David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
History and Philosophy of Logic 14 (1):39-66 (1993)
Tarski 1968 makes a move in the course of providing an account of ?definitionally equivalent? classes of algebras with a businesslike lack of fanfare and commentary, the significance of which may accordingly be lost on the casual reader. In ?1 we present this move as a response to a certain difficulty in the received account of what it is to define a function symbol (or ?operation symbol?). This difficulty, which presents itself as a minor technicality needing to be got around especially for the case of symbols for zero-place functions (for ?distinguished elements?), has repercussions?not widely recognised?for the account of functional completeness in sentential logic. A similarly stark comment in Church 1956 reveals an appreciation of this difficulty, though not every subsequent author on the topic has taken the point. We fill out this side of the picture in ?2. The discussion of functional completeness in ?2 is supplemented by some remarks on what is involved in defining a connective, which have been included in an Appendix. The emphasis throughout is on conceptual clarification rather than on proving theorems, and the main body of the paper may be regarded as an elaboration on the remarks just mentioned by Tarski and Church. The Appendix (?3) is intended to be similarly clarificatory, though this time with some corrective intent, of remarks made in and about Makinson 1973
|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
Alonzo Church (1956). Introduction to Mathematical Logic. Princeton, Princeton University Press.
Alonzo Church (1944). Introduction to Mathematical Logic. London, H. Milford, Oxford University Press.
Irving M. Copi (1956). Another Variant of Natural Deduction. Journal of Symbolic Logic 21 (1):52-55.
Karel Louis de Bouvère (1959). A Method in Proofs of Undefinability. Amsterdam, North-Holland Pub. Co..
Citations of this work BETA
Lloyd Humberstone (2008). Béziau's Translation Paradox. Theoria 71 (2):138-181.
I. L. Humberstone (1998). Choice of Primitives: A Note on Axiomatizing Intuitionistic Logic. History and Philosophy of Logic 19 (1):31-40.
P. D'Altan, J.-J. Ch Meyer & R. J. Wieringa (1996). An Integrated Framework for Ought-to-Be and Ought-to-Do Constraints. Artificial Intelligence and Law 4 (2):77-111.
Similar books and articles
D. C. McCarty (1996). Undecidability and Intuitionistic Incompleteness. Journal of Philosophical Logic 25 (5):559 - 565.
Richard Kaye (2007). The Mathematics of Logic: A Guide to Completeness Theorems and Their Applications. Cambridge University Press.
Douglas N. Hoover (1987). An Analytic Completeness Theorem for Logics with Probability Quantifiers. Journal of Symbolic Logic 52 (3):802-816.
Rafał Urbaniak (2006). On Representing Sentential Connectives of Lesniewski's Elementary Protothetic. Journal of Logic and Computation 16 (4):451-460.
Alfred Tarski, Jan Tarski & Jan Woleński (1995). Some Current Problems in Metamathematics1. History and Philosophy of Logic 16 (2):159-168.
Xavier Caicedo & Roberto Cignoli (2001). An Algebraic Approach to Intuitionistic Connectives. Journal of Symbolic Logic 66 (4):1620-1636.
Torben Braüner (2005). Proof-Theoretic Functional Completeness for the Hybrid Logics of Everywhere and Elsewhere. Studia Logica 81 (2):191 - 226.
Henri Galinon (2009). A Note on Generalized Functional Completeness in the Realm of Elementrary Logic. Bulletin of the Section of Logic 38 (1):1-9.
C. Caleiro, W. A. Carnielli, M. E. Coniglio, A. Sernadas & C. Sernadas (2003). Fibring Non-Truth-Functional Logics: Completeness Preservation. [REVIEW] Journal of Logic, Language and Information 12 (2):183-211.
I. L. Humberstone (1990). Expressive Power and Semantic Completeness: Boolean Connectives in Modal Logic. Studia Logica 49 (2):197 - 214.
Added to index2010-08-10
Total downloads10 ( #157,089 of 1,140,320 )
Recent downloads (6 months)1 ( #140,127 of 1,140,320 )
How can I increase my downloads?