David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 39 (4):625-637 (1974)
For each $n > 0$ , two alternative axiomatizations of the theory of strings over n alphabetic characters are presented. One class of axiomatizations derives from Tarski's system of the Wahrheitsbegriff and uses the n characters and concatenation as primitives. The other class involves using n character-prefixing operators as primitives and derives from Hermes' Semiotik. All underlying logics are second order. It is shown that, for each n, the two theories are synonymous in the sense of deBouvere. It is further shown that each member of one class is synonymous with each member of the other class; thus that all of the theories are synonymous with each other and with Peano arithmetic. Categoricity of Peano arithmetic then implies categoricity of each of the above theories
|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
Gualtiero Piccinini (2010). The Mind as Neural Software? Understanding Functionalism, Computationalism, and Computational Functionalism. Philosophy and Phenomenological Research 81 (2):269-311.
John Corcoran & José Miguel Sagüillo (2011). The Absence of Multiple Universes of Discourse in the 1936 Tarski Consequence-Definition Paper. History and Philosophy of Logic 32 (4):359 - 374.
Gualtiero Piccinini (2007). Computational Modeling Vs. Computational Explanation: Is Everything a Turing Machine, and Does It Matter to the Philosophy of Mind? Australasian Journal of Philosophy 85 (1):93 – 115.
Gualtiero Piccinini (2008). Computers. Pacific Philosophical Quarterly 89 (1):32–73.
John Corcoran (1980). Categoricity. History and Philosophy of Logic 1 (1):187-207.
Similar books and articles
Robert Batterman (1992). Quantum Chaos and Semiclassical Mechanics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:50 - 65.
Volker Halbach (1999). Conservative Theories of Classical Truth. Studia Logica 62 (3):353-370.
Nikolaj Jang Lee Linding Pedersen & Marcus Rossberg (2010). Open-Endedness, Schemas and Ontological Commitment. Noûs 44 (2):329-339.
Pasquale Frascolla (1997). The Tractatus System of Arithmetic. Synthese 112 (3):353-378.
Shmuel Lifsches & Saharon Shelah (1997). Peano Arithmetic May Not Be Interpretable in the Monadic Theory of Linear Orders. Journal of Symbolic Logic 62 (3):848-872.
P. X. Monaghan (2010). A Novel Interpretation of Plato's Theory of Forms. Metaphysica 11 (1):63-78.
Sergei Artëmov & Franco Montagna (1994). On First-Order Theories with Provability Operator. Journal of Symbolic Logic 59 (4):1139-1153.
J. Michael Dunn (1980). Quantum Mathematics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:512 - 531.
Added to index2009-01-28
Total downloads60 ( #25,459 of 1,101,655 )
Recent downloads (6 months)3 ( #116,934 of 1,101,655 )
How can I increase my downloads?