Logic and Existence
(Existence Predicates in Logic)

Luis Estrada-González

Institute for Philosophical Research
National Autonomous University of Mexico (UNAM)

Giovanni Mion

Department of Philosophy
Istanbul Technical University (ITU), Turkey

 

Bibliography

Session 1
Berto, Franz (2012): Existence as a Real Property: The Ontology of Meinongianism, Berlin-New York: Springer.
Berto, Franz (forthcoming): ““There is an ‘Is’ in ‘There is’”: Meinongian quantification and existence”, in Alessandro Torza (ed.), Quantifiers, Quantifiers, Quantifiers, Springer.
Dunn, J. Michael (1996): “Is existence a (relevant) predicate?”, Philosophical Topics 24, 1–34.
Lewis, David (1990): “Noneism or allism?”, Mind 99, 23–31.
Priest, Graham (2005): Towards Non-Being, Oxford: Oxford University Press.
Priest, Graham (2008): “The closing of the mind: How the particular quantifier became existentially loaded behind our backs”, The Review of Symbolic Logic 1, 42–55.

 

 

 

The tutorial is divided into three sections:

In the first section, we first recapitulate the steps that led to an existential interpretation of the particular quantifier. Then, we critically evaluate some of Priest/Berto’s arguments against such an interpretation. Finally, we also engage some of their philosophical arguments in favor of the introduction of an existence predicate.


In the second session of the tutorial we present some standard examples of logics with existence predicates, viz. the three major families of free logics –negative, neuter and positive. We also study the dialogical approach, that provides a very general framework to reformulate those logics and according to which their existence predicates are entirely dispensable and gives a new perspective on the issue of ontological commitment.


In the third session we present another family of examples of logics, which come principally from mathematics and specifically from category theory, in which existence predicates are seemingly needed or, at least, provide the most natural and convenient treatment of certain issues. We extend the dialogical approach of the second session to cover those logics.

 

 

 

 

Session 2
Fontaine, Matthieu and Juan Redmond (2012): “To be is to be chosen: A dialogical understanding of ontological commitment”, in Cristina Barés, Sébastien Magniez and Francisco Salguero (eds.), Logic of Knowledge. Theory and Applications, London: College Publications.
Nolt, John (2006): “Free logics,” in Dale Jacquette, ed., Philosophy of Logic (Series: Volume 5 of the Handbook of the Philosophy of Science), Amsterdam: Elsevier, 2006, pp. 1023–1060.
Rahman, Shahid and Laurent Keif (2004): “On how to be a dialogician”. In D. Vanderveken (ed.), Logic, Thought and Action, Dordrecht: Springer, pp. 359–408.
Rahman, Shahid and Tero Tulenheimo (2006): “From games to dialogues and back: towards a general frame for validity”, in Ondrej Majer, Ahti-Veikko Pietarinen and Tero Tulenheimo (eds.), Games: Unifying Logic, Language, and Philosophy, Dordrecht: Springer, pp. 153–208.

Session 3
Barwise, Jon and John Etchemendy (1999): Language, Proof and Logic, Stanford/New York/London: CSLI Publications/Seven Bridges Press.
Fontaine, Matthieu and Juan Redmond (2012): “To be is to be chosen: A dialogical understanding of ontological commitment”, in Cristina Barés, Sébastien Magniez and Francisco Salguero (eds.), Logic of Knowledge. Theory and Applications, London: College Publications.
Goldblatt, Robert (1984): Topoi. The Categorial Analysis of Logic, revised edition, Amsterdam: North Holland.
Lambek, Joachim and Philip J. Scott (1986): Introduction to High Order Categorical Logic, Cambridge: Cambridge University Press.
Rahman, Shahid and Laurent Keif (2004): “On how to be a dialogician”, in Daniel Vanderveken (ed.), Logic, Thought and Action, Dordrecht: Springer, pp. 359–408.
Rahman, Shahid and Tero Tulenheimo (2006): “From games to dialogues and back: towards a general frame for validity”, in Ondrej Majer, Ahti-Veikko Pietarinen and Tero Tulenheimo (eds.), Games: Unifying Logic, Language, and Philosophy, Dordrecht: Springer, pp. 153–208.
Scott, Dana (1979): “Identity and existence in intuitionistic logic”,  in Michael Fourman, Christopher Mulvey and Dana Scott (eds.), Applications of Sheaves, Springer Lectures Notes 753; pp. 660–696.