Mind 118 (469):71-100 (2009)

Authors
Volker Halbach
Oxford University
Abstract
In philosophical logic necessity is usually conceived as a sentential operator rather than as a predicate. An intensional sentential operator does not allow one to express quantified statements such as 'There are necessary a posteriori propositions' or 'All laws of physics are necessary' in first-order logic in a straightforward way, while they are readily formalized if necessity is formalized by a predicate. Replacing the operator conception of necessity by the predicate conception, however, causes various problems and forces one to reject many philosophical accounts involving necessity that are based on the use of operator modal logic. We argue that the expressive power of the predicate account can be restored if a truth predicate is added to the language of first-order modal logic, because the predicate 'is necessary' can then be replaced by 'is necessarily true'. We prove a result showing that this substitution is technically feasible. To this end we provide partial possible-worlds semantics for the language with a predicate of necessity and perform the reduction of necessities to necessary truths. The technique applies also to many other intensional notions that have been analysed by means of modal operators
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DOI 10.1093/mind/fzn030
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References found in this work BETA

Two Dogmas of Empiricism.Willard V. O. Quine - 1951 - Philosophical Review 60 (1):20–43.
Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
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Citations of this work BETA

Non‐Classical Knowledge.Ethan Jerzak - 2019 - Philosophy and Phenomenological Research 98 (1):190-220.
Deontic Modals and Hyperintensionality.Federico L. G. Faroldi - 2019 - Logic Journal of the IGPL 27 (4):387-410.
Paradoxes and Contemporary Logic.Andrea Cantini - 2008 - Stanford Encyclopedia of Philosophy.

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