Triviality Results and the Relationship between Logical and Natural Languages

Mind 128 (510):485-526 (2019)
  Copy   BIBTEX


Inquiry into the meaning of logical terms in natural language (‘and’, ‘or’, ‘not’, ‘if’) has generally proceeded along two dimensions. On the one hand, semantic theories aim to predict native speaker intuitions about the natural language sentences involving those logical terms. On the other hand, logical theories explore the formal properties of the translations of those terms into formal languages. Sometimes, these two lines of inquiry appear to be in tension: for instance, our best logical investigation into conditional connectives may show that there is no conditional operator that has all the properties native speaker intuitions suggest if has. Indicative conditionals have famously been the source of one such tension, ever since the triviality proofs of both Lewis (1976) and Gibbard (1981) established conclusions which are in prima facie tension with ordinary judgments about natural language indicative conditionals. In a recent series of papers, Branden Fitelson has strengthened both triviality results (Fitelson 2013, 2015, 2016), revealing a common culprit: a logical schema known as IMPORT-EXPORT. Fitelson’s results focus the tension between the logical results and ordinary judgments, since IMPORT-EXPORT seems to be supported by intuitions about natural language. In this paper, we argue that the intuitions which have been taken to support IMPORT-EXPORT are really evidence for a closely related, but subtly different, principle. We show that the two principles are independent by showing how, given a standard assumption about the conditional operator in the formal language in which IMPORT-EXPORT is stated, many existing theories of indicative conditionals validate one, but not the other. Moreover, we argue that once we clearly distinguish these principles, we can use propositional anaphora to show that IMPORT-EXPORT is in fact not valid for natural language indicative conditionals (given this assumption about the formal conditional operator). This gives us a principled and independently motivated way of rejecting a crucial premise in many triviality results, while still making sense of the speaker intuitions which appeared to motivate that premise. We suggest that this strategy has broad application and an important lesson: in theorizing about the logic of natural language, we must pay careful attention to the translation between the formal languages in which logical results are typically proved, and natural languages which are the subject matter of semantic theory.

Similar books and articles

Conditionals, indeterminacy, and triviality.Justin Khoo - 2013 - Philosophical Perspectives 27 (1):260-287.
Subjunctive Credences and Semantic Humility.Sarah Moss - 2012 - Philosophy and Phenomenological Research 87 (2):251-278.
Hurford Conditionals.Matthew Mandelkern & Jacopo Romoli - 2018 - Journal of Semantics 35 (2):357-367.
The Probabilities of Conditionals Revisited.Igor Douven & Sara Verbrugge - 2013 - Cognitive Science 37 (4):711-730.
Logical Consequence and Natural Language.Michael Glanzberg - 2015 - In Colin R. Caret & Ole T. Hjortland (eds.), Foundations of Logical Consequence. Oxford University Press. pp. 71-120.
The Logic of Indicative Conditionals.Chhanda Chakraborti - 1995 - Dissertation, The University of Utah
Triviality Pursuit.Alan Hájek - 2011 - Topoi 30 (1):3-15.
Embedding If and Only If.Adam Sennet & Jonathan Weisberg - 2012 - Journal of Philosophical Logic 41 (2):449-460.
Conditionals and Actuality.Timothy Williamson - 2009 - Erkenntnis 70 (2):135 - 150.
Linguistics and natural logic.George Lakoff - 1970 - Synthese 22 (1-2):151 - 271.


Added to PP

537 (#25,893)

6 months
87 (#27,037)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Justin Khoo
Massachusetts Institute of Technology
Matthew Mandelkern
New York University

References found in this work

Studies in the way of words.Herbert Paul Grice - 1989 - Cambridge: Harvard University Press.
The Foundations of Mathematics and Other Logical Essays.Frank Plumpton Ramsey - 1925 - London, England: Routledge & Kegan Paul. Edited by R. B. Braithwaite.
A philosophical guide to conditionals.Jonathan Bennett - 2003 - New York: Oxford University Press.

View all 86 references / Add more references