O fenômeno da vagueza é quase onipresente na linguagem natural. Por um lado, a vagueza abrange variadas categorias lógicas, incluindo predicados, termos singulares e quantificadores. Por outro, é argumentável que a maioria das expressões em cada uma destas categorias, principalmente termos singulares e predicados, é vaga. Isto não seria um problema, não tivesse o fenômeno da vagueza relacionado ao paradoxo sorites, que supostamente mostra a incoerência destas expressões. O Supervalorativismo fornece uma explicação do fenômeno, acompanhado de uma solução (...) do paradoxo, que é interessante por pelo menos duas razões. Primeiro, é argumentável que esta teoria é a que melhor acomoda certa imagem intuitiva da vagueza, conhecida como indecisão semântica. Segundo, ela é relativamente conservadora com respeito à lógica clássica. Ao contrário de algumas rivais, como a Teoria Trivalente e o Gradualismo, o Supervalorativismo nos permite manter tanto o terceiro excluído como a não contradição. A despeito de suas aparentes vantagens, no entanto, a teoria carrega alguns sérios problemas. Com foco na categoria dos predicados vagos, meu objetivo neste artigo é mostrar que o Supervalorativismo falha em satisfazer pelo menos um de três critérios de adequação para uma teoria ideal da vagueza: o critério da precisão. O artigo é dividido em quatro seções. Na primeira, apresento o paradoxo sorites e três critérios de adequação para uma teoria ideal da vagueza: o critério do sorites, o critério da coerência e o critério da precisão. Na segunda e terceira, apresento o Supervalorativismo e sua solução para o paradoxo sorites. Por fim, argumento que, mesmo que a teoria satisfaça os dois primeiros critérios de adequação, ela certamente não satisfaz o terceiro. (shrink)

Há pelo menos duas coisas que tornam o fenômeno da vagueza interessante. Primeiro, a vagueza está espalhada por toda a linguagem natural. Uma parte significativa das expressões de nossa linguagem são vagas e podemos encontrar a vagueza em expressões de diferentes categorias lógicas, como termos singulares, predicados e quantificadores. Por razões de simplicidade, contudo, ao longo deste artigo considero apenas o caso dos predicados vagos. Segundo, o fenômeno da vagueza está por trás de um difícil paradoxo, conhecido como (...) class='Hi'>Paradoxo Sorites. Atualmente, há muitas tentativas de explicar esse fenômeno e resolver o Sorites, sendo uma delas a Teoria Trivalente da Vagueza. Essa teoria é interessante não apenas porque fornece uma explicação elegante da vagueza, acompanhada de uma solução engenhosa para o paradoxo em questão, mas também porque serve de base para a compreensão de outras teorias clássicas da vagueza. Tanto o Gradualismo como o Supervalorativismo, por exemplo, incorporam parte significativa de suas ideias centrais. A despeito disso, existem alguns sérios obstáculos para a Teoria Trivalente. Acredito que o principal deles é que ela falha em satisfazer pelo menos um dos três critérios de adequação para uma teoria ideal da vagueza: o critério da precisão. Meu objetivo é apresentar essa teoria e mostrar como essa dificuldade surge para ela. (shrink)

Este artigo é uma introdução crítica ao problema da vagueza. Não vou explicar ou avaliar as teorias da vagueza aqui. Meu objetivo é introduzir e discutir o próprio problema, com o intuito de alcançar uma formulação clara do mesmo. Minha formulação tornará claro quais condições uma teoria ideal da vagueza deveria satisfazer, assim como os principais obstáculos para desenvolver teorias que satisfaçam estas condições.

A sorites argument is a symptom of the vagueness of the predicate with which it is constructed. A vague predicate admits of at least one dimension of variation (and typically more than one) in its intended range along which we are at a loss when to say the predicate ceases to apply, though we start out confident that it does. It is this feature of them that the sorites arguments exploit. Exactly how is part of the subject of (...) this paper. The majority of philosophers writing on vagueness take it to be a kind of semantic phenomenon. If we are right, they are correct in this assumption, which is surely the default position, but they have not so far provided a satisfactory account of the implications of this or a satisfactory diagnosis of the sorites arguments. Other philosophers have urged more exotic responses, which range from the view that the fault lies not in our language, but in the world, which they propose to be populated with vague objects which our semantics precisely reflects, to the view that the world and language are both perfectly in order, but that the fault lies with our knowledge of the properties of the words we use (epistemicism). In contrast to the exotica to which some philosophers have found themselves driven in an attempt to respond to the sorites puzzles, we undertake a defense of the commonsense view that vague terms are semantically vague. Our strategy is to take fresh look at the phenomenon of vagueness. Rather than attempting to adjudicate between different extant theories, we begin with certain pre-theoretic intuitions about vague terms, and a default position on classical logic. The aim is to see whether (i) a natural story can be told which will explain the vagueness phenomenon and the puzzling nature of soritical arguments, and, in the course of this, to see whether (ii) there arises any compelling pressure to give up the natural stance. We conclude that there is a simple and natural story to be told, and we tell it, and that there is no good reason to abandon our intuitively compelling starting point. The importance of the strategy lies in its dialectical structure. Not all positions on vagueness are on a par. Some are so incredible that even their defenders think of them as positions of last resort, positions to which we must be driven by the power of philosophical argument. We aim to show that there is no pressure to adopt these incredible positions, obviating the need to respond to them directly. If we are right, semantic vagueness is neither surprising, nor threatening. It provides no reason to suppose that the logic of natural languages is not classical or to give up any independently plausible principle of bivalence. Properly understood, it provides us with a satisfying diagnosis of the sorites argumentation. It would be rash to claim to have any completely novel view about a topic so well worked as vagueness. But we believe that the subject, though ancient, still retains its power to inform and challenge us. In particular, we will argue that taking seriously the central phenomenon of predicate vagueness—the “boundarylessness” of vague predicates—on the commonsense assumption that vagueness is semantic, leads ineluctably to the view that no sentences containing vague expressions (henceforth ‘vague sentences’) are truth-evaluable. This runs counter to much of the literature on vagueness, which commonly assumes that, though some applications of vague predicates to objects fail to be truth-evaluable, in clear positive and negative cases vague sentences are unproblematically true or false. It is clarity on this, and related points, that removes the puzzles associated with vagueness, and helps us to a satisfying diagnosis of why the sorites arguments both seem compelling and yet so obviously a bit of trickery. We give a proof that semantically vague predicates neither apply nor fail-to-apply to anything, and that consequently it is a mistake to diagnose sorites arguments, as is commonly done, by attempting to locate in them a false premise. Sorites arguments are not sound, but not unsound either. We offer an explanation of their appeal, and defend our position against a variety of worries that might arise about it. The plan of the paper is as follows. We first introduce an important distinction in terms of which we characterize what has gone wrong with vague predicates. We characterize what we believe to be our natural starting point in thinking about the phenomenon of vagueness, from which only a powerful argument should move us, and then trace out the consequences of accepting this starting point. We consider the charge that among the consequences of semantic vagueness are that we must give up classical logic and the principle of bivalence, which has figured prominently in arguments for epistemicism. We argue there are no such consequences of our view: neither the view that the logic of natural languages is classical, nor any plausible principle of bivalence, need be given up. Next, we offer a diagnosis of what has gone wrong in sorites arguments on the basis of our account. We then present an argument to show that our account must be accepted on pain of embracing (in one way or another) the epistemic view of “vagueness”, i.e., of denying that there are any semantically vague terms at all. Next, we discuss some worries that may arise about the intelligibility of our linguistic practices if our account is correct. We argue none of these worries should force us from our intuitive starting point. Finally, we cast a quick glance at other forms of semantic incompleteness. (shrink)

Ethics in the tradition of Derek Parfit’s Reasons and Persons is riddled with sorites-like arguments, which lead us by what seem innocent steps to seemingly false conclusions. Take, for example, spectrum arguments for the Repugnant Conclusion that appeal to slight differences in quality of life. Several authors have taken the view that, since spectrum arguments are structurally analogous to sorites arguments, the correct response to spectrum arguments is structurally analogous to the correct response to sorites arguments. This (...) sorites analogy is here argued against. There are potential structural disanalogies between spectrum arguments and sorites arguments. But even if these arguments are relevantly structurally analogous, they differ in their content in ways that show the sorites analogy to be implausible. Two content-based disanalogies are here explored—one is inspired by Parfit’s work on reductionism, and the other involves hypersensitivity. The chapter concludes with a methodological lesson. (shrink)

Is there an interesting relation between the Preface paradox and the Sorites paradox that might be used to illuminate either or both of those paradoxes and the phenomena of rationality and vagueness with which they, respectively, are bound up? In particular, if we consider the analogy alongside a familiar response to the Preface Paradox that employs degrees of belief, does this give any support to the thought that we should adopt some kind of degree-theoretic treatment of vagueness and the (...) sorites? This chapter argues that it does not; indeed exploring the disanalogies contributes to a case against such a treatment of vagueness more generally. Among other views, it considers Edgington’s account of vagueness that employs a probabilistic structure of “verities”. It then contends that appeal to the framework of supervaluationism yields a better guide to reasoning in vague language than the degree-theoretic treatment can sustain. (shrink)

What I hope to show here is that the costs of taking sorites arguments seriously, in particular the costs with respect to hopes for precise replacement are significantly greater than proponents of sorites arguments have estimated.

The first part of the chapter surveys some of the main ways in which the Sorites Paradox has figured in arguments in practical philosophy in recent decades, with special attention to arguments where the paradox is used as a basis for criticism. Not coincidentally, the relevant arguments all involve the transitivity of value in some way. The second part of the chapter is more probative, focusing on two main themes. First, I further address the relationship between the Sorites (...) Paradox and the main arguments discussed in the first part, by elucidating in what sense they rely on (something like) tolerance principles. Second, I briefly discuss the prospect of rejecting the respective principles, aiming to show that we can do so for some of the arguments but not for others. The reason is that in the latter cases the principles do not function as independent premises in the reasoning but, rather, follow from certain fundamental features of the relevant scenarios. I also argue that not even adopting what is arguably the most radical way to block the Sorites Paradox – that of weakening the consequence relation – suffices to invalidate these arguments. (shrink)

The presentation of the “dual picture of vagueness” in my earlier work is supplemented here with a number of additional considerations. I emphasize how the picture lends itself naturally to treatments of the contribution of a typical degree adjective to propositional content and to truth conditions. A number of reasonable refinements of the picture are presented, especially concerning occasions of use of a degree adjective in which a class containing a sorites series is somehow involved in content fixing, but (...) in such a way that an extension ultimately gets fixed for the predicate. I also develop the observation that standard theories of the logical and semantic paradoxes rely on the idea that the content-fixing mechanisms for the paradoxical expressions work well in general but fail in some localized cases, and that while standard theories of the sorites paradox are clearly not based on this idea at all, the dual theory is fully based on the idea. Next, I offer a few remarks on some recent theories of vagueness and the sorites that are broadly in the spirit of the dual picture, emphasizing the aspects where the latter compares favorably against those recent theories. Finally, the question whether the dual theory is statable with truth according to the theory itself is considered in more detail than in my earlier presentation. (shrink)

On some accounts of vagueness, predicates like “is a heap” are tolerant. That is, their correct application tolerates sufficiently small changes in the objects to which they are applied. Of course, such views face the sorites paradox, and various solutions have been proposed. One proposed solution involves banning repeated appeals to tolerance, while affirming tolerance in any individual case. In effect, this solution rejects the reasoning of the sorites argument. This paper discusses a thorny problem afflicting this approach (...) to vagueness. In particular, it is shown that, on the foregoing view, whether an object is a heap will sometimes depend on factors extrinsic to that object, such as whether its components came from other heaps. More generally, the paper raises the issue of how to count heaps in a tolerance-friendly framework. (shrink)

This paper responds to Theron Pummer’s distinction between Sorites arguments and repugnant conclusion arguments by presenting a Sorites overpopulation argument. Also I present a Sorites argument in favour of myths of genius.

Neutralism is the broad view that philosophical progress can take place when (and sometimes only when) a thoroughly neutral, non-specific theory, treatment, or methodology is adopted. The broad goal here is to articulate a distinct, specific kind of sorites paradox (The Observational Sorites Paradox) and show that it can be effectively treated via Neutralism.

ABSTRACT: This paper offers a generic revenge-proof solution to the Sorites paradox that is compatible with several philosophical approaches to vagueness, including epistemicism, supervaluationism, psychological contextualism and intuitionism. The solution is traditional in that it rejects the Sorites conditional and proposes a modally expressed weakened conditional instead. The modalities are defined by the first-order logic QS4M+FIN. (This logic is a modal companion to the intermediate logic QH+KF, which places the solution between intuitionistic and classical logic.) Borderlineness is introduced (...) modally as usual. The solution is innovative in that its modal system brings out the semi-determinability of vagueness. Whether something is borderline and whether a predicate is vague or precise is only semi-determinable: higher-order vagueness is columnar. Finally, the solution is based entirely on two assumptions. (1) It rejects the Sorites conditional. (2) It maintains that if one specifies borderlineness in terms of the ‒suitably interpreted‒ modal logic QS4M+FIN, then one can explain why the Sorites appears paradoxical. From (1)+(2) it results that one can tell neither where exactly in a Sorites series the borderline zone starts and ends nor what its extension is. Accordingly, the solution is also called agnostic. (shrink)

Problems for 'precise replacements' as a way out of sorites paradoxes.

The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to (...) the other, each intermediate stage constituting an overlap in certain proportion of both contraries. Hence, degrees in the possession of a property give rise to simple contradictions. The reason why I have chosen those two questions is that they provide the main philosophical motivation for a particular brand of an infinite valued and paraconsistent logic. I will claim that Classical logic (CL) is not adequate to handle fuzzy situations, and, being deficient, is in need of being expanded to make room for degrees of truth and weak contradictions. One can hardly deny the importance of the debate, since what is ultimately at stake is what the limits of truth, rationality, intelligibility and possibility are. The main disciplines within which the research moves are the philosophy of language, philosophy of logic, and ontology. (shrink)

Vagueness does not necessarily come in with vague predicates, nor need it be expressed by them , but undoubtedly 'vague predicates' are traditionally in the focus of main stream discussions of vagueness. In her current modal logic presentation and discussion of the Sorites paradox Susanne Bobzien[1] lists among the properties of a Sorites series a rather weak modal tolerance principle governing the 'grey zone' containing the borderline cases of the Sorites series, which later proves crucial for her (...) solution of the Sorites paradox by use of epistemic interpreted modal operators in 1st order modal logic. We suggest (for different research interest) instead a non-modal description of the switch in the grey zone (respecting tolerance), by resort to similarity sequences, thus getting tangent to two other areas of research in the field. Let's say -any way- the Sorites paradox vanishes, the Sorites series does not. (shrink)

When you and I seriously argue over whether a man of seventy is old enough to count as an "old man", it seems that we are appealing neither to our own separate standards of oldness nor to a common standard that is already fixed in the language. Instead, it seems that both of us implicitly invoke an ideal, shared standard that has yet to be agreed upon: the place where we ought to draw the line. As with other normative standards, (...) it is hard to know whether such borderlines exist prior to our coming to agree on where they are. But epistemicists plausibly argue that they must exist whether we ever agree on them or not, as this provides the only logically acceptable response to the sorites paradox. This paper argues that such boundaries do typically exist as hypothetical ideals, but not as determinate features of the present actual world. There is in fact no general solution to the paradox, but attention to practice in resolving vague disagreements shows that its instances can be dealt with separately, as they arise, in many reasonable ways. (shrink)

Resumo Embora controversa, o contextualismo epistêmico alega oferecer a melhor explicação para alguns fenômenos analisados em epistemologia contemporânea, por exemplo: alega responder ou explicar o apelo de certos paradoxos e, ao mesmo tempo, manter a verdade de nossas alegações ordinárias de conhecimento. Conforme alegado por contextualistas, a vantagem de sua teoria ao explicar o apelo de certos paradoxos reside no fato de que nenhum princípio lógico precisa ser rejeitado. O paradoxo do prefácio – que consiste na aparente incoerência lógica (...) que ocorre quando o autor de um livro declara em seu prefácio que, apesar de acreditar que é altamente provável que tudo o que o livro afirma seja verdadeiro, também é altamente provável que o livro contenha, pelo menos, algum erro – parece não ter sido explorado o suficiente pelos contextualistas. Portanto, pretendemos sugerir uma versão do paradoxo do prefácio apresentando um argumento análogo ao argumento que os contextualistas costumam apresentar para explicar o paradoxo cético. Desta maneira, pretendemos oferecer, por meio de uma análise contextualista, uma explicação para o paradoxo do prefácio. Se a resposta contextualista é ou não adequada para esse paradoxo, isso será questão de disputa e não nos caberá discuti-la aqui. Meu objetivo é apenas sugerir que uma análise contextualista semelhante à aplicada ao paradoxo cético pode ser construída para explicar o paradoxo do prefácio. Palavras-chave: Contextualismo; Paradoxo do prefácio; Paradoxo cético. (shrink)

É comumente aceito, atualmente, que Aristóteles não teria enfrentado ou tentado seriamente resolver o famoso paradoxo do mentiroso, embora ele tenha sido formulado por Eubúlides de Mileto, membro da escola megárica e rival filosófico de Aristóteles. No máximo, assim reza a visão tradicional, ele parece apenas fazer uma menção desse paradoxo nas Refutações sofísticas, Capítulo 25, talvez esboçando a sua solução. O meu intento, no presente artigo, é desafiar essa opinião geral mostrando que o Estagirita fornece uma explicação (...) implícita para duas versões do paradoxo do mentiroso, a saber, a versão autorreferencial (que pode ser apresentada pela declaração: “esta declaração é falsa”), e a versão anafórica (que pode ser apresentada por meio de duas declarações mutuamente referentes como estas: “a próxima declaração é verdadeira” e “a declaração anterior é falsa”). A minha alegação é que a solução aristotélica para essas duas versões do paradoxo encontra-se no núcleo de sua refutação de duas teses, as quais denominei como tese da synalethia (que defende que toda declaração é verdadeira) e como tese da sympseudia (que defende que toda declaração é falsa). Tal refutação é realizada no oitavo capítulo do quarto Livro da Metafísica, um texto até agora subestimado pelos intérpretes modernos, mesmo sendo a parte final de um dos mais importantes escritos de Aristóteles. A solução aristotélica, assim defendo, é levada a cabo por meio dos seguintes princípios: (i) toda declaração é sempre precedida por um operador de verdade da forma ‘é verdade que...’, ou seja, toda declaração, qualquer que seja o que ela possa declarar a mais, primariamente assevera a sua própria verdade; e, em conformidade com o princípio anterior, (ii) toda declaração que assevera a sua própria falsidade ou acarreta a verdade de sua contraditória é necessariamente falsa. Através desses princípios, a refutação de Aristóteles da synalethia e da sympseudia é bem-sucedida. Mostrarei que obtemos uma boa solução para as versões do mentiroso acima mencionadas (e implicitamente presentes nas posições refutadas), apenas aplicando esses mesmos princípios a elas. Esse tipo de solução ao mentiroso tanto quanto para as teses antes citadas é muito parecido com aquele explicitamente encontrado nas obras de diversos filósofos, a saber, Guilherme de Sherwood, Tomás Bradwardine, João Buridano, Alberto da Saxônia, Paulo Venetus, Charles S. Peirce e Arthur Prior. Assim, também defendo que essa linhagem tem as suas raízes na solução de Aristóteles. (shrink)

The semantic paradoxes are a family of arguments – including the liar paradox, Curry’s paradox, Grelling’s paradox of heterologicality, Richard’s and Berry’s paradoxes of definability, and others – which have two things in common: first, they make an essential use of such semantic concepts as those of truth, satisfaction, reference, definition, etc.; second, they seem to be very good arguments until we see that their conclusions are contradictory or absurd. These arguments raise serious doubts concerning the coherence of the concepts (...) involved. This article will offer an introduction to some of the main theories that have been proposed to solve the paradoxes and avert those doubts. Included is also a brief history of the semantic paradoxes from Eubulides to Tarski and Curry. (shrink)

Noniterative approaches to the sorites paradox accept single steps of soritical reasoning, but deny that these can be combined into valid chains of soritical reasoning. The distributed sorites is a puzzle designed to undermine noniterative approaches to the sorites paradox, by deriving an inconsistent conclusion using only single steps, but not chains, of soritical reasoning. This paper shows how a dialetheist version of the noniterative approach, the strict-tolerant approach, also solves the distributed sorites paradox, at no (...) further cost, by accepting the inconsistent conclusion. (shrink)

Gender is both indeterminate and multifaceted: many individuals do not fit neatly into accepted gender categories, and a vast number of characteristics are relevant to determining a person's gender. This article demonstrates how these two features, taken together, enable gender to be modeled as a multidimensional sorites paradox. After discussing the diverse terminology used to describe gender, I extend Helen Daly's research into sex classifications in the Olympics and show how varying testosterone levels can be represented using a (...) class='Hi'>sorites argument. The most appropriate way of addressing the paradox that results, I propose, is to employ fuzzy logic. I then move beyond physiological characteristics and consider how gender portrayals in reality television shows align with Judith Butler's notion of performativity, thereby revealing gender to be composed of numerous criteria. Following this, I explore how various elements of gender can each be modeled as individual sorites paradoxes such that the overall concept forms a multidimensional paradox. Resolving this dilemma through fuzzy logic provides a novel framework for interpreting gender membership. (shrink)

Definida como beleza lógica e forma do paradoxo, a ironia romântica de Friedrich Schlegel (1772-1829) assimila a antiga ironia socrática e a reinterpreta, inserindo-a como elemento central de sua teorização crítico-literária. O presente artigo analisa a ironia romântica, buscando situar sua alteração e abrangência no final do século XVIII, quando o conceito passa a significar metacrítica, reflexão filosófica, ruptura ficcional, distância estética e forma de exposição da arte literária. Defined as logical beauty and form of paradox, Friedrich Schlegel's (1772-1829) (...) romantic irony incorporates ancient Socratic irony and reinterprets it, inserting it as a nuclear element of his theorization on literary criticism. The current paper analyses the concept of romantic irony seeking to situate its alterations at the end of 18th century, when it changed its meaning for metacritics, philosophical reflexion, fictional rupture, aesthetical distance and form of art exposition. (shrink)

As Leibniz points out in the Méditation sur la notion commune de la jus tice, justice—defined as charity of the wise and universal benevolence—belongs “to the necessary and eternal truths about the nature of things, as numbers and proportions.” According to the interpretation of Patrick Riley, from this perspective the two manuscripts usually regarded as belonging to the Méditation should be seen as complementary parts of a unitary Platonizing work. According to Riley, the manuscript that now constitutes the first part (...) of the Méditation is concerned with definitions of ethical concepts viewed as “quasi-mathematical, demonstrable ‘eternal verities’”, whereas the manuscript that now constitutes the second part of the Méditation is concerned “with Platonic ‘ascent’, in the manner of Phaedrus and Symposium,” which recommends the transition from mere negative forbearance from harm to doing positive good. In formulating these claims, Riley uses scare quotes to indicate that he uses the terms “eternal verities” and “ascent” in an unusual way that diverges from the views of the historical Plato. According to his interpretation, Leibniz’s modifications of Platonism are restricted to peripheral parts such as the doctrine of the pre-existence of the soul or Pythagorean components such as the doctrine of metempsychosis. Therefore, Riley claims that when Leibniz is talking about knowing eternal truths, what he has in mind is literally the view that we know the same truths as the truths that the gods know and love but do not cause or change. (shrink)

Agent relativists about vagueness (henceforth ‘agent relativists’) hold that whether or not an object x falls in the extension of a vague predicate ‘P’ at a time t depends on the judgemental dispositions of a particular competent agent at t. My aim in this paper is to critically examine arguments that purport to support agent relativism by appealing to data from forced-march Sorites experiments. The most simple and direct versions of such forced-march Sorites arguments rest on the following (...) (implicit) premise: If competent speakers' judgements vary in a certain way, then the extensions of ‘P’ as used by these speakers must vary in the same way. This premise is in need of independent support, since otherwise opponents of agent relativism can simply reject it. In this paper, I focus on the idea that one cannot plausibly reject this premise, as that would commit one to implausible claims about linguistic competence. Against this, I argue that one can accommodate the data from forced-march Sorites experiments in a way that is compatible with a plausible picture of linguistic competence, without going agent relativist. Thus, there is reason to be sceptical of the idea that such data paired with considerations about linguistic competence can be invoked in order to lend any solid support to agent relativism. Forced-march Sorites arguments of this kind can, and should be, resisted. (shrink)

A person with one dollar is poor. If a person with n dollars is poor, then so is a person with n + 1 dollars. Therefore, a person with a billion dollars is poor. True premises, valid reasoning, a false a conclusion. This is an instance of the Sorites-paradox. (There are infinitely many such paradoxes. A man with an IQ of 1 is unintelligent. If a man with an IQ of n is unintelligent, so is a man with an (...) IQ of n+1. Therefore a man with an IQ of 200 is unintelligent.) Most attempts to solve this paradox reject some law of classical logic, usually the law of bivalence. I show that this paradox can be solved while holding on to all the laws of classical logic. Given any predicate that generates a Sorites-paradox, significant use of that predicate is actually elliptical for a relational statement: a significant token of "Bob is poor" means that Bob is poor compared to x, for some value of x. Once a value of x is supplied, a definite cutoff line between having and not having the paradox-generating predicate is supplied. This neutralizes the inductive step in the associated Sorites argument, and the would-be paradox is avoided. (shrink)

The non-transitivity of the relation looks the same as has been used to argue that the relation has the same phenomenal character as is non-transitive—a result that jeopardizes certain theories of consciousness. In this paper, I argue against this conclusion while granting the premise by dissociating lookings and phenomenology; an idea that some might find counter-intuitive. However, such an intuition is left unsupported once phenomenology and cognitive access are distinguished from each other; a distinction that is conceptually and empirically grounded.

Sergio Tenenbaum and Diana Raffman contend that ‘vague projects’ motivate radical revisions to orthodox, utility-maximising rational choice theory. Their argument cannot succeed if such projects merely ground instances of the paradox of the sorites, or heap. Tenenbaum and Raffman are not blind to this, and argue that Warren Quinn’s Puzzle of the Self-Torturer does not rest on the sorites. I argue that their argument both fails to generalise to most vague projects, and is ineffective in the case of (...) the Self-Torturer itself. (shrink)

T. A. Heinrichs sustentou que a análise de Hobbes da experiência e do pensamento dá origem a um aparente paradoxo. O paradoxo consiste no fato de que Hobbes teria reivindicado descobertas que a sua teoria implica que não poderiam ser feitas. Para resolver o problema, Heinrichs argumenta que a teoria hobbesiana da experiência e pensamento deveria ser interpretada com base em sua teoria da linguagem, no sentido forte de que suas descobertas são de fato descobertas sobre a linguagem. (...) Neste artigo será defendido, contra Heinrichs, que a interpretação mais plausível é que Hobbes baseou sua análise da linguagem em sua analise do pensamento e experiência. Portanto, a solução de Heinrichs para o paradoxo deve ser rejeitada. (shrink)

Smarandache Hypothesis states that there is no speed limit of anything, including light and particles. While the idea is quite simple and based on known hypothesis of quantum mechanics, called Einstein-Podolski-Rosen paradox, in reality such a superluminal physics seems still hard to accept by majority of physicists. Here we review some experiments to support superluminal physics and also findings to explain Smarandache Quantum Paradoxes and Quantum Sorites Paradox. We also touch briefly on new experiment on magneton, supporting SubQuantum Kinetic (...) Model of Electron. (shrink)

Contrary to the great bulk of philosophical work on vagueness, the core of vagueness is not to be found in vague monadic predicates such as ‘bald’, ‘tall’, or ‘old’. The true source of vagueness – at least vagueness of the type that typically appears in the sorites – lies beneath these, in a mechanism using a buried quantifier operative over the comparatives ‘balder’, ‘taller’ and ‘older’.

The solution to the Sorites Paradox is discussed.

The article makes an analysis of a paraconsistent solution to the liar paradox, namely, Priest’s solution. Paraconsistent logics are characterized, in opposition to classical logic, as rejecting the Principle of Explosion, which says that “from a contradiction everything follows”. Priest, in turn, is a dialetheist, an interpretation of paraconsistency that admits the truth of contradictions. His answer to the liar paradox, therefore, accepts the liar sentence as being a truly paradoxical sentence using LP, the “Logic of Paradox. Then, we propose (...) some critiques of his position. Finally, we evaluate Priest’s solution to the paradox in comparison with Tarski and Kripke canonical solutions. (shrink)

Is logic a normative science for reasoning? Do its principles play any role in the rationality of our beliefs? Being logically consistent is supposed to be a principle for the theoretical reasoning. Furthermore, it seems that logical consistency imposes a constraint on rational belief. However, the preface paradox puts this principle to the test, since the ‘state of preface’ would be a rational state. We will present an analysis according to a Bayesian model of degrees of belief in order to (...) exemplify a (dis)solution of the paradox and, simultaneously, the maintenance of the principle of consistency. (shrink)

Eu li muitas discussões recentes sobre os limites da computação e do universo como computador, na esperança de encontrar alguns comentários sobre o trabalho surpreendente do físico polimatemático e teórico da decisão David Wolpert, mas não encontrei uma única citação e assim que eu apresento este muito breve Resumo. Wolpert provou alguma impossibilidade impressionante ou teoremas da incompletude (1992 a 2008-Veja arxiv dot org) nos limites à inferência (computação) que são tão gerais que são independentes do dispositivo que faz a (...) computação, e mesmo independente das leis da física, para que eles se apliquem em computadores, física e comportamento humano. Eles fazem uso da diagonalização de cantor, o paradoxo mentiroso e worldlines (linhas do mundo) para fornecer o que pode ser o teorema final na teoria da máquina de Turing, e, aparentemente, fornecer insights sobre a impossibilidade, incompletude, os limites da computação, e do universo como computador, em todos os universos possíveis e todos os seres ou mecanismos, gerando, entre outras coisas, um princípio de incerteza mecânica não quântica e uma prova de monoteísmo. Há umas conexões óbvias ao trabalho clássico de Chaitin, Solomonoff, Komolgarov e Wittgenstein e à noção que nenhum programa (e assim nenhum dispositivo) pode gerar uma seqüência (ou dispositivo) com maior complexidade do que possui. Pode-se dizer que este corpo de trabalho implica ateísmo, uma vez que não pode haver qualquer entidade mais complexa do que o universo físico e do ponto de vista Wittgensteiniano, ' mais complexo ' é sem sentido (não tem condições de satisfação, ou seja, criador de verdade ou teste). Mesmo um ' Deus ' (ou seja, um ' dispositivo ' com tempo ilimitado/espaço e energia) não pode determinar se um determinado ' número ' é ' aleatório ', nem encontrar uma determinada maneira de mostrar que uma determinada ' fórmula ', ' teorema ' ou ' sentença ' ou ' Device ' (todos estes sendo linguagem complexa jogos) faz parte de um determinado «sistema». Aqueles que desejam um quadro até à data detalhado para o comportamento humano da opinião moderna dos dois sistemas consultar meu livros Falando Macacos 3ª Ed (2019), A Estrutura Lógica da Filosofia, Psicologia, Mente e Linguagem em Ludwig Wittgenstein e John Searle 2a Ed (2019), Suicídio Pela Democracia,4aEd(2019), Entendendo as Conexões entre Ciência, Filosofia, Psicologia, Religião, Política e Economia Artigos e Análises 2006-2019 (2019), Ilusões Utópicas Suicidas no 21St século 5a Ed (2019), A Estrutura Lógica do Comportamento Humano (2019), e A Estrutura Lógica da Consciência (2019) y outras. (shrink)

Atribuindo à ironia a possibilidade de exercício e desenvolvimento da liberdade subjetiva, Kierkegaard sublinha a negatividade absoluta como característica do referido processo em Sócrates, convergindo para assinalar o absoluto e irredutível valor do indivíduo em um movimento que implica o início absoluto da vida pessoal entre criar-se e deixar-se criar. Dessa forma, contrapondo-se à dissolução da existência humana nas fronteiras da pura conceituação intelectual, Kierkegaard assinala a tensão inaplacável entre existência e transcendência em um movimento que implica a interioridade e (...) guarda correspondência com a necessidade de tornar-se subjetivo, tendo em vista a perspectiva que defende que a verdade consiste na transformação do sujeito em si mesmo entre a vertigem da liberdade e o paradoxo da fé em um processo que encerra angústia e desespero e converge para a transição do ético ao religioso. (shrink)

Abstract: Using a critical review of the literature, we study a challenge from philosophical anarchism to J. Raz's theory of legal authority: it would be irrational to follow an order with which one disagrees, since it would mean acting against what is considered more justified. Through references from decision theory and epistemology, and deploying examples about tools for assisting in routine decision-making, we sketch two possible answers: first, it may be justifiable to put yourself in a situation that leads to (...) irrationally acting; second, according to the “blindspots” theory, we outline some restrictions from a theory of rationality to the authority. (shrink)

‘Puzzles’, ‘word games’, ‘logical anomalies’, whatever we call them, they perplex us and challenge our familiar patterns of reasoning. One of these puzzles, among many others, originated from the mind of an ancient Megarian logician, Eubulides of Miletus, and endures to the modern day.1 Its name, ‘sorites’, can be traced to the Greek word soros, meaning ‘heap.’ The answer to whether one grain of sand ‘is a heap’ or ‘is not a heap’ seems quite simple: it is not a (...) heap. However, as we add grains to the one, at what future point does the non-heap become a heap? Our decision is fraught with uncertainty. Are the objects or the language we are using to describe them vague? In academic philosophy, the ancient Greek puzzle has gained the status of a paradox, as philosophers apply stoic and modern logic to these propositions considered to have vague predicates. The current debate has developed quite serious and wide-ranging implications, such as whether sorites issues provide adequate grounds for abandoning our standard ontology (or our understanding of what really exists), 2 and (germinating into another discipline) whether vagueness in the language of legal rules can generate disagreement as to whether there are right answers to questions of law. 3 Several unique solutions to the paradox have been proposed, yet all suffer from specific inadequacies that might, upon further reflection, disappear in the event that we endeavour to produce a synthesis. When we say that we are attempting to derive a synthesis, we seek to combine elements of two solutions for the sake of creating a new (and hopefully, though not necessarily, a better) one. The paradox of the sorites, or ‘the heap’, appeals to us because it challenges our assumption that we may categorically describe clear cases and their negations, yet fail to distinguish the borderline ones. I will demonstrate that some combinations of solutions are easy fits while others are extremely weak and awkward as attempts at resolving the paradox. Nonetheless, the process of synthesis produces three noteworthy combinations. (shrink)

Segundo Kierkegaard, a verdade se sobrepõe ao caráter objetivo que encerra desde uma investigação histórica até um exercício especulativo, guardando correspondência com a subjetividade em um movimento que implica a condição-limite da interioridade. Detendo-se em tal princípio hermenêutico-existencial, o artigo assinala a espiritualidade enquanto experiência epistêmico-existencial envolvendo a verdade como paradoxo em Kierkegaard, que se sobrepõe à mediação lógico-discursiva e implica uma construção dialético-subjetiva que transcende a razão histórico-objetiva (ou finita). Dessa forma, caracterizando a espiritualidade enquanto experiência epistêmico-existencial que (...) encerra como único tipo de evidência a evidência de caráter não racional, o artigo recorre à perspectiva fenomenológica de Rudolf Otto, que sublinha o sagrado e a sua distinção absoluta em relação à realidade natural e ao seu caráter perceptível em uma construção que enfatiza o elemento não racional e a sua natureza suprarracional e implica o numinoso, que escapa aos processos lógico-racionais e, emergindo como a priori, converge para a apreensão do racional e do não racional na noção da Divindade. Assim, se a relação com Deus se sobrepõe às fronteiras que encerram a subjetividade e a objetividade, convergindo para a superação do referido esquema estrutural epistêmico, o artigo, baseado na perspectiva teológico-filosófica de Paul Tillich, detém-se no conceito de Presença Espiritual que, caracterizando a vida sem ambiguidade, implica a união transcendente, correlacionando ágape e gnosis enquanto experiência epistêmico-existencial envolvendo a relação com o sagrado como presença de Deus através de um movimento extático-religioso que converge para a automanifestação, a autorrevelação e a autocomunicação do Absoluto e Transcendente como Deus. (shrink)

Este trabalho é uma investigação sobre os conceitos de espaço presentes tanto no livro IV da Física de Aristóteles, bem como no Livro 1, parte 2, do Tratado da Natureza Humana de David Hume. Nosso ponto de partida são os paradoxos de Zenão. Sabemos que Aristóteles debate diretamente com Zenão no livro IV da Física, enquanto Hume, no Tratado da Natureza Humana discute com a posição de Zenão acerca do espaço renovada por Bayle. Tendo isto em vista, o principal objetivo (...) deste trabalho é o de expor como Aristóteles enfrenta o paradoxo proposto por Zenão acerca do lugar, e como Hume enfrentou o paradoxo proposto por Bayle sobre a constituição do espaço, através de uma apropriação do método de Zenão. (shrink)

My main aim at this paper is to present Lewis Carrol’s Paradox on the justification of logical principles inasmuch as some attempts of solving it. This is important because if there are basic logical principles, it also seems necessary to exist some justification for them. By considering some observations from Ryle, Devitt and Kripke about the theme, we intend to briefly display their theories and their core critics among themselves and, mainly, the critics against adoption theory.

On swizzle sticks, sorites paradoxes, and precise replacements.

Fine (2017) proposes a new logic of vagueness, CL, that promises to provide both a solution to the sorites paradox and a way to avoid the impossibility result from Fine (2008). The present paper presents a challenge to his new theory of vagueness. I argue that the possibility theorem stated in Fine (2017), as well as his solution to the sorites paradox, fail in certain reasonable extensions of the language of CL. More specifically, I show that if we (...) extend the language with any negation operator that obeys reductio ad absurdum, we can prove a new impossibility result that makes the kind of indeterminacy that Fine takes to be a hallmark of vagueness impossible. I show that such negation operators can be conservatively added to CL and examine some of the philosophical consequences of this result. Moreover, I demonstrate that we can define a particular negation operator that behaves exactly like intuitionistic negation in a natural and unobjectionable propositionally quantified extension of CL. Since intuitionistic negation obeys reductio, the new impossibility result holds in this propositionally quantified extension of CL. In addition, the sorites paradox resurfaces for the new negation. (shrink)

In his essay ‘“Wang’s Paradox”’, Crispin Wright proposes a solution to the Sorites Paradox (in particular, the form of it he calls the ‘Paradox of Sharp Boundaries’) that involves adopting intuitionistic logic when reasoning with vague predicates. He does not give a semantic theory which accounts for the validity of intuitionistic logic (and the invalidity of stronger logics) in that area. The present essay tentatively makes good the deficiency. By applying a theorem of Tarski, it shows that intuitionistic logic (...) is the strongest logic that may be applied, given certain semantic assumptions about vague predicates. The essay ends with an inconclusive discussion of whether those semantic assumptions should be accepted. (shrink)

Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when dealing (...) with the so-called paradoxes of higher-order vagueness. We offer a proposal that makes strides on both issues. We argue that the intuitionist’s characteristic rejection of any third alethic value alongside true and false is best elaborated by taking the normal modal system S4M to be the sentential logic of the operator ‘it is clearly the case that’. S4M opens the way to an account of higher-order vagueness which avoids the paradoxes that have been thought to infect the notion. S4M is one of the modal counterparts of the intuitionistic sentential calculus and we use this fact to explain why IPC is the correct sentential logic to use when reasoning with vague statements. We also show that our key results go through in an intuitionistic version of S4M. Finally, we deploy our analysis to reply to Timothy Williamson’s objections to intuitionistic treatments of vagueness. (shrink)

What the Sorites has to tell us is a simple truth regarding our categories. It appears to saddle us with something other than a simple truth—something worse, a contradiction or a problem or a paradox—only when we insist on viewing it through a discrete logic of categories. Discrete categories and discrete logic are for robots. We aren’t robots, and the simple truth is that we don’t handle categories in the way any discrete logic would demand. For us non-robots, what (...) the Sorites has to offer is a straightforward truth regarding how incapable robots and their logic are of handling categories like ours. (shrink)

The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to (...) the other, each intermediate stage constituting an overlap in certain proportion of both contraries. Hence, degrees in the possession of a property give rise to simple contradictions. The reason why I have chosen those two questions is that they provide the main philosophical motivation for a particular brand of an infinite valued and paraconsistent logic. I will claim that Classical logic (CL) is not adequate to handle fuzzy situations, and, being deficient, is in need of being expanded to make room for degrees of truth and weak contradictions. One can hardly deny the importance of the debate, since what is ultimately at stake is what the limits of truth, rationality, intelligibility and possibility are. The main disciplines within which the research moves are the philosophy of language, philosophy of logic, and ontology. (shrink)