This category needs an editor. We encourage you to help if you are qualified.
Volunteer, or read more about what this involves.
Related categories
Siblings:
23 found
Search inside:
(import / add options)   Sort by:
  1. Jesus Alcolea (2012). Kitcher's Naturalistic Epistemology and Methodology of Mathematics. Poznan Studies in the Philosophy of the Sciences and the Humanities 101 (1):295-326.
    With his book The Nature of Mathematical Knowledge (1983), Ph. Kitcher, that had been doing extensive research in the history of the subject and in the contemporary debates on epistemology, saw clearly the need for a change in philosophy of mathematics. His goal was to replace the dominant, apriorist philosophy of mathematics with an empiricist philosophy. The current philosophies of mathematics all appeared, according to his analysis, not to fit well with how mathematicians actually do mathematics. A shift in orientation (...)
    Remove from this list |
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  2. Carlo Cellucci (1996). Mathematical Logic: What has It Done for the Philosophy of Mathematics? In Piergiorgio Odifreddi (ed.), Kreiseliana. About and Around Georg Kreisel, pp. 365-388. A K Peters.
    onl y to discuss some claims concerning the relationship between mathematical logic and the philosophy of mathematics that repeatedly occur in his writings. Although I do not know to what extent they are representative of his present position, they correspond to widespread views of the logical community and so seem worth discussing anyhow. Such claims will be used as reference to make some remarks about the present state of relations between mathematical logic and the philosophy of mathematics.
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  3. Carlo Cellucci (1993). From Closed to Open Systems. In J. Czermak (ed.), Philosophy of Mathematics, pp. 206-220. Hölder-Pichler-Tempsky.
    While Gödel's (first) incompleteness theorem has been used to refute the main contentions of Hilbert's program, it does not seem to have been generally used to stress that a basic ingredient of that program, the concept of formal system as a closed system - as well as the underlying view, embodied in the axiomatic method, that mathematical theories are deductions from first principles must be abandoned. Indeed the logical community has generally failed to learn Gödel's lesson that Hilbert's concept of (...)
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  4. Justin Clarke-Doane, Flawless Disagreement in Mathematics.
    A disagrees with B with respect to a proposition, p, flawlessly just in case A believes p and B believes not-p, or vice versa, though neither A nor B is guilty of a cognitive shortcoming – i.e. roughly, neither A nor B is being irrational, lacking evidence relevant to p, conceptually incompetent, insufficiently imaginative, etc.
    Remove from this list |
    Translate to English
    | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  5. Helen De Cruz & Johan De Smedt (2013). Mathematical Symbols as Epistemic Actions. Synthese 190 (1):3-19.
    Recent experimental evidence from developmental psychology and cognitive neuroscience indicates that humans are equipped with unlearned elementary mathematical skills. However, formal mathematics has properties that cannot be reduced to these elementary cognitive capacities. The question then arises how human beings cognitively deal with more advanced mathematical ideas. This paper draws on the extended mind thesis to suggest that mathematical symbols enable us to delegate some mathematical operations to the external environment. In this view, mathematical symbols are not only used to (...)
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  6. Lieven Decock (2010). Mathematical Entities. In Robrecht Vanderbeeken & Bart D'Hooghe (eds.), Worldviews, Science and Us. World Scientific. 224-241.
  7. Michael Deutsch (2007). Ontologie Und Methode der Mathematik. Universitätsdruckerei Bremen.
    Remove from this list |
    Translate to English
    |
     
    My bibliography  
     
    Export citation  
  8. William M. Farmer (1995). Reasoning About Partial Functions with the Aid of a Computer. Erkenntnis 43 (3):279 - 294.
    Partial functions are ubiquitous in both mathematics and computer science. Therefore, it is imperative that the underlying logical formalism for a general-purpose mechanized mathematics system provide strong support for reasoning about partial functions. Unfortunately, the common logical formalisms — first-order logic, type theory, and set theory — are usually only adequate for reasoning about partial functionsin theory. However, the approach to partial functions traditionally employed by mathematicians is quite adequatein practice. This paper shows how the traditional approach to partial functions (...)
    Remove from this list | Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  9. Giambattista Formica (2013). Da Hilbert a von Neumann: La Svolta Pragmatica Nell'assiomatica. Carocci.
    Remove from this list |
    Translate to English
    |
     
    My bibliography  
     
    Export citation  
  10. Joseph S. Fulda (2009). Rendering Conditionals in Mathematical Discourse with Conditional Elements. Journal of Pragmatics 41 (7):1435-1439.
    In "Material Implications" (1992), mathematical discourse was said to be different from ordinary discourse, with the discussion centering around conditionals. This paper shows how.
    Remove from this list |
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  11. M. Giaquinto (2011). Crossing Curves: A Limit to the Use of Diagrams in Proofs. Philosophia Mathematica 19 (3):281-307.
    This paper investigates the following question: when can one reliably infer the existence of an intersection point from a diagram presenting crossing curves or lines? Two cases are considered, one from Euclid's geometry and the other from basic real analysis. I argue for the acceptability of such an inference in the geometric case but against in the analytic case. Though this question is somewhat specific, the investigation is intended to contribute to the more general question of the extent and limits (...)
    Remove from this list | Direct download (11 more)  
     
    My bibliography  
     
    Export citation  
  12. Jaakko Hintikka (2012). Which Mathematical Logic is the Logic of Mathematics? Logica Universalis 6 (3-4):459-475.
    The main tool of the arithmetization and logization of analysis in the history of nineteenth century mathematics was an informal logic of quantifiers in the guise of the “epsilon–delta” technique. Mathematicians slowly worked out the problems encountered in using it, but logicians from Frege on did not understand it let alone formalize it, and instead used an unnecessarily poor logic of quantifiers, viz. the traditional, first-order logic. This logic does not e.g. allow the definition and study of mathematicians’ uniformity concepts (...)
    Remove from this list | Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  13. Philip Kitcher (1989). Innovation and Understanding in Mathematics. Journal of Philosophy 86 (10):563-564.
    Remove from this list | Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  14. Jean-Pierre Marquis (2006). A Path to the Epistemology of Mathematics: Homotopy Theory. In Jeremy Gray & Jose Ferreiros (eds.), Architecture of Modern Mathematics. Oxford University Press. 239--260.
    Remove from this list | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  15. Jean-Pierre Marquis (1999). Mathematical Engineering and Mathematical Change. International Studies in the Philosophy of Science 13 (3):245 – 259.
    In this paper, I introduce and examine the notion of “mathematical engineering” and its impact on mathematical change. Mathematical engineering is an important part of contemporary mathematics and it roughly consists of the “construction” and development of various machines, probes and instruments used in numerous mathematical fields. As an example of such constructions, I briefly present the basic steps and properties of homology theory. I then try to show that this aspect of contemporary mathematics has important consequences on our conception (...)
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  16. Mark McEvoy (2013). Experimental Mathematics, Computers and the a Priori. Synthese 190 (3):397-412.
    In recent decades, experimental mathematics has emerged as a new branch of mathematics. This new branch is defined less by its subject matter, and more by its use of computer assisted reasoning. Experimental mathematics uses a variety of computer assisted approaches to verify or prove mathematical hypotheses. For example, there is “number crunching” such as searching for very large Mersenne primes, and showing that the Goldbach conjecture holds for all even numbers less than 2 × 1018. There are “verifications” of (...)
    Remove from this list | Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  17. Jaroslav Peregrin, Diagonalization.
    It is a trivial fact that if we have a square table filled with numbers, we can always form a column which is not yet contained in the table. Despite its apparent triviality, this fact underlies the foundations of most of the path-breaking results of logic in the second half of the nineteenth and the first half of the twentieth century. We explain how this fact can be used to show that there are more sequences of natural numbers than there (...)
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  18. Georg Schiemer (2010). Fraenkel's Axiom of Restriction: Axiom Choice, Intended Models and Categoricity. In Benedikt L.öwe & Thomas Müller (eds.), PhiMSAMP. Philosophy of Mathematics: Sociological Aspects and Mathematical Practice. College Publications. 307{340.
  19. David Sherry (2006). Mathematical Reasoning: Induction, Deduction and Beyond. Studies in History and Philosophy of Science Part A 37 (3):489-504.
  20. David Sherry (1993). Don't Take Me Half the Way: On Berkeley on Mathematical Reasoning. Studies in the History and Philosophy of Science 24 (2):207-225.
  21. Jörgen Sjögren (2011). Indispensability, the Testing of Mathematical Theories, and Provisional Realism. Polish Journal of Philosophy 5 (2):99-116.
    Mathematical concepts are explications, in Carnap's sense, of vague or otherwise non-clear concepts; mathematical theories have an empirical and a deductive component. From this perspective, I argue that the empirical component of a mathematical theory may be tested together with the fruitfulness of its explications. Using these ideas, I furthermore give an argument for mathematical realism, based on the indispensability argument combined with a weakened version of confirmational holism.
    Remove from this list | Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  22. Jamie Tappenden, Proof Style and Understanding in Mathematics I: Visualization, Unification and Axiom Choice.
    Mathematical investigation, when done well, can confer understanding. This bare observation shouldn’t be controversial; where obstacles appear is rather in the effort to engage this observation with epistemology. The complexity of the issue of course precludes addressing it tout court in one paper, and I’ll just be laying some early foundations here. To this end I’ll narrow the field in two ways. First, I’ll address a specific account of explanation and understanding that applies naturally to mathematical reasoning: the view proposed (...)
    Remove from this list | Direct download  
     
    My bibliography  
     
    Export citation  
  23. Dag Westerståhl (2004). Perspectives on the Dispute Between Intuitionistic and Classical Mathematics. In Christer Svennerlind (ed.), Ursus Philosophicus. Essays dedicated to Björn Haglund on his sixtieth birthday. Philosophical Communications.
    It is not unreasonable to think that the dispute between classical and intuitionistic mathematics might be unresolvable or 'faultless', in the sense of there being no objective way to settle it. If so, we would have a pretty case of relativism. In this note I argue, however, that there is in fact not even disagreement in any interesting sense, let alone a faultless one, in spite of appearances and claims to the contrary. A position I call classical pluralism is sketched, (...)
    Remove from this list |
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation