The Principle of Sufficient Reason Defended: There Is No Conjunction of All Contingently True Propositions


Toward the end of his classic treatise An Essay on Free Will, Peter van Inwagen offers a modal argument against the Principle of Sufficient Reason which he argues shows that the principle “collapses all modal distinctions.” In this paper, a critical flaw in this argument is shown to lie in van Inwagen’s beginning assumption that there is such a thing as the conjunction of all contingently true propositions. This is shown to follow from Cantor’s theorem and a property of conjunction with respect to contingent propositions. Given the failure of this assumption, van Inwagen’s argument against the Principle of Sufficient Reason cannot succeed, at least not without the addition of some remarkable and previously unacknowledged qualifications.

This is a preview of subscription content, log in to check access.


  1. 1.

    Since van Inwagen takes mutually entailed propositions to be identical (“... if it both entailed and were entailed by P, it would be P...”), another way of stating this condition is to say that no contingent proposition can be sufficient reason for itself.

  2. 2.

    Van Inwagen (1983), p. 203

  3. 3.

    Van Inwagen (1983), p. 203-204

  4. 4.

    Grim (1984), p. 207

  5. 5.

    Van Inwagen (1983), p. 203

  6. 6.

    It perhaps ought to be said that this N needn’t be the same proposition for every \(C_{\mathcal {X}}\). It is possible to get a unique N for every collection \(C_{\mathcal {X}}\), if desired. Simply draw such necessary propositions from the deep well of mathematics, which will afford any cardinality of them one might need.

  7. 7.

    Oppy (2000) agrees with this assessment: “For example, despite the claims of Gale and Pruss to the contrary, one might wonder whether the [conjunction of all contingently true propositions] for a world can differ from the [conjunction of all true propositions] for that world: since a conjunction of a necessary proposition and a contingent proposition is contingent, the conjunction of all contingent propositions will ‘include’ all of the necessary propositions.”

  8. 8.

    Many kind thanks to Michael Lynch, Peter van Inwagen, Chad Marxen, Christopher Menzel, Josh Rasmussen, two anonymous referees for Philosophia, and audiences at 2014 Meeting of the North Carolina Philosophical Association, the IX Annual Mark L. Shapiro Graduate Philosophy Conference at Brown University, and the 2014 Eastern Division Meeting of the APA for their supportive yet challenging comments on earlier drafts of this paper.


  1. Gale, R., & Pruss, A. (1999). A New Cosmological Argument. Religious Studies, 35(4), 461–476.

    Article  Google Scholar 

  2. Grim, P. (1984). There Is No Set of All Truths. Analysis, 44(4), 206–208.

    Article  Google Scholar 

  3. Grim, P. (1986). On Sets and Worlds: A Reply to Menzel. Analysis, 46(4), 186–191.

    Article  Google Scholar 

  4. Oppy, G. (2000). On A New Cosmological Argument. Religious Studies, 36(3), 345–353.

    Article  Google Scholar 

  5. Pruss, A. (2006). The Principle of Sufficient Reason: A Reassessment. New York: Cambridge University Press.

    Google Scholar 

  6. Van Inwagen, P. (1983). An Essay on Free Will. Oxford: Claredon Press.

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Christopher M. P. Tomaszewski.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

P. Tomaszewski, C.M. The Principle of Sufficient Reason Defended: There Is No Conjunction of All Contingently True Propositions. Philosophia 44, 267–274 (2016).

Download citation


  • Principle of sufficient reason
  • Free will
  • Cantor’s theorem
  • Propositions
  • Modality