An Argument for Completely General Facts
Generalized Molecular Formulas in Logical Atomism
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.
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.
The Public Knowledge Project recommends the use of the Creative Commons license. The Journal for the History of Analytical Philosophy requires authors to agree to a Creative Commons Attribution /Non-commercial license. Authors who publish with the Journal for the History of Analytical Philosophy agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons BY-NC license.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access)
This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.