David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Studia Logica 49 (1):47-65 (1990)
Da Costa's C systems are surveyed and motivated, and significant failings of the systems are indicated. Variations are then made on these systems in an attempt to surmount their defects and limitations. The main system to emerge from this effort, system CC , is investigated in some detail, and dual-intuitionistic semantical analyses are developed for it and surrounding systems. These semantics are then adapted for the original C systems, first in a rather unilluminating relational fashion, subsequently in a more illuminating way through the introduction of impossible situations where and and or change roles. Finally other attempts to break out of impasses for the original and expanded C systems, by going inside them, are looked at, and further research directions suggested.
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References found in this work BETA
Stephen Cole Kleene (1952). Introduction to Metamathematics. North Holland.
Haskell B. Curry (1963/1977). Foundations of Mathematical Logic. Dover Publications.
Newton C. A. Da Costa (1974). On the Theory of Inconsistent Formal Systems. Notre Dame Journal of Formal Logic 15 (4):497-510.
A. Heyting (1956). Intuitionism. Amsterdam, North-Holland Pub. Co..
Evert Willem Beth (1959). The Foundations of Mathematics. Amsterdam, North-Holland Pub. Co..
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