An Argument for Completely General Facts
Generalized Molecular Formulas in Logical Atomism
DOI:
https://doi.org/10.15173/jhap.v9i7.4439Abstract
In his 1918 logical atomism lectures, Russell argued that there are no molecular facts. But he posed a problem for anyone wanting to avoid molecular facts: we need truth-makers for generalizations of molecular formulas, but such truth-makers seem to be both unavoidable and to have an abominably molecular character. Call this the problem of generalized molecular formulas. I clarify the problem here by distinguishing two kinds of generalized molecular formula: incompletely generalized molecular formulas and completely generalized molecular formulas. I next argue that, if empty worlds are logically possible, then the model-theoretic and truth-functional considerations that are usually given address the problem posed by the first kind of formula, but not the problem posed by the second kind. I then show that Russell’s commitments in 1918 provide an answer to the problem of completely generalized molecular formulas: some truth-makers will be non-atomic facts that have no constituents. This shows that the neo-logical atomist goal of defending the principle of atomicity—the principle that only atomic facts are truth-makers—is not realizable.
References
Armstrong, D. M., 1978a. A Theory of Universals: Universals & Scientific Realism. New York: Cambridge University Press.
———, 1978b. Nominalism & Realism: Universals & Scientific Realism. New York: Cambridge University Press.
———, 1997. A World of States of Affairs. Cambridge: Cambridge University Press.
———, 2004. Truth and Truthmakers. Cambridge: Cambridge University Press.
Barker, Stephen and Mark Jago, 2012. “Being Positive About Negative Facts.” Philosophy and Phenomenological Research LXXXV: 117–38.
Baronett, Stan, 2013. Logic, Second edition. New York: Oxford University Press.
Benacerraf, Paul, 1973. “Mathematical Truth.” The Journal of Philosophy 70(19): 661–79.
Cameron, Ross P., 2005. “Truthmaker Necessitarianism and Maximalism.” 48(189/192): 43–56.
———, 2008. “How to be a Truthmaker Maximalist.” Noûs 42(3): 410–21.
Campbell, Keith, 1997. “The Metaphysic of Abstract Particulars.” In Mellor and Oliver (1997), pp. 125–39.
Church, Alonzo, 1956. Introduction to Mathematical Logic. Princeton, NJ: Princeton University Press.
Cocchiarella, Nino B., 2007. Formal Ontology and Conceptual Realism, edited by Vincent F. Hendricks and John Symons. New York: Springer.
Coggins, Geraldine, 2010. Could There Have Been Nothing? Against Metaphysical Nihilism. London: Palgrave Macmillan.
David, Marian, 2016. The Correspondence Theory of Truth. Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/archives/fall2016/entries/truth-correspondence/.
Efird, David and Tom Stoneham, 2009. “Justifying Metaphysical Nihilism: A Response to Cameron.” The Philosophical Quarterly 59: 132–37.
Elkind, Landon D. C. and Gregory Landini, eds., 2018. The Philosophy of Logical Atomism: A Centenary Reappraisal. London: Palgrave MacMillan.
Elkind, Landon D. C., 2018. “On Russell’s Logical Atomism.” In Elkind and Landini (2018), pp. 3–37.
Goldrei, Derek, 2005. Propositional and Predicate Calculus. Boca Raton, FL: CRC Press.
Griffin, Nicholas, 1980. “Russell on the Nature of Logic.” Synthese 45(1): 117–88.
Hunter, Geoffrey, 1973. Metalogic: An Introduction to the Metatheory of Standard First Order Logic. Berkeley, CA: University of California Press.
Jago, Mark, 2011. “Setting the Facts Straight.” Journal of Philosophical Logic 40(1): 33–54.
Klement, Kevin C., 2004. “Putting Form Before Function: Logical Grammar in Frege, Russell, and Wittgenstein.” 4(2): 1–47.
———, 2015. “The Constituents of the Propositions of Logic.” In Acquaintance, Knowledge, and Logic: New Essays on Bertrand Russell’s The Problems of Philosophy, edited by Donovan Wishon and Bernard Linsky, pp. 189–230. Stanford, CA: CSLI Publications.
Kripke, Saul, 1980. Naming and Necessity. Cambridge, MA: Harvard University Press.
Lambert, Karel, 2002. “The Philosophical Foundations of Free Logic.” In Free Logic: Selected Essays, pp. 122–75. Cambridge: Cambridge University Press.
Lewis, David K., 1968. “Counterpart Theory and Quantified Modal Logic.” The Journal of Philosophy 65: 113–26.
———, 2001. “Truthmaking and Difference-Making.” Noûs 35(4): 602–15.
MacBride, Fraser, 2016. Truthmakers. Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/archives/fall2016/entries/truthmakers/.
Maclean, Gülberk Koç, 2018. “Logical Atomism in Russell’s Later Works.” In Elkind and Landini (2018), pp. 69–90.
Maddy, Penelope, 2014. The Logical Must: Wittgenstein on Logic. Oxford: Oxford University Press.
Mellor, D. H. and Alex Oliver, eds., 1997. Properties. New York: Oxford University Press.
Mendelson, Elliott, 1997. Introduction to Mathematical Logic, fourth edition. London: Chapman & Hall.
Menzel, Christopher, 2017. Possible Worlds. Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/archives/win2017/entries/possible-worlds/.
Mulligan, Kevin, Peter Simons and Barry Smith, 1984. “Truth-Makers.” Philosophy and Phenomenological Research 44(3): 287–321.
Nolan, Daniel, 2011. “The Extent of Metaphysical Necessity.” Philosophical Perspectives 25: 313–39.
Parent, Ted, 2012. Modal Metaphysics. Internet Encyclopedia of Philosophy, https://www.iep.utm.edu/mod-meta/.
Perovic, Katarina, 2018. “Can We Be Positive About Russell’s Negative Facts?” In Elkind and Landini (2018), pp. 199–218.
Quine, W. V., 1954. “Quantification and the Empty Domain.” The Journal of Symbolic Logic 19(3): 177–79.
Restall, Greg, 2008. “Truth-Makers, Entailment and Necessity.” In Truth and Truth-Making, edited by E. J. Lowe and A. Rami, pp. 87–97. Montreal: McGill-Queen’s University Press.
Rodriguez-Pereyra, Gonzalo, 2006. “Truthmakers.” Philosophy Compass 1(2): 186–200.
Russell, Bertrand, 1905/1994. “Necessity and Possibility.” In Foundations of Logic, 1903-05, edited by Alasdair Urquhart, pp. 507–20.
———, 1908/2014. “ “If" and “Imply", A Reply to Mr. MacColl.” In Toward “Principia Mathematica", 1905-08, edited by Gregory H. Moore, pp. 581–84. New York: Routledge.
———, 1913/1984. Theory of Knowledge: The 1913 Manuscript, edited by Elizabeth Ramsden Eames. Winchester, MA: George Allen and Unwin Ltd.
———, 1918/1986. “The Philosophy of Logical Atomism.” In The Philosophy of Logical Atomism and Other Essays, 1914-19, edited by John G. Slater, pp. 155–244. New York: George Allen and Unwin Ltd.
———, 1919. Introduction to Mathematical Philosophy. New York: George Allen and Unwin Ltd.
———, 1937. The Principles of Mathematics, 2nd edition. New York: George Allen and Unwin Ltd.
———, 1940/1973. An Inquiry into Meaning and Truth. London: Penguin University Books.
———, 1948/1967. Human Knowledge: Its Scope and Limits. Forge Village, MA: Simon and Schuster.
Shoemaker, Sydney, 1997. “Causality and Properties.” In Mellor and Oliver (1997), pp. 228–54.
Simons, Peter, 1992. “Logical Atomism and its Ontological Refinement: A Defense.” In Language, Truth, and Ontology, edited by Kevin Mulligan, pp. 157–79. Dordrecht: Kluwer.
Stevens, Graham, 2011. The Theory of Descriptions, edited by Michael Beaney. London: Palgrave MacMillan.
Tomassi, Paul, 1999. Logic. London: Routledge.
Williams, Donald C., 1997. “On the Elements of Being: I.” In Mellor and Oliver (1997), pp. 112–24.
Williamson, Timothy, 1999. “A Note on Truth, Satisfaction, and the Empty Domain.” Analysis 59(1): 3–8.
———, 2013. Modal Logic as Metaphysics. Oxford: Oxford University Press.
Wittgenstein, Ludwig, 1913/2009. “Notes on Logic.”: 276–95.
———, 1922/1971. Tractatus Logico-Philosophicus, Second edition, edited by D. F. Pears and B. F. McGuinness. London: Routledge & Kegan Paul.
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