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26 results in The Metaphysics of Logic

Page 1 of 2

  • Chapter 11 - Bolzano’s logical realism

  • from Part II - History and Authors
  • Edited by Penelope Rush, University of Tasmania
  • Book:
    The Metaphysics of Logic
    Published online:
    05 October 2014
    Print publication:
    16 October 2014, pp 189-208

  • Summary

    Bolzano's Theory of Science presents the first explicit and methodical espousal of internal logical realism. It also contains a formidable number of theoretical innovations. They include: the first account of the distinction between sense and reference; definitions of analyticity and consequence, i.e. deducibility based on a new substitutional procedure that anticipates Quine's and Tarski's, respectively; and an account of mathematical knowledge that excludes, contra Kant. In Bolzano's case, one of the main purposes in introducing propositions in themselves is to achieve precise and satisfactory definitions. By way of consequence, on Bolzano's own account the success of the endeavour depends on whether his commitment to propositions allows him to deliver a good theory of logic, or at least one that is preferable to its rivals. Bolzano did have views on epistemic modality, though unfortunately, there is no place for a discussion of the latter here.

  • Chapter 13 - Glutty theories and the logic of antinomies

  • from Part III - Specific Issues
  • Edited by Penelope Rush, University of Tasmania
  • Book:
    The Metaphysics of Logic
    Published online:
    05 October 2014
    Print publication:
    16 October 2014, pp 224-232

  • Summary

    A transcendental philosophy as described and practiced by Kant is itself a logic. It is not intended to decide such factual questions as whether there is a God or humans are free, but to address semantical issues like what the meaning of God or freedom is. Within the semantical space where the (transcendental) logical enterprise is located, one can take different words as primitives and establish a network of semantical relations and dependencies based on those primitives. A logic is a self-organizing structure, self-enclosed and self-referential, that provides the bare scaffolding of a world and, if given enough data, even a large part of its actual construction. Logic is a highly ambitious theory: one that attempts to construct a universal language. In and by itself, this theory will be found persuasive only by those who are already committed to the particular view it expresses and articulates.

  • Chapter 9 - The problem of universals and the subject matter of logic

  • from Part II - History and Authors
  • Edited by Penelope Rush, University of Tasmania
  • Book:
    The Metaphysics of Logic
    Published online:
    05 October 2014
    Print publication:
    16 October 2014, pp 160-177

  • Summary

    The idea that there may be more than one correct logic has recently attracted considerable interest. The most notorious bone of contention in the discussion of logical correctness is the law of excluded middle. The connections between sequent calculus, constructive proof transformation, structural completeness, and lem are fixtures from logical knowledge store, but they cannot seriously be thought of as a network of consequences in some allegedly correct logic. The author indicates logic's modern contours, highlighting the fact that the deepest observations logic has to offer come with no ties to preconceptions about its essence. The richness of logic comes into view only when we stop looking for such an essence and focus instead on the accumulation of applications and conceptual changes that have made current logical investigations possible. The study of logic might be the best practical antidote to the view of it that we have inherited.

  • Chapter 2 - A defense of logical conventionalism

  • from Part I - The Main Positions
  • Edited by Penelope Rush, University of Tasmania
  • Book:
    The Metaphysics of Logic
    Published online:
    05 October 2014
    Print publication:
    16 October 2014, pp 32-48

  • Summary

    Our logical practices, it seems, already exhibit "truth by convention". A visible part of contemporary research in logic is the exploration of non classical logical systems. It's sad that almost no one notices that Quine's refutation of the conventionality of logic is a dilemma. The famous Lewis Carroll infinite regress assails only one horn of this dilemma, the horn that presupposes that the infinitely many needed conventions are all explicit. One of the oldest ways of begging the question against proponents of alternative logics (as well as a popular way of begging the question against logical conventionalism) is to implicitly adopt a lofty metalanguage stance, and then use the very words that are under contention against the opponent. That doing this is so intuitive evidently contributes to the continued popularity of the fallacy.

  • Chapter 7 - Wittgenstein and the covert Platonism of mathematical logic

  • from Part I - The Main Positions
  • Edited by Penelope Rush, University of Tasmania
  • Book:
    The Metaphysics of Logic
    Published online:
    05 October 2014
    Print publication:
    16 October 2014, pp 128-144

  • Summary

    This chapter discusses a kind of relativism or pluralism concerning logic. It explores a core metaphysical issue concerning logic, the extent to which logic is objective. The chapter adopts a Hilbertian perspective, either the original version where consistency is the only formal, mathematical requirement on legitimate theories, or the liberal orientation where there are no formal requirements on legitimacy at all. It explores the ramifications for what the author takes to be a longstanding intuition that logic is objective. This chapter explains the matter of objectivity with the present folk-relativism concerning logic in focus. Sometimes it concentrates on general logical matters, such as validity and consistency, as such, and sometimes it deals with particular instances of the folk-relativism, such as classical validity, intuitionistic consistency, and the like. The chapter limits the discussion to Wright's axes of epistemic constraint and cognitive command.

  • Chapter 6 - Logical nihilism

  • from Part I - The Main Positions
  • Edited by Penelope Rush, University of Tasmania
  • Book:
    The Metaphysics of Logic
    Published online:
    05 October 2014
    Print publication:
    16 October 2014, pp 109-127

  • Summary

    Our logical practices, it seems, already exhibit "truth by convention". A visible part of contemporary research in logic is the exploration of non classical logical systems. It's sad that almost no one notices that Quine's refutation of the conventionality of logic is a dilemma. The famous Lewis Carroll infinite regress assails only one horn of this dilemma, the horn that presupposes that the infinitely many needed conventions are all explicit. One of the oldest ways of begging the question against proponents of alternative logics (as well as a popular way of begging the question against logical conventionalism) is to implicitly adopt a lofty metalanguage stance, and then use the very words that are under contention against the opponent. That doing this is so intuitive evidently contributes to the continued popularity of the fallacy.

  • Chapter 1 - Logical realism

  • from Part I - The Main Positions
  • Edited by Penelope Rush, University of Tasmania
  • Book:
    The Metaphysics of Logic
    Published online:
    05 October 2014
    Print publication:
    16 October 2014, pp 13-31

  • Summary

    Logic might chart the rules of the world itself; the rules of rational human thought; or both. Husserl had a very broad concept of logic that embraces our usual modern idea of logic as well as something he called pure logic, which we can loosely characterise as something like the fundamental forms of experience. For Husserl, the fundamental forms of pure logic are an in-eliminable part of experience: i.e. experience encompasses direct apprehension of these inferential relationships. The apprehended structures are abstract and platonic; discovered, rather than constructed. Theory, empirical observation, and experience are in this sense fallible: they may or may not get it right and reveal the actual independent structure of logic. Both logic and mathematics as they are characterised by Husserl, should encounter the realist problem of independence, neither are the sort of thing we can simply take as part of human cognition.

  • Chapter 5 - A Second Philosophy of logic

  • from Part I - The Main Positions
  • Edited by Penelope Rush, University of Tasmania
  • Book:
    The Metaphysics of Logic
    Published online:
    05 October 2014
    Print publication:
    16 October 2014, pp 93-108

  • Summary

    Logic might chart the rules of the world itself; the rules of rational human thought; or both. Husserl had a very broad concept of logic that embraces our usual modern idea of logic as well as something he called pure logic, which we can loosely characterise as something like the fundamental forms of experience. For Husserl, the fundamental forms of pure logic are an in-eliminable part of experience: i.e. experience encompasses direct apprehension of these inferential relationships. The apprehended structures are abstract and platonic; discovered, rather than constructed. Theory, empirical observation, and experience are in this sense fallible: they may or may not get it right and reveal the actual independent structure of logic. Both logic and mathematics as they are characterised by Husserl, should encounter the realist problem of independence, neither are the sort of thing we can simply take as part of human cognition.

  • Chapter 4 - Logic, mathematics, and conceptual structuralism

  • from Part I - The Main Positions
  • Edited by Penelope Rush, University of Tasmania
  • Book:
    The Metaphysics of Logic
    Published online:
    05 October 2014
    Print publication:
    16 October 2014, pp 72-92

  • Summary

    Logic is integral to mathematics and, to the extent that is the case, a philosophy of logic should be integral to a philosophy of mathematics. The aim of the mathematician working in the mainstream is to establish truths about mathematical concepts by means of proofs as the principal instrument. There are other dimensions of mathematical practice that reward metamathematical study motivated by the philosophy of conceptual structuralism. One is the open-ended nature of certain principles such as that of induction for the integers and comprehension for sets. This accords with the fact that in the development of mathematics what concepts are recognized to be definite evolve with time. Thus one cannot fix in advance all applications of these open-ended schematic principles by restriction to those instances definable in one or another formal language, as is currently done in the study of formal systems.

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