We look at two recent accounts of the indefiniteextensibility of set, and compare them with a linguistic model of the indefiniteextensibility. I suggest the linguistic model has much to recommend over extant accounts of the indefiniteextensibility of set, and we defend it against three prima facie objections.
A number of authors have noted that the key steps in Fitch’s argument are not intuitionistically valid, and some have proposed this as a reason for an anti-realist to accept intuitionistic logic (e.g. Williamson 1982, 1988). This line of reasoning rests upon two assumptions. The first is that the premises of Fitch’s argument make sense from an anti-realist point of view – and in particular, that an anti-realist can and should maintain the principle that all truths are knowable. The second (...) is that we have some independent reason for thinking that classical logic is not appropriate in this area. This paper explores these two assumptions in the context of Michael Dummett’s version of anti-realism, with particular reference to the argument from indefiniteextensibility developed at various points in Dummett’s writings (e.g. Dummett 1991 Ch. 24). -/- Dummett argues that certain concepts, the indefinitely extensible concepts, are such that we cannot form a clear and determinate conception of all the objects that fall under them. The most familiar examples of indefinitely extensible concepts are mathematical. Dummett discusses the concepts ordinal number, real number, and natural number, which are indefinitely extensible because any conception that one might form of their complete extension can be extended to a more inclusive conception (as, for example, in Cantor’s proof of the non-denumerability of the set of real numbers). This paper argues that the concept of a truth is indefinitely extensible. This gives a Dummettian anti-realist an independent motivation for rejecting the classical understanding of the quantifiers in this area. At the same time, however, it places in doubt the admissibility of the knowability principle, which seems to involve quantification over the “totality” of truths. As Dummett is at pains to point out (1991: 316), some sentences that purport to quantify over the extension of an indefinitely extensible concept plainly have a truth-value (we can truly say, for example, that every ordinal number has a successor, even though when we say that we are not quantifying over the set of all ordinals). But is the knowability principle one of these sentences? (shrink)
The Monist’s call for papers for this issue ended: “if formalism is true, then it must be possible in principle to mechanize meaning in a conscious thinking and language-using machine; if intentionalism is true, no such project is intelligible”. We use the Grelling-Nelson paradox to show that natural language is indefinitely extensible, which has two important consequences: it cannot be formalized and model theoretic semantics, standard for formal languages, is not suitable for it. We also point out that object-object mapping (...) theories of semantics, the usual account for the possibility of non intentional semantics, doesn’t seem able to account for the indefinitely extensible productivity of natural language. (shrink)
Over the last few decades Michael Dummett developed a rich program for assessing logic and the meaning of the terms of a language. He is also a major exponent of Frege's version of logicism in the philosophy of mathematics. Over the last decade, Neil Tennant developed an extensive version of logicism in Dummettian terms, and Dummett influences other contemporary logicists such as Crispin Wright and Bob Hale. The purpose of this paper is to explore the prospects for Fregean logicism within (...) a broadly Dummettian framework. The conclusions are mostly negative: Dummett's views on analyticity and the logical/non-logical boundary leave little room for logicism. Dummett's considerations concerning manifestation and separability lead to a conservative extension requirement: if a sentence S is logically true, then there is a proof of S which uses only the introduction and elimination rules of the logical terms that occur in S. If basic arithmetic propositions are logically true - as the logicist contends - then there is tension between this conservation requirement and the ontological commitments of arithmetic. It follows from Dummett's manifestation requirements that if a sentence S is composed entirely of logical terminology, then there is a formal deductive system D such that S is analytic, or logically true, if and only if S is a theorem of D. There is a deep conflict between this result and the essential incompleteness, or as Dummett puts it, the indefiniteextensibility, of arithmetic truth. (shrink)
Patrick Grim has put forward a set theoretical argument purporting to prove that omniscience is an inconsistent concept and a model theoretical argument for the claim that we cannot even consistently define omniscience. The former relies on the fact that the class of all truths seems to be an inconsistent multiplicity (or a proper class, a class that is not a set); the latter is based on the difficulty of quantifying over classes that are not sets. We first address the (...) set theoretical argument and make explicit some ways in which it depends on mathematical Platonism. Then we sketch a non Platonistic account of inconsistent multiplicities, based on the notion of indefiniteextensibility, and show how Grim’s set theoretical argument could fail to be conclusive in such a context. Finally, we confront Grim’s model theoretical argument suggesting a way to define a being as omniscient without quantifying over any inconsistent multiplicity. (shrink)
The purpose of this paper is to assess the prospects for a neo-logicist development of set theory based on a restriction of Frege's Basic Law V, which we call (RV): PQ[Ext(P) = Ext(Q) [(BAD(P) & BAD(Q)) x(Px Qx)]] BAD is taken as a primitive property of properties. We explore the features it must have for (RV) to sanction the various strong axioms of Zermelo–Fraenkel set theory. The primary interpretation is where ‘BAD’ is Dummett's ‘indefinitely extensible’. 1 Background: what and why? (...) 2 Framework 3 GOOD candidates, indefiniteextensibility 4 The framework of (RV) alone, or almost alone 5 The axioms 6 Brief closing. (shrink)
The paper examines Dummett's argument for the indefiniteextensibility of the concepts set, ordinal, real number, set of natural numbers, and natural number. In particular it investigates how the indefiniteextensibility of the concept set affects our understanding of the notion of real number and whether the argument to the indefiniteextensibility of the reals is cogent. It claims that Dummett is right to think of the universe of sets as an indefinitely extensible domain (...) but questions the cogency of the further claim that this fact raises an issue as to what sets or real numbers there are. (shrink)
A central theme in the foundational debates in the early Twentieth century in response to the paradoxes was to invoke the notion of the indefiniteextensibility of certain concepts e,g. definability (the Richard paradox) and class (the Zermelo-Russell contradiction). Dummett has recently revived the notion, as the real lesson of the paradoxes and the source of Frege's error in basic law five of the Grundgesetze. The paper traces the historical and conceptual evolution of the concept and critices Dummett's (...) argument that the proper lesson of the paradoxes is that set theory is a theory of indefinitely extensible domains. (shrink)
In a well-known passage in the last chapter of Frege: Philosophy of Mathematics Michael Dummett suggests that Frege’s major “mistake”—the key to the collapse of the project of Grundgesetze—consisted in “his supposing there to be a totality containing the extension of every concept defined over it; more generally [the mistake] lay in his not having the glimmering of a suspicion of the existence of indefinitely extensible concepts” (Dummett [1991, 317]). Now, claims of the form, Frege fell into paradox because……. are (...) notoriously difficult to assess even when what replaces the dots is relatively straightforward. Offerings have included, for instance, that — (A) Unrestricted quantification: Frege fell into paradox because he allowed himself to quantify over a single, all-inclusive domain of objects (Russell, Dummett). (shrink)
Assuming the indefiniteextensibility of any domain of quantification leads to reasoning with extensible domain semantics. It is showed that some theorems (e.g. Thomson's) in conventional semantics logic are not theorems in a logic provided with this new semantics.
Structure is central to the realist view of mathematical disciplines with intended interpretations and categoricity is a model-theoretic notion that captures the idea of the determination of structure by theory. By considering the cases of arithmetic and (pure) set theory, I investigate how categoricity results might offer support from within to the realist view. I argue, amongst other things, that second-order quantification is essential to the support the categoricity results provide. I also note how the findings on categoricity relate to (...) a fundamental feature of the realist position. (shrink)
Of all the cases made against classical logic, Michael Dummett's is the most deeply considered. Issuing from a systematic and original conception of the discipline, it constitutes one of the most distinctive achievements of twentieth century British philosophy. Although Dummett builds on the work of Brouwer and Heyting, he provides the case against classical logic with a new, explicit and general foundation in the philosophy of language. Dummett's central arguments, widely celebrated if not widely endorsed, concern the implications of the (...) relation between meaning and use for both the inference rules that govern logical connectives and the relation between truth and its recognition. It is less often noted that Dummett has a further argument against classical logic, one based on the semantic and set-theoretic paradoxes. That is the topic of this paper. (shrink)
The use of tensed language and the metaphor of set ‘formation’ found in informal descriptions of the iterative conception of set are seldom taken at all seriously. Both are eliminated in the nonmodal stage theories that formalise this account. To avoid the paradoxes, such accounts deny the Maximality thesis, the compelling thesis that any sets can form a set. This paper seeks to save the Maximality thesis by taking the tense more seriously than has been customary (although not literally). A (...) modal stage theory, MST, is developed in a bimodal language, governed by a tenselike logic. Such a language permits a very natural axiomatisation of the iterative conception, which upholds the Maximality thesis. It is argued that the modal approach is consonant with mathematical practice and a plausible metaphysics of sets and shown that MST interprets a natural extension of Zermelo set theory less the axiom of Infinity and, when extended with a further axiom concerning the extent of the hierarchy, interprets Zermelo–Fraenkel set theory. (shrink)
Cantor’s proof that the powerset of the set of all natural numbers is uncountable yields a version of Richard’s paradox when restricted to the full definable universe, that is, to the universe containing all objects that can be defined not just in one formal language but by means of the full expressive power of natural language: this universe seems to be countable on one account and uncountable on another. We argue that the claim that definitional contexts impose restrictions on the (...) scope of quantifiers reveals a natural way out. (shrink)
The generality relativist has been accused of holding a self-defeating thesis. Kit Fine proposed a modal version of generality relativism that tries to resist this claim. We discuss his proposal and argue that one of its formulations is self-defeating.
The Anselmian Thesis is the thesis that God is that than which nothing greater can be thought. In this paper, I argue that such a notion of God is incoherent due to greatness being indefinitely extensible: roughly, for any great being that can be, there is another one that is greater, so there cannot be a being than which nothing greater can be. Someone will say that it is impossible to produce the best, because there is no perfect creature, and (...) that it is always possible to produce one which would be more perfect.’ G.W. Leibniz. Theodicy. Edited by A. Farrer (Chicago, IL: Open Court, 1985. Pp. 249.). (shrink)
Dummctt argues that classical quantification is illegitimate when the domain is given as the objects which fall under an indefinitely extensible concept, since in such cases the objects are not the required definite totality. The chief problem in understanding this complex argument is the crucial but unexplained phrase 'definite totality' and the associated claim that it follows from the intuitive notion of set that the objects over which a classical quantifier ranges form a set. 'Definite totality' is best understood as (...) disguised plural talk like Cantor's 'consistent multiplicity', although this does not help in understanding how a totality could be anything other than definite. Moreover, contrary to his claims, Dummett's own notion of set is not intuitive and he does not demystify the set-theoretic paradoxes. In conclusion, it is argued that Dummett's context principle is responsible for the incoherent projection of the haziness of a conception of some objects onto reality. (shrink)
TABLE OF CONTENTS Introduction: Art, Metaphysics, & The Paradox of Standards (Christy Mag Uidhir) GENERAL ONTOLOGICAL ISSUES 1. Must Ontological Pragmatism be Self-Defeating? (Guy Rohrbaugh) 2. Indication, Abstraction, & Individuation (Jerrold Levinson) 3. Destroying Artworks (Marcus Rossberg) INFORMATIVE COMPARISONS 4. Artworks & IndefiniteExtensibility (Roy T. Cook) 5. Historical Individuals Like Anas platyrhynchos & ‘Classical Gas’ (P.D. Magnus) 6. Repeatable Artworks & Genericity (Shieva Kleinschmidt & Jacob Ross) ARGUMENTS AGAINST & ALTERNATIVES TO 7. Against Repeatable Artworks (Allan Hazlett) (...) 8. How to be a Nominalist & a Fictional Realist (Ross Cameron) 9. Platonism vs. Nominalism in Musical Ontology (Andrew Kania) ABSTRACTA ACROSS THE ARTS 10. Reflections on the Metaphysics of Sculpture (Hud Hudson) 11. Installation Art & Performance: A Shared Ontology (Sherri Irvin) 12. What Type of ‘Type’ is a Film? (David Davies) 13. Musical Works: A Metaphysical Mash-Up (Joseph Moore) . (shrink)
In Michael Dummett's celebrated essay on Gödel's theorem he considers the threat posed by the theorem to the idea that meaning is use and argues that this threat can be annulled. In my essay I try to show that the threat is even less serious than Dummett makes it out to be. Dummett argues, in effect, that Gödel's theorem does not prevent us from "capturing" the truths of arithmetic; I argue that the idea that meaning is use does not require (...) that we be able to "capture" these truths anyway. Towards the end of my essay I relate what I have been arguing first to Dummett's concept of indefiniteextensibility and then to some of Wittgenstein's remarks on Gödel's theorem. (shrink)
Noun phrases (NPs) beginning with the or a/an are prototypical definite and indefinite NPs in English. The two main theories about the meaning of definiteness are uniqueness and familiarity. Both properties characterize most occurrences of definite descriptions although there are examples which defy one or the other or both theories. Existential sentences have become criterial for distinguishing indefinites from definites, and have led to broadening of both categories to include a variety of other NP forms. Information status approaches propose (...) a hierarchy of NP types, rather than a simple binary distinction. The expression of definiteness varies from language to language. (shrink)
Working on the assumption that ideas are embedded in socio-technical arrangements which actualize them, this essay sheds light on the way the Open Method of Co-ordination (OMC) achieves the Lisbon strategic goal: to become the most competitive and dynamic knowledge-based economy in the world . Rather than framing the issue in utilitarian terms, it focuses attention on quantified indicators, comparable statistics and common targets resulting from the increasing practice of intergovernmental benchmarking, in order to tackle the following questions: how does (...) the OMC go about co-ordinating Member States through the benchmarking of national policies? And to what extent does this managerial device impact the path of European construction? Beyond the ideological and discursive construction of the competitive imperative, this technology of government transforms it into an indefinite discipline (Foucault) which constantly urges decision-makers to hit the top of the charts. This contribution thus argues that the practice of intergovernmental benchmarking is far from being neutral in purpose and effect. On the contrary, it lays the foundation for building a competitive Europe which unites Member States through competition. (shrink)
This paper presents a restructured set of axioms for categorical logic. In virtue of it, the syllogistic with indefinite terms is deduced and proved, within the categorical logic boundaries. As a result, the number of all the conclusive syllogisms is deduced through a simple and axiomatic methodology. Moreover, the distinction between immediate and mediate inferences disappears, which reinstitutes the unity of Aristotelian logic.
Sentences containing pronouns and indefinite noun phrases can be said toexpress open propositions, propositions which display gaps to be filled.This paper addresses the question what is the linguistic content ofthese expressions, what information they can be said to provide to ahearer, and in what sense the information of a speaker can be said tosupport their utterance. We present and motivate first order notions ofcontent, update and support. The three notions are each defined in acompositional fashion and brought together within (...) a single and coherentframework. (shrink)
An analysis of indefinite probability statements has been offered by Jackson and Pargetter (1973). We accept that this analysis will assign the correct probability values for indefinite probability claims. But it does so in a way which fails to reflect the epistemic state of a person who makes such a claim. We offer two alternative analyses: one employing de re (epistemic) probabilities, and the other employing de dicto (epistemic) probabilities. These two analyses appeal only to probabilities which are (...) accessible to a person who makes an indefinite probability judgment, and yet we prove that the probabilities which either of them assigns will always be equivalent to those assigned by the Jackson and Pargetter analysis. (shrink)
In this paper, we examine the properties of a novel kind of nominal ellipsis in Greek, which we call indefinite argument drop (IAD), concentrating on its manifestation in object positions. We argue that syntactically these null objects are present as pro, and we show that semantically they are licensed only by weak DP antecedents (in the sense of Milsark 1974). We compare IAD with NP- internal ellipsis, as attested also in English among many other languages, and show that IAD (...) has distinct syntactic and semantic properties. Finally, we compare our account with a number of proposals regarding null objects in the literature, and show that IAD cannot be reduced to any of these. (shrink)
The main purpose of this paper is to define and study a particular variety of Montague-Scott neighborhood semantics for modal propositional logic. We call this variety the first-order neighborhood semantics because it consists of the neighborhood frames whose neighborhood operations are, in a certain sense, first-order definable. The paper consists of two parts. In Part I we begin by presenting a family of modal systems. We recall the Montague-Scott semantics and apply it to some of our systems that have hitherto (...) be uncharacterized. Then, we define the notion of a first-order indefinite semantics, along with the more specific notion of a first-order uniform semantics, the latter containing as special cases the possible world semantics of Kripke. In Part II we prove consistency and completeness for a broad range of the systems considered, with respect to the first-order indefinite semantics, and for a selected list of systems, with respect to the first-order uniform semantics. The completeness proofs are algebraic in character and make essential use of the finite model property. A by-product of our investigations is a result relating provability in S-systems and provability in T-systems, which generalizes a known theorem relating provability in the systems S 2° and C 2. (shrink)
Both proposals acknowledge that definite descriptions differ from indefinites in their implications. (Two parenthetical clarifications: (i) "implication" is to be understood here and below as neutral between semantic and pragmatic conveyance; (ii) "semantic" is to be understood to mean "conventional", that is including, in addition to truth conditional impact, anything else that is linguistically encoded.) One of these implications is what is commonly termed "familiarity" ? an assumption that the denotation of the NP has already been introduced, as such, to (...) the addressee of the utterance. The other is uniqueness, or more properly exhaustive application, within the salient discourse context, of the descriptive content of the NP to the intended denotation. However both analyses attempt to derive one or both of these implications pragmatically. Ludlow & Segal propose that familiarity is a conventional implicature and uniqueness a conversational implicature. Szabó concurs with Ludlow & Segal that familiarity is more essential to definite descriptions, but attempts to derive both implications pragmatically. (shrink)
Grice introduced generalized conversational implicatures with the following example: "Anyone who uses a sentence of the formX is meeting tz woman this evening would normally implicate that the person to be met was someone other than X’s wife, mother, sister, or perhaps even close platonic friend" (1975 : 37). Concerning this example, he suggested the following account: When someone, by using the form of expression an JQ implicates that the X does not belong to or is not otherwise closely connected (...) with some identifiable person, the implicature is present because the speaker has failed to be specific in a way in which he might have been expected to be specific. (Grice 1975: 38.) Grice went on to sketch an explanation as to why such an implicature should arise, involving the different ways in which we behave towards things that are closely related to.. (shrink)
Isaac Levi and I have different views of probability and decision making. Here, without addressing the merits, I will try to answer some questions recently asked by Levi (1985) about what my view is, and how it relates to his.
Defining structural constraints on coindexing proved fruitful. Its semantic import, however, remains unclear.1 Syntactic work in the late seventies and early eighties extended the use of indexing to capture the ‘arbitrariness’ of examples like (1a) (Chomsky and Lasnik 1977, Chomsky 1980), (1b) or (1c) (Suñer 1983). The semantic import of this type of indexing is not less unclear.
This paper is an attempt to take up the prompt in Derrida's work concerning the necessity for a deconstruction of anthropocentrism. Working through an example from Hegel's Philosophy of Right concerning animality, the paper takes up Derrida's project and connects it to the larger concern of what happens to the philosophical once it is no longer premised on the animal's exclusion but has to acknowledge the inclusion of an already present thus recalcitrant animality.
In the first part of this paper a logic is defined for propositions whose probability of being true may not be known. A speaker's beliefs about which propositions are true are still interesting in this case. The meaning of propositions is determined by the consequences of asserting them: in this logic there are debates which incur certain costs for the protagonists.The second part of the paper describes the mathematics of the resulting logic which displays several novel features.
This squib aims to show that the acceptability status of sluicing examples with an implicit antecedent in islands varies and discusses what is responsible for this variability. After investigating two representative structural approaches to sluicing that posit unpronounced structure in ellipsis sites, namely, Chung et al.’s (Nat Lang Semant 3:239–282, 1995; in Mikkelsen et al. (eds) Representing language: Essays in honor of Judith Aissen, 2010) LF-recovery analysis and Merchant’s (The syntax of silence: Sluicing, islands, and identity in ellipsis. Oxford: Oxford (...) University Press 2001) PF-deletion analysis, we demonstrate that the acceptability data presented are challenging for both of them. Acceptable sluicing examples with implicit correlates in islands cast doubt on Chung, Ladusaw, and McCloskey’s strict locality requirement, while unacceptable or degraded sluicing examples necessitate additional constraints for Merchant, who employs E-type anaphora as an escape hatch for island violations in sluicing. The gradient nature of the acceptability status of the examples under discussion calls for a non-structural factor that controls their acceptability. We speculate that it is discourse activation of implicit correlates that plays this crucial role. (shrink)
Contemporary discussions do not always clearly distinguish two different forms of vagueness. Sometimes focus is on the imprecision of predicates, and sometimes the indefiniteness of statements. The two are intimately related, of course. A predicate is imprecise if there are instances to which it neither definitely applies nor definitely does not apply, instances of which it is neither definitely true nor definitely false. However, indefinite statements will occur in everyday discourse only if speakers in fact apply imprecise predicates to (...) such indefinite instances. (What makes an instance indefinite is, it should be clear, predicate-relative.) The basic issue in the present inquiry is whether this indefiniteness ever really occurs; the basic question is, Why should it ever occur? (shrink)
According to the so-called “Folk Theorem” for repeated games, stable cooperative relations can be sustained in a Prisoner’s Dilemma if the game is repeated an indefinite number of times. This result depends on the possibility of applying strategies that are based on reciprocity, i.e., strategies that reward cooperation with subsequent cooperation and punish defectionwith subsequent defection. If future interactions are sufficiently important, i.e., if the discount rate is relatively small, each agent may be motivated to cooperate by fear of (...) retaliation in the future. For finite games, however, where the number of plays is known beforehand, there is a backward induction argument showing that rational agents will not be able to achieve cooperation. On behalf of the Hobbesian “Foole”, who cannot see any advantage in cooperation, Gregory Kavka (1983, 1986) has presented an argument that significantly extends the range of the backward induction argument. He shows that, for the backward induction argument to be effective, it is not necessary that the precise number of future interactions be known. It is sufficient that there is a known definite upper bound on the number of interactions. A similar argument is developed by John W. Carroll (1987). We will here question the assumption of a known upper bound. When the assumption is made precise in the way needed for the argument to go through, its apparent plausibility evaporates. We then offer a reformulation of the argument, based on weaker, and more plausible, assumptions. (shrink)
This paper investigates the truth conditions of sentences containing indefinite noun phrases, focusing on occurrences in attitude reports, and, in particular, a puzzle case due to Walter Edelberg. It is argued that indefinites semantically contribute the (thought-)object they denote, in a manner analogous to attributive definite descriptions. While there is an existential reading of attitude reports containing indefinites, it is argued that the existential quantifier is contributed by the de re interpretation of the indefinite (as the de re (...) reading adds existential quantification to the interpretation of definites on Kaplan’s analysis). (shrink)
After describing the philosophical background of Kerry?s work, an account is given of the way Kerry proposed to supplement Bolzano?s conception of logic with a psychological account of the mental acts underlying mathematical judgements.In his writings Kerry criticized Frege?s work and Kerry?s views were then attacked by Frege.The following two issues were central to this controversy: (a) the relation between the content of a concept and the object of a concept; (b) the logical roles of the definite article.Not only did (...) Frege in 1892 offer an unconvincing solution to Kerry?s puzzle concerning ?the concept horse? but he also overlooked the many criticisms levelled by Kerry against the notion of an (indefinite) extension on which his own definition of number was based. (shrink)
This paper will defend the claim that, under certain circumstances, the material vehicles responsible for an agent’s conscious experience can be partly constituted by processes outside the agent’s body. In other words, the consciousness of the agent can extend. This claim will be supported by the Extended Mind Thesis (EMT) example of the artist and their sketchpad (Clark 2001, 2003). It will be argued that if this example is one of EMT, then this example also supports an argument for consciousness (...) extension. Clark (2009) rejects claims of consciousness extension. This paper will challenge Clark and argue that he fails to show that the material vehicles responsible for consciousness must be internal to the agent. (shrink)
Demonstrative noun phrases (e.g. this; that guy over there ) are intimately connected to the context of use in that their reference is determined by demonstrations and/or the speaker's intentions. The semantics of demonstratives therefore has important implications not only for theories of reference, but for questions about how information from the context interacts with formal semantics. First treated by Kaplan as directly referential , demonstratives have recently been analyzed as quantifiers by King, and the choice between these two approaches (...) is a matter of ongoing controversy. Meanwhile, linguists and psychologists working from a variety of perspectives have gathered a wealth of data on the form, meaning, and use of demonstratives in many languages. Demonstratives thus provide a fruitful topic for graduate study for two reasons. On the one hand, they serve as an entry point to foundational issues in reference and the semantics–pragmatics interface. On the other hand, they are an especially promising starting point for interdisciplinary research, which brings the results of linguistics and related fields to bear on the philosophy of language. Author Recommends Kaplan, David. 'Demonstratives.' 1977. Themes from Kaplan . Ed. J. Almong, J. Perry, and H. Wettstein. Oxford: Oxford UP, 1989. 481–563. The seminal work on the semantics of demonstratives and indexicals, such as I, here , and now . Kaplan introduces a distinction between content (which maps from possible circumstances to extensions) and character (which maps from possible contexts to contents). He argues that demonstratives and indexicals are directly referential : given a possible context, their character fixes their extension. Kaplan, David. 'Afterthoughts.' Themes from Kaplan . Ed. J. Almong, J. Perry, and H. Wettstein. Oxford: Oxford UP, 1989. 565–614. An elaboration on the theory developed in 'Demonstratives.' Kaplan considers the connection between direct reference and rigid designation; raises the issue of whether demonstratives depend on demonstrations or speaker intentions; and discusses implications of the analysis for formal semantics and for epistemology. King, Jeffrey C. Complex Demonstratives . Cambridge, MA: MIT Press, 2001. In perhaps the most influential challenge to date to the direct reference theory of demonstratives, King argues that complex demonstratives (i.e. demonstrative determiners with nominal complements) are best analyzed as quantifiers. Braun, David. 'Complex Demonstratives and Their Singular Contents.' Linguistics and Philosophy 31 (2008): 57–99. This recent Kaplanian analysis of complex demonstratives shows the 'state of the art' of direct reference approaches and responds to some of the objections to such approaches raised by King. Elbourne, Paul. 'Demonstratives as Individual Concepts.' Linguistics and Philosophy 31 (2008): 409–466. The most recent analysis of demonstratives as individual concepts, contrasting with both the direct reference and quantificational approaches. Fillmore, Charles. Lectures on Deixis . Stanford, CA: CSLI, 1997. In this collection of lectures, originally delivered in 1971, Fillmore considers demonstratives and indexical expressions in many languages to describe the types of information about the context (e.g. locations in space, time, and discourse) that are encoded in natural language. Gundel, Jeanette K., Nancy Hedberg, and Ron Zacharski. 'Cognitive Status and the Form of Referring Expressions in Discourse.' Language 69 (1993): 274–307. Perhaps the most detailed pragmatic alternative to formal semantic theories of demonstratives and other referring expressions. The authors argue that demonstratives are best described as imposing a condition of use in which the referent of the demonstrative has a certain level of salience for the interlocutors. Online Materials http://plato.stanford.edu/entries/indexicals/ Indexicals (David Braun) http://plato.stanford.edu/entries/reference/ Reference (Marga Reimer) http://plato.stanford.edu/entries/rigid-designators/ Rigid designators (Joseph LaPorte) http://philpapers.org/browse/indexicals-and-demonstratives/ Online bibliography of papers on indexicals and demonstratives Sample Syllabus The following syllabus can be used in entirety for a survey course on demonstratives; in addition, each of the three units is self-contained and can be used alone. Unit 1: Demonstratives and Indexicality Week 1: Indexicals 1. Kaplan, Demonstratives 2. Kaplan, Afterthoughts Week 2: Issues for Indexical Reference 1. Reimer, Marga. 'Do Demonstrations Have Semantic Significance?' Analysis 51 (1991): 177–83. 2. Bach, Kent. 'Intentions and Demonstrations.' Analysis 52 (1992): 140–46. 3. Nunberg, Geoffrey. 'Indexicality and Deixis.' Linguistics and Philosophy 16.1 (1993): 1–43. Week 3: Optional detour: Monsters 1. Schlenker, Philippe. 'A Plea for Monsters.' Linguistics and Philosophy 26 (2003): 29-120. Week 4: Demonstratives as Quantifiers 1. King. Complex Demonstratives , chapters 1–3. Week 5: Indexical and Non-Indexical Demonstratives 1. Braun, David. 'Complex Demonstratives and Their Singular Contents.' Linguistics and Philosophy 31 (2008): 57–99. Optional additional reading 2. Roberts, Craige. 'Demonstratives as Definites.' Information Sharing . Ed. Kees van Deemter and Roger Kibble. Stanford, CA: CSLI Press, 2002. 3. Wolter, Lynsey. 'That's That: The Semantics and Pragmatics of Demonstrative Noun Phrases.' Diss. University of California, Santa Cruz, 2006, chapters 2–3. 4. Elbourne, Paul. 'Demonstratives as Individual Concepts.' Linguistics and Philosophy 31 (2008): 409–66. Unit 2: Demonstratives, Proximity, Salience Week 6: Demonstratives and Proximity 1. Fillmore, Charles. 'Deixis I.' in Lectures on Deixis . Stanford, CA: CSLI, 1997. 59–76. 2. Fillmore, Charles. 'Deixis II.' in Lectures on Deixis . Stanford, CA: CSLI, 1997. 103–26. Optional additional reading 3. Prince, Ellen. 'On the Inferencing of Indefinite- this NPs.' Elements of Discourse Understanding . Ed. Aravind K. Joshi, Bonnie L. Weber, and Ivan A. Sag. Cambridge: Cambridge University Press, 1981. 231–50. Week 7: Demonstratives and Salience 1. Gundel, Jeanette K., Nancy Hedberg, and Ron Zacharski. 'Cognitive Status and the Form of Referring Expressions in Discourse.' Language 69 (1993): 274–307. Optional additional reading 2. Brown-Schmidt, Sarah, Donna K. Byron, and Michael K. Tanenhaus. 'Beyond Salience: Interpretation of Personal and Demonstrative Pronouns.' Journal of Memory and Language 53 (2005): 292–313. Note: readers new to psycholinguistics should concentrate on the Introduction. Unit 3: Demonstratives and Copular Sentences Week 8: Background on the Typology of Copular Sentences 1. Higgins, F. Roger. 'The Pseudo-Cleft Construction in English.' Diss. MIT, 1973, chapter 5. Week 9: Demonstratives in Copular Sentences 1. Mikkelsen, Line. 'Specifying Who: On the Structure, Meaning, and Use of Specificational Copular Clauses.' Diss. University of California, Santa Cruz, 2004, chapter 8.2 (Truncated Clefts). 2. Heller, Daphna and Lynsey Wolter. ' That is Rosa : Identificational Sentences as Intensional Predication.' Proceedings of Sinn und Bedeutung 12 . Ed. Atle Grønn. Oslo: Department of Literature, Area Studies and European Languages, University of Oslo, 2008. Week 10: Demonstratives, Copular Sentences, Modals 1. Birner, Betty J., Jeffrey P. Kaplan, and Gregory Ward. 'Functional Compositionality and the Interaction of Discourse Constraints.' Language 83 (2007): 317–43. Focus Questions 1. Which of the following expressions are indexicals? Which are demonstratives? Why? (a) a pencil (b) the pencil (c) this pencil (d) Mary Smith (e) Mary's pencil (f ) my pencil (g) we (h) you (i) here (j) there (k) now (l) then 2. Do demonstratives ever interact with scope-taking operators to give rise to two or more truth-conditionally distinct readings? If so, under what circumstances? 3. (a) If demonstratives (sometimes or always) interact with scope-taking operators to give rise to two or more truth-conditionally distinct readings, to what extent can a direct reference theory of demonstratives be maintained? (b) If demonstratives never interact with scope-taking operators to give rise to two or more truth-conditionally distinct readings, to what extent can a quantificational theory of demonstratives be maintained? 4. What kind of thing is a demonstration? Is it a pointing gesture? An indication of the speaker's focus of attention? Something more abstract? 5. What information do English demonstratives convey about proximity? What is 'proximity'– physical closeness to the speaker, or something more abstract? What is the status of this information: is it entailed, presupposed, or something else? 6. Do demonstratives that are accompanied by a physical gesture of demonstration have the same semantic value as anaphoric demonstratives, such as that in (a)? Why or why not? (a) John made a peanut butter sandwich and ate it quickly. Next he took an apple from the fridge. He ate that more slowly. (shrink)
This essay critically reviews Andy Clark’s new book Supersizing the Mind: Embodiment, Action, and Cognitive Extension, in which he argues that there are circumstances in which the mind, properly considered, is found to supervene on not only the brain, but the body and the external environment as well. This review summarizes Clark’s major contributions to this viewpoint for the general reader, then raises a few critical points that help to contextualize Clark’s claims, aims, and methods, while highlighting the book’s strengths (...) and weaknesses. (shrink)
The view that mathematical objects are indefinite in nature is presented and defended, hi the first section, Field's argument for fictionalism, given in response to Benacerraf's problem of identification, is closely examined, and it is contended that platonists can solve the problem equally well if they take the view that mathematical objects are indefinite. In the second section, two general arguments against the intelligibility of objectual indefiniteness are shown erroneous, hi the final section, the view is compared to (...) mathematical structuralism, and it is shown that a version of structuralism should be understood as embracing the same view. (shrink)
Summary Verbs of creation (create, make, paint) are not transparent. The object created does not exist during the event time but only thereafter. We may call this type of opacity temporal opacity. I is to be distinguished from modal opacity, which is found in verbs like owe or seek. (Dowty, 1979) offers two analyses of creation verbs. One analysis predicts that no object of the sort created exists before the time of the creation. The other analysis says that the object (...) exists throughout the act of creation. I investigate three theories: Theory I says that no object of the sort created and which is caused by the very act of creation exists before the creation. In this theory, verbs of creation must embed a property. Theory II can regard the indefinite object of a creation verb as a quantifier and gives it wide scope with respect to the verb. The theory has to make sure that the objects quantified over exist only after the event. While Theory I and II start from the assumption that the extension of all nouns depend on time, Theory III says that Individual Level predicates do not depend on time. This ontology will enable us to treat verbs of creation as first order relations. The theory will entail that a picture does not mean the same as there is a picture. The paper discusses various approaches to the problem: Krifka, Parsons, Landman, Kratzer and Zucchi. (shrink)
The prototypes of definiteness and indefiniteness in English are the definite article the and the indefinite article a/an, and singular noun phrases (NPs)1 determined by them. That being the case it is not to be predicted that the concepts, whatever their content, will extend satisfactorily to other determiners or NP types. However it has become standard to extend these notions. Of the two categories definites have received rather more attention, and more than one researcher has characterized the category of (...) definite NPs by enumerating NP types. Westerståhl (1985), who is concerned only with determiners in the paper cited, gives a very short list: demonstrative NPs, possessive NPs, and definite descriptions. Prince (1992) lists proper names and personal pronouns, as well as NPs with the, a demonstrative, or a possessive NP as determiner. She notes, in addition, that “certain quantifiers (e.g. all, every) have been argued to be definite” (Prince 1992: 299). This list, with the quantifiers added, agrees with that given by Birner & Ward (1998, 114). Ariel (1988, 1990) adds null anaphoric NPs. (shrink)
A mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics is proposed. For this a Hilbert space H of functions of four variables x,t furnished with an additional indefinite inner product invariant under Poincare transformations is introduced. For a class of functions in H that are well localized in the time variable the usual formalism of non-relativistic quantum mechanics is derived. In particular, the interference in time for these functions is suppressed; a motion in H (...) becomes the usual Shrodinger evolution with t as a parameter. The relativistic invariance of the construction is proved. The usual theory of relativity on Minkowski space-time is shown to be ``isometrically and equivariantly embedded'' into H. That is, classical space-time is isometrically embedded into H, Poincare transformations have unique extensions to isomorphisms of H and the embedding commutes with Poincare transformations. (shrink)
In the Corpus Hippocraticum and in tragedy, γκος is difficult to translate, for it corresponds to a very primitive notion, intuitively implying a confusion between two aspects that were gradually distinguished: 1) a thing's bulk or extension, and 2) an appreciation, as a function of its bulk and its extension, of the load represented by this thing, or its weight. This explains why the term usually designates something that has a certain mass. As an indefinite quantity of formless matter, (...) this is probably a notion which was used by medio-Platonists, strongly influenced by Stoicism, to understand matter the Timaeus . In Plotinus' polemic against the Stoics, γκος, which refers to a magnitude with resistance bereft of qualities, is thus situated at a level intermediate between matter (λη), bereft of all determination, and the body (σμα), which is endowed with magnitude and qualities. In the Sentences , Porphyry uses the term γκος 30 times in its technical sense, almost as often as Plotinus in the whole of the Enneads . This is probably because he felt uncomfortable with Plotinus' notion of matter bereft of all determination, including magnitude. (shrink)
The paper shows that in the Art of Thinking (The Port Royal Logic) Arnauld and Nicole introduce a new way to state the truth-conditions for categorical propositions. The definition uses two new ideas: the notion of distributive or, as they call it, universal term, which they abstract from distributive supposition in medieval logic, and their own version of what is now called a conservative quantifier in general quantification theory. Contrary to the interpretation of Jean-Claude Parienté and others, the truth-conditions do (...) not require the introduction of a new concept of ?indefinite? term restriction because the notion of conservative quantifier is formulated in terms of the standard notion of term intersection. The discussion shows the following. Distributive supposition could not be used in an analysis of truth because it is explained in terms of entailment, and entailment in terms of truth. By abstracting from semantic identities that underlie distribution, the new concept of distributive term is definitionally prior to truth and can, therefore, be used in a non-circular way to state truth-conditions. Using only standard restriction, the Logic?s truth-conditions for the categorical propositions are stated solely in terms of (1) universal (distributive) term, (2) conservative quantifier, and (3) affirmative and negative proposition. It is explained why the Cartesian notion of extension as a set of ideas is in this context equivalent to medieval and modern notions of extension. (shrink)
I attempt to show, via considering Schlesinger’s device of putting the word ‘now’ in capitals, that the transient view of time can explicate temporal extensivity without presupposing it, and the static view can’t. The argument hinges on the point that duration is generated by continuance of the present—such that ‘the present’ here is used in a nontechnical, nonindexical, and nonreflexive sense, which Schlesinger and others unknowingly give to the word ‘now’ (by “NOW” or “Now” or “’now’”).
In Humanity’s End: Why We Should Reject Radical Enhancement, Nicholas Agar presents a novel argument against the prospect of radical life-extension. Agar’s argument hinges on the claim that extended lifespans will result in people’s lives being dominated by the fear of death. Here we examine this claim and the surrounding issues in Agar’s discussion. We argue, firstly, that Agar’s view rests on empirically dubious assumptions about human rationality and attitudes to risk, and secondly, that even if those assumptions are granted, (...) the fears that Agar adverts to are unlikely to dominate people’s lives if and when radical life-extension is made possible. Further, we claim that the structure of the decision-making process around life-extension is unlikely to be the way that it would have to be in order for Agar’s claims about fear of death to make sense. Finally, we argue that Agar is implicitly committed to a narrow conception of human value. In response, we suggest that the pursuit of life-extension can itself be seen as an expression of certain important aspects of our distinctively human nature. (shrink)
According to certain kinds of semantic dispositionalism, what an agent means by her words is grounded by her dispositions to complete simple tasks. This sort of position is often thought to avoid the finitude problem raised by Kripke against simpler forms of dispositionalism. The traditional objection is that, since words possess indefinite (or infinite) extensions, and our dispositions to use words are only finite, those dispositions prove inadequate to serve as ground for what we mean by our words. I (...) argue that, even if such positions (emphasizing simple tasks) avoid the traditional form of Kripke's charge, they still succumb to special cases of the finitude problem. Furthermore, I show how such positions can be augmented so as to avoid even these special cases. Doing so requires qualifying the dispositions of interest as those possessed by the abstracted version of an actual agent (in contrast to, say, an idealized version of the agent). In addition to avoiding the finitude problem in its various forms, the position that results provides new materials for appreciating the role that abstracting models can play for a dispositionalist theory of meaning. (shrink)
The development of the typical cladomothallus of the red algae Antithaminion plumula (Ellis) Le Jolis [= Pterothamnion plumula (Ellis) Nägcli], (Rhodophyceae, Ceramiales) is simulated with the help of a formal language called L-systems. Two types of uniseriate filaments are distinguished: axial filaments of cladomes with indefinite growth and branching and pleuridia with definite growth and branching. The rythmical acropetal formation of secondary axes with basitonic arrangement contrasts with the intercalary basitonic formation of pleuridia, resulting in an acrotonic arrangement within (...) an axial segment. Five types of cells and two types of cell divisions intervene in the system. In addition, for the graphical representations, some morphological particularities of A. plumula are taken into account: the curvature of axial filaments, the extension of growth zones, variable cell generation times, and segment length variability along an axis. The incidence of these variables on the generated thallus form is emphasized, pointing to the singularities of A. plumula. (shrink)
Truth values are, properly understood, merely proxies for the various relations that can hold between language and the world. Once truth values are understood in this way, consideration of the Liar paradox and the revenge problem shows that our language is indefinitely extensible, as is the class of truth values that statements of our language can take – in short, there is a proper class of such truth values. As a result, important and unexpected connections emerge between the semantic paradoxes (...) and the set-theoretic paradoxes. (shrink)
It might be thought that we could argue for the consistency of a mathematical theory T within T, by giving an inductive argument that all theorems of T are true and inferring consistency. By Gödel's second incompleteness theorem any such argument must break down, but just how it breaks down depends on the kind of theory of truth that is built into T. The paper surveys the possibilities, and suggests that some theories of truth give far more intuitive diagnoses of (...) the breakdown than do others. The paper concludes with some morals about the nature of validity and about a possible alternative to the idea that mathematical theories are indefinitely extensible. (shrink)
Would be fairer to call Peirce’s philosophy of language “extensionalist” or “intensionalist”? The extensionalisms of Carnap and Quine are examined, and Peirce’s view is found to be prima facie similar, except for his commitment to the importance of “hypostatic abstraction”. Rather than dismissing this form of abstraction (famously derided by Molière) as useless scholasticism, Peirce argues that it represents a crucial (though largely unnoticed) step in much working inference. This, it is argued, allows Peirce to transcend the extensionalist-intensionalist dichotomy itself, (...) through his unique triadic analysis of reference and meaning, by transcending the distinction between (as Quine put it) “things” and “attributes”. (shrink)
Crosslinguistically, questions frequently make crucial use of morphosyntactic elements which also occur outside of questions. Chief among these are focus, disjunctions, and wh-words with indefinite semantics. This paper provides a compositional account of the semantics of wh-, alternative, and polar questions in Yucatec Maya (YM), which are composed primarily of these elements. Key to the account is a theory of disjunctions and indefinites (extending work by others) which recognizes the inherently inquisitive nature of these elements. While disjunctions and indefinites (...) are inquisitive, they differ from questions since they are also truth-conditionally informative. Compositionally, then, the role of focus in YM questions is to presuppose the informative component of an indefinite wh-word or disjunction, rendering the inquisitive component the question’s only new contribution to the discourse. In addition to deriving question denotations compositionally, the account also captures a potentially surprising fact: focused disjunctions in YM can function as either questions or assertions, depending solely on the discourse context. (shrink)
Our concern for nonhuman nature can be justified in terms of a human right to liberty of ecological conscience. This right is analogous to the right to religious liberty, and is equally worthy of recognition as that fundamental liberty. The liberty of ecological conscience, like religious liberty, is a negative right against interference. Each ecological conscience supports a claim to protection of the parts of nonhuman nature that are current or potential sites of its active pursuit of natural value. If (...) we acknowledge the fallibility of each conscience in its pursuit of genuine natural value, a policy of indefinitely extensive conservation can be justified. Destruction of an object of current or potential natural value is like destroying a church, mosque, temple, or other holy place. This justification for environmental conservation is analogous to the standard justification for individual negative rights, as upheld by the liberal tradition of Locke, Mill, and Rawls. (shrink)
Extension is probably the most general natural property. Is it a fundamental property? Leibniz claimed the answer was no, and that the structureless intuition of extension concealed more fundamental properties and relations. This paper follows Leibniz's program through Herbart and Riemann to Grassmann and uses Grassmann's algebra of points to build up levels of extensions algebraically. Finally, the connection between extension and measurement is considered.
This paper evaluates the Natural-Kinds Argument for cognitive extension, which purports to show that the kinds presupposed by our best cognitive science have instances external to human organism. Various interpretations of the argument are articulated and evaluated, using the overarching categories of memory and cognition as test cases. Particular emphasis is placed on criteria for the scientific legitimacy of generic kinds, that is, kinds characterized in very broad terms rather than in terms of their fine-grained causal roles. Given the current (...) state of cognitive science, I conclude that we have no reason to think memory or cognition are generic natural kinds that can ground an argument for cognitive extension. (shrink)