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PURE LOGIC OF ITERATED FULL GROUND

Published online by Cambridge University Press:  13 July 2018

JON ERLING LITLAND
JON ERLING LITLAND*
Affiliation:
Department of Philosophy, University of Texas at Austin
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF TEXAS AT AUSTIN STOP C3500 TX 78712, AUSTIN E-mail: [email protected]
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Abstract

This article develops the Pure Logic of Iterated Full Ground (plifg), a logic of ground that can deal with claims of the form “ϕ grounds that (ψ grounds θ)”—what we call iterated grounding claims. The core idea is that some truths Γ ground a truth ϕ when there is an explanatory argument (of a certain sort) from premisses Γ to conclusion ϕ. By developing a deductive system that distinguishes between explanatory and nonexplanatory arguments we can give introduction rules for operators for factive and nonfactive full ground, as well as for a propositional “identity” connective. Elimination rules are then found by using a proof-theoretic inversion principle.

Keywords

03A0503F99grounditerated groundexplanationlogic of groundinversion principlenatural deduction
Type
Research Article
Information
The Review of Symbolic Logic , Volume 11 , Issue 3 , September 2018 , pp. 411 - 435
Copyright
Copyright © Association for Symbolic Logic 2018 

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References

BIBLIOGRAPHY

Audi, P. (2012). Grounding: Towards a theory of the in virtue of relation. Journal of Philosophy, 109(12), 685–711.CrossRefGoogle Scholar
Bennett, K. (2011). By our bootstraps. Philosophical Perspectives, 25(1), 27–41.CrossRefGoogle Scholar
Bliss, R. (2014). Viciousness and circles of ground. Metaphilosophy, 45(2), 245–256.CrossRefGoogle Scholar
Bliss, R. & Trogdon, K. (2016). Metaphysical grounding. In Zalta, E. N., editor. The Stanford Encyclopedia of Philosophy (Winter 2016 edition). Available at https://plato.stanford.edu/archives/win2016/entries/grounding/.Google Scholar
Correia, F. (2010). Grounding and truth-functions. Logique et Analyse, 53(211), 251–279.Google Scholar
Correia, F. (2014). Logical grounds. Review of Symbolic Logic, 7(1), 31–59.CrossRefGoogle Scholar
Correia, F. (2017). An impure logic of representational grounding. Journal of Philosophical Logic, 46(5), 507–538.CrossRefGoogle Scholar
Daly, C. (2012). Scepticism about grounding. In Correia, F. and Schnieder, B., editors. Metaphysical Grounding. Cambridge: Cambridge University Press, pp. 81–100.CrossRefGoogle Scholar
Dasgupta, S. (2014a). On the plurality of grounds. Philosophers’ Imprint, 14(20), 1–28.Google Scholar
Dasgupta, S. (2014b). The possibility of physicalism. Journal of Philosophy, 111(9/10), 557–592.CrossRefGoogle Scholar
deRosset, L. (2013a). Grounding explanations. Philosophers’ Imprint, 13(7), 1–26.Google Scholar
deRosset, L. (2013b). What is weak ground? Essays in Philosophy, 14(1), 7–18.CrossRefGoogle Scholar
deRosset, L. (2014). On weak ground. Review of Symbolic Logic, 7(4), 713–744.CrossRefGoogle Scholar
Dorr, C. (2016). To be F is to be G. Philosophical Perspectives, 30, 39–134.CrossRefGoogle Scholar
Fine, K. (1994a). Essence and modality. Philosophical Perspectives, 8, 1–16.CrossRefGoogle Scholar
Fine, K. (1994b). Senses of essence. In Raffman, D., Sinnott Armstrong, W., and Asher, N., editors. Modality, Morality, and Belief: Essays in Honor of Ruth Barcan Marcus. Chicago: University of Chicago Press, pp. 53–73.Google Scholar
Fine, K. (2001). The Question of realism. Philosophers’ Imprint, 1(1), 1–30.Google Scholar
Fine, K. (2010). Some puzzles of ground. Notre Dame Journal of Formal Logic, 51(1), 97–118.CrossRefGoogle Scholar
Fine, K. (2012a). Guide to ground. In Correia, F. and Schnieder, B., editors. Metaphysical Grounding. Cambridge: Cambridge University Press. pp. 37–80.CrossRefGoogle Scholar
Fine, K. (2012b). The pure logic of ground. The Review of Symbolic Logic, 5(1), 1–25.CrossRefGoogle Scholar
Gentzen, G. (1969). The Collected Papers of Gerhard Gentzen. Amsterdam: North-Holland.Google Scholar
Hofweber, T. (2009). Ambitious, yet modest, metaphysics. In Chalmers, D., Manley, D., and Wasserman, R., editors. Metametaphysics: New Essays on the Foundations of Ontology. New York: Oxford University Press, pp. 269–289.Google Scholar
Jenkins, C. (2011). Is metaphysical dependence irreflexive? The Monist, 94(2), 267–276.CrossRefGoogle Scholar
Krämer, S. (2013). A simpler puzzle of ground. Thought, 2(2), 85–89.Google Scholar
Litland, J. E. (2013). On some counterexamples to the transitivity of grounding. Essays in Philosophy, 14(1), 19–32.CrossRefGoogle Scholar
Litland, J. E. (2015). Grounding, explanation, and the limit of internality. Philosophical Review, 124(4), 481–532.CrossRefGoogle Scholar
Litland, J. E. (2016). Pure logic of many-many ground. Journal of Philosophical Logic, 45(5), 531–577.CrossRefGoogle Scholar
Litland, J. E. (2017a). Could the grounds’s grounding the grounded ground the grounded? Analysis, 78(1), 56–65.CrossRefGoogle Scholar
Litland, J. E. (2017b). Grounding ground. Oxford Studies in Metaphysics, 10, 279–316.CrossRefGoogle Scholar
Litland, J. E. (forthcoming). Bicollective ground: Towards a (hyper)graphic account. In Bliss, R. and Priest, G., editors. Reality and Its Structure: Essays in Fundamentality. New York: Oxford University Press, pp. 140–163.Google Scholar
Poggiolesi, F. (2016). On defining the notion of complete and immediate formal grounding. Synthese, 193(10), 3147–3167.CrossRefGoogle Scholar
Poggiolesi, F. (2018). On constructing a logic for the notion of complete and immediate formal grounding. Synthese, 195(3), 1231–1254.CrossRefGoogle Scholar
Raven, M. J. (2013). Is ground a strict partial order. American Philosophical Quarterly, 50(2), 191–199.Google Scholar
Rayo, A. (2013). The Construction of Logical Space. Oxford: Oxford University Press.CrossRefGoogle Scholar
Read, S. (2010). General-elimination harmony and the meaning of the logical constants. Journal of Philosophical Logic, 39(5), 557–576.CrossRefGoogle Scholar
Rosen, G. (2015). Real definition. Analytic Philosophy, 56, 189–209.CrossRefGoogle Scholar
Schaffer, J. (2012). Grounding, transitivity, and contrastivity. In Correia, F. and Schnieder, B., editors. Metaphysical Grounding. Cambridge: Cambridge University Press, pp. 122–138.CrossRefGoogle Scholar
Schnieder, B. (2011). A Logic for “Because”. Review of Symbolic Logic, 4(3), 445–465.CrossRefGoogle Scholar
Schroeder-Heister, P. (1984). A natural extension of natural deduction. Journal of Symbolic Logic, 49, 1284–1300.CrossRefGoogle Scholar
Wilsch, T. (2015a). The deductive-nomological account of metaphysical explanation. Australasian Journal of Philosophy, 94(1), 1–23.CrossRefGoogle Scholar
Wilsch, T. (2015b). The nomological account of ground. Philosophical Studies, 12(172), 3293–3312.CrossRefGoogle Scholar
Wilson, J. M. (2014). No work for a theory of grounding. Inquiry, 57(5–6), 535–579.CrossRefGoogle Scholar
Wilson, J. M. (2016). Grounding-based formulations of physicalism. Topoi, https://doi.org/10.1007/s11245-016-9435-7.Google Scholar
Yablo, S. & Rosen, G. (forthcoming). Solving the caesar problem—with metaphysics. In Miller, A., editor. Logic, Language and Metaphysics. Essays in Honor of Crispin Wright. Oxford: Oxford University Press.Google Scholar