thought. Oxford: Oxford University Press.CrossRefGoogle Scholar
Berto, F., French, R., Priest, G., & Ripley, D. (2018). ‘Williamson on Counterpossibles’. Journal of Philosophical Logic, 47, 693–713.CrossRefGoogle ScholarPubMed
Berto, F., & Jago, M. (2019). Impossible Worlds. Oxford: Oxford University Press.CrossRefGoogle Scholar
Berto, F., & Jago, M. (2022). ‘Impossible Worlds’. In Zalta, E. N., & Nodelman, U. (Eds.), The Stanford Encyclopedia of Philosophy (Winter 2022 ed.). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/win2022/entries/impossible-worlds/.Google Scholar
Berto, F., & Nolan, D. (2021). ‘Hyperintensionality’. In Zalta, E. N. (Ed.), The Stanford Encyclopedia of Philosophy (Summer 2021 ed.). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/sum2021/entries/hyperintensionality/.Google Scholar
Bjerring, J. C. (2013). ‘Impossible Worlds and Logical Omniscience: An Impossibility Result’. Synthese, 190, 2505–2524.CrossRefGoogle Scholar
Bjerring, J. C. (2014). ‘On Counterpossibles’. Philosophical Studies, 168, 327–353.CrossRefGoogle Scholar
Bjerring, J. C., & Schwarz, W. (2017). ‘Granularity Problems’. Philosophical Quarterly, 67(266), 22–37.CrossRefGoogle Scholar
Cotnoir, A. (2018). ‘Logical Nihilism’. In Kellen, N., Pedersen, N., & Wyatt, J. (Eds.), Pluralisms in Truth and Logic (pp. 301–329). London: Palgrave Macmillan.CrossRefGoogle Scholar
Cresswell, M. (1995). ‘S1 Is Not So Simple’. In Sinnott-Armstrong, E., Raffiman, D., & Asher, N. (Eds.), Modality, Morality and Belief: Essays in Honor of Ruth Barcan Marcus (pp. 29–40). Cambridge: Cambridge University Press.Google Scholar
Elliot, E. (2019). ‘Impossible Worlds and Partial Beliefs’. Synthese, 196, 3433–3458.CrossRefGoogle Scholar
Estrada-González, L. (2012). ‘Models of Possibilism and Trivialism’. Logic and Logical Philosophy, 21(2), 175–205.Google Scholar
Fouché, C. (2022). ‘Hybrid Modal Realism Debugged’. Erkenntnis, Online First.Google Scholar
French, R., Girard, P., & Ripley, D. (2022). ‘Classical Counterpossibles’. The Review of Symbolic Logic, 15(1), 259–275.CrossRefGoogle Scholar
Girard, P., & Tanaka, K. (2016). ‘Paraconsistent Dynamics’. Synthese, 193(1), 1–14.CrossRefGoogle Scholar
Goodman, J. (2004). ‘An Extended Lewis/Stalnaker Semantics and the New Problem of Counterpossibles’. Philosophical Papers, 33(1), 35–66.CrossRefGoogle Scholar
Hintikka, J. (1962). Knowledge and Belief. Ithaca: Carnell University Press.Google Scholar
Jacob, P. (2023). ‘Intentionality’. In Zalta, E. N., & Nodelman, U. (Eds.), The Stanford Encyclopedia of Philosophy (Spring 2023 ed.). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/spr2023/entries/intentionality/.Google Scholar
Jago, M. (2007). ‘Hintikka and Cresswell on Logical Omniscience’. Logic and Logical Philosophy, 15, 325–354.CrossRefGoogle Scholar
Jago, M. (2009). ‘Logical Information and Epistemic Space’. Synthese, 167, 327–341.CrossRefGoogle Scholar
Jago, M. (2013a). ‘The Content of Deduction’. Journal of Philosophical Logic, 42, 317–334.CrossRefGoogle Scholar
Jago, M. (2013b). ‘Impossible Worlds’. Noûs, 47, 713–728.Google Scholar
Jago, M. (2014). The Impossible. Oxford: Oxford University Press.CrossRefGoogle Scholar
Kabay, P. (2010). On the Plenitude of Truth: A Defense of Trivialism. London: Lambert Academic.Google Scholar
Kasirzadeh, A. (2023). ‘Counter Countermathematical Explanations’. Erkenntnis, 88, 2537–2560.CrossRefGoogle Scholar
Kiourti, I. (2019). ‘An Excess of Dialetheias: In Defence of Genuine Impossible Worlds’. In Rieger, A., & Young, G. (Eds.), Dialetheism and Its Applications (pp. 81–100). Cham: Springer.CrossRefGoogle Scholar
Kocurek, A., & Jerzak, E. (2021). ‘Counterlogicals as Counterconventionals’. Journal of Philosophical Logic, 50, 673–704.CrossRefGoogle Scholar
Kouri Kissel, T. (2019). ‘Metalinguistic Negotiation and Logical Pluralism’. Synthese, 198(Suppl 20), 4801–4812.CrossRefGoogle Scholar
Kratzer, A. (1977). ‘What “Must” and “Can” Must and Can Mean’. Linguistics and Philosophy, 1(3), 337–355.CrossRefGoogle Scholar
Kripke, S. (1965). ‘Semantical Analysis of Modal Logic II. Non-Normal Modal Propositional Calculi’. In Addison, J., Henkin, L., & Tarski, A. (Eds.), The Theory of Models (pp. 206–220). Amsterdam: North-Holland.Google Scholar
Lemmon, E. J. (1957). ‘New Foundations for Lewis Modal Systems’. The Journal of Symbolic Logic, 22, 176–186.CrossRefGoogle Scholar
Lewis, C. I. (1918). A Survey of Symbolic Logic. Berkeley: University of California Press.CrossRefGoogle Scholar
Lewis, D. (1973). Counterfactuals. Oxford: Blackwell.Google Scholar
Lewis, D. (1979). ‘Counterfactual Dependence and Time’s Arrow’. Noûs, 13, 455–476.CrossRefGoogle Scholar
Lewis, D. (1981). ‘Are We Free to Break the Laws?’. Theoria, 47, 113–121.CrossRefGoogle Scholar
Lewis, D. (1986). Philosophical Papers (Vol. 2). Oxford: Oxford University Press.Google Scholar
Lynch, M. (2009). Truth as One and Many. Oxford: Oxford University Press.CrossRefGoogle Scholar
Mares, E. (1997). ‘Who’s Afraids of Impossible Worlds?’. Notre Dame Journal of Formal Logic, 38, 516–526.CrossRefGoogle Scholar
Mortensen, C. (1989). ‘Anything Is Possible’. Erkenntnis, 30, 319–337.CrossRefGoogle Scholar
Mortensen, C. (1995). Inconsistent Mathematics. Dordrecht: Kluwer.CrossRefGoogle Scholar
Nolan, D. (1997). ‘Impossible Worlds: A Modest Approach’. Notre Dame Journal of Formal Logic, 38, 535–572.CrossRefGoogle Scholar
Nolan, D. (2013). ‘Impossible Worlds’. Philosophy Compass, 8, 360–372.CrossRefGoogle Scholar
Nolan, D. (2014). ‘Hyperintensional Metaphysics’. Philosophical Studies, 171(1), 149–160.CrossRefGoogle Scholar
Nolan, D. (2017). ‘Causal Counterfactuals and Impossible Worlds’. In Beebee, H., Hitchcock, C., & Price, H. (Eds.), Making a Difference: Essays on the Philosophy of Causation (pp. 14–32). Oxford: Oxford University Press.Google Scholar
Priest, G. (1979). ‘Logic of Paradox’. Journal of Philosophical Logic, 8, 219–241.CrossRefGoogle Scholar
Priest, G. (1992). ‘What Is a Non-Normal World?’. Logique et Analyse, 35, 291–302.Google Scholar
Priest, G. (1997a). ‘Inconsistent Models of Arithmetic Part I: Finite Models’. Journal of Philosophical Logic, 26(2), 223–235.CrossRefGoogle Scholar
Priest, G. (1997b). ‘Sylvan’s Box’. Notre Dame Journal of Formal Logic, 38(4), 573–582.Google Scholar
Priest, G. (2000). ‘Inconsistent Models of Arithmetic Part II: The General Case’. The Journal of Symbolic Logic, 65(4), 1519–1529.CrossRefGoogle Scholar
Priest, G. (2001). ‘Logic: One or Many?’. In Woods, J., & Brown, B. (Eds.), Logical Consequences: Rival Approaches (pp. 23–38). Oxford: Hermes Scientific.Google Scholar
Priest, G. (2005). Towards Non-Being. Oxford: Oxford University Press.CrossRefGoogle Scholar
Priest, G. (2008). An Introduction to Non-Classical Logic (2nd ed.). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Priest, G. (2013). ‘Mathematical Pluralism’. Logic Journal of the IGPL, 21(1), 4–13.CrossRefGoogle Scholar
Priest, G. (2016a). ‘Thinking the Impossible’. Philosophical Studies, 173, 2649–2662.CrossRefGoogle Scholar
Priest, G. (2016b). Towards Non-Being (2nd ed.). Oxford: Oxford University Press.CrossRefGoogle Scholar
Priest, G. (202+). ‘Mission Impossible’. In Weiss, Y., & Padró, R. (Eds.), Saul Kripke on Modal Logic. New York: Springer.Google Scholar
Priest, G., Tanaka, K., & Weber, Z. (2022). ‘Paraconsistent Logic’. In Zalta, E. N., & Nodelman, U. (Eds.), The Stanford Encyclopedia of Philosophy (Spring 2022 ed.). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/entries/logic-paraconsistent/.Google Scholar
Rantala, V. (1982a). ‘Impossible Worlds Semantics and Logical Omniscience’. Acta Philosophica Fennica, 35, 18–24.Google Scholar
Rantala, V. (1982b). ‘Quantified Modal Logic: Non-Normal Worlds and Propositional Attitudes’. Studia Logica, 41, 41–65.CrossRefGoogle Scholar
Restall, G. (1997). ‘Ways Things Can’t Be’. Notre Dame Journal of Formal Logic, 38(4), 583–596.CrossRefGoogle Scholar
Routley, R., & Meyer, R. (1973). ‘The Semantics of Entailment – I’. In Leblanc, H. (Ed.), Truth, Syntax and Modality (pp. 199–243). Amsterdam: North-Holland.CrossRefGoogle Scholar
Routley, R., Plumwood, V., Meyer, R. K., & Brady, R. T. (1982). Relevant Logics and Their Rivals. Atascadero: Ridgeview.Google Scholar
Routley, R., & Routley, V. (1972). ‘The Semantics of First Degree Entailment’. Noûs, 6, 335–359.CrossRefGoogle Scholar
Russell, G. (2008). ‘One True Logic?’. Journal of Philosophical Logic, 37(6), 593–611.CrossRefGoogle Scholar
Russell, G. (2017). ‘An Introduction to Logical Nihilism’. In Leitgeb, H., Niiniluoto, I., Seppälä, P., & Sober, E. (Eds.), Logic, Methodology and Philosophy of Science – Proceedings of the 15th International Congress (pp. 125–135). London: College Publications.Google Scholar
Russell, G. (2018). ‘Logical Nihilism: Could There Be No Logic?’. Philosophical Issues, 28, 308–324.CrossRefGoogle Scholar
Sandgren, A., & Tanaka, K. (2020). ‘Two Kinds of Logical Impossibility’. Noûs, 54(4), 795–806.CrossRefGoogle Scholar
Stalnaker, R. (1968). ‘A Theory of Conditionals’. In Rescher, N. (Ed.), Studies in Logical Theory (pp. 98–112). Oxford: Blackwell.Google Scholar
Stalnaker, R. (1981). ‘Indexical Belief’. Synthese, 49, 129–151.CrossRefGoogle Scholar
Stalnaker, R. (2008). Our Knowledge of the Internal World. Oxford: Oxford University Press.CrossRefGoogle Scholar
Tanaka, K. (2013). ‘Making Sense of Paraconsistent Logic: The Nature of Logic, Classical Logic and Paraconsistent Logic’. In Tanaka, K., Berto, F., Mares, E., and Paoli, F. et al. (Eds.), Paraconsistency: Logic and Applications (pp. 15–25). Dordrecht: Springer.CrossRefGoogle Scholar
Tanaka, K. (2018). ‘Logically Impossible Worlds’. Australasian Journal of Logic, 15(2), 489–497.CrossRefGoogle Scholar
Tanaka, K. (202+). ‘Impossibility Happens!’. (A paper presented to the 2023 Australasian Association of Philosophy conference.)Google Scholar
Tanaka, K., & Girard, P. (2023). ‘Against Classical Paraconsistent Metatheory’. Analysis, 83(2), 285–294.CrossRefGoogle Scholar
Tversky, A., & Kahneman, D. (1981). ‘The Framing of Decisions and the Psychology of Choice’. Science, 211, 453–458.CrossRefGoogle ScholarPubMed
Vander Laan, D. (1997). ‘The Ontology of Impossible Worlds’. Notre Dame Journal of Formal Logic, 38, 597–620.CrossRefGoogle Scholar
Weber, Z. (2021). Paradoxes and Inconsistent Mathematics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Weber, Z., & Omori, H. (2019). ‘Observations on the Trivial World’. Erkenntnis, 84, 975–994.CrossRefGoogle Scholar
Williamson, T. (2007). The Philosophy of Philosophy. Oxford: Oxford University Press.CrossRefGoogle Scholar
Williamson, T. (2010). ‘Modal Logic Within Counterfactual Logic’. In Hale, B. and Hoffmann, A. (Eds.), Modality: Metaphysics, Logic, and Epistemology (pp. 81–96). Oxford: Oxford University Press.CrossRefGoogle Scholar
Williamson, T. (2013). Modal Logic as Metaphysics. Oxford: Oxford University Press.CrossRefGoogle Scholar
Williamson, T. (2020). Suppose and Tell. Oxford: Oxford University Press.CrossRefGoogle Scholar
Williamson, T. (2021). ‘Degrees of Freedom: Is Good Philosophy Bad Science?’. Disputatio, 13(61), 73–94.CrossRefGoogle Scholar
Williamson, T. L., & Sandgren, A. (2021). ‘Law-Abiding Causal Decision Theory’. The British Journal for the Philosophy of Science, Online First.Google Scholar
Yagisawa, T. (2010). Worlds and Individuals. Oxford: Oxford University Press.Google Scholar
Zalta, E. (1997). ‘A Classically-Based Theory of Impossible Worlds’. Notre Dame Journal of Formal Logic, 38, 640–660.CrossRefGoogle Scholar

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