Abstract
Thomas Bradwardine’s solution to the semantic paradoxes, presented in his Insolubilia written in Oxford in the early 1320s, turns on two main principles: that a proposition is true only if things are wholly as it signifies; and that signification is closed under consequence. After exploring the background in Walter Burley’s account of the signification of propositions, I consider the extent to which Bradwardine’s theory is compatible with the compositional principles of the distribution of truth over conjunction, disjunction, negation and the conditional.
Presented at the Conference on ‘Truth at Work’, Paris 20–23 June 2011. This work is supported by Research Grant AH/F018398/1 (Foundations of Logical Consequence) from the Arts and Humanities Research Council, UK.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
(Raine 1843), p. xii: “Dubito certe annon in te solum cudatur proverbium Asinus ad lyram. At profecto tu non dignus es qui esses procurator in sophistarum scholis: sic enim insurgit quidam sophista contra Procuratorem; ‘Qui dicit te esse animal dicit verum; at qui dicit te esse asinum dicit te esse animal ergo, qui dicit te esse asinum dicit verum.’ ‘Concedo totum,’ inquit Procurator: ‘non ausus sum negare pro auribus.’ Videtis, itaque, Procurator fatetur se esse asinum per confessionem auricularem.” I am grateful to my colleague, Professor Sarah Broadie, for her help in trying to capture the subtlety of the original Latin in English. The proverb comes from Aesop’s Fables. ‘Auricular confession’ apparently means confession made vocally by the penitent to a priest, as distinct from silently addressed to God. Presumably there’s a supposed threat that if he says he’s not a donkey then they’ll make it true that he’s not a donkey by cutting off his (donkey’s) ears.
- 2.
- 3.
The Abstractiones are as yet unpublished; a preliminary edition can be found online at (Ricardus n.d.).
- 4.
Burley’s treatise was edited in (Burley 1955), and translated into English in (Burley 2000). The counter-example also appears in the treatise on ‘Consequences’ of 1302 attributed to Burley and edited in (Green-Pedersen 1980, p. 113), but the later passage of the Shorter Treatise is little more than a verbatim repetition of the earlier text. The example is discussed, rather inconsequentially, in (Jacquette 2007a) (which is a shorter version of (Jacquette 2007b)).
- 5.
(Burley 1955, p. 200 ff.): “Quidquid sequitur ad consequens, sequitur ad antecedens.”
- 6.
(Burley 1955, p. 205), my own translation.
- 7.
- 8.
- 9.
“Cum superius sit dicere te esse animal quam dicere te esse asinum.”
- 10.
“Et non ualet: te esse animal est uerum, ergo omnis dicens te esse animal dicit uerum; sed est fallacia figurae dictionis; commutatur enim unus modus supponendi in alium.”
- 11.
- 12.
(Brown 1973, § 1.03): “Oratio in mente componitur ex rebus patet per Commentatorem, VI Metaphysicae, in fine, qui dicit quod entia vera, cuiusmodi sunt propositiones, facta sunt ab intellectu quando dividit ea ab invicem vel componit ea ad invicem.”
- 13.
See (Bradwardine 2010, ‘Introduction’ § 4).
- 14.
\(p\to(q\to r)\) entails \((p{ \wedge} q)\to r\) (but not vice versa) in the logics of strict implication S2 (and stronger) and of relevant implication, R: on the latter, see, e.g., (Anderson and Belnap 1975, § 29.3.1, R30 and R31).
- 15.
Buridan famously rejected this claim in his later writings, saying not that every proposition signifies its own truth, but that it virtually implies it. His main reason for doing so was his rejection of the notion of the complexly signifiable (complexe significabile), what is signifiable only by a complexum, that is, a proposition. Given the similarity between this doctrine and Burley’s notion of the real proposition, Bradwardine would not share Buridan’s worries, if he did indeed accept Burley’s semantic account. See, e.g. (Klima 2009, Chaps. 9–10, esp. § 10.2).
- 16.
- 17.
See Lib. I Questiones 7–9 § 10 (Andrews et al. 2004, I p. 181): “Quaelibet propositio significat se esse veram, ergo ista ‘tu eris albus cras’ significat se esse veram. Antecedens patet, quia ad omnem propositionem veram sequitur suum dictum fore verum. Similiter contradictorium affirmativae ut ista ‘tu non eris albus’ infert hanc ‘“te non fore album” est verum’. Utrumque igitur contradictoriorum in illis de futuro significat se esse determinate veram.” This occurs as part of an objection, but in his response Scotus does not question the basic principle.
- 18.
Quaestiones disputatae de mysterio Trinitatis, q1 a1, translated in (Wippel and Wolter 1969, pp. 310–311).
- 19.
(Geulincx 1663, Chap. 1; Land 1891, II p. 25): “Sit enunciatio quaecunque, nempe A. Dico quod A dicat se esse veram. Quia A dicit esse, et dicit esse quod dicit esse, sed esse id, quod A esse dicit, est A esse veram. Cum igitur A prius dicat, dicit etiam posterius, seu A dicet A, id est seipsam, veram esse.” Cf. (Geulincx 1662, II.i.1.4; Land 1891, I p. 234]) and (Nuchelmans 1988, p. 280]). Similar proofs are found in Albert of Saxony and John Buridan. See, e.g., (Read 2002, § 3]).
- 20.
See, e.g., (Yrjönsuuri 1993).
- 21.
See (Read 2008, p. 217).
- 22.
- 23.
See (Roure 1962, p. 262).
- 24.
So called by (Geach 1955): in symbols, from \(p\to (p\to q)\) infer \(p\to q\); nowadays usually referred to as “contraction”.
- 25.
(Del Punta and McCord Adams 1978, p. 74), my translation.
- 26.
We can capture this in a generalisation of (P2): if s signifies that p 1 and signifies that p 2, and p 1 and p 2 (jointly) entail r, then s signifies that r.
References
Anderson, A., & Belnap, N. (1975). Entailment: The logic of relevance and necessity (Vol. 1). Princeton: Princeton University Press.
Andrews, R., Etzkorn, G., Gál, G., Green, G., Noone, T., Plevano, R., Traver, R., & Wood, R. (2004). B. Ioannis Duns Scoti: Opera Philosophica. St. Bonaventure: The Franciscan Institute.
Arnauld, A., & Nicole, P. (1662). La logique ou l’art de penser. Paris: Charles Savreux.
Bradwardine, T. (2010). Insolubilia (trans: S. Read). Leuven: Peeters.
Brown, S. (1973). Walter Burley’s middle commentary on Aristotle’s Perihermenias.Franciscan Studies, 33, 42–134.
Buridan, J. (2001). Summulae de Dialectica (trans: G. Klima). New Haven: Yale University Press.
Buridan, J. (2004). Summulae de Practica Sophismatum (Ed. F. Pironet). Turnhout: Brépols.
Burley, W. (1955). De Puritate Artis Logicae Tractatus Longior, with a revised edition of the Tractatus Brevior. St. Bonaventure: The Franciscan Institute.
Burley, W. (2000). On the purity of the art of logic (trans: P. V. Spade). New Haven: Yale University Press.
Cesalli, L. (2007). Le réalisme propositionnel. Paris: Vrin.
Conti, A. (2011). Walter Burley. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy. (Fall 2014 edition) http://plato.stanford.edu/archives/fall2014/entries/burley/.
Curry, H. (1942). On the inconsistency of certain formal logics. Journal of Symbolic Logic, 7, 115–117.
De Rijk, L. (1972). Peter of Spain: Tractatus. Assen: Van Gorcum.
Del Punta, F., & McCord Adams, M. (1978). Pauli Veneti Logica Magna: Secunda Pars, Tractatus de Veritate et Falsitate Propositionis, et Tractatus de Significato Propositionis. Oxford: Oxford University Press for the British Academy.
Field, H. (2008). Saving truth from paradox. Oxford: Oxford University Press.
Frege, G. (1997). Thoughts. In M. Beaney (Ed.), A Frege Reader (pp. 325–345). Oxford: Blackwell.
Geach, P. (1955). On insolubilia. Analysis, 15, 71–72.
Geulincx, A. (1662). Logica fundamentis suis, a quibus hactenus collapsa fuerat, restituta. Leiden: Henricus Verbiest. (Reprinted in (Land 1891, Vol. I, pp. 165–454)).
Geulincx, A. (1663). Methodus inveniendi argumenta. Leiden: Issacus deWael. (Reprinted in (Land 1891, vol. II, pp. 1–111)).
Green-Pedersen, N. J. (1980). Walter Burley’s De consequentiis: An edition. Franciscan Studies, 40, 102–166.
Hamilton, W. (1863). On presentative and representative knowledge. In W. Hamilton (Ed.), The works of Thomas Reid (Vol. 2, pp. 804–815). Edinburgh: MacLachlan and Stewart.
Jacquette, D. (2007a). Burleigh’s fallacy. Philosophy, 82, 437–448.
Jacquette, D. (2007b). Deductivism and the informal fallacies. Argumentation, 21, 335–347.
King, J. (2007). The nature and structure of content. Oxford: Oxford University Press.
Klima, G. (2009). John Buridan. Oxford: Oxford University Press.
Land, J. (Ed.). (1891). Arnold Geulincx: Opera Philosophica (3 volumes). The Hague: Martinus Nijhoff.
Maudlin, T. (2004). Truth and paradox. Oxford: Oxford University Press.
Nuchelmans, G. (1988). Geulincx’ containment theory of logic. Medelingen van de Afdeling Letterkunde. Amsterdam: Koninklijke Nederlandse Akademie van Wetenschappen, NS51, no. 8, pp. 266–317.
Nuchelmans, G. (1994). Walter Burleigh on the conclusion that you are an ass. Vivarium, 32, 90–101.
Raine, J. (Ed.). (1843). The correspondence of Dr. Matthew Hutton, Archbishop of York. London: Publications of the Surtees Society 17. J.B. Nichols and Son.
Read, S. (2002). The liar paradox from John Buridan back to Thomas Bradwardine. Vivarium, 40, 189–218.
Read, S. (2008). Further thoughts on Tarski’s T-scheme and the Liar. In J. Rahman, T. Tulenheimo, & E. Genot (Eds.), Unity, truth and the liar: The modern relevance of medieval solutions to the liar paradox (pp. 205–225). Berlin: Springer.
Ricardus. (n.d.). Abstractiones (Ed. P. King). http://www.hs-augsburg.de/~harsch/Chronologia/Lspost13/RicardusSophista/ricabst.html.
Roure, M.-L. (1962). Le traité “Des Propositions Insolubles” de Jean de Celaya. Archives d’Histoire Doctrinale et Littéraire du Moyen Age, 29, 235–336.
Roure, M.-L. (1970). La problématique des propositions insolubles au XIIIe siècle et au début du XIVe, suivie de l’édition des traités de W. Shyreswood, W. Burleigh et Th. Bradwardine. Archives d’Histoire Doctrinale et Littéraire du Moyen Age, 37, 205–326.
Russell, B. (1903). The principles of mathematics. London: George Allen & Unwin.
Spade, P. (1981). ‘Insolubilia’ and Bradwardine’s theory of signification. Medioevo, 7, 115–134.
Wippel, J., & Wolter, A. (Eds.). (1969). Medieval philosophy. NewYork: The Free Press.
Yrjönsuuri, M. (1993). Expositio as a method of solving sophisms. In S. Read (Ed.), Sophisms in medieval logic and grammar (pp. 202–216). Dordrecht: Kluwer.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Read, S. (2015). Truth, Signification and Paradox. In: Achourioti, T., Galinon, H., Martínez Fernández, J., Fujimoto, K. (eds) Unifying the Philosophy of Truth. Logic, Epistemology, and the Unity of Science, vol 36. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9673-6_20
Download citation
DOI: https://doi.org/10.1007/978-94-017-9673-6_20
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-017-9672-9
Online ISBN: 978-94-017-9673-6
eBook Packages: Humanities, Social Sciences and LawPhilosophy and Religion (R0)