3 results
4 - Overview of My Proposal
- from Part I
-
- Book:
- A Logical Foundation for Potentialist Set Theory
- Published online:
- 10 February 2022
- Print publication:
- 17 February 2022, pp 42-56
-
- Chapter
- Export citation
2 - Actualist Set Theory
- from Part I
-
- Book:
- A Logical Foundation for Potentialist Set Theory
- Published online:
- 10 February 2022
- Print publication:
- 17 February 2022, pp 13-30
-
- Chapter
- Export citation
Frege's unofficial arithmetic
-
- Journal:
- The Journal of Symbolic Logic / Volume 67 / Issue 4 / December 2002
- Published online by Cambridge University Press:
- 12 March 2014, pp. 1623-1638
- Print publication:
- December 2002
-
- Article
- Export citation
-
I show that any sentence of nth-order (pure or applied) arithmetic can be expressed with no loss of compositionality as a second-order sentence containing no arithmetical vocabulary, and use this result to prove a completeness theorem for applied arithmetic. More specifically. I set forth an enriched second-order language L. a sentence
of L (which is true on the intended interpretation of L), and a compositionally recursive transformation Tr defined on formulas of L, and show that they have the following two properties: (a) in a universe with at least ℶn−2 objects, any formula of nth-order (pure or applied) arithmetic can be expressed as a formula of L, and (b) for any sentence 
of 
is a second-order sentence containing no arithmetical vocabulary, and 
of 
of 
is a second-order sentence containing no arithmetical vocabulary, and 
