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.

De um modo geral, queríamos mostrar que a filosofia tem suas próprias áreas, mas tem também subáreas em interdisciplinaridade com as ciências. As ciências e as disciplinas acadêmicas em geral têm problemas, cuja a solução pode ser encontrada empiricamente, por meio de experimentos, entrevistas, documentos, ou formalmente, por meio de cálculos etc, porém os problemas das filosofias dessas disciplinas são justamente os problemas mais fundamentais dessas disciplinas, que fundam o quadro conceitual e de pesquisa das mesmas, e que só poderiam (...) ser respondidos por meio de uma extensa argumentação. A filosofia de cada uma dessas disciplinas é uma mistura (a) de metafísica da disciplina, perguntando-se qual a natureza e justificação das entidades que formam o quadro teórico da disciplina, i.e., quais delas realmente existem na realidade (não sendo meros instrumentos para obter resultados) e quais as suas categorizações fundamentais, naturezas e funções teóricas, (b) de epistemologia dessa disciplina, ao nos perguntarmos sobre como tal área poderia obter conhecimento de modo confiável e se ela de fato o faz, e (c) de teorias do valor, ao nos perguntarmos, por exemplo, sobre qual o valor moral do desenvolvimento de uma certa disciplina e, finalmente, (d) a lógica, que perpassa tudo, ao nos perguntarmos sobre a consistência das teses assumidas pela disciplina. Não é à toa que falamos que a filosofia é mãe de todas as ciências. Ela é mãe tanto num sentido geracional, pois a maioria das ciências foram desenvolvimentos particulares, empíricos ou de cálculo, das questões filosóficas sobre um certo tema, quanto num sentido fundamental, pois é a filosofia que fornece os fundamentos mais gerais, metafísicos, epistêmicos, valorativos e lógicos, na construção do quadro teórico de cada ciência e na qualidade dos métodos para se aproximar da verdade que a disciplina utiliza. A biologia, por exemplo, foi criada por Aristóteles, tal como os primeiros desenvolvimentos da meteorologia (na verdade, esta começa com os pré-socráticos), e grande parte do fundamento da física atual jaz nas discussões de filosofia da física. Sendo você filósofo ou cientista de outra área, a filosofia promete te dar as bases para uma reflexão geral ou sobre sua área, que seja muito mais informada e profunda do que aquilo que você poderia realizar sem ela. /// In general, we wanted to show that philosophy has its own areas, but it also has subareas in interdisciplinarity with the sciences. The sciences and academic disciplines in general have problems, the solution of which can be found empirically, through experiments, interviews, documents, or formally, through calculations etc., but the problems of the philosophies of these disciplines are precisely the most fundamental problems. of these disciplines, which build their conceptual and research framework, and which could only be answered through extensive argumentation. The philosophy of each of these disciplines is a mixture (a) of metaphysics of the discipline, asking what is the nature and justification of the entities that form the theoretical framework of the discipline, ie, which ones really exist in reality (not being mere instruments for achieving results) and what are its fundamental categorizations, natures and theoretical functions, (b) the epistemology of this discipline, when we ask ourselves how such an area could obtain knowledge reliably and if it does, and (c) theories of value, when we ask ourselves, for example, about the moral value of the development of a certain discipline and, finally, (d) the logic, which permeates everything, when we ask ourselves about the consistency of the theses assumed by the discipline. It is not for nothing that we say that philosophy is the mother of all sciences. It is a mother both in a generational sense, as most sciences were particular empirical or formal developments of philosophical questions on a certain topic, and in a fundamental sense, as it is philosophy that provides the most general, metaphysical, epistemic, evaluative and logical foundations, in the construction of the theoretical framework of each science and in the quality of the methods to approach the truth that the discipline uses. Biology, for example, was created by Aristotle, like the first developments in meteorology (in fact, it starts with the pre-Socratics), and much of the foundation of current physics lies in discussions of the philosophy of physics. Whether you are a philosopher or scientist from another area, philosophy promises to give you the basis for a general reflection or about your area, which is much more informed and profound than what you could accomplish without it. (shrink)

This book proposes a new solution to the problem of vagueness. There are several different ways of addressing this problem and no clear agreement on which one is correct. The author proposes that it should be understood as the problem of explaining vague predicates in a way that systematizes six intuitions about the phenomenon and satisfies three criteria of adequacy for an ideal theory of vagueness. The third criterion, which is called the “criterion of precisification”, is the most controversial one. (...) It is based on the intuition that a predicate is vague only if it is imprecise. The author considers some different definitions of linguistic imprecision, proposing that a predicate is imprecise if and only if there is no sharp boundary between objects to which its application yields some particular truth-value and objects to which its application does not yield that truth-value. The volume critically reviews the current theories of vagueness and proposes a new one, the Theory of Vagueness as Arbitrariness, which defines a vague predicate as an arbitrary predicate that must be precisified in order to contribute to a sentence that has truth-conditions. The main advantages of this theory over the current alternatives are that it satisfies all three criteria and systematizes the relevant intuitions. (shrink)

Development of decision-support and intelligent agent systems necessitates mathematical descriptions of uncertainty and fuzziness in order to model vagueness. This paper seeks to present an outline of Peirce’s triadic logic as a practical new way to model vagueness in the context of artificial intelligence. Charles Sanders Peirce was an American scientist–philosopher and a great logician whose triadic logic is a culmination of the study of semiotics and the mathematical study of anti-Cantorean model of continuity and infinitesimals. After presenting Peircean semiotics (...) within AI perspective, a mathematical formulation of a Peircean triadic set is given in relationship with classical and fuzzy sets. Using basic logical operators, all possible respective implication operators, bi-equivalence operators, valid rules of inference, and associative, distributive and commutative logical properties are derived and verified through the truth function approach. In order to suggest practical directions, aggregation operators for Peirce’s triadic logic have been formulated. A mathematical formulation of a medical diagnostic problem and ER diagram of a library management system using Peirce’s triadic relation show potential for further applications of the proposed triadic set and triadic logic. Alongside, a classical AI game—The Wumpus World—is implemented to show practical efficacy in comparison with binary implementation. Besides giving some preliminary formulations for trichotomous set theory and definition of finite automaton, development of hybrid architectures for intelligent agents and evolutionary computations are discussed as potential practical avenues for Peirce’s triadic logic. (shrink)

The sorites paradox is the name given to a class of paradoxical arguments, also known as little by little arguments, which arise as a result of the indeterminacy surrounding limits of application of the predicates involved. For example, the concept of a heap appears to lack sharp boundaries and, as a consequence of the subsequent indeterminacy surrounding the extension of the predicate ‘is a heap’, no one grain of wheat can be identified as making the difference between being a heap (...) and not being a heap. Given then that one grain of wheat does not make a heap, it would seem to follow that two do not, thus three do not, and so on. In the end it would appear that no amount of wheat can make a heap. We are faced with paradox since from apparently true premises by seemingly uncontroversial reasoning we arrive at an apparently false conclusion. (shrink)

The PhD thesis advances a new approach to vagueness as dispersion, comparing it with the main philosophical theories of vagueness in the analytic tradition.