Abstract
The fourteenth-century theorist Jean Buridan claimed that in a thoroughly bivalent framework central semantic concepts such as truth and signification are both free of paradox and ungrounded. This paper outlines and defends Buridan’s approach and suggests that it may give reason to think that ungroundedness is not problematic in semantics or in metaphysics.
I would like to thank, first, Magali Roques for organizing the wonderful meeting out of which this paper grew and for her patience with me while I revised it. I would also like to thank both the participants in the conference for their comments, and Hans Herzberger and Deborah J. Brown, sine quibus non.
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Notes
- 1.
Exactly what is on the left and right of that ‘because’ is controverted. Buridan insists that the bearers of truth are sentences and that what is signified by sentences are individual substances and qualities. For much of what follows we may abstract away from these claims.
- 2.
None of these claims is entirely uncontroversial. I suspect that this is because several quite distinct concepts are being conflated in the grounding literature. For one of these notions, one might, for example, appeal to the theory of per se or essentially ordered causes developed by such medieval figures as Thomas Aquinas and John Duns Scotus and summarized in Scotus’s Treatise on the First Principle where, distinguishing such an order from what may seem to us a more familiar notion of causation, he writes: “Per se or essentially ordered causes differ from accidentally ordered causes in three ways. The first difference is that in per se [ordered causes] the second, insofar as it causes, depends on the first. In accidentally [ordered causes] this is not so, although [the second] may depend [on the first] in being or in some other way. The second [difference] is that in things ordered per se there is causality of another ratio and order. In accidentally [ordered causes] it is not so. This [difference] follows from the first for no cause depends essentially in causing on another cause of the same ratio because in causation one of a single ratio suffices. A third [difference] follows—that all causes ordered per se are necessarily required at the same time for causing [the effect]; otherwise some causality per se to the effect would be lacking. Accidentally ordered [causes] are not required [to act] at the same time.” (Duns Scotus, A Treatise on God as First Principle 3.11, tr. Allan Wolter [Chicago, 1982], p. 47).
- 3.
Hans Herzberger, “Paradoxes of Grounding in Semantics,” Journal of Philosophy 67 no. 6 (1970), 147–48.
- 4.
Ibid., p. 148.
- 5.
Steven Yablo, “Paradox without Self-Reference,” Analysis 53 (1993), 251–52.
- 6.
Saul Kripke, “Outline of a Theory of Truth,” Journal of Philosophy 72, no. 19 (1975), 690–716. Anil Gupta, “Truth and Paradox,” Journal of Philosophical Logic 11 (1982), 1–60.
- 7.
P.T. Geach, Reference and Generality (Ithaca, NY, 1980), p. 10.
- 8.
John Buridan, Summulae de dialectica, trans. Gyula Klima (New Haven, 2001), p. 938.
- 9.
For a quick overview see my “Buridan’s Ontology,” in How Things Are, ed. James Bogen and James E. McGuire (Dordrecht, 1985), pp. 189–203.
- 10.
Here I am heavily indebted to Hans Herzberger, “Dimensions of Truth,” Journal of Philosophical Logic 2 (1973) 535–56. Buridan does not accept such items as facts or states of affairs and likely would resist even talk of “ways” things might be. Hence the unusual use of ‘howsoever’ (qualitercumque) to avoid a noun.
- 11.
John Buridan, Summulae de dialectica, trans. Gyula Klima (New Haven, 2001), p. 830. References to Buridan’s Summulae will be to this translation.
- 12.
Cf. John Buridan, Summulae de dialectica, p. 972.
- 13.
Buridan’s concept of entailment runs on correspondence not truth. Thus a set of sentences A entails a sentence B iff it is impossible for things to be as the conjunction of the sentences in A has it and not be as B has it. This has consequences. For example, given Buridan’s tokenism and the requirement that a sentence must exist to be true, it is impossible that ‘No sentence is negative’ be true and so impossible that it be true and that ‘God is Satan’ be false. Nonetheless, if there were no sentences, things could be as ‘No sentence is negative’ has it and not be as ‘God is Satan’ has it.
- 14.
Stephen Read, “The Liar Paradox from John Buridan Back to Thomas Bradwardine,” Vivarium 40, no. 2 (2002), 189–219, esp. pp. 199–203. See also his “The Truth Schema and the Liar,” in Unity, Truth and the Liar, ed. Shahid Rahman, Tero Tulenheimo, and Emmanuel Genot (Berlin, 2008), pp. 3–18, and “Further Thoughts on Tarski’s T-Scheme and the Liar,” also in Unity Truth and the Liar, pp. 205–25.
- 15.
Terence Parsons, “Comments on Stephen Read’s “The Truth-Schema and the Liar,” in Unity, Truth and the Liar, ed. Shahid Rahman, Tero Tulenheimo, and Emmanuel Genot (Berlin, 2008), pp. 129–34.
- 16.
This is suggested to me by his discussion of Sophism 10 of Chap. 8 of his Sophismata (Summulae de dialectica, trans. Klima, p. 977). There Buridan reasons (against the background of a case in which there are two uncontroversially true sentences and one uncontroversially false one) that if the only other sentence is ‘There are as many truths as falsehoods” that sentence is false because if we suppose things to be as that would have it (i.e. that there are not the same number of truths and falsehoods) then take with the claim that the sentence itself is true entails that it is false. For a different view see G.E. Hughes, John Buridan on Self-Reference (Cambridge, 1982), p. 123, and the review of it by Richard L. Epstein in History and Philosophy of Logic 6 (1985), 117–25, at p. 125.
- 17.
Perhaps, in line with the previous note, we can say more. If we suppose the correspondence condition for TT to not be met and we add the claim that TT is true we get a contradiction. Hence we need suppose the correspondence condition is met and so have no reason to deny truth to TT.
- 18.
I begin the tale in “Externalism, Singular Thought and Nominalist Ontology,” in The Demonic Temptations of Medieval Nominalism, ed. Gyula Klima and Alexander Hall (Newcastle-on-Tyne, 2011), pp. 137–47. Deborah Brown and I continue it a little in “On Bits and Pieces in the History of Philosophy,” in Composition as Identity, ed. Aaron J. Cotnoir and Donald L. Baxter (Oxford, 2014), pp. 34–47.
Works Cited
Medieval Sources
Buridan, John. 2001. Summulae de dialectica. Trans. G. Klima. New Haven: Yale University Press.
Duns Scotus, John. 1982. In De primo principio, ed. Allan Wolter. Chicago: Franciscan Herald Press.
Modern Sources
Epstein, Richard L. 1985. Review of John Buridan on Self-Reference by G.E. Hughes. History and Philosophy of Logic 6: 117–125.
Geach, P.T. 1980. Reference and Generality. Ithaca, NY: Cornell University Press.
Gupta, Anil. 1982. Truth and Paradox. Journal of Philosophical Logic 11: 1–60.
Herzberger, Hans. 1973. Dimensions of Truth. Journal of Philosophical Logic 2: 535–556.
———. 1970. Paradoxes of Grounding in Semantics. Journal of Philosophy 67 (6): 145–167.
Hughes, G.E. 1982. John Buridan on Self-Reference. Cambridge: Cambridge University Press.
Kripke, Saul. 1975. Outline of a Theory of Truth. Journal of Philosophy 72 (19): 690–716.
Normore, Calvin. 1985. Buridan’s Ontology. In How Things Are, ed. James Bogen and James E. McGuire, 189–203. Dordrecht: Reidel.
———. 2011. Externalism, Singular Thought and Nominalist Ontology. In The Demonic Temptations of Medieval Nominalism, ed. Gyula Klima and Alexander Hall, 137–147. Newcastle-on-Tyne: Cambridge Scholars Publishing.
Normore, Calvin, and Deborah Brown. 2014. On Bits and Pieces in the History of Philosophy. In Composition as Identity, ed. Aaron J. Cotnoir and Donald L. Baxter, 34–47. Oxford: Oxford University Press.
Parsons, Terence. 2008. Comments on Stephen Read’s “The Truth-Schema and the Liar”. In Unity, Truth and the Liar, ed. Shahid Rahman, Tero Tulenheimo, and Emmanuel Genot, 129–134. Berlin: Springer.
Read, Stephen. 2008a. Further Thoughts on Tarski’s T-Schema and the Liar. In Unity, Truth and the Liar, ed. Shahid Rahman, Tero Tulenheimo, and Emmanuel Genot, 205–225. Berlin: Springer.
———. 2002. The Liar Paradox from John Buridan Back to Thomas Bradwardine. Vivarium 40 (2): 189–219.
———. 2008b. The Truth Schema and the Liar. In Unity, Truth and the Liar, ed. Shahid Rahman, Tero Tulenheimo, and Emmanuel Genot, 3–18. Berlin: Springer.
Yablo, Steven. 1993. Paradox without Self-Reference. Analysis 53: 251–252.
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Normore, C.G. (2024). Up in the Air: Buridan’s Principled Rejection of Grounding. In: Normore, C.G., Schmid, S. (eds) Grounding in Medieval Philosophy. Historical-Analytical Studies on Nature, Mind and Action, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-031-53666-3_11
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