Reforming logic (and set theory)
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
1. Frege’s mistake Frege is justifiably considered the most important thinker in the development of our contemporary “modern” logic. One corollary to this historical role of Frege’s is that his mistakes are found in a magnified form in the subsequent development of logic. This paper examines one such mistake and its later history. Diagnosing this history also reveals ways of overcoming some of the limitations that Frege’s mistake has unwittingly imposed on current forms of modern logic. Frege’s mistake concerns the semantics (meaning) of quantifiers. The mistake is to assume that this semantics is exhausted by the quantifiers’ (quantified variables’) ranging over a class of values. These values are the members of the domain (universe of discourse) of the language to which the quantifiers belong. The entire job description of the quantifiers is to indicate whither or not at least one member of the domain has a certain (possible complex) predicate (existential quantifier) and to indicate whether all of them have one (universal quantifier). In other words, quantifiers are higher order predicates indicating whether or not a given lower-order predicate is nonempty or exceptionless. This is in fact precisely how Frege proposes to treat quantifiers in his logical theory. (See Frege 1984, pp. 153-154, pp. 26-27 of the original.) This is obviously part of the semantical task of quantifiers. However, it is not the only one. Quantifiers have another function in language. There is a task that any language must be capable of fulfilling if it is to serve as a language of science and for that matter as a language suitable for innumerable purposes in everyday life. This task is to..
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
Jaakko Hintikka (2011). What is the Axiomatic Method? Synthese 183 (1):69-85.
Similar books and articles
Fredrik Engström (2012). Generalized Quantifiers in Dependence Logic. Journal of Logic, Language and Information 21 (3):299-324.
Martin Hackl (2009). On the Grammar and Processing of Proportional Quantifiers: Most Versus More Than Half. [REVIEW] Natural Language Semantics 17 (1):63--98.
Lauri Hella, Jouko Väänänen & Dag Westerståhl (1997). Definability of Polyadic Lifts of Generalized Quantifiers. Journal of Logic, Language and Information 6 (3):305-335.
Edward L. Keenan (1992). Beyond the Frege Boundary. Linguistics and Philosophy 15 (2):199 - 221.
Stephen Read (1997). Completeness and Categoricity: Frege, Gödel and Model Theory. History and Philosophy of Logic 18 (2):79-93.
Juha Kontinen & Jakub Szymanik (2011). Characterizing Definability of Second-Order Generalized Quantifiers. In L. Beklemishev & R. de Queiroz (eds.), Proceedings of the 18th Workshop on Logic, Language, Information and Computation, Lecture Notes in Artificial Intelligence 6642. Springer.
Johan van Benthem & Dag Westerståhl (1995). Directions in Generalized Quantifier Theory. Studia Logica 55 (3):389-419.
Wiebe Van Der Hoek & Maarten De Rijke (1993). Generalized Quantifiers and Modal Logic. Journal of Logic, Language and Information 2 (1):19-58.
Added to index2009-09-11
Total downloads10 ( #141,181 of 1,096,632 )
Recent downloads (6 months)0
How can I increase my downloads?