David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
History and Philosophy of Logic 33 (3):215-243 (2012)
Fitch's basic logic is an untyped illative combinatory logic with unrestricted principles of abstraction effecting a type collapse between properties (or concepts) and individual elements of an abstract syntax. Fitch does not work axiomatically and the abstraction operation is not a primitive feature of the inductive clauses defining the logic. Fitch's proof that basic logic has unlimited abstraction is not clear and his proof contains a number of errors that have so far gone undetected. This paper corrects these errors and presents a reasonably intuitive proof that Fitch's system K supports an implicit abstraction operation. Some general remarks on the philosophical significance of basic logic, especially with respect to neo-logicism, are offered, and the paper concludes that basic logic models a highly intensional form of logicism
|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
Wayne Aitken & Jeffrey A. Barrett (2004). Computer Implication and the Curry Paradox. Journal of Philosophical Logic 33 (6):631-637.
Wayne Aitken & Jeffrey A. Barrett (2007). Stability and Paradox in Algorithmic Logic. Journal of Philosophical Logic 36 (1):61 - 95.
G. A. Antonelli (2010). Notions of Invariance for Abstraction Principles. Philosophia Mathematica 18 (3):276-292.
Peter Apostoli (2000). The Analytic Conception of Truth and the Foundations of Arithmetic. Journal of Symbolic Logic 65 (1):33-102.
George Bealer (1982). Quality and Concept. Oxford University Press.
Citations of this work BETA
No citations found.
Similar books and articles
Frederic B. Fitch (1957). A Definition of Existence in Terms of Abstraction and Disjunction. Journal of Symbolic Logic 22 (4):343-344.
Uwe Petersen (2000). Logic Without Contraction as Based on Inclusion and Unrestricted Abstraction. Studia Logica 64 (3):365-403.
Frederic B. Fitch (1950). A Further Consistent Extension of Basic Logic. Journal of Symbolic Logic 14 (4):209-218.
Frederic B. Fitch (1956). Recursive Functions in Basic Logic. Journal of Symbolic Logic 21 (4):337-346.
Frederic B. Fitch (1948). An Extension of Basic Logic. Journal of Symbolic Logic 13 (2):95-106.
Frederic B. Fitch (1953). A Simplification of Basic Logic. Journal of Symbolic Logic 18 (4):317-325.
Frederic B. Fitch (1954). A Definition of Negation in Extended Basic Logic. Journal of Symbolic Logic 19 (1):29-36.
Frederic B. Fitch (1958). An Extensional Variety of Extended Basic Logic. Journal of Symbolic Logic 23 (1):13-21.
Alan Ross Anderson, Ruth Barcan Marcus, R. M. Martin & Frederic B. Fitch (eds.) (1975). The Logical Enterprise. Yale University Press.
Frederic B. Fitch (1942). A Basic Logic. Journal of Symbolic Logic 7 (3):105-114.
Frederic B. Fitch (1949). The Heine-Borel Theorem in Extended Basic Logic. Journal of Symbolic Logic 14 (1):9-15.
M. W. Bunder (2000). Expedited Broda-Damas Bracket Abstraction. Journal of Symbolic Logic 65 (4):1850-1857.
Sabine Broda & Luís Damas (1997). Compact Bracket Abstraction in Combinatory Logic. Journal of Symbolic Logic 62 (3):729-740.
Paolo Maffezioli, Alberto Naibo & Sara Negri (2013). The Church–Fitch Knowability Paradox in the Light of Structural Proof Theory. Synthese 190 (14):2677-2716.
Wayne Aitken & Jeffrey A. Barrett (2008). Abstraction in Algorithmic Logic. Journal of Philosophical Logic 37 (1):23 - 43.
Added to index2012-02-18
Total downloads147 ( #6,131 of 1,102,092 )
Recent downloads (6 months)4 ( #91,808 of 1,102,092 )
How can I increase my downloads?