Necessities and Necessary Truths: A Prolegomenon to the Use of Modal Logic in the Analysis of Intensional Notions
Mind 118 (469):71-100 (2009)
| 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 | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,709 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesMax Cresswell (2013). Axiomatising the Prior Future in Predicate Logic. Logica Universalis 7 (1):87-101.
David H. Sanford (1975). Borderline Logic. American Philosophical Quarterly 12 (1):29-39.
Edward N. Zalta (1997). The Modal Object Calculus and its Interpretation. In M. de Rijke (ed.), Advances in Intensional Logic. Kluwer.
Max A. Freund (2004). A Modal Sortal Logic. Journal of Philosophical Logic 33 (3):237-260.
H. Kushida & M. Okada (2003). A Proof-Theoretic Study of the Correspondence of Classical Logic and Modal Logic. Journal of Symbolic Logic 68 (4):1403-1414.
Ulrich Nortmann (2002). The Logic of Necessity in Aristotle--An Outline of Approaches to the Modal Syllogistic, Together with a General Account of de Dicto - and de Re -Necessity. History and Philosophy of Logic 23 (4):253-265.
Volker Halbach, Hannes Leitgeb & Philip Welch (2003). Possible-Worlds Semantics for Modal Notions Conceived as Predicates. Journal of Philosophical Logic 32 (2):179-223.
Beomin Kim (2008). The Translation of First Order Logic Into Modal Predicate Logic. Proceedings of the Xxii World Congress of Philosophy 13:65-69.
D. M. Gabbay & G. Malod (2002). Naming Worlds in Modal and Temporal Logic. Journal of Logic, Language and Information 11 (1):29-65.
Heinrich Wansing (1999). Predicate Logics on Display. Studia Logica 62 (1):49-75.
Leon Horsten & Hannes Leitgeb (2001). No Future. Journal of Philosophical Logic 30 (3):259-265.
Holger Sturm & Frank Wolter (2001). First-Order Expressivity for S5-Models: Modal Vs. Two-Sorted Languages. Journal of Philosophical Logic 30 (6):571-591.
Yannis Stephanou (2001). Indexed Actuality. Journal of Philosophical Logic 30 (4):355-393.
Richard Otte (1982). Modality as a Metalinguistic Predicate. Philosophical Studies 41 (2):153 - 159.
Analytics
Monthly downloads |
Added to index2010-09-14Total downloads8 ( #123,255 of 549,699 )Recent downloads (6 months)1 ( #63,425 of 549,699 )How can I increase my downloads? |
My notes
Discussion
