David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
1. Two kinds of logic. To a first approximation there are two main kinds of pursuit in logic. The first is the traditional one going back two millennia, concerned with characterizing the logically valid inferences. The second is the one that emerged most systematically only in the twentieth century, concerned with the semantics of logical operations. In the view of modern, model-theoretical eyes, the first requires the second, but not vice-versa. According to Tarski’s generally accepted account of logical consequence (1936), inference from some statements as hypotheses to a statement as conclusion is logically valid if the truth of the hypotheses ensures the truth of the conclusion, in a way that depends only on the form of the statements involved, not on their content. Interpreted model-theoretically this means that every model of the hypotheses is a model of the conclusion. However, there is an ambiguity in Tarski’s explication, as he himself emphasized, since for the specification of form one needs to determine what are the logical notions. Once those are isolated and their semantical roles are settled, one can see how the truth of a statement (in a given model and relative to given assignments) is composed from the truth of its basic parts, in whatever way those are specified. The problem of what are the logical notions is an unsettled and controversial one (cf. Feferman 1999, Gómez-Torrente 2002). In the classical truthfunctional perspective, proposals range from those of first-order logic to generalized quantifiers to second and higher-order quantifiers to infinitary languages and beyond. Many of these stronger semantical notions have been treated in the volume Model Theoretic Logics (Barwise and Feferman 1987). In a series of singular, thought-provoking publications in recent years, Jaakko Hintikka has vigorously promoted consideration of an extension of first-order logic called IF logic, along with claims that its adoption promises to have revolutionary consequences..
|Keywords||No keywords specified (fix it)|
No categories specified
(categorize this paper)
|Through your library||Only published papers are available at libraries|
Similar books and articles
Mario Gómez-Torrente (2000). A Note on Formality and Logical Consequence. Journal of Philosophical Logic 29 (5):529-539.
Jaakko Hintikka (2012). Which Mathematical Logic is the Logic of Mathematics? Logica Universalis 6 (3-4):459-475.
Theo M. V. Janssen (2013). Compositional Natural Language Semantics Using Independence Friendly Logic or Dependence Logic. Studia Logica 101 (2):453-466.
Alexander Paseau (2010). Pure Second-Order Logic with Second-Order Identity. Notre Dame Journal of Formal Logic 51 (3):351-360.
Kevin C. Klement, Propositional Logic. Internet Encyclopedia of Philosophy.
J. Väänänen (2007). Dependence Logic: A New Approach to Independence Friendly Logic. Cambridge University Press.
Matthew W. McKeon (2010). The Concept of Logical Consequence: An Introduction to Philosophical Logic. Peter Lang Pub..
John P. Burgess (2011). Kripke Models. In Alan Berger (ed.), Saul Kripke. Cambridge University Press.
Alessandro Torza (2013). How to Lewis a Kripke-Hintikka. Synthese 190 (4):743-779.
Jaakko Hintikka (2002). Quantum Logic as a Fragment of Independence-Friendly Logic. Journal of Philosophical Logic 31 (3):197-209.
Pietro Galliani & Allen L. Mann (2013). Lottery Semantics: A Compositional Semantics for Probabilistic First-Order Logic with Imperfect Information. Studia Logica 101 (2):293-322.
Ken Akiba (1996). Logic as Instrument: The Millian View on the Role of Logic. History and Philosophy of Logic 17 (1-2):73-83.
Robert Hanna (2008). Husserl's Arguments Against Logical Psychologism (Prolegomena, §§ 17–61). In Verena Mayer (ed.), Edmund Husserl: Logische Untersuchungen. 27-42.
Fredrik Engström (2012). Generalized Quantifiers in Dependence Logic. Journal of Logic, Language and Information 21 (3):299-324.
Added to index2010-12-22
Total downloads10 ( #118,316 of 1,004,688 )
Recent downloads (6 months)1 ( #64,743 of 1,004,688 )
How can I increase my downloads?