The Tree Theory and Isomorphism
Analysis 41 (1):6-11 (1981)
| Abstract | A main thesis of Fred Sommers' type theory, is that an isomorphism exists between any natural language and the categories discriminated by that language. Here the author gives an explanation of what this claim comes to. And then it is argued that, so understood, the claim is incompatible with Zermelo-Fraenkel set theory. Finally, it is argued against trying to salvage the isomorphism thesis by appealing to some other set theory. | |||||||||
| Keywords | Sommers sommers type theory set theory | |||||||||
| Categories | ||||||||||
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Charles Sayward (1976). A Defense of Sommers. Philosophical Studies 29 (5):343 - 347.
Charles Sayward (1978). Are There Infinitely Many Sorts of Things? Philosophia 8 (1):17-30.
Stephen H. Voss & Charles Sayward (1980). The Structure of Type Theory. Journal of Philosophy 77 (5):241-259.
George Englebretsen (1985). Semantic Considerations for Sommers' Logic. Philosophy Research Archives 11:281-318.
Charles Sayward & Stephen H. Voss (1972). Absurdity and Spanning. Philosophia 2 (3):227-238.
George Englebretsen (1975). Sommers' Tree Theory and Possible Things. Philosophical Studies 24:131-139.
David Massie (1967). Sommers' Tree Theory: A Reply to de Sousa. Journal of Philosophy 64 (6):185-193.
Charles Sayward (1978). Strawson on Categories. Journal of Critical Analysis 7 (3):83-87.
J. P. Studd (2012). The Iterative Conception of Set: A (Bi-)Modal Axiomatisation. Journal of Philosophical Logic.
Bart Jacobs (1989). The Inconsistency of Higher Order Extensions of Martin-Löf's Type Theory. Journal of Philosophical Logic 18 (4):399 - 422.
Colin McLarty (1993). Anti-Foundation and Self-Reference. Journal of Philosophical Logic 22 (1):19 - 28.
Fred Sommers (1959). The Ordinary Language Tree. Mind 68 (270):160-185.
Nicola Gambino & Peter Aczel (2006). The Generalised Type-Theoretic Interpretation of Constructive Set Theory. Journal of Symbolic Logic 71 (1):67 - 103.
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