Synthese

, Volume 193, Issue 6, pp 1703–1753 | Cite as

New foundations for imperative logic III: A general definition of argument validity

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Abstract

Besides pure declarative arguments, whose premises and conclusions are declaratives (“you sinned shamelessly; so you sinned”), and pure imperative arguments, whose premises and conclusions are imperatives (“repent quickly; so repent”), there are mixed-premise arguments, whose premises include both imperatives and declaratives (“if you sinned, repent; you sinned; so repent”), and cross-species arguments, whose premises are declaratives and whose conclusions are imperatives (“you must repent; so repent”) or vice versa (“repent; so you can repent”). I propose a general definition of argument validity: an argument is valid exactly if, necessarily, every fact that sustains its premises also sustains its conclusion, where a fact sustains an imperative exactly if it favors the satisfaction over the violation proposition of the imperative, and a fact sustains a declarative exactly if, necessarily, the declarative is true if the fact exists. I argue that this definition yields as special cases the standard definition of validity for pure declarative arguments and my previously defended definition of validity for pure imperative arguments, and that it yields intuitively acceptable results for mixed-premise and cross-species arguments.

Keywords

Argument validity Imperative logic Inconsistency 
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Notes

Acknowledgments

I am grateful to Daniel Boisvert, Joseph Fulda, Alan Hájek, Casey Hart, Ryan Millsap, David O’Brien, Josh Parsons, Manidipa Sanyal, Michael Titelbaum, and especially Aviv Hoffmann, Joshua Schechter, and several anonymous reviewers for comments. Thanks also to Martin Barrett, John Bengson, John Bishop, Anna Brożek, Heather Dyke, Branden Fitelson, Molly Gardner, Paula Gottlieb, Casey Helgeson, Jacek Jadacki, Matt Kopec, Jonathan Lang, John Mackay, Andrew Moore, Jakub Motrenko, Charles Pigden, Gina Schouten, Benjamin Schwan, Larry Shapiro, Elliott Sober, Ivan Soll, Reuben Stern, and Berislav Žarnić for interesting questions, and to my mother for typing the bulk of the paper. Material from this paper was presented at the 7th Formal Epistemology Workshop (September 2010), the University of Otago (December 2011, via Skype), the 2012 Central APA Meeting (February 2012), the University of Wisconsin-Madison (Department of Mathematics, April 2012, and Department of Philosophy, May 2012), the University of Warsaw (May 2012), and the Beijing Normal University (August 2012)..

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Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of Wisconsin-MadisonsMadisonUSA

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