VBTOs such as 'the', 'the set of objects such that', 'the least number such that'.

What is it about?

1972. Variable Binding Term Operators, (Co-authors Wm. Hatcher, John Herring) Zeitschrift f"ur mathematische Logik und Grundlagen der Mathematik 18, 177–82. MR0305970 (46 #5098) Reprint 2006. Mathematical Logic Quarterly.18: 177–182. https://www.academia.edu/s/71e709b704?source=link A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. Kalish-Montague 1964 proposed using vbtos to formalize definite descriptions “the x: x+x=2”, set abstracts {x: F}, minimization in recursive function theory “the least x: x+x>2”, etc. However, they gave no semantics for vbtos. Hatcher 1968 gave a semantics but one that has flaws described in the 1971 paper and admitted by Hatcher. In 1971 we give a correct semantic analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture, proved in this paper with Hatcher’s help, was proved independently about the same time by Newton da Costa. The 1983 paper by Newton da Costa brings us up to date. http://www.tandfonline.com/doi/pdf/10.1080/01445348308837045

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Why is it important?

Russell said how to eliminate 'the', but he did not give the semantic analysis or even the full syntactic analyysis of what he was eliminating. He did not even say why 'the' should be eliminated and not taken at face value.

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