The Source of Logical Necessities

Hale Bob

in Necessary Beings

Published in print September 2013 | ISBN: 9780199669578
Published online January 2014 | e-ISBN: 9780191765186 | DOI:
The Source of Logical Necessities

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  • Philosophy of Mathematics and Logic


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When it is necessary that p, what makes it so? In Michael Dummett’s words, what is the source of necessity? Some old arguments of Quine and Dummettare rehearsed, which show that not all necessities can be the product of conventions, and a further argument is given to show that none can. These arguments apply most clearly to conventionalism, but can be extended to cover looser versions of the linguistic theory which claim that necessity reduces to truth in virtue of meaning. Since matters of meaning and convention are contingent, defenders of conventionalism and truth in virtue of meaning must reject the S4 principle that what is necessary is necessarily so. As against this, it is argued that the logic of absolute necessity is the yet stronger modal logic S5. To complete the discussion of Blackburn’s Dilemma (see Ch.3), it is argued that the necessity-horn of that dilemma overlooks the possibility of non-transmissive explanations of necessity. Such explanations may be given in terms of the nature or essence of the logical functions.

Keywords: conventionalism; truth-in-virtue-of-meaning; Quine’s regress; Dummett’s objection; S4; S5; Blackburn’s Dilemma; non-transmissive explanation

Chapter.  16840 words. 

Subjects: Metaphysics ; Philosophy of Mathematics and Logic

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