Whatever the attractions of Tolkein's world, irrealists about fictions do not believe literally that Bilbo Baggins is a hobbit. Instead, irrealists believe that, according to The Lord of the Rings {Bilbo is a hobbit}. But when irrealists want to say something like “I am taller than Bilbo”, there is nowhere good for them to insert the operator “according to The Lord of the Rings”. This is an instance of the operator problem. In this paper, I outline and criticise Sainsbury's (2006) (...) spotty scope approach to the operator problem. Sainsbury treats the problem as syntactic, but the problem is ultimately metaphysical. (shrink)

(1) Every miner went to a meeting. It seems that (1) can mean either that there was one meeting that every miner went to, or that every miner went to at least one meeting with no guarantee that they all went to the same meeting. In the language of first-order logic we can represent these two readings as a matter of the universal and existential quantifiers having different scope with respect to each other.

Specificity has been defined in the linguistic literature according to two different criteria: one corresponding to Quine's opaque and transparent contexts, and the other to criteria closely related to Donellan's referential/attributive distinction. The paper argues that only the former definition is a semantic one since it alone manifests linguistic correlates. The meaning changes involving referential/attributive factors are pragmatic in nature. In the concluding section is is argued that the semantics of specificity is completely independent of the relative scope interpretation of (...) an indefinite noun phrase in relation to other quantified nouns in the sentence. This is demonstrated using sentences which contain an indefinite interacting with both an opaque operator and a second quantifier. It is shown that such sentences can be four ways ambiguous. (shrink)

Online collection of papers by Devitt, Dretske, Guarino, Hochberg, Jackson, Petitot, Searle, Tye, Varzi and other leading thinkers on philosophy and the foundations of cognitive Science. Topics dealt with include: Wittgenstein and Cognitive Science, Content and Object, Logic and Foundations, Language and Linguistics, and Ontology and Mereology.

Winter (2000) argues that so-called co-distributive or cumulative readings do not involve polyadic quantification (contra proposals by Krifka, Schwarzschild, Sternefeld, and others). Instead, he proposes that all such readings involve a hidden anaphoric dependency or a lexical mechanism. We show that Winter's proposal is insufficient for a number of cases of cumulative readings, and that Krifka's and Sternefeld's polyadic **-operator is needed in addition to dependent definites. Our arguments come from new observations concerning dependent plurals and clause-boundedness effects with cumulative (...) readings. (shrink)

As a celebration of theTractatus100th anniversary it might be worth revisiting its relation to the later writings. From the former to the latter, David Pears recalls that “everyone is aware of the holistic character of Wittgenstein’s later philosophy, but it is not so well known that it was already beginning to establish itself in theTractatus” (The False Prison, 1987). From the latter to the former, Stephen Hilmy’s (The Later Wittgenstein, 1987) extensive study of theNachlasshas helped removing classical misconceptions such as (...) Hintikka’s claim that “Wittgenstein in thePhilosophical Investigationsalmost completely gave up the calculus analogy.” Hilmy points out that even in theInvestigationsone finds the use of the calculus/game paradigm to the understanding of language, such as “in operating with the word” (Part I, §559) and “it plays a different part in the calculus”. Hilmy also quotes from a late (1946) unpublished manuscript (MS 130) “this sentence has use in the calculus of language”, which seems to be compatible with “asking whether and how a proposition can be verified is only a particular way of asking ‘How do you mean?’” Central in this back and forth there is an aspect which seems to deserve attention in the discussion of a semantics for the language of mathematics which might be based on (normalisation of) proofs and/or Hintikka/Lorenzen game-dialogue: the explication of consequences. Such a discussion is substantially supported by the use of the open and searchableThe Wittgenstein Archives at the University of Bergen. These findings are framed within the discussion of the meaning of logical constants in the context of natural deduction style rules of inference. (shrink)

This paper argues against the view that the standard explanation of phase transitions in statistical mechanics may be considered a causal explanation, a distortion that can nevertheless successfully represent causal relations.

Recent work on the acquisition of number words has emphasized the importance of integrating linguistic and developmental perspectives [Musolino, J. (2004). The semantics and acquisition of number words: Integrating linguistic and developmental perspectives. Cognition93, 1-41; Papafragou, A., Musolino, J. (2003). Scalar implicatures: Scalar implicatures: Experiments at the semantics-pragmatics interface. Cognition, 86, 253-282; Hurewitz, F., Papafragou, A., Gleitman, L., Gelman, R. (2006). Asymmetries in the acquisition of numbers and quantifiers. Language Learning and Development, 2, 76-97; Huang, Y. T., Snedeker, J., Spelke, (...) L. (submitted for publication). What exactly do numbers mean?]. Specifically, these studies have shown that data from experimental investigations of child language can be used to illuminate core theoretical issues in the semantic and pragmatic analysis of number terms. In this article, I extend this approach to the logico-syntactic properties of number words, focusing on the way numerals interact with each other (e.g. Three boys are holding two balloons) as well as with other quantified expressions (e.g. Three boys are holding each balloon). On the basis of their intuitions, linguists have claimed that such sentences give rise to at least four different interpretations, reflecting the complexity of the linguistic structure and syntactic operations involved. Using psycholinguistic experimentation with preschoolers (n=32) and adult speakers of English (n=32), I show that (a) for adults, the intuitions of linguists can be verified experimentally, (b) by the age of 5, children have knowledge of the core aspects of the logical syntax of number words, (c) in spite of this knowledge, children nevertheless differ from adults in systematic ways, (d) the differences observed between children and adults can be accounted for on the basis of an independently motivated, linguistically-based processing model [Geurts, B. (2003). Quantifying kids. Language Acquisition, 11(4), 197-218]. In doing so, this work ties together research on the acquisition of the number vocabulary with a growing body of work on the development of quantification and sentence processing abilities in young children [Geurts, 2003; Lidz, J., Musolino, J. (2002). Children's command of quantification. Cognition, 84, 113-154; Musolino, J., Lidz, J. (2003). The scope of isomorphism: Turning adults into children. Language Acquisition, 11(4), 277-291; Trueswell, J., Sekerina, I., Hilland, N., Logrip, M. (1999). The kindergarten-path effect: Studying on-line sentence processing in young children. Cognition, 73, 89-134; Noveck, I. (2001). When children are more logical than adults: Experimental investigations of scalar implicature. Cognition, 78, 165-188; Noveck, I., Guelminger, R., Georgieff, N., & Labruyere, N. (2007). What autism can tell us about every. . . not sentences. Journal of Semantics,24(1), 73-90. On a more general level, this work confirms the importance of integrating formal and developmental perspectives [Musolino, 2004], this time by highlighting the explanatory power of linguistically-based models of language acquisition and by showing that the complex structure postulated by linguists has important implications for developmental accounts of the number vocabulary. (shrink)

In this paper I examine a cluster of concepts relevant to the methodology of truth theories: 'informative definition', 'recursive method', 'semantic structure', 'logical form', 'compositionality', etc. The interrelations between these concepts, I will try to show, are more intricate and multi-dimensional than commonly assumed.

In this paper it is argued that Hintikka's game theoreticalsemantics for Independence Friendly logic does not formalize theintuitions about independent choices; it rather is aformalization of imperfect information. Furthermore it is shownthat the logic has several remarkable properties (e.g.,renaming of bound variables is not allowed). An alternativesemantics is proposed which formalizes intuitions aboutindependence.

We introduce generalized quantifiers, as defined in Tarskian semantics by Mostowski and Lindström, in logics whose semantics is based on teams instead of assignments, e.g., IF-logic and Dependence logic. Both the monotone and the non-monotone case is considered. It is argued that to handle quantifier scope dependencies of generalized quantifiers in a satisfying way the dependence atom in Dependence logic is not well suited and that the multivalued dependence atom is a better choice. This atom is in fact definably equivalent (...) to the independence atom recently introduced by Väänänen and Grädel. (shrink)

Over the last two decades, semantic theory has been marked by a continuing shift from a static view of meaning to a dynamic one. The increasing interest in extending semantic analysis from isolated sentences to larger units of discourse has fostered the intensive study of anaphora and coreference, and this has engendered a shift from viewing meaning as truth conditions to viewing it as the potential to change the "informational context".

The paper offers a new analysis of the difficulties involved in the construction of a general and substantive correspondence theory of truth and delineates a solution to these difficulties in the form of a new methodology. The central argument is inspired by Kant, and the proposed methodology is explained and justified both in general philosophical terms and by reference to a particular variant of Tarski's theory. The paper begins with general considerations on truth and correspondence and concludes with a brief (...) outlook on the "family" of theories of truth generated by the new methodology. (shrink)

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 negations match the distinction existing in (...) natural languages between sentential and constituent negation. As a corollary, I derive the fact that there are no mechanical rules for forming the contradictory negation of an English sentence. (shrink)

Independence Friendly Logic, introduced by Hintikka, is a logic in which a quantifier can be marked for being independent of other quantifiers. Dependence logic, introduced by Väänänen, is a logic with the complementary approach: for a quantifier it can be indicated on which quantifiers it depends. These logics are claimed to be useful for many phenomena, for instance natural language semantics. In this contribution we will compare these two logics by investigating their application in a compositional analysis of the de (...) dicto - de re ambiguity in natural language. It will be argued that Independence Friendly logic is suitable, whereas Dependence Logic is not. (shrink)

§1. The mission of axiomatic set theory. What is set theory needed for in the foundations of mathematics? Why cannot we transact whatever foundational business we have to transact in terms of our ordinary logic without resorting to set theory? There are many possible answers, but most of them are likely to be variations of the same theme. The core area of ordinary logic is by a fairly common consent the received first-order logic. Why cannot it take care of itself? (...) What is it that it cannot do? A large part of every answer is probably that first-order logic cannot handle its own model theory and other metatheory. For instance, a first-order language does not allow the codification of the most important semantical concept, viz. the notion of truth, for that language in that language itself, as shown already in Tarski. In view of such negative results it is generally thought that one of the most important missions of set theory is to provide the wherewithal for a model theory of logic. For instance Gregory H. Moore asserts in his encyclopedia article “Logic and set theory” thatSet theory influenced logic, both through its semantics, by expanding the possible models of various theories and by the formal definition of a model; and through its syntax, by allowing for logical languages in which formulas can be infinite in length or in which the number of symbols is uncountable. (shrink)

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.

Still, some may still want to say it. If so, my replies may gain nothing better than a stalemate against such persistence, though I can hope that earlier revelations will discourage others from persisting. But two replies are possible. Both come down, one circuitously, to an issue with us from the beginning: whether the language of the right side of (10) is suspect. For if (10) is to support instances for (6) which are about objects, that clause must itself be (...) about objects. (These would be ones assigned by variants of I it mentions to constants it mentions.) Yet Barwise and I would call it implicitly about functions. Ironically, the discussion surrounding (10), hoping to settle that issue, could only do so if the issue were already settled, revealing decisively the ontology of (10). If irritating, this is also inevitable, given the Tarskian spirit of the ensivioned semantics for QLB.A second reply begins by noting that a QLB semantics which implies (10) cannot simply be assumed. Even a QL semantics augmented to imply (11) is not trivial to frame, as I will let readers confirm. On the QLB project, Barwise comments thus:It is not possible to explain the meaning of an essential use of branching quantification ... inductively, by treating one quantifier at a time in a first-order fashion. Some use of higher-type abstract objects is essential. (BQE75)But believers in a modest ontology for QLB can claim a non sequitur here. For (10), as they read it, succeeds without mentioning abstract objects, though not in the “one quantifier at a time” way which Barwise rightly finds impossible. This is not yet to say the same about a QLB semantics implying (10). But that too can be said, as it happens, with as good a conscience as with (10). A suitable treatment can begin by somehow linearizing non QL sentences like (6). Still assuming prefixes whose rows each consist, speaking loosely, of n universal quantifiers followed by a single existential, we could simply line up these rows in any order, with unique deconcatenatability being assured. From then on, it gets both tedious and complex. A full syntax is essential, and some surprising categories arose in mine. I will spare readers all details, except to say that one can indeed “treat one quantifier at a time”, if not “in first-order fashion”: schematic rules for treating n quantifiers at once can be eschewed. Unsurprisingly, heavy use is made of the “depending only on” idiom seen in (10). Nor does it surprise me that this semantics can succeed, with that idiom available. Roughly, if open talk about functions works in a semantics for QLF, what I read as implicit talk about them should work in a semantics for QLB See [6] for a start on a semantics aspiring to handle sentences like (6) without invoking abstract objects. See also my comments on its notion of dependence, in [9]. . So even from a bare sketch, we can see that this new semantics settles nothing. It just leads back to the stalemate. Barwise and I will read crucial clauses as talking implicitly about functions, but this general charge against an idiom is equally deniable wherever the idiom occurs: in a reading for (6), say, or in the metalanguage can hardly repress a motherhood slogan: better dead than obscurely read. But that just denies the denial, unhelpfully. A better comment is the reminder that the claim stays alive only in a form which no one has ever imagined for it. The QLB quantifiers that cannot be shown not to range over objects are not the items anyone would ever have pointed to in illustrating the unkillable claim. (shrink)

Jaakko Hintikka points out the power of Skolem functions to affect both what there is and what we know. There is a tension in his presupposition that these functions actually extend the realm of logic. He claims to have resolved the tension by “reconstructing constructivism” along epistemological lines, instead of by a typical ontological construction; however, after the collapse of the distinction between first and second order, that resolution is not entirely satisfactory. Still, it does throw light on the conceptual (...) analysis Hintikka proposes. (shrink)

Following Henkin's discovery of partially-ordered (branching) quantification (POQ) with standard quantifiers in 1959, philosophers of language have attempted to extend his definition to POQ with generalized quantifiers. In this paper I propose a general definition of POQ with 1-place generalized quantifiers of the simplest kind: namely, predicative, or "cardinality" quantifiers, e.g., "most", "few", "finitely many", "exactly α", where α is any cardinal, etc. The definition is obtained in a series of generalizations, extending the original, Henkin definition first to a general (...) definition of monotone-increasing (M↑) POQ and then to a general definition of generalized POQ, regardless of monotonicity. The extension is based on (i) Barwise's 1979 analysis of the basic case of M↑ POQ and (ii) my 1990 analysis of the basic case of generalized POQ. POQ is a non-compositional Ist-order structure, hence the problem of extending the definition of the basic case to a general definition is not trivial. The paper concludes with a sample of applications to natural and mathematical languages. (shrink)