The conceptual spaces approach has recently emerged as a novel account of concepts. Its guiding idea is that concepts can be represented geometrically, by means of metrical spaces. While it is generally recognized that many of our concepts are vague, the question of how to model vagueness in the conceptual spaces approach has not been addressed so far, even though the answer is far from straightforward. The present paper aims to fill this lacuna.
Edgington has proposed a solution to the sorites paradox in terms of ‘verities’, which she defines as degrees of closeness to clear truth. Central to her solution is the assumption that verities are formally probabilities. She is silent on what verities might derive from and on why they should be probabilities. This paper places Edgington’s solution in the framework of a spatial approach to conceptualization, arguing that verities may be conceived of as deriving from how our concepts relate to each (...) other. Building on work by Kamp and Partee, this paper further shows how verities, thus conceived of, may plausibly be assumed to have probabilistic structure. The new interpretation of verities is argued to also help answer the question of what the verities of indicative conditionals are, a question which Edgington leaves open. Finally, the question of how to accommodate higher-order vagueness, given this interpretation, is addressed. (shrink)
This paper considers Kamp and Partee's account of graded membership within a conceptual spaces framework and puts the account to the test in the domain of colors. Three experiments are reported that are meant to determine, on the one hand, the regions in color space where the typical instances of blue and green are located and, on the other hand, the degrees of blueness/greenness of various shades in the blue–green region as judged by human observers. From the locations of the (...) typical blue and typical green regions in conjunction with Kamp and Partee's account follow degrees of blueness/greenness for the color shades we are interested in. These predicted degrees are compared with the judged degrees, as obtained in the experiments. The results of the comparison support the account of graded membership at issue. (shrink)
It has seemed natural to model phenomena related to vagueness in terms of graded membership. However, so far no satisfactory answer has been given to the question of what graded membership is nor has any attempt been made to describe in detail a procedure for determining degrees of membership. We seek to remedy these lacunae by building on recent work on typicality and graded membership in cognitive science and combining some of the results obtained there with a version of the (...) conceptual spaces framework. (shrink)
In a famous critique, Goodman dismissed similarity as a slippery and both philosophically and scientifically useless notion. We revisit his critique in the light of important recent work on similarity in psychology and cognitive science. Specifically, we use Tversky’s influential set-theoretic account of similarity as well as Gärdenfors’s more recent resuscitation of the geometrical account to show that, while Goodman’s critique contained valuable insights, it does not warrant a dismissal of similarity.
The standard approach to the so-called paradoxes of identity has been to argue that these paradoxes do not essentially concern the notion of identity but rather betray misconceptions on our part regarding other metaphysical notions, like that of an object or a property. This paper proposes a different approach by pointing to an ambiguity in the identity predicate and arguing that the concept of identity that figures in many ordinary identity claims, including those that appear in the paradoxes, is not (...) the traditional philosophical concept but one that can be defined in terms of relevant similarity. This approach to the paradoxes will be argued to be superior to the standard one. (shrink)
Quine's views on indispensability arguments in mathematics are scrutinised. A weak indispensability argument is distinguished from a strong indispensability thesis. The weak argument is the combination of the criterion of ontological commitment, holism and a mild naturalism. It is used to refute nominalism. Quine's strong indispensability thesis claims that one should consider all and only the mathematical entities that are really indispensable. Quine has little support for this thesis. This is even clearer if one takes into account Maddy's critique of (...) Quine's strong indispensability thesis. Maddy's critique does not refute Quine's weak indispensability argument. We are left with a weak and almost unassailable indispensability argument. (shrink)
In recent years philosophers have been interested in the methodology of metaphysics. Most of these developments are related to formal work in logic or physics, often against the backdrop of the Carnap-Quine debate on ontology. Drawing on Quine’s later work, I argue that a psychological or cognitive perspective on metaphysical topics may be a valuable addition to contemporary metametaphysics. The method is illustrated by means of cognitive studies of the notions “identity,” “vagueness,” and “object” and is compared to other extant (...) metametaphysical positions. (shrink)
Putnam’s internal realism is aimed at reconciling realist and antirealist intuitions about truth and the nature of reality. A common complaint about internal realism is that it has never been stated with due precision. This paper attempts to render the position precise by drawing on the literature on conceptual spaces as well as on earlier work of the authors on the notion of identity.
The Interplay of Logic, Set Theory and Semantics in Quine's Philosophy L. Decock. In philosophy of science Quine's name is linked to the so-called Quine- Duhem thesis. The discussion of this thesis still continues even after several decades.9 ...
This paper argues that phenomenal or internal metrical spaces are redundant posits. It is shown that we need not posit an internal space-time frame, as the physical space-time suffices to explain geometrical perception, memory and planning. More than the internal space-time frame, the idea of a phenomenal colour space has lent credibility to the idea of internal spaces. It is argued that there is no phenomenal colour space that underlies the various psychophysical colour spaces; it is parasitic upon physical and (...) psychophysical colour spaces. The argumentation is further extended to other sensory spaces and generalised quality spaces. (shrink)
In recent years, neologicists have demonstrated that Hume's principle, based on the one-to-one correspondence relation, suffices to construct the natural numbers. This formal work is shown to be relevant for empirical research on mathematical cognition. I give a hypothetical account of how nonnumerate societies may acquire arithmetical knowledge on the basis of the one-to-one correspondence relation only, whereby the acquisition of number concepts need not rely on enumeration (the stable-order principle). The existing empirical data on the role of the one-to-one (...) correspondence relation for numerical abilities is assessed and additional empirical tests are proposed. In the final part, it is argued that the fact that the successor relation and the one-to-one correspondence relation can play independent roles in number concept acquisition may be a complication for testing the Whorfian hypothesis. (shrink)
This article addresses two questions related to colour categorization, to wit, the question what a colour category is, and the question how we identify colour categories. We reject both the relativist and universalist answers to these questions. Instead, we suggest that colour categories can be identified with the help of the criterion of psychological saliency, which can be operationalized by means of consistency and consensus measures. We further argue that colour categories can be defined as well-structured entities that optimally partition (...) colour space. We provide some empirical support for this claim by presenting experimental results, which indicate that internal structure is a better predictor of colour categories than perceptual saliency. (shrink)
I analyze Quine’s later writings on analyticity from a linguistic point of view. In Word and Object Quine made room for a “strictly vegetarian” notion of analyticity. In later years, he developed this notion into two more precise notions, which I have coined “stimulus analyticity” and “behaviorist analyticity.” The latter characterization is in many respects similar to Carnap’s characterization of analyticity based on semantic rules and can be seamlessly incorporated in a Carnapian project of explication. I explain why Quine failed (...) to see the importance of analyticity thus defined. I argue that Quine’s views on language are deeply rooted in the American structuralist tradition in linguistics and that the resulting strict descriptivism and the strong emphasis on language change bring down the usefulness of analyticity. (shrink)
Color qualia inversion scenarios have played a key role in various philosophical debates. Most notably perhaps, they have figured in skeptical arguments for the fundamental unknowability of other persons’ color experiences. For these arguments to succeed, it must be assumed that a person's having inverted color qualia may go forever unnoticed. This assumption is now generally deemed to be implausible. The present paper defines a variant of color qualia inversion—termed ‘‘color qualia compression’’—and argues that the possibility of undetectable color qualia (...) compression is immune to the objections that have been levelled against color qualia inversion arguments, and that color qualia compression scenarios support full-blown skepticism regarding other people's color experiences. (shrink)
Traditionally, epistemologists have held that only truth-related factors matter in the question of whether a subject can be said to know a proposition. Various philosophers have recently departed from this doctrine by claiming that the answer to this question also depends on practical concerns. They take this move to be warranted by the fact that people’s knowledge attributions appear sensitive to contextual variation, in particular variation due to differing stakes. This paper proposes an alternative explanation of the aforementioned fact, one (...) that allows us to stick to the orthodoxy. The alternative applies the conceptual spaces approach to the concept of knowledge. With knowledge conceived of spatially, the variability in knowledge attributions follows from recent work on identity, according to which our standards for judging things (including concepts) to be identical are context-dependent. On the proposal to be made, it depends on what is at stake in a context whether it is worth distinguishing between knowing and being at least close to knowing. (shrink)
Rips et al. argue that the construction of math schemas roughly similar to the Dedekind/Peano axioms may be necessary for arriving at arithmetical skills. However, they neglect the neo-Fregean alternative axiomatization of arithmetic, based on Hume's principle. Frege arithmetic is arguably a more plausible start for a top-down approach in the psychological study of mathematical cognition than Peano arithmetic.
The volume assembles thirteen essays on logic, language and meaning, and is preceded by an introduction by Paul Gochet. Most of the papers were published between 1981 and 2000 in European journals such as Dialectica, Logique et Analyse, and Erkenntnis. The papers stand alone, yet throughout the book an overarching view of the relationship between pragmatics and semantics transpires clearly. Callaway defends a midway position between American analytic philosophy and American pragmatism. The result is a blend of Quine's scientific philosophy (...) and Dewey's social pragmatism. In addition other thinkers such as Frege, Peirce, Davidson, Putnam, Fodor and Haack are critically discussed. (shrink)
I want to analyse the Quine-Carnap discussion on analyticity with regard to logical, mathematical and set-theoretical statements. In recent years, the renewed interest in Carnap’s work has shed a new light on the analytic-synthetic debate. If one fully appreciates Carnap’s conventionalism, one sees that there was not a metaphysical debate on whether there is an analytic-synthetic distinction, but rather a controversy on the expedience of drawing such a distinction. However, on this view, there can be no longer a single analytic-synthetic (...) distinction, because several kinds of statements could be regarded as analytic (L-determinate). L-equivalence between extra-logical linguistic predicates has already been heavily debated. The recent consensus states that Quine’s rejection of this analytic-synthetic is pragmatically grounded in his linguistic behaviorism. However, Carnap’s logical frameworks also contain other kinds of statements, and it is worthwhile to compare both Quine and Carnap’s grounds for considering these statements as analytic or not analytic. First, I will discuss logical statements. I will argue that Quine draws a very sharp distinction between first order logic and set theory, which should be regarded as a (pragmatic) analytic-synthetic distinction (as Quine admits in an interview, see Theoria, 40, 1994, p. 199). In fact, Quine’s major worry is whether identity statements are analytic. Second, I will discuss mathematical statements. In Carnap’s Foundations of Logic and Mathematics, it is clear that mathematical statements are analytic. For Quine, all mathematical statements are reducible to set-theoretical statements. Third, I discuss the analyticity of set-theoretical statements. For Quine, the membership predicate should be regarded as an interpreted extra-logical predicate. Quine’s work in set theory and his later philosophy of set theory naturally lead to the view that set-theoretical statements cannot be analytic. A major complication for the Quine-Carnap comparison is that Carnap has no elaborate reflections on set theory, while the influence of set theory on Quine’s views can hardly be underestimated. I conclude with some lessons for the contemporary debate on analyticity. (shrink)
This paper traces the development of Quine's ontological ideas throughout his early logical work in the period before 1948. It shows that his ontological criterion critically depends on this work in logic. The use of quantifiers as logical primitives and the introduction of general variables in 1936, the search for adequate comprehension axioms, and problems with proper classes, all forced Quine to consider ontological questions. I also show that Quine's rejection of intensional entities goes back to his generalisation of Principia (...) Mathematica in 1932. (shrink)
In two papers in the mid-seventies, Quine has discussed an ontological deba-cle, the reduction of ontology to an ontology of pure sets only. This debacle, which weakened Quine’s interest in ontology, is the natural outcome of on-tological relativity, or, more precisely, the proxy-function argument. It is ex-plained how Quine unavoidably came to this conclusion. Moreover, it is ar-gued that the result is even more damaging for Quine’s philosophy than has hitherto been assumed. It is shown that in addition to an (...) ontological debacle, there is an ideological debacle, reducing the ideology of science to the ideology of set theory. The ideological debacle results from applying ex-tensional substitution of predicates within a scientific theory that is reinter-preted by means of proxy-functions to a theory with a set-theoretic ontology. Though Quine has recognized the possibility of an ideological debacle, his rebuttal is unconvincing. As a result, his tenet of extensionalism is under heavy pressure. (shrink)
Reflectance physicalism only provides a partial picture of the ontology of color. Byrne & Hilbert’ account is unsatisfactory because the replacement of reflectance functions by productance functions is ad hoc, unclear, and only leads to new problems. Furthermore, the effects of color contrast and differences in illumination are not really taken seriously: Too many “real” colors are tacitly dismissed as illusory, and this for arbitrary reasons. We claim that there cannot be an all-embracing ontology for color.
Contents: Introduction. NATURALIZED EPISTEMOLOGY. Ton DERKSEN: Naturalistic Epistemology, Murder and Suicide? But what about the Promises! Christopher HOOKWAY: Naturalism and Rationality. Mia GOSSELIN: Quine's Hypothetical Theory of Language Learning. A Comparison of Different Conceptual Schemes of Their Logic. THE NATURE OF PERCEPTUAL KNOWLEDGE. Jaap van BRAKEL: Quine and Innate Similarity Spaces. Dirk KOPPELBERG: Quine and Davidson on the Structure of Empirical Knowledge. Eva PICARDI: Empathy and Charity. ONTOLOGY. Sandra LAUGIER: Quine: Indeterminacy, ‘Robust Realism', and Truth. Roger VERGAUWEN: Quine and Putnam (...) on Conceptual Relativity and Reference: Theft or Honest Toil? Igor DOUVEN: Empiricist Semantics and Indeterminism of Reference. Lieven DECOCK: Domestic Ontology and Ideology. Paul GOCHET: Canonical Notation, Predication and Ontology. About the Authors. (shrink)
Contra Shepard we argue, first, that his presentation of a three-dimensional representational (psychological or phenomenal) colour space is at odds with many results in colour science, and, second, that there is insufficient evidence for Shepard's stronger claim that the three-dimensionality of colour perception has resulted from natural selection, moulded by the particulars of the solar spectrum and its variations. [Shepard].
The development and changes in Quine's ideas on universais are analysed, and especially the interplay of the notions of attribute, set and predicate is highlighted. In a first logico-mathematical part it is shown how Quine banned attributes as a result of extensionalism, and how set-theoretic solutions for Russell's paradox disturbed the easy view of each predicate determining a class. Quine even tried to formulate nominalistic theories without universais (sets). It is further shown how linguistic considerations played a role in Quine's (...) ideas on universais. The role of predicates is scrutinised, and it is shown how they are torn between logical and linguistic demands. It is suggested that the role of attributes has been taken over by predicates. This semantic role of predicates is quite unstable. I conclude with the suggestion that Quine should separate set theory and linguistics more radically. (shrink)