Switch to: References

Add citations

You must login to add citations.
  1. Impurity in Contemporary Mathematics.Ellen Lehet - 2021 - Notre Dame Journal of Formal Logic 62 (1):67-82.
    Purity has been recognized as an ideal of proof. In this paper, I consider whether purity continues to have value in contemporary mathematics. The topics (e.g., algebraic topology, algebraic geometry, category theory) and methods of contemporary mathematics often favor unification and generality, values that are more often associated with impurity rather than purity. I will demonstrate this by discussing several examples of methods and proofs that highlight the epistemic significance of unification and generality. First, I discuss the examples of algebraic (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Ontological Purity for Formal Proofs.Robin Martinot - forthcoming - Review of Symbolic Logic:1-40.
    Purity is known as an ideal of proof that restricts a proof to notions belonging to the ‘content’ of the theorem. In this paper, our main interest is to develop a conception of purity for formal (natural deduction) proofs. We develop two new notions of purity: one based on an ontological notion of the content of a theorem, and one based on the notions of surrogate ontological content and structural content. From there, we characterize which (classical) first-order natural deduction proofs (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
    		•
  • The Calculus of Natural Calculation.René Gazzari - 2021 - Studia Logica 109 (6):1375-1411.
    The calculus of Natural Calculation is introduced as an extension of Natural Deduction by proper term rules. Such term rules provide the capacity of dealing directly with terms in the calculus instead of the usual reasoning based on equations, and therefore the capacity of a natural representation of informal mathematical calculations. Basic proof theoretic results are communicated, in particular completeness and soundness of the calculus; normalisation is briefly investigated. The philosophical impact on a proof theoretic account of the notion of (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  • Direct Proofs of Lindenbaum Conditionals.René Gazzari - 2014 - Logica Universalis 8 (3-4):321-343.
    We discuss the problem raised by Miller to re-prove the well-known equivalences of some Lindenbaum theorems for deductive systems without an application of the Axiom of Choice. We present five special constructions of deductive systems, each of them providing some partial solutions to the mathematical problem. We conclude with a short discussion of the underlying philosophical problem of deciding, whether a given proof satisfies our demand that the Axiom of Choice is not applied.
    $47.60 new   $52.55 used   $54.99 from Amazon    (collection)    View on Amazon.com
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
    		•
  • Science-Driven Mathematical Explanation.Alan Baker - 2012 - Mind 121 (482):243-267.
    Philosophers of mathematics have become increasingly interested in the explanatory role of mathematics in empirical science, in the context of new versions of the Quinean ‘Indispensability Argument’ which employ inference to the best explanation for the existence of abstract mathematical objects. However, little attention has been paid to analysing the nature of the explanatory relation involved in these mathematical explanations in science (MES). In this paper, I attack the only articulated account of MES in the literature (an account sketched by (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   42 citations  
  • Proof theory in philosophy of mathematics.Andrew Arana - 2010 - Philosophy Compass 5 (4):336-347.
    A variety of projects in proof theory of relevance to the philosophy of mathematics are surveyed, including Gödel's incompleteness theorems, conservation results, independence results, ordinal analysis, predicativity, reverse mathematics, speed-up results, and provability logics.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • On the relationship between plane and solid geometry.Andrew Arana & Paolo Mancosu - 2012 - Review of Symbolic Logic 5 (2):294-353.
    Traditional geometry concerns itself with planimetric and stereometric considerations, which are at the root of the division between plane and solid geometry. To raise the issue of the relation between these two areas brings with it a host of different problems that pertain to mathematical practice, epistemology, semantics, ontology, methodology, and logic. In addition, issues of psychology and pedagogy are also important here. To our knowledge there is no single contribution that studies in detail even one of the aforementioned areas.
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   29 citations  
  • L'infinité des nombres premiers : une étude de cas de la pureté des méthodes.Andrew Arana - 2011 - Les Etudes Philosophiques 97 (2):193.
    Une preuve est pure si, en gros, elle ne réfère dans son développement qu’à ce qui est « proche » de, ou « intrinsèque » à l’énoncé à prouver. L’infinité des nombres premiers, un théorème classique de l’arithmétique, est un cas d’étude particulièrement riche pour les recherches philosophiques sur la pureté. Deux preuves différentes de ce résultat sont ici considérées, à savoir la preuve euclidienne classique et une preuve « topologique » plus récente proposée par Furstenberg. D’un point de vue (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark  
    		•