Publisher’s note: This volume is an accessible introduction to the subject of many-valued and fuzzy logic suitable for use in relevant advanced undergraduate and graduate courses. The text opens with a discussion of the philosophical issues that give rise to fuzzy logic – problems arising from vague language – and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. The major fuzzy logical systems – Lukasiewicz, Godel, and product logics – are then presented as generalizations of three-valued systems that successfully address the problems of vagueness. Semantic and axiomatic systems for three-valued and fuzzy logics are examined along with an introduction to the algebras characteristic of those systems. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, ask students to continue proofs begun in the text, and engage them in the comparison of logical systems.
Virtues of the Mind: An Inquiry Into the Nature of Virtue and the Ethical Foundations of Knowledge.
lmost all theories of knowledge and justified belief employ moral concepts and forms of argument borrowed from moral theories, but none of them pay attention to the current renaissance in virtue ethics. This remarkable book is the first attempt to establish a theory of knowledge based on the model of virtue theory in ethics. The book develops the concept of an intellectual virtue, and then shows how the concept can be used to give an account of the major concepts in epistemology, including the concept of knowledge. This highly original work of philosophy for professionals will also provide students with an excellent introduction to epistemology, virtue theory, and the relationship between ethics and epistemology.
On the metaphysics of quantum mechanics
Abstract: Many solutions have been proposed for solving the problem of macroscopic superpositions of wave function ontology. A possible solution is to assume that, while the wave function provides the complete description of the system, its temporal evolution is not given by the Schroedinger equation. The usual Schroedinger evolution is interrupted by random and sudden “collapses”. The most promising theory of this kind is the GRW theory, named after the scientists that developed it: Gian Carlo Ghirardi, Alberto Rimini and Tullio Weber. It seems tempting to think that in GRW we can take the wave function ontologically seriously and avoid the problem of macroscopic superpositions just allowing for quantum jumps. In this paper it is argued that such “bare” wave function ontology is not possible, neither for GRW nor for any other quantum theory: quantum mechanics cannot be about the wave function simpliciter. All quantum theories should be regarded as theories in which physical objects are constituted by a primitive ontology. The primitive ontology is mathematically represented in the theory by a mathematical entity in three-dimensional space, or space-time.
Animal Action in the Space of Reasons
Abstract: I defend the view that we should not overintellectualize the mind. Nonhuman animals can occupy islands of practical rationality: they can have contextbound reasons for action even though they lack full conceptual abilities. Holism and the possibility of mistake are required for such reasons to be the agent’s reasons, but these requirements can be met in the absence of inferential promiscuity. Empirical work with animals is used to illustrate the possibility that reasons for action could be bound to symbolic or social contexts, and connections are made to simulationist accounts of cognitive skills.
The Metaphysics of Squaring Scientific Realism with Referential Indeterminacy
Introduction: Scientific realism and the claim that there is radical referential indeterminacy are important and compelling philosophical theses. Each thesis has advocates and for good reason. On cursory examination, however, it seems that these theses are at odds with one another. It seems that one cannot both claim that science seeks to describe an objective reality and yet deny that reality is objectively structured in such a way as to determine the referents of our terms. Since there are compelling reasons in favour of each thesis and since it appears that some philosophers actually advocate both theses (Quine himself may be one such example), finding a way to square the theses would be multiply advantageous. On this paper, the author argues that despite the prima facie tension between them, these theses are indeed cotenable.
Essentialism and the Necessity of the Laws of Nature
Abstract: In this paper the author discusses and evaluates different arguments for the view that the laws of nature are metaphysically necessary. She conclude that essentialist arguments from the nature of natural kinds fail to establish that essences are ontologically more basic than laws, and fail to offer an a priori argument for the necessity of all causal laws. Similar considerations carry across to the argument from the dispositionalist view of properties, which may end up placing unreasonable constraints on property identity across possible worlds. None of her arguments preclude the possibility that the laws may turn out to be metaphysically necessary after all, but she argues that this can only be established by a posteriori scientific investigation. She argues for what may seem to be a surprising conclusion: that a fundamental metaphysical question – the modal status of laws of nature – depends on empirical facts rather than purely on a priori reasoning.
A Quantified Temporal Logic for Ampliation and Restriction
Abstract: Temporal logic as a modern discipline is separate from classical logic; it is seen as an addition or expansion of the more basic propositional and predicate logics. This approach is in contrast with logic in the Middle Ages, which was primarily intended as a tool for the analysis of natural language. Because all natural language sentences have tensed verbs, medieval logic is inherently a temporal logic. This fact is most clearly exemplified in medieval theories of supposition. As a case study, we look at the supposition theory of Lambert of Lagny (Auxerre), extracting from it a temporal logic and providing a formalization of that logic.
Models and Logical Consequence
Abstract: This paper deals with the adequacy of the model-theoretic definition of logical consequence. Logical consequence is commonly described as a necessary relation that can be determined by the form of the sentences involved. In this paper, necessity is assumed to be a metaphysical notion, and formality is viewed as a means to avoid dealing with complex metaphysical questions in logical investigations. Logical terms are an essential part of the form of sentences and thus have a crucial role in determining logical consequence.
Gila Sher and Stewart Shapiro each propose a formal criterion for logical terms within a model-theoretic framework, based on the idea of invariance under isomorphism. The two criteria are formally equivalent, and thus we have a common ground for evaluating and comparing Sher and Shapiro philosophical justification of their criteria. It is argued that Shapiro’s blended approach, by which models represent possible worlds under interpretations of the language, is preferable to Sher’s formal-structural view, according to which models represent formal structures. The advantages and disadvantages of both views’ reliance on isomorphism are discussed.
The Concept of Voluntariness – A Reply
Abstract: In his paper on ‘The Concept of Voluntariness’, Ben Colburn helpfully takes up the task of developing my view about the sense of voluntariness that is relevant for judgments of substantive responsibility, or judgments about individuals’ liability to pick up some costs of their choices. On my view, a necessary condition for holding people responsible for their choices is that those choices be voluntary in the sense that they are not made because there is no acceptable alternative, where the standard for the acceptability of options is an objective standard of well-being. […] Colburn’s first point is entirely well-taken. By way of endorsing it, I ask whether we are justified in taking some but not all kinds of beliefs to affect the voluntariness of choice, as his elaboration of my view suggests. However, I find Colburn’s second point less convincing, and argue that we should allow for the moral character of options to affect the voluntariness of choice.
Wisdom, Knowledge and Rationality
Abstract: After surveying the strengths and weaknesses of several well-known approaches to wisdom, I argue for a new theory of wisdom that focuses on being epistemically, practically, and morally rational. My theory of wisdom, The Deep Rationality Theory of Wisdom, claims that a wise person is a person who is rational and who is deeply committed to increasing his or her level of rationality. This theory is a departure from theories of wisdom that demand practical and/or theoretical knowledge. The Deep Rationality Theory salvages all that is attractive, and avoids all that is problematic, about theories of wisdom that require wise people to be knowledgeable.