I wish to present a proof that vagueness is impossible. Of course, vagueness is possible; and so there must be something wrong with the proof. But it is far from clear where the error lies and, indeed, all of the assumptions upon which the proof depends are ones that have commonly been accepted. This suggests that we may have to radically alter our current conception of vagueness if we are to make proper sense of what it is.

It is generally supposed that borderline cases account for the tolerance of vague terms, yet cannot themselves be sharply bounded, leading to infinite levels of higher order vagueness. This higher order vagueness subverts any formal effort to make language precise. However, it is possible to show that tolerance must diminish at higher orders. The attempt to derive it from indiscriminability founders on a simple empirical test, and we learn instead that there is no limit to how small higher order tolerance (...) may become. That means there is no limit to how precisely we may draw the boundaries of borderline cases, thus forestalling any requirement for higher order vagueness. (shrink)

Varzi has recently joined a thread of arguments originating in an attempt by Sorensen (1985) to demonstrate that the predicate ‘vague’ is itself vague. Sorensen's conclusion is significant in that it has provided the basis for a subsequent effort by Hyde (1994) to defend the legitimacy of supposing higher-order vagueness. Varzi's contribution to this debate is twofold. First, contra earlier criticism by Deas (1989), he claims that Sorensen's result is sound so far as it goes. Second, he argues that despite (...) this it cannot be used as Hyde wishes on pain of circularity. I am not interested in the latter argument—it is examined in Hyde (2003)—but rather wish to defend and elaborate Deas's criticism of Sorensen against Varzi's repudiation. (shrink)

In §2-4, I survey three extant ways of making sense of indeterminate truth and find each of them wanting. All the later sections of the paper are concerned with showing that the most promising way of making sense of indeterminate truth is via either a theory of truthmaker gaps or via a theory of truthmaking gaps. The first intimations of a truthmaker–truthmaking gap theory of indeterminacy are to be found in Quine (1981). In §5, we see how Quine proposes to (...) solve Unger’s problem of the many via positing the possibility of groundless truth. In §6, I elaborate the truthmaker gap model of indeterminacy first sketched by Sorensen (2001, ch.11) and use it to give a reductive analysis of indeterminate truth. In §7, I briefly assess what kind of formal framework can best express the possibility of truthmaker gaps. In §8, I contrast what I dub ‘the ordinary conception of worldly indeterminacy’ with Williamson’s conception of worldly indeterminacy. In §9, I show how one can distinguish linguistic from worldly indeterminacy on a truthmaker gap conception. In §10, I briefly sketch the relationship between truthmaker gaps and ignorance. In §11, I assess whether a truthmaker gap conception of vagueness is really just a form of epistemicism. In §12, I propose that truthmaker gaps can yield a plausible model of (semantic) presupposition failure. In §13, in response to the worry that a truthmaker gap conception of indeterminacy is both parochial and controversial—since it commits us to an implausibly strong theory of truthmaking—I set forth a truthmaking gap conception of indeterminacy. In §14, I answer the worry that groundless truths, of whatever species, are just unacceptably queer. A key part of this answer is that a truthmaker–truthmaking gap model of indeterminacy turns out to be considerably less queer than any model of indeterminacy which gives up on Tarski’s T-schema for truth (and cognate schemas). (shrink)

This extended abstract summarises some of the basic points of AI ethics and policy as they present themselves now. We explain the notion of AI, the main ethical issues in AI and the main policy aims and means.

A discussion on this so debatable and debated concept, Higher Order Vagueness. After going through the issues that make Higher Order Vagueness an object of scientific attention, we conclude that vagueness is undesirable in logical systems but desirable in language, and the Semiotics Universe splits into three other universes inside of the universe of the Computer Science Systems. We create a new way of addressing problems with sigmatoids, and define vagueness in an almost mathematical fashion.

Sorensen has argued that one can exploit the vagueness of an ordinary predicate like ‘small’ to induce a sort of vagueness in ‘vague’, by constructing a series of predicates of the form ‘n-small’, where x is n- small if and only if x is small or x n. The resulting ‘Sorensen’ed’ predicates present a Sorites case for ‘vague’ ; hence the vagueness of ‘vague’. Hyde argues that this demonstrates that all vague predicates are higher-order vague. Others doubt whether Sorensen’s series (...) really delivers such a result, claiming Hyde’s argument to be either: unsound, because it misidentifies the true source of vagueness in Sorensen’s Sorites ; invalid, because it fails to generalize to all vague predicates ; or circular, because it presupposes the very thing it tries to prove, namely, higher-order vagueness. This paper contributes to the Sorensen-Hyde vs. Tye-Deas-Hull-Varzi debate by clarifying the relations between vague vagueness and higher-order vagueness. I show how claims of higher-order vagueness are derivable from claims of vague vagueness. This is the missing piece needed to complete Hyde’s argument and overcome the objections presented by Deas, Hull, Tye, and Varzi. I then show how Sorensen’s considerations, once properly generalized, pose more far-reaching consequences about the vagueness of ‘vague’ than either defenders or critics of Hyde’s argument have appreciated. (shrink)

What sort of logic do we get if we adopt a supervaluational semantics for vagueness? As it turns out, the answer depends crucially on how the standard notion of validity as truth preservation is recasted. There are several ways of doing that within a supervaluational framework, the main alternative being between “global” construals (e.g., an argument is valid iff it preserves truth-under-all-precisifications) and “local” construals (an argument is valid iff, under all precisifications, it preserves truth). The former alternative is by (...) far more popular, but I argue in favor of the latter, for (i) it does not suffer from a number of serious objections, and (ii) it makes it possible to restore global validity as a defined notion. (shrink)

Die gegenwärtig unter dem Titel ›Realismus‹ geführten Debatten in der Philosophie befinden sich nach allgemeiner Ansicht in einem Zustand größter Verwirrung, so daß es nützlich erscheint, ein wenig Ordnung in die theoretischen Optionen zu bringen bevor man für die eine oder andere Auffassung Partei ergreift. In der vorliegenden Arbeit wird dafür argumentiert, daß sich ein systematisch zusammenhängendes Zentrum dieser Debatten mit Hilfe des Begriffes der Referenz ordnen läßt. Nach der Analyse einiger klassischer Positionen soll ein Rahmen erstellt werden, innerhalb dessen (...) die Positionen eingeordnet und die zentralen Probleme fruchtbar diskutiert werden können. Zu diesem Zwecke ist es erforderlich, für die Einordnung der Positionen theoretische Kriterien zu benennen, die sich an den Problemen orientieren von denen hier argumentiert wird, das sie zentral seien. Sehr knapp ausgedrückt wird hier die Auffassung vertreten, Realismus sei als metaphysische These aufzufassen, welche eine von menschlichen epistemischen und semantischen Möglichkeiten unabhängige Existenz behauptet; in den gegenwärtigen Debatten typischerweise die Existenz einer Art von Dingen, nicht die eines individuellen Gegenstandes. Diese metaphysische These wird jedoch in der gegenwärtigen Debatte mit semantischen Argumenten untermauert, bzw. angegriffen und jene semantischen Argumente wiederum verwenden epistemische Erwägungen – die Frage betreffend, was man wissen kann und was nicht. Der Beginn der gegenwärtigen Realismusdebatten mit der soeben skizzierten zentralen Stellung semantischer Argumente ist, der hier vertretenen Auffassung zufolge, die Kritik am traditionellen Fregeschen Referenzbegriff durch Kripke und den frühen Putnam um 1970 (Kap. 2). Aus dieser neu zu bewertenden Kritik und der von den Autoren daraus entwickelten externalistischen realistischen Semantik für Artausdrücke läßt sich das erste Kriterium für eine Position in einer Realismusdebatte ableiten und klären (Kap. 3): Hält man die fragliche Art für eine natürliche Art und meint also, sie habe ihren ›Zusammenhalt‹ von Natur aus? Wenn ja, dann ist die fragliche Position eine realistische (das Kriterium ist dank des engen Zusammenhangs von Realismus und Externalismus sowohl hinreichend als auch notwendig). Hält man die Art nicht für eine natürliche Art, ist man Antirealist. Damit geht jeweils not- wendig eine bestimmte Semantik für den auf die Art referierenden Ausdruck einher. Es zeigt sich zugleich, daß es zwei Varianten des Realismus zu unterscheiden gilt, die hier als klassischer bzw. als moderater Realismus bezeichnet werden. Im folgenden (Kap. 4.1) wird argumentiert, daß der Begriff der Wahrheit nicht eigentlich der zentrale Punkt in den in Frage stehenden Realismusdebatten sein sollte, wie vielfach behauptet wurde, sondern seine Brisanz vielmehr aus zugrundeliegenden semantischen Fragen gewinnt die also in der weiteren Aufdeckung der Kriterien die zentrale Rolle spielen müssen. In der Analyse der Kritik an der in Kap. 3 entwickelten Position des ›klassischen Realismus‹ läßt sich ein zweites unterscheidendes Kriterium für Positionen in Realismusdebatten entwickeln: begriffliche Relativität. Nach der Ablehnung von Putnams Auffassungen zu diesem Thema, werden zwei Varianten vorgeschlagen, starke und schwache begriffliche Relativität (Kap. 4.2). Die Anwendung dieses Merkmals zwingt, so wird argumentiert, in einigen Fällen zu einer Kombination einer realistischen Auffassung von Arten als natürliche mit begrifflicher Relativität. Diese mittlere Position zwischen klassischem Realismus und Antirealismus wird als »moderater Realismus« bezeichnet. Der im ersten Kriterium verwendete Begriff der natürlichen Art, und damit die Optionen in den Debatten, wird schließlich mittels einer Dis- kussion des Phänomens der Vagheit noch weiter verdeutlicht (Kap. 4.3). Ab- schließend werden die drei Optionen zusammenfassend dargestellt und ein Versuch unternommen, ihre Fruchtbarkeit für diverse Realismusdebatten anzudeuten. (shrink)

A rejoinder to G. Hull’s reply to my Mind 2003. Hull argues that Sorensen’s purported proof that ‘vague’ is vague--which I defended against certain familiar objections--fails. He offers three reasons: (i) the vagueness exhibited by Sorensen’s sorites is just the vagueness of ‘small’; (ii) the general assumption underlying the proof, to the effect that predicates which possess borderline cases are vague, is mistaken; (iii) the conclusion of the proof is unacceptable, for it is possible to create Sorensen-type sorites even for (...) predicates that are paradigmatically precise. I argue that each of these points involves fallacious reasoning. (shrink)

In this paper I develop a framework for understanding ontic vagueness. The project of the paper is two-fold. I first outline a definitional account of ontic vagueness – one that I think is an improvement on previous attempts because it remains neutral on other, independent metaphysical issues. I then develop one potential manifestation of that basic definitional structure. This is a more robust (and much less neutral) account which gives a fully classical explication of ontic vagueness via modal concepts. The (...) overarching aim is to systematically investigate the puzzling question of what exactly it could be for the world itself to be vague. (shrink)

In this paper I present two arguments against the thesis that we experience qualia. I argue that if we experienced qualia then these qualia would have to be essentially vague entities. And I then offer two arguments, one a reworking of Gareth Evans' argument against the possibility of vague objects, the other a reworking of the Sorites argument, to show that no such essentially vague entities can exist. I consider various objections but argue that ultimately they all fail. In particular (...) I claim that the stock responses to the Sorites argument fail against my reworking of the argument because they require us to make a distinction between a determinate reality and how that reality appears to us, whereas in the case of qualia we can make no such distinction. I conclude that there can be no such things as qualia. (shrink)

In this book, I present the results of an investigation which began with an extended stay at Oxford's Balliol College during the first half of 1995. My visit to Oxford was made possible by a grant from the Spanish Ministerio de Educaci6n y Ciencia. My sincere thanks go to Joseph Raz who served as my supervisor in Oxford. For several points of the present study, conversations with Timothy Endicott in Oxford were also of great help. The book is part of (...) a larger project of investigation, directed by Albert Calsami glia, which is a joint effort of a group of legal philosophers from the Universitat Pom peu Fabra and the Universitat de Girona, and which also receives financial support from the Spanish Ministerio de Educaci6n y Ciencia. An earlier version of the manuscript was presented in June 1996 to the selection committee for a tenured professorship in Legal Philosophy at the Universitat de Girona. The members of the committee were Francisco Laporta, Albert Calsamiglia, Gregorio Peces-Barba, Camilo J. Cela Conde, and Francesca Puigpelat. I am grateful to all of them for their comments, which have been extremely useful in preparing the final ver sion of this book. (shrink)

This book, provides a critical approach to all major logical paradoxes: from ancient to contemporary ones. There are four key aims of the book: 1. Providing systematic and historical survey of different approaches – solutions of the most prominent paradoxes discussed in the logical and philosophical literature. 2. Introducing original solutions of major paradoxes like: Liar paradox, Protagoras paradox, an unexpected examination paradox, stone paradox, crocodile, Newcomb paradox. 3. Explaining the far-reaching significance of paradoxes of vagueness and change for philosophy (...) and ontology. 4. Proposing a novel, well justified and, as it seems, natural classification of paradoxes. (shrink)

Philosophy Compass 2: 896-909. (Link to Philosophy Compass.).

R. Sorensen’s argument to the effect that ’vague’ is a vague predicate has been used by D. Hyde to infer that vague predicates suffer from higher-order vagueness. M. Tye has objected (convincingly) that this is too strong: all that follows from Sorensen’s result is that there are some border border cases, but not necessarily border border cases of every vague predicate. I argue that this is still too strong: Sorensen’s proof presupposes the existence of border border cases, hence cannot be (...) used to establish that fact on pain of circularity. (shrink)