•  143
    What is Logic?
    with Hintikka Jaakko
    In Dale Jacquette (ed.), Philosophy of Logic, North Holland. pp. 13--39. 2006.
    It is far from clear what is meant by logic or what should be meant by it. It is nevertheless reasonable to identify logic as the study of inferences and inferential relations. The obvious practical use of logic is in any case to help us to reason well, to draw good inferences. And the typical form the theory of any part of logic seems to be a set of rules of inference. This answer already introduces some structure into a discussion of the nature of logic, for in an inference we can distinguish …Read more
  •  138
    The fallacies of the new theory of reference
    with Jaakko Hintikka
    Synthese 104 (2). 1995.
    The so-called New Theory of Reference (Marcus, Kripke etc.) is inspired by the insight that in modal and intensional contexts quantifiers presuppose nondescriptive unanalyzable identity criteria which do not reduce to any descriptive conditions. From this valid insight the New Theorists fallaciously move to the idea that free singular terms can exhibit a built-in direct reference and that there is even a special class of singular terms (proper names) necessarily exhibiting direct reference. This…Read more
  •  102
    What is a quantifier?
    with Jaakko Hintikka
    Synthese 98 (1). 1994.
  •  100
    Some aspects of negation in English
    Synthese 99 (3). 1994.
    I introduce a formal language called the language of informational independence (IL-language, for short) that extends an ordinary first-order language in a natural way. This language is interpreted in terms of semantical games of imperfect information. In this language, one can define two negations: (i) strong or dual negation, and (ii) weak or contradictory negation. The latter negation, unlike the former, can occur only sentence-initially. Then I argue that, to a certain extent, the two negati…Read more
  •  95
    If-logic and truth-definition
    Journal of Philosophical Logic 27 (2): 143-164. 1998.
    In this paper we show that first-order languages extended with partially ordered connectives and partially ordered quantifiers define, under a certain interpretation, their own truth-predicate. The interpretation in question is in terms of games of imperfect information. This result is compared with those of Kripke and Feferman
  •  84
    Aspects of compositionality
    with Jaakko Hintikka
    Journal of Logic, Language and Information 10 (1): 49-61. 2001.
    We introduce several senses of the principle ofcompositionality. We illustrate the difference between them with thehelp of some recent results obtained by Cameron and Hodges oncompositional semantics for languages of imperfect information.
  •  83
    Signalling In Languages With Imperfect Information
    Synthese 127 (1): 21-34. 2001.
    This paper is a short survey of different languages with imperfect information introduced in. The imperfect information concerns both quantifiers and connectives. At the end, I will sketch a connection between these languages and linear logic.
  •  76
    The paper argues that there are two main kinds of joint action, direct joint bringing about (or performing) something (expressed in terms of a DO-operator) and jointly seeing to it that something is the case (expressed in terms of a Stit-operator). The former kind of joint action contains conjunctive, disjunctive and sequential action and its central subkinds. While joint seeing to it that something is the case is argued to be necessarily intentional, direct joint performance can also be noninte…Read more
  •  74
    The article presents Erik Stenius' conception of logical constants and compares it with the standard approach.
  •  65
    Henkin quantifiers and the definability of truth
    with Tapani Hyttinen
    Journal of Philosophical Logic 29 (5): 507-527. 2000.
    Henkin quantifiers have been introduced in Henkin (1961). Walkoe (1970) studied basic model-theoretical properties of an extension $L_{*}^{1}$ (H) of ordinary first-order languages in which every sentence is a first-order sentence prefixed with a Henkin quantifier. In this paper we consider a generalization of Walkoe's languages: we close $L_{*}^{1}$ (H) with respect to Boolean operations, and obtain the language L¹(H). At the next level, we consider an extension $L_{*}^{2}$ (H) of L¹(H) in whic…Read more
  •  62
    Partially interpreted relations and partially interpreted quantifiers
    Journal of Philosophical Logic 27 (6): 587-601. 1998.
    Logics in which a relation R is semantically incomplete in a particular universe E, i.e. the union of the extension of R with its anti-extension does not exhaust the whole universe E, have been studied quite extensively in the last years. (Cf. van Benthem (1985), Blamey (1986), and Langholm (1988), for partial predicate logic; Muskens (1996), for the applications of partial predicates to formal semantics, and Doherty (1996) for applications to modal logic.) This is not so with semantically incom…Read more
  •  58
    Logic and semantics in the twentieth century
    with Tuomo Aho
    In Leila Haaparanta (ed.), The Development of Modern Logic, Oxford University Press. pp. 562. 2008.
    This chapter explores logical semantics, that is, the structural meaning of logical expressions like connectives, quantifiers, and modalities. It focuses on truth-theoretical semantics for formalized languages, a tradition emerging from Carnap's and Tarski's work in the first half of the last century that specifies the meaning of these expressions in terms of the truth-conditions of the sentences in which they occur. It considers Tarski-style definitions of the semantics of a given language in a…Read more
  •  55
    Uses and Misuses of Frege’s Ideas
    with Jaakko Hintikka
    The Monist 77 (3): 278-293. 1994.
    Frege has one magnificent achievement to his credit, viz. the creation of modern formal logic. As a philosopher and as a theoretical logician, he was nevertheless as parochial as he was, geographically speaking. Hence Frege’s concepts and problems offer singularly unfortunate starting points for constructive work in the foundations of logic and mathematics. Even if he is right in some of his views, they depend on severely restrictive assumptions that have to be noted and eliminated. These restri…Read more
  •  55
    Deflationism and arithmetical truth
    with Tapani Hyttinen
    Dialectica 58 (3). 2004.
  •  54
  •  52
    On the logic of informational independence and its applications
    Journal of Philosophical Logic 22 (1). 1993.
    We shall introduce in this paper a language whose formulas will be interpreted by games of imperfect information. Such games will be defined in the same way as the games for first-order formulas except that the players do not have complete information of the earlier course of the game. Some simple logical properties of these games will be stated together with the relation of such games of imperfect information to higher-order logic. Finally, a set of applications will be outlined
  •  51
    Jaakko Hintikka in memoriam
    Theoria 81 (4): 289-292. 2015.
  •  49
    Minimalism and the Definability of Truth
    The Proceedings of the Twentieth World Congress of Philosophy 2000 143-153. 2000.
    In this paper I am going to inquire to what extent the main requirements of a minimalist theory of truth and falsity (as formulated, for example, by Horwich and Field) can be consistently implemented in a formal theory. I will discuss several of the existing logical theories of truth, including Tarski-type (un)definability results, Kripke’s partial interpretation of truth and falsity, Barwise and Moss’ theory based upon non-well-founded sets, McGee’s treatment of truth as a vague predicate, and …Read more
  •  46
    Between proof and truth
    with Julien Boyer
    Synthese 187 (3): 821-832. 2012.
    We consider two versions of truth as grounded in verification procedures: Dummett's notion of proof as an effective way to establish the truth of a statement and Hintikka's GTS notion of truth as given by the existence of a winning strategy for the game associated with a statement. Hintikka has argued that the two notions should be effective and that one should thus restrict one's attention to recursive winning strategies. In the context of arithmetic, we show that the two notions do not coincid…Read more
  •  45
    Erratum to: Between proof and truth
    with Julien Boyer
    Synthese 187 (3): 973-974. 2012.
  •  42
    From Lagrange to Frege: Functions and Expressions
    In Gabriel Sandu, Marco Panza & Hourya Benis-Sinaceur (eds.), Functions and Generality of Logic, Springer Verlag. 2015.
    Both Frege's Grundgesetze, and Lagrange's treatises on analytical functions pursue a foundational purpose. Still, the former's program is not only crucially different from the latter's. It also depends on a different idea of what foundation of mathematics should be like . Despite this contrast, the notion of function plays similar roles in their respective programs. The purpose of my paper is emphasising this similarity. In doing it, I hope to contribute to a better understanding of Frege's logi…Read more
  •  36
    Independence‐Friendly logic introduced by Hintikka and Sandu studies patterns of dependence and independence of quantifiers which exceed those found in ordinary first‐order logic. The present survey focuses on the game‐theoretical interpretation of IF‐logic, including connections to solution concepts in classical game theory, but we shall also present its compositional interpretation together with its connections to notions of dependence and dependence between terms
  •  28
    This collects some of the remarks made at the 2016 Pacific APA Memorial session for Patrick Suppes and Jaakko Hintikka. The full list of speakers on behalf of these two philosophers: Dagfinn Follesdal; Dana Scott; Nancy Cartwright; Paul Humphreys; Juliet Floyd; Gabriel Sandu; John Symons.
  •  25
    Equilibrium semantics
    with Merlijn Sevenster
    Annals of Pure and Applied Logic. forthcoming.