Switch to: References

Add citations

You must login to add citations.
  1. Set Existence Principles and Closure Conditions: Unravelling the Standard View of Reverse Mathematics.Benedict Eastaugh - 2019 - Philosophia Mathematica 27 (2):153-176.
    It is a striking fact from reverse mathematics that almost all theorems of countable and countably representable mathematics are equivalent to just five subsystems of second order arithmetic. The standard view is that the significance of these equivalences lies in the set existence principles that are necessary and sufficient to prove those theorems. In this article I analyse the role of set existence principles in reverse mathematics, and argue that they are best understood as closure conditions on the powerset of (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  • Review of John Stillwell, Reverse Mathematics: Proofs From the Inside Out. [REVIEW]Benedict Eastaugh - 2020 - Philosophia Mathematica 28 (1):108-116.
    Review of John Stillwell, Reverse Mathematics: Proofs from the Inside Out. Princeton, NJ: Princeton University Press, 2018, pp. 200. ISBN 978-0-69-117717-5 (hbk), 978-0-69-119641-1 (pbk), 978-1-40-088903-7 (e-book).
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  • Incompleteness Via Paradox and Completeness.Walter Dean - 2020 - Review of Symbolic Logic 13 (3):541-592.
    This paper explores the relationship borne by the traditional paradoxes of set theory and semantics to formal incompleteness phenomena. A central tool is the application of the Arithmetized Completeness Theorem to systems of second-order arithmetic and set theory in which various “paradoxical notions” for first-order languages can be formalized. I will first discuss the setting in which this result was originally presented by Hilbert & Bernays and also how it was later adapted by Kreisel and Wang in order to obtain (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  • Strict Finitism, Feasibility, and the Sorites.Walter Dean - 2018 - Review of Symbolic Logic 11 (2):295-346.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Computational Reverse Mathematics and Foundational Analysis.Benedict Eastaugh - manuscript
    Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational analysis, which explores the limits of different foundations for mathematics in a formally precise manner. This paper gives a detailed account of the motivations and methodology of foundational analysis, which have heretofore been largely left implicit in the practice. It then shows how this account can be fruitfully applied in the (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark