If structured propositions are logical procedures then how are procedures individuated?
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This paper deals with two issues. First, it identifies structured propositions with logical procedures. Second, it considers various rigorous definitions of the granularity of procedures, hence also of structured propositions, and comes out in favour of one of them. As for the first point, structured propositions are explicated as algorithmically structured procedures. I show that these procedures are structured wholes that are assigned to expressions as their meanings, and their constituents are sub-procedures occurring in executed mode (as opposed to displayed mode). Moreover, procedures are not mere aggregates of their parts; rather, procedural constituents mutually interact. As for the second point, there is no universal criterion of the structural isomorphism of meanings, hence of co-hyperintensionality, hence of synonymy for every kind of language. The positive result I present is an ordered set of rigorously defined criteria of fine-grained individuation in terms of the structure of procedures. Hence procedural semantics provides a solution to the problem of the granularity of co-hyperintensionality.
KeywordsProcedural semantics Transparent intensional logic Structured propositions Mereology of structured procedures Unity of propositions synonymy Co-hyperintensionality Procedural isomorphism
The research reported here in was supported by the Grant Agency of the Czech Republic, Project No. GA15-13277S, Hyperintensional logic for natural language analysis, and by the internal grant agency of VSB-TU Ostrava, Project SGS No. SP2017/133, “Knowledge modelling and its applications in software engineering III”. 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. I want to thank Bjørn Jespersen for great comments along the way, and not least two anonymous referees for Synthese.
- Bolzano, B. (1837). Wissenschaftslehre. Sulzbach: von Seidel.Google Scholar
- Carnap, R. (1947). Meaning and necessity. Chicago: Chicago University Press.Google Scholar
- Church, A. (1941). The calculi of lambda conversion. Princeton: Princeton University Press.Google Scholar
- Church, A. (1951). The need for abstract entities. American Academy of Arts and Sciences Proceedings, 80, 100–113.Google Scholar
- Church, A. (1956). Introduction to mathematical logic. Princeton: Princeton University Press.Google Scholar
- Cohen, M. R., & Nagel, E. (1934). An introduction to logic and scientific method. London: Routledge and Kegan Paul.Google Scholar
- Duží, M. (2014). A procedural interpretation of the Church-Turing Thesis. In A. Olszewski, B. Brożek, P. Urbańczyk (Eds.), Church’s Thesis: Logic, mind and nature. Copernicus Center Press, Krakow 2013.Google Scholar
- Duží, M. (2017a). Logic of dynamic discourse; anaphora resolution. In Proceedings of the 27th international conference on information modelling and knowledge bases-EJC 2017, Thailand.Google Scholar
- Duží, M. (2017b). Presuppositions and two kinds of negation. Logique & Analyse, the special issue on How to Say ‘Yes’ and ‘No’ (Vol. 239, pp. 245–263).Google Scholar
- Duží, M. (2003). Notional attitudes (on wishing, seeking and finding). ORGANON F, 10(3), 237–260.Google Scholar
- Duží, M. (2014a). Communication in a multi-cultural world. ORGANON F, 21(2), 198–218.Google Scholar
- Duží, M. (2014b). Structural isomorphism of meaning and synonymy. Computación y Sistemas, 18(3), 439–453.Google Scholar
- Duží, M., Jespersen, B., & Materna, P. (2009). ‘\(\pi \)’ in the sky. In G. Primiero & S. Rahman (Eds.), Acts of knowledge: History, philosophy and logic. Essays dedicated to Göran Sundholm. London: College Publications Tribute Series 1.Google Scholar
- Duží, M., Jespersen, B., & Materna, P. (2010). Procedural semantics for hyperintensional logic. Foundations and applications of transparent intensional logic. Berlin: Springer.Google Scholar
- Duží, M., & Kosterec, M. (2017). A valid rule of \(\beta \)-conversion for the logic of partial functions. ORGANON F, 24(1), 10–36.Google Scholar
- Duží, M., Macek, J., & Vích, L. (2014). Procedural isomorphism and synonymy. In M. Dančák & V. Punčochář (Eds.), Logica yearbook 2013 (pp. 15–33). London: College Publications.Google Scholar
- Duží, M., & Materna, P. (2017). Validity and applicability of Leibniz’s law of substitution of identicals. In P. Arazim & T. Lavička (Eds.), The logica yearbook 2016 (pp. 17–35). London: College Publications.Google Scholar
- Jespersen, B. (2015b). Should propositions proliferate? Thought, 4, 243–251.Google Scholar
- Jespersen, B. (2017a). Anatomy of a proposition. Synthese, S.I. Unity of structured propositions, published online August 2017. https://doi.org/10.1007/s11229-017-1512-y.
- Jespersen, B. (2017b). Is predication an act or an operation? In P. Stalmaszczyk (Ed.), Philosophy and logic of predication, studies in philosophy of language and linguistics (Vol. 7, pp. 223–245). Peter Lang GmbH: Frankfurt/Main.Google Scholar
- King, J. C. (2014). Structured propositions. In E. N. Zalta (ed.) The Stanford encyclopedia of philosophy (Spring 2014 Edition). http://plato.stanford.edu/archives/spr2014/entries/propositions-structured/.
- Materna, P. (1998). Concepts and objects (Vol. 63). Helsinki: Acta Philosophica Fennica.Google Scholar
- Materna, P. (2004). Conceptual systems. Berlin: Logos.Google Scholar
- Mates, B. (1952). Synonymity. In L. Linsky (Ed.), Semantics and the philosophy of language (pp. 111–138). Urbana, IL: University of Illinois Press.Google Scholar
- Moschovakis, Y. N. (1994). Sense and denotation as algorithm and value. In J. Väänänen & J. Oikkonen (Eds.), Lecture notes in logic (Vol. 2, pp. 210–249). Berlin: Springer.Google Scholar
- Richard, M. (2001). Analysis, synonymy and sense. In: A. Anderson, M. Zelëny (Eds.), Logic, meaning and computation, essays in memory of Alonzo Church. Synthese Library 305 (vol. III, pp. 545–572).Google Scholar
- Russell, B. (1903). The principles of mathematics. New York: Norton paperback edition 1996. Norton & Company.Google Scholar
- Soames, S. (2012). What is meaning?. Princeton: Princeton University Press.Google Scholar
- Tichý, P. (2004). Collected papers in logic and philosophy. In V. Svoboda, B. Jespersen, C. Cheyne (Eds.), Prague: Filosofia, Czech Academy of Sciences and Dunedin: University of Otago Press.Google Scholar
- van Lambalgen, M., & Hamm, F. (2004). Moschovakis’ notion of meaning as applied to linguistics. In M. Baaz, S. Friedman, J. Krajicek (Eds.), Logic Colloquium’01. Digital Academic Repository. Amsterdam: University of Amsterdam. http://dare.uva.nl/record/123675/. Accessed 13 September 2017.