Switch to: References

Add citations

You must login to add citations.
  1. Is Frege's Definition of the Ancestral Adequate?Richard G. Heck - 2016 - Philosophia Mathematica 24 (1):91-116.
    Why should one think Frege's definition of the ancestral correct? It can be proven to be extensionally correct, but the argument uses arithmetical induction, and that seems to undermine Frege's claim to have justified induction in purely logical terms. I discuss such circularity objections and then offer a new definition of the ancestral intended to be intensionally correct; its extensional correctness then follows without proof. This new definition can be proven equivalent to Frege's without any use of arithmetical induction. This (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Poincaré: Mathematics & logic & intuition.Colin Mclarty - 1997 - Philosophia Mathematica 5 (2):97-115.
    often insisted existence in mathematics means logical consistency, and formal logic is the sole guarantor of rigor. The paper joins this to his view of intuition and his own mathematics. It looks at predicativity and the infinite, Poincaré's early endorsement of the axiom of choice, and Cantor's set theory versus Zermelo's axioms. Poincaré discussed constructivism sympathetically only once, a few months before his death, and conspicuously avoided committing himself. We end with Poincaré on Couturat, Russell, and Hilbert.
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  • Continuity, causality and determinism in mathematical physics: from the late 18th until the early 20th century.Marij van Strien - 2014 - Dissertation, University of Ghent
    It is commonly thought that before the introduction of quantum mechanics, determinism was a straightforward consequence of the laws of mechanics. However, around the nineteenth century, many physicists, for various reasons, did not regard determinism as a provable feature of physics. This is not to say that physicists in this period were not committed to determinism; there were some physicists who argued for fundamental indeterminism, but most were committed to determinism in some sense. However, for them, determinism was often not (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
    		•