Anatomy of a proposition
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This paper addresses the mereological problem of the unity of structured propositions. The problem is how to make multiple parts interact such that they form a whole that is ultimately related to truth and falsity. The solution I propose is based on a Platonist variant of procedural semantics. I think of procedures as abstract entities that detail a logical path from input to output. Procedures are modeled on a function/argument logic, but are not functions (mappings). Instead they are higher-order, fine-grained structures. I identify propositions with particular kinds of molecular procedures containing multiple sub-procedures as parts. Procedures are among the basic entities of my ontology, while propositions are derived entities. The core of a structured proposition is the procedure of predication, which is an instance of the procedure of functional application. The main thesis I defend is that procedurally conceived propositions are their own unifiers detailing how their parts interact so as to form a unit. They are not unified by one of their constituents, e.g., a relation or a sub-procedure, on pain of regress. The relevant procedural semantics is Transparent Intensional Logic, a hyperintensional, typed \(\lambda \)-calculus, whose \(\lambda \)-terms express four different kinds of procedures. While demonstrating how the theory works, I place my solution in a wider historical and systematic context.
KeywordsProposition Unity Structure Predication Procedural semantics Transparent Intensional Logic Type theory Lambda-calculus
The research reported herein was supported by Marie Curie Fellowship FP-7-PEOPLE-2013-IEF628170, Grant Agency of the Czech Republic Project No. GA15-13277S, and VSB-TU Ostrava Project No. SP2017/133. Versions of this paper were read at the Barcelona Workshop on Reference 9 (BW9): Unity and Individuation of Structured Propositions, Barcelona, 22–24 June 2015; Institute of Culture and Society, University of Aarhus, 11 April 2014; ILLC, University of Amsterdam, 18 May 2016; Department of Philosophy, Groningen University, GroLog, 12 May 2016; Department of Philosophy, Lingnan University, Hong Kong, 30 September 2015; Department of Philosophy, National University of Singapore, 23 September 2015; Department of Philosophy, Stockholm University, 24 April 2015; Department of Computer Science, TU Ostrava, 27 March 2014; Department of Philosophy, UNAM, Mexico City, 11 March 2015; Department of Logic and Philosophy of Science, UC Irvine, C-ALPHA, 6 March 2015; Department of Logic, History and Philosophy of Science, Logos, University of Barcelona, 18 February 2015. I wish to thank the following for great comments along the way: Marie Duží, Manuel García-Carpintero, Bryan Pickel the various audiences, and not least two anonymous referees for Synthese.
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