Abstract
This paper examines the potential for abstracting propositions – an as yet untested way of defending the realist thesis that propositions as abstract entities exist. I motivate why we should want to abstract propositions and make clear, by basing an account on the neo-Fregean programme in arithmetic, what ontological and epistemological advantages a realist can gain from this. I then raise a series of problems for the abstraction that ultimately have serious repercussions for realism about propositions in general. I first identify problems about the number of entities able to be abstracted using these techniques. I then focus on how issues of language relativity result in problems akin to the Caesar problem in arithmetic by exposing circularity and modal concern over the status of the criterion of identity for propositions.
Similar content being viewed by others
References
J Barwise J Perry (1983) Situations and Attitudes MIT Press Cambridge Mass
G. Bealer (1998) ArticleTitle‘Propositions’ Mind 107 1–32 Occurrence Handle10.1093/mind/107.425.1
M. Beaney (Eds) (1997) The Frege Reader Blackwell Oxford
Ben-Chorin S., (1981), ‘Sentence Meanings as a Formal Basis for Intensional Logic’, in Mordechay S, (ed.): 1981 UCLA Working Papers in Semantics.
Boolos G., (1987a), ‘Saving Frege from Contradiction’. in The Proceedings of the Aristotelian Society 87, 137–151
G. Boolos (1987b) ‘The Consistency of Frege’s Foundations of Arithmetic’ J Thomson (Eds) 1987 On Being and Saying: Essays in Honor of Richard Cartwright The MIT Press Cambridge Mass 3–20
G. Boolos (1990a) ‘The Standard of Equality of Numbers’ Boolos (Eds) 1990b, Meaning and Method: Essays in Honor of Hilary Putnam Cambridge University Press Cambridge 261–277
G. Boolos (1997) ‘Is Hume’s Principle Analytic?’ Heck (Eds) 1997, Language, Thought and Logic Oxford University Press Oxford 245–262
R. Carnap (1947) Meaning and Necessity Chicago University Press Chicago
N. Chomsky (1957) Syntactic Structures Mouton The Hague
N. Chomsky (1965) Aspects of the Theory of Syntax The MIT Press Cambridge Mass
I Copi (1954) Symbolic Logic, 1970 EditionNumber3 Macmillan London
M. Davies (1981) Meaning, Quantification Necessity Routledge and Keegan Paul London
M. Dummett (1973) Frege: Philosophy of Language Duckworth London
J. Fodor (1987) Psychosemantics The MIT Press Cambridge, Mass
Frege G., (1892), ‘Uber Sinn und Bedeutung’, reprinted in Beaney (ed.): 1997, 151–171
Frege G., (1918), ‘Der Gedanke’, reprinted in Beaney (ed.): 1997, 325–345
P. Gochet (1980) Outline of a Nominalist Theory of Propositions Reidel Dordrecht
H.P. Grice P.F Strawson (1956) ArticleTitle‘In Defence of a Dogma’ The Philosophical Review 65 141–158 Occurrence Handle10.2307/2182828
B. Hale (1987) Abstract Objects Blackwell Oxford
B. Hale (1996) ArticleTitleCritical Notice of Demopoulos Frege’s Philosophy of Mathematics The Philosophical Quarterly 49 92–104 Occurrence Handle10.1111/1467-9213.00132
B. Hale (2000) ArticleTitle‘Reals by abstraction’ Philosophia Mathematica 8 100–123
B. Hale C Wright (2001) The Reason’s Proper Study Oxford University Press Oxford
J.J. Katz (1981) Language and Other Abstract Objects Rowman and Littlefield New Jersey
S. Kripke (1980) Naming and Necessity Blackwell Oxford
D. Lewis (1972) ‘Languages and Language’ Lewis (Eds) 1983, Philosophical Papers Vol. I Oxford University Press Oxford 163–188
D. Lewis (1986) On The Plurality of Worlds Blackwell Oxford
Montague R., (1974), Formal Philosophy: Selected Papers of Richard Montague Thomason R. H. (ed.), Yale University Press, New Haven.
Peacocke C., (1978), ‘Necessity and Truth Theories’, in The Journal of Philosophical Logic 7, 473–500
C. Peacocke (1992) A Study of Concepts The MIT Press Cambridge Mass
W.V.O. Quine (1951) ArticleTitle‘Two Dogmas of Empiricism’ The Philosophical Review 60 20–43 Occurrence Handle10.2307/2181906
W.V.O. Quine (1960) Word and Object The MIT Press Cambridge Mass
Russell B., (1903), Principles of Mathematics, Allen and Unwin, London. (1912) The Problems of Philosophy (Oxford. Oxford University Press).
B. Russell (1940) An Inquiry into Meaning and Truth Allen and Unwin London
S. Shapiro (2000) ArticleTitle‘Frege meets Dedekind: A neo-logicist treatment of real analysis’ Notre Dame Journal of Formal Logic 41 335–364 Occurrence Handle10.1305/ndjfl/1038336880
S. Shapiro A Weir (2000) ArticleTitle‘Neo-logicist logic is not epistemically innocent’ Philosophia Mathematica 8 160–189 Occurrence Handle10.1093/0195139305.001.0001
C. Wright (1983) Frege’s Conception of Numbers as Objects Aberdeen University Press Aberdeen
C. Wright (1986) ’Inventing Logical Necessity’ J. Butterfield (Eds) Language, Mind and Logic Cambridge University Press Cambridge 187–209
C. Wright (1999) ArticleTitle‘Is Hume’s Principle Analytic?’ Notre Dame Journal of Formal Logic 40 1 Occurrence Handle10.1305/ndjfl/1039096301
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wrigley, A. Abstracting Propositions. Synthese 151, 157–176 (2006). https://doi.org/10.1007/s11229-004-2249-y
Issue Date:
DOI: https://doi.org/10.1007/s11229-004-2249-y