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 $n > 0$ , 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
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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.
John Corcoran (1980). Categoricity. History and Philosophy of Logic 1 (1):187-207.
Gualtiero Piccinini (2008). Computers. Pacific Philosophical Quarterly 89 (1):32–73.
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