David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Symbolic Logic 39 (4):625-637 (1974)
For each positive n , 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 definitionally equivalent [or 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 definitionally equivalent with each other and with Peano arithmetic. Categoricity of Peano arithmetic then implies categoricity of each of the above theories
|Keywords||Syntax concatenation foundations of logic juxtaposition Wahrheitsbegriff truth-definition categoricity second-order logic definitionally equivalent character-prefixing|
|Categories||categorize this paper)|
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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.
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