Uncertainty behind the veil of ignorance

This paper argues that the decision problem in the original position should be characterized as a decision problem under uncertainty even when it is assumed that the denizens of the original position know that they have an equal chance of ending up in any given individual's place. It argues for this claim by arguing that (a) the continuity axiom of decision theory does not hold between all of the outcomes the denizens of the original position face and that (b) neither us nor the denizens of the original position can know the exact point where discontinuity sets in, because the language we employ in comparing different outcomes is ineradicably vague. It is also argued that the account underlying (b) can help proponents of superiority in value theory defend their view against arguments offered by Norcross and Griffin

Personhood, Vagueness and Abortion

In a recent paper, Lee Kerckhove and Sara Waller (hereafter K & W) argue that the concept of personhood is irrelevant for the abortion debate.1 Surprisingly, this irrelevance is due merely to the fact that the predicate ‘being a person’ — hereafter ‘personhood’ — is inherently vague. This vagueness, they argue, reduces ‘personhood’ to incoherency and disqualifies the notion from being a useful moral concept. In other words, if ‘personhood’ isn’t a precise notion with well-defined boundaries, then it cannot be of any use in the debate over the permissibility of abortion. This argument is mistaken. While it may be true that ‘personhood’ is irrelevant for the debate over abortion (a substantive issue not dealt with in this paper), it is not true that ‘personhood’ should be disqualified merely because it is vague. Section 2 of the paper is a quick survey in which I briefly review the importance of ‘personhood’ in some of the more recent literature concerning the moral status of abortion. Section 3 is a reconstruction of K & W’s argument against the relevancy of ‘personhood’ and a criticism showing why their argument fails. Section 4 approaches the use of a vague predicate in moral debate and explores the application of ‘personhood’ given three contemporary solutions to vagueness: degree theory, epistemicism and supervaluationism

The use of Rough Set and Spatial Statistic in evaluating the Periurban Fringe

The distinction among urban, peri-urban and rural areas inside a territory represents a classical example of uncertainty in land classification. The transition among the three classes is not much clear and can be described with Sorites Paradox, considering the residential buildings and the settlements. Peri-urban fringe can be considered as a transition zone between urban and rural areas, as an area with its own intrinsic organic rules, as a built area without formal organisation or as an abandoned rural area contiguous to urban centres. In any case, concepts as density of buildings, services and infrastructures or the degree of rural, residential and industrial activities, will lead to uncertainty in defining classes, due to the uncertainty in combining some properties. One of the methods which can be utilized is the rough sets theory, which represents a different mathematical approach to uncertainty capturing the indiscernibility. The definition of a set is connected to information knowledge and perception about phenomena. Some phenomena can be classified only in the context of the information available about them. Two different phenomena can be indiscernible in some contexts and classified in the same way (Pawlak 83). The rough sets approach to data analysis hinges on two basic concepts, the lower approximation which considers all the elements that doubtlessly belong to the class, and the upper approximation which includes all the elements that possibly belong to the class. The rough sets theory furthermore takes into account only properties which are independent. This approach has been tested in the case of study of Potenza Province. This area, located in Southern Italy, is particularly suitable to the application of this theory, because it includes 100 municipalities with different number of inhabitants, quantity of services and distance from the main road infrastructures.

Vagueness, Logic and Use: Four Experimental Studies on Vagueness

Although arguments for and against competing theories of vagueness often appeal to claims about the use of vague predicates by ordinary speakers, such claims are rarely tested. An exception is Bonini et al. (1999), who report empirical results on the use of vague predicates by Italian speakers, and take the results to count in favor of epistemicism. Yet several methodological difficulties mar their experiments; we outline these problems and devise revised experiments that do not show the same results. We then describe three additional empirical studies that investigate further claims in the literature on vagueness: the hypothesis that speakers confuse ‘P’ with ‘definitely P’, the relative persuasiveness of different formulations of the inductive premise of the Sorites, and the interaction of vague predicates with three different forms of negatio

“Almost Identical with Itself” : A Search for a Logic of Fuzzy Identity

This thesis grows out of a fascination with the vagueness of natural language, its manifestation in the ancient Sorites paradox, and the way in which the paradox is dealt with in fuzzy logic. It is an attempt to resolve the tension between two versions of the paradox, and the related problem of whether identity can be fuzzy. If it can be fuzzy, then the most popular argument against vague objects is mistaken, which would be great news for those who hold that there can be vagueness in the world independently of our representation or knowledge of it. The standard Sorites is made up of conditionals about an ordinary predicate (e.g. “heap”) by the rule of modus ponens. It is typically solved in fuzzy logic by interpreting the predicate as a fuzzy relation and showing that the argument fails as a result. There is another, less known version of the paradox, based on the identity predicate and the rule of substitutivity of identicals. The strong analogy between the two versions suggests that their solutions might be analogical as well, which would make identity just as vague as any relation. Yet the idea of vague identity has traditionally been rejected on both formal and philosophical grounds. Even Nicholas J. J. Smith, who is known for his positive attitude toward fuzzy relations in general, denies that identity could be fuzzy. The opposite position is taken by Graham Priest, who argues for a fuzzy interpretation of identity as a similarity relation. Following Priest, I aim to show that there is a perfectly sensible logic of fuzzy identity and that a fuzzy theoretician of vagueness therefore cannot rule out fuzzy identity on logical grounds alone. I compare two fuzzy solutions to the identity Sorites: Priest’s solution, based on the notion of local validity, and B. Jack Copeland’s solution, based on the failure of contraction in sequent calculus. I provide a synthesis of the two solutions, suggesting that Priest’s local validity counts as a genuine kind of validity even if he might not think so himself. The substitutivity of identicals is not locally valid in Priest’s logic, however; his solution only applies to a special case with the rule of transitivity. Applying L. Valverde’s representation theorem and other mathematical results, I lay the foundation for a stronger logic where the substitutivity rule is locally valid and the two Sorites merge into one paradox with one solution. Finally, I defend fuzzy identity against Gareth Evans’ argument that vague identity leads to contradiction, and Smith’s argument that vague identity is not really identity. The former relies on a fallacious application of the substitutivity rule; to the latter, my principal response is to question Smith’s understanding of identity and argue for a broader one. I conclude that not only is fuzzy identity logically possible, but it also has potential applicability in metaphysics and elsewhere

Insignificant differences : the paradox of the heap

This study investigates six theoretical approaches offered as solutions to the paradox of the heap (sorites paradox), a logic puzzle dating back to the ancient Greek philosopher Eubulides. Those considered are: Incoherence Theory, Epistemic Theory, Supervaluation Theory, Many-Valued Logic, Fuzzy Logic, and Non-Classical Semantics. After critically examining all of these, it is concluded that none of the attempts to explain the sorites are fully adequate, and the paradox remains unresolved.Philosophy, Practical and Systematic TheologyM.A. (Philosophy

Vagueness: Subvaluationism

Supervaluationism is a well known theory of vagueness. Subvaluationism is a less well known theory of vagueness. But these theories cannot be taken apart, for they are in a relation of duality that can be made precise. This paper provides an introduction to the subvaluationist theory of vagueness in connection to its dual, supervaluationism. A survey on the supervaluationist theory can be found in the Compass paper of Keefe (2008); our presentation of the theory in this paper will be short to get rapidly into the logical issues. This paper is relatively self-contained. A modest background on propositional modal logic is, though not strictly necessary, advisable. The reader might find useful the Compass papers Kracht (2011) and Negri (2011) (though these papers cover issues of more complexity than what is demanded to follow this paper

Standpoint Logic: A Logic for Handling Semantic Variability, with Applications to Forestry Information

It is widely accepted that most natural language expressions do not have precise universally agreed definitions that fix their meanings. Except in the case of certain technical terminology, humans use terms in a variety of ways that are adapted to different contexts and perspectives. Hence, even when conversation participants share the same vocabulary and agree on fundamental taxonomic relationships (such as subsumption and mutual exclusivity), their view on the specific meaning of terms may differ significantly. Moreover, even individuals themselves may not hold permanent points of view, but rather adopt different semantics depending on the particular features of the situation and what they wish to communicate. In this thesis, we analyse logical and representational aspects of the semantic variability of natural language terms. In particular, we aim to provide a formal language adequate for reasoning in settings where different agents may adopt particular standpoints or perspectives, thereby narrowing the semantic variability of the vague language predicates in different ways. For that purpose, we present standpoint logic, a framework for interpreting languages in the presence of semantic variability. We build on supervaluationist accounts of vagueness, which explain linguistic indeterminacy in terms of a collection of possible interpretations of the terms of the language (precisifications). This is extended by adding the notion of standpoint, which intuitively corresponds to a particular point of view on how to interpret vague terminology, and may be taken by a person or institution in a relevant context. A standpoint is modelled by sets of precisifications compatible with that point of view and does not need to be fully precise. In this way, standpoint logic allows one to articulate finely grained and structured stipulations of the varieties of interpretation that can be given to a vague concept or a set of related concepts and also provides means to express relationships between different systems of interpretation. After the specification of precisifications and standpoints and the consideration of the relevant notions of truth and validity, a multi-modal logic language for describing standpoints is presented. The language includes a modal operator for each standpoint, such that \standb{s}\phi means that a proposition $\phi$ is unequivocally true according to the standpoint $s$ --- i.e.\ $\phi$ is true at all precisifications compatible with $s$. We provide the logic with a Kripke semantics and examine the characteristics of its intended models. Furthermore, we prove the soundness, completeness and decidability of standpoint logic with an underlying propositional language, and show that the satisfiability problem is NP-complete. We subsequently illustrate how this language can be used to represent logical properties and connections between alternative partial models of a domain and different accounts of the semantics of terms. As proof of concept, we explore the application of our formal framework to the domain of forestry, and in particular, we focus on the semantic variability of `forest'. In this scenario, the problematic arising of the assignation of different meanings has been repeatedly reported in the literature, and it is especially relevant in the context of the unprecedented scale of publicly available geographic data, where information and databases, even when ostensibly linked to ontologies, may present substantial semantic variation, which obstructs interoperability and confounds knowledge exchange