Reforming logic (and set theory)

Abstract
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)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index Translate to english
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 11,392
External links
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
Similar books and articles
Analytics

Monthly downloads

Added to index

2009-09-11

Total downloads

10 ( #148,640 of 1,102,929 )

Recent downloads (6 months)

0

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.