David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Stanford Encyclopedia of Philosophy (2008)
Traditionally, expressions in formal systems have been regarded as signifying finite inscriptions which are—at least in principle—capable of actually being written out in primitive notation. However, the fact that (first-order) formulas may be identified with natural numbers (via "Gödel numbering") and hence with finite sets makes it no longer necessary to regard formulas as inscriptions, and suggests the possibility of fashioning "languages" some of whose formulas would be naturally identified as infinite sets . A "language" of this kind is called an infinitary language : in this article I discuss those infinitary languages which can be obtained in a straightforward manner from first-order languages by allowing conjunctions, disjunctions and, possibly, quantifier sequences, to be of infinite length. In the course of the discussion it will be seen that, while the expressive power of such languages far exceeds that of their finitary (first-order) counterparts, very few of them possess the "attractive" features (e.g., compactness and completeness) of the latter. Accordingly, the infinitary languages that do in fact possess these features merit special attention.
|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
Rohan French (forthcoming). An Argument for the Ontological Innocence of Mereology. Erkenntnis:1-22.
Colin Howson (2014). A Continuum-Valued Logic of Degrees of Probability. Erkenntnis 79 (5):1001-1013.
Similar books and articles
H. Jerome Keisler (1971). Model Theory for Infinitary Logic. Amsterdam,North-Holland Pub. Co..
Yoshihito Tanaka (2007). An Infinitary Extension of Jankov's Theorem. Studia Logica 86 (1):111 - 131.
James F. Lynch (1997). Infinitary Logics and Very Sparse Random Graphs. Journal of Symbolic Logic 62 (2):609-623.
Herman Ruge Jervell (1972). Herbrand and Skolem Theorems in Infinitary Languages. Oslo,Universitetet I Oslo, Matematisk Institutt.
Attila Máté (1971). Incompactness in Infinitary Languages with Respect to Boolean-Valued Interpretations. Szeged,University of Szeged Bolyai Mathematical Institute.
John Gregory (1971). Incompleteness of a Formal System for Infinitary Finite-Quantifier Formulas. Journal of Symbolic Logic 36 (3):445-455.
David Booth (1991). Logical Feedback. Studia Logica 50 (2):225 - 239.
Matthew J. Donald, Finitary and Infinitary Mathematics, the Possibility of Possibilities and the Definition of Probabilities.
Added to index2009-01-28
Total downloads45 ( #93,410 of 1,907,383 )
Recent downloads (6 months)1 ( #466,442 of 1,907,383 )
How can I increase my downloads?