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4 results

  • 10 - Quantification

  • Edwin Mares, Victoria University of Wellington
  • Book:
    The Logic of Entailment and its History
    Published online:
    08 February 2024
    Print publication:
    15 February 2024, pp 192-214

  • Summary

    The model theory for quantified relevant logic developed by Robert Goldblatt and Mares is adapted to the present semantical framework. A universally quantified statement ‘For all x A(x)’ is taken to mean that there is some proposition in the present theory that entails every instance of A(x). An axiomatization of the logic is given, and completeness is proven in the Appendix to the book. Identity, the nature of domains, and higher-order quantification are also discussed.

Mathematical Anti-Realism and Modal Nothingism

Mathematical Anti-Realism and Modal Nothingism
  • Mark Balaguer
  • Published online:
    02 December 2022
    Print publication:
    05 January 2023
  • This Element defends mathematical anti-realism against an underappreciated problem with that view-a problem having to do with modal truthmaking. Part I develops mathematical anti-realism, it defends that view against a number of well-known objections, and it raises a less widely discussed objection to anti-realism-an objection based on the fact that (a) mathematical anti-realists need to commit to the truth of certain kinds of modal claims, and (b) it's not clear that the truth of these modal claims is compatible with mathematical anti-realism. Part II considers various strategies that anti-realists might pursue in trying to solve this modal-truth problem with their view, it argues that there's only one viable view that anti-realists can endorse in order to solve the modal-truth problem, and it argues that the view in question-which is here called modal nothingism-is true.
Divine Ideas

Divine Ideas
  • Thomas M. Ward
  • Published online:
    13 August 2020
    Print publication:
    03 September 2020
  • This Element defends a version of the classical theory of divine ideas, the containment exemplarist theory of divine ideas. The classical theory holds that God has ideas of all possible creatures, that these ideas partially explain why God's creation of the world is a rational and free personal action, and that God does not depend on anything external to himself for having the ideas he has. The containment exemplarist version of the classical theory holds that God's own nature is the exemplar of all possible creatures, and therefore that God's ideas of possible creatures are in some sense ideas of himself. Containment exemplarism offers a monotheism fit for metaphysics, insofar as it is coherent, simple, and explanatorily powerful; and offers a metaphysics fit for monotheism, insofar as it leaves God truly worthy of the unconditional worship which Christians, along with Jews and Muslims, aspire to offer to God.
God and Abstract Objects

God and Abstract Objects
  • Einar Duenger Bøhn
  • Published online:
    19 July 2019
    Print publication:
    08 August 2019
  • Some believe that there is a God who is the source of all things; and some believe that there are necessarily existing abstract objects. But can one believe both these things? That is the question of this Element. First, Einar Duenger Bøhn clarifies the concepts involved, and the problem that arises from believing in both God and abstract objects. Second, he presents and discusses the possible kinds of solutions to that problem. Third, Bøhn discusses a new kind of solution to the problem, according to which reality is most fundamentally made of information.