Abstract
Perhaps the most powerful argument that has been made in favour of the view that some contradictions are true (dialetheism) is that it allows for a solution to the logical paradoxes which is immune to the well-known problem of revenge. The version of the view which would seem to have the best chance of avoiding the problem is a particularly thoroughgoing dialetheism, most prominently defended by Graham Priest, which takes paraconsistent set theory as its working metatheory. The purpose of this paper is to characterise a revenge problem for this thoroughgoing dialetheism, involving the notion of invalidity. I argue that the inconsistency of the metatheory commits dialetheists of this sort to accepting as contradictory, not only truth, but validity: in other words, some inference principles are both valid and invalid. I show that, depending on the details of the theory, all, or ‘almost all’ (in a sense to be explained), inference principles can be shown to be dialetheically invalid. I argue that this gives rise to a revenge problem for dialetheism, since it makes the notion of invalidity inexpressible for the dialetheist and deprives them of the ability to express crucial semantic claims about their theory.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In fact, it is very common in the literature for Yablo’s paradox to be expressed in this, strengthened form, employing untruth instead of falsity. Indeed, Yablo’s original formulation of the paradox in his [13] was characterised in this way.
References
Batens, D. (1990). Against global paraconsistency. Studies in Soviet Thought, 39(3–4), 209–229.
Beall, J. C. (2009). Spandrels of truth. Oxford University Press.
Beall, J. C. (2013). Shrieking against gluts: the solution to the ‘just true’ problem. Analysis, 73(3), 438–445.
Berto, F. (2014). Absolute contradiction, dialetheism, and revenge. Review of Symbolic Logic, 7(2), 193–207.
Field, H. (2008). Saving truth from paradox. Oxford University Press.
Heck, R. (2007). Self-reference and the languages of arithmetic. Philosophia Mathematica, 15(1), 1–29.
Littman, G., & Simmons, K. (2004). A critique of dialetheism. In G. Priest, J. C. Beall, & B. Armour-Garb (Eds.), The law of non-contradiction. Oxford University Press.
Parsons, T. (1990). True contradictions. Canadian Journal of Philosophy, 20(3), 335–353.
Priest, G. (2006). In contradiction: A study of the transconsistent. Oxford University Press.
Priest, G. (2010). Hopes fade for saving truth. Philosophy, 85(1), 109–140.
Priest, G., & Berto, F. (2017, Spring). Dialetheism. In E. N. Zalta (Ed.), The stanford encyclopedia of philosophy. https://plato.stanford.edu/archives/spr2017/entries/dialetheism/.
Shapiro, S. (2004). Simple truth, contradiction, and consistency. In The law of non- contradiction. Oxford University Press.
Yablo, S. (1985). Truth and reflection. Journal of Philosophical Logic., 14, 279.
Young, G. (2015). Shrieking, just false and exclusion. Thought: A Journal of Philosophy, 4(4), 269–276 (2015).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Young, G. (2019). A Revenge Problem for Dialetheism. In: Rieger, A., Young, G. (eds) Dialetheism and its Applications. Trends in Logic, vol 52. Springer, Cham. https://doi.org/10.1007/978-3-030-30221-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-30221-4_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-30220-7
Online ISBN: 978-3-030-30221-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)