11 found
  1.  75
    Frege and Hilbert on Consistency.Patricia A. Blanchette - 1996 - Journal of Philosophy 93 (7):317-336.
  2. Frege on Consistency and Conceptual Analysis.Patricia A. Blanchette - 2007 - Philosophia Mathematica 15 (3):321-346.
    Gottlob Frege famously rejects the methodology for consistency and independence proofs offered by David Hilbert in the latter's Foundations of Geometry. The present essay defends against recent criticism the view that this rejection turns on Frege's understanding of logical entailment, on which the entailment relation is sensitive to the contents of non-logical terminology. The goals are (a) to clarify further Frege's understanding of logic and of the role of conceptual analysis in logical investigation, and (b) to point out the extent (...)
    Direct download (8 more)  
    Export citation  
    Bookmark   14 citations  
  3. Models and modality.Patricia A. Blanchette - 2000 - Synthese 124 (1-2):45-72.
    This paper examines the connection between model-theoretic truth and necessary truth. It is argued that though the model-theoretic truths of some standard languages are demonstrably ''''necessary'''' (in a precise sense), the widespread view of model-theoretic truth as providing a general guarantee of necessity is mistaken. Several arguments to the contrary are criticized.
    Direct download (5 more)  
    Export citation  
    Bookmark   12 citations  
  4.  47
    Frege on Formality and the 1906 Independence-Test.Patricia A. Blanchette - 2014 - In Godehard Link (ed.), Formalism and Beyond: On the Nature of Mathematical Discourse. Boston: De Gruyter. pp. 97-118.
  5.  68
    Frege's reduction.Patricia A. Blanchette - 1994 - History and Philosophy of Logic 15 (1):85-103.
    This paper defends the view that Frege’s reduction of arithmetic to logic would, if successful, have shown that arithmetical knowledge is analytic in essentially Kant’s sense. It is argued, as against Paul Benacerraf, that Frege’s apparent acceptance of multiple reductions is compatible with this epistemological thesis. The importance of this defense is that (a) it clarifies the role of proof, definition, and analysis in Frege’s logicist works; and (b) it demonstrates that the Fregean style of reduction is a valuable tool (...)
    Direct download (3 more)  
    Export citation  
    Bookmark   10 citations  
  6. Logical consequence.Patricia A. Blanchette - 2001 - In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Malden, Mass.: Wiley-Blackwell. pp. 2001--115.
  7. Axioms in Frege.Patricia A. Blanchette - 2019 - In Philip A. Ebert & Marcus Rossberg (eds.), Essays on Frege's Basic Laws of Arithmetic. Oxford: Oxford University Press.
  8.  45
    Frege On Shared Belief and Total Functions.Patricia A. Blanchette - 2012 - Journal of Philosophy 109 (1-2):9-39.
  9.  8
    Logical Consequence.Patricia A. Blanchette - 2001 - In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Malden, Mass.: Wiley-Blackwell. pp. 115–135.
    Whenever one asserts a claim of any kind, one engages in a commitment not just to that claim itself, but to a variety of other claims that follow in its wake, claims that, as we tend to say, follow logically from the original claim. To say that Smith and Jones are both great basketball players is to say something from which it follows that Smith is a great basketball player, that someone is a great basketball player, that there is something (...)
    No categories
    Direct download  
    Export citation  
    Bookmark   1 citation  
  10. Logicism Reconsidered.Patricia A. Blanchette - 1990 - Dissertation, Stanford University
    This thesis is an examination of Frege's logicism, and of a number of objections which are widely viewed as refutations of the logicist thesis. In the view offered here, logicism is designed to provide answers to two questions: that of the nature of arithmetical truth, and that of the source of arithmetical knowledge. ;The first objection dealt with here is the view that logicism is not an epistemologically significant thesis, due to the fact that the epistemological status of logic itself (...)
    Export citation  
  11.  42
    Realism and Paradox.Patricia A. Blanchette - 2000 - Notre Dame Journal of Formal Logic 41 (3):227-241.
    This essay addresses the question of the effect of Russell's paradox on Frege's distinctive brand of arithmetical realism. It is argued that the effect is not just to undermine Frege's specific account of numbers as extensions (courses of value) but more importantly to undermine his general means of explaining the object-directedness of arithmetical discourse. It is argued that contemporary neo-Fregean attempts to revive that explanation do not successfully avoid the central problem brought to light by the paradox. Along the way, (...)
    Direct download (6 more)  
    Export citation