Skip to main content Accessibility help
×
  1. Home
  2. Books
  3. The Metaphysics of Logic
  4. Content listing

Refine listing

Refine listing

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

26 results in The Metaphysics of Logic

Page 2 of 2

  • Chapter 10 - Logics and worlds

  • 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 178-188

  • Summary

    Wittgenstein's thought on mathematics had undergone a major, if often undetected, change. The idea that adopting an algorithm like "plus" determines in some physical, mental, or metaphysical way one's response to infinitely many exercises is nothing but covert Platonism, in many ways worse than the Platonism of objects. Wittgenstein agrees entirely with the Intuitionist critique of the law of excluded middle. For the Goldbach conjecture to be true in the sense of classical mathematics, we have to say that the operations of arithmetic determine in advance that every even number, no matter how large, can be partitioned into two primes. The law of excluded middle cannot be regarded as a hardened regularity in cases in which it is applied it to a putative infinite totality. But precisely because of this, there is no direct comparison possible between empirical observations and mathematical theorems in this type of proof.

  • Chapter 12 - Revising logic

  • 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 211-223

  • Summary

    The semantic notions of truth and logical validity in predicate logic, being dependent on what the correlates of our universal terms are, demand at least a certain semantic clarification of the issue of universals. Apparently, the primary issue concerning universals is ontological. It should be clear that these objective concepts are non-conventionally objective. It should also be clear that the laws of logic in the framework are supposed to be fundamentally different from the laws of psychology. For while the former are the laws of the logical relations among objective concepts, the latter are the laws of the causal relations among formal concepts. Thus, whereas logic can be normative, prescribing the laws of valid inference, cognitive psychology can only be descriptive, describing and perhaps explaining the psychological mechanisms that can make us prone to certain types of logical errors.

  • Chapter 8 - Logic and its objects: a medieval Aristotelian view

  • 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 147-159

  • Summary

    In general, the Second Philosopher's epistemological investigations take the form of asking how human beings, as described in biology, physiology, psychology, linguistics, and so on come to have reliable beliefs about the world as described in physics, chemistry, botany, astronomy, and so on. Second Philosopher's focus is somewhat broader; not only does she study how people come to form beliefs about the world, she also takes it upon herself to match these beliefs up with what her other inquiries have told her about how the world actually is, and to assess which types of belief-forming processes, in which circumstances, are reliable. After all, even Second Philosophy and Second Philosopher are used to describe her and her behavior. In any case, philosophy or not, the Second Philosopher's investigations do tell us something about the nature of the inference about the foreign coin.

  • Chapter 14 - The metaphysical interpretation of logical truth

  • 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 233-248

  • 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 3 - Pluralism, relativism, and objectivity

  • 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 49-71

  • 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.

Page 2 of 2