Zero-place operations and functional completeness, and the definition of new connectives

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)
DOI 10.1080/01445349308837209
 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
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 27,613
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
Mathematical Logic.Joseph R. Shoenfield - 1967 - Reading, Mass., Addison-Wesley Pub. Co..
Introduction to Mathematical Logic.Alonzo Church - 1944 - London: Oxford University PRess.
Introduction to Mathematical Logic.Alonzo Church - 1956 - Princeton: Princeton University Press.
Introduction to Logic.Suppes Patrick - 1957 - Dover Publications.

View all 26 references / Add more references

Citations of this work BETA
Béziau's Translation Paradox.Lloyd Humberstone - 2005 - Theoria 71 (2):138-181.
Béziau's Translation Paradox.Lloyd Humberstone - 2005 - Theoria 71 (2):138-181.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

20 ( #247,256 of 2,168,955 )

Recent downloads (6 months)

6 ( #49,748 of 2,168,955 )

How can I increase my downloads?

My notes
Sign in to use this feature

There  are no threads in this forum
Nothing in this forum yet.

Other forums