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Kit Fine (2005). Our Knowledge of Mathematical Objects.

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  1.  62
    Sets and Supersets.Toby Meadows - 2016 - Synthese 193 (6):1875-1907.
    It is a commonplace of set theory to say that there is no set of all well-orderings nor a set of all sets. We are implored to accept this due to the threat of paradox and the ensuing descent into unintelligibility. In the absence of promising alternatives, we tend to take up a conservative stance and tow the line: there is no universe. In this paper, I am going to challenge this claim by taking seriously the idea that we can (...)
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  2.  54
    To Bridge Gödel’s Gap.Eileen S. Nutting - 2016 - Philosophical Studies 173 (8):2133-2150.
    In “Mathematical Truth,” Paul Benacerraf raises an epistemic challenge for mathematical platonists. In this paper, I examine the assumptions that motivate Benacerraf’s original challenge, and use them to construct a new causal challenge for the epistemology of mathematics. This new challenge, which I call ‘Gödel’s Gap’, appeals to intuitive insights into mathematical knowledge. Though it is a causal challenge, it does not rely on any obviously objectionable constraints on knowledge. As a result, it is more compelling than the original challenge. (...)
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  3.  19
    Solving Prior’s Problem with a Priorean Tool.Martin Pleitz - 2016 - Synthese 193 (11):3567-3577.
    I will show how a metaphysical problem of Arthur Prior’s can be solved by a logical tool he developed himself, but did not put to any foundational use: metric logic. The broader context is given by the key question about the metaphysics of time: Is time tenseless, i.e., is time just a structure of instants; or is time tensed, because some facts are irreducibly tensed? I take sides with Prior and the tensed theory. Like him, I therefore I have to (...)
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  4. Unrestricted Quantification.Salvatore Florio - 2014 - Philosophy Compass 9 (7):441-454.
    Semantic interpretations of both natural and formal languages are usually taken to involve the specification of a domain of entities with respect to which the sentences of the language are to be evaluated. A question that has received much attention of late is whether there is unrestricted quantification, quantification over a domain comprising absolutely everything there is. Is there a discourse or inquiry that has absolute generality? After framing the debate, this article provides an overview of the main arguments for (...)
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  5.  45
    Review of S. Centrone, Logic and Philosophy of Mathematics in the Early Husserl[REVIEW]Matteo Plebani - 2011 - Dialectica 65 (3):477-482.
  6.  4
    Logic and Philosophy of Mathematics in the Early Husserl – By Stefania Centrone.Matteo Plebani - 2011 - Dialectica 65 (3):477-482.
  7. Logic and Philosophy of Mathematics in the Early Husserl - By Stefania Centrone.Matteo Plebani - 2011 - Dialectica 65 (3):477-482.
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    Honest Toil or Sheer Magic?Alan Weir - 2007 - Dialectica 61 (1):89-115.
    In this article I discuss the ‘procedural postulationist’ view of mathematics advanced by Kit Fine in a recent paper. I argue that he has not shown that this view provides an avenue to knowledge of mathematical truths, at least if such truths are objective truths. In particular, more needs to be said about the criteria which constrain which types of entities can be postulated. I also argue that his reliance on second‐order quantification means that his background logic is not free (...)
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    Honest Toil or Sheer Magic?Alan Weir - 2006 - Dialectica 61 (1):89–115.
    In this article I discuss the ‘procedural postulationist’ view of mathematics advanced by Kit Fine in a recent paper. I argue that he has not shown that this view provides an avenue to knowledge of mathematical truths, at least if such truths are objective truths. In particular, more needs to be said about the criteria which constrain which types of entities can be postulated. I also argue that his reliance on second‐order quantification means that his background logic is not free (...)
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