Degree supervaluational logic

Supervaluationism is often described as the most popular semantic treatment of indeterminacy. There???s little consensus, however, about how to fill out the bare-bones idea to include a characterization of logical consequence. The paper explores one methodology for choosing between the logics: pick a logic that norms belief as classical consequence is standardly thought to do. The main focus of the paper considers a variant of standard supervaluational, on which we can characterize degrees of determinacy. It applies the methodology above to focus on degree logic. This is developed first in a basic, single-premise case; and then extended to the multipremise case, and to allow degrees of consequence. The metatheoretic properties of degree logic are set out. On the positive side, the logic is supraclassical???all classical valid sequents are degree logic valid. Strikingly, metarules such as cut and conjunction introduction fail

A future for the thin red line

The thin red line (TRL) is a theory about the semantics of future-contingents. The central idea is that there is such a thing as the ‘actual future’, even in the presence of indeterminism. It is inspired by a famous solution to the problem of divine foreknowledge associated with William of Ockham, in which the freedom of agents is argued to be compatible with God’s omniscience. In the modern branching time setting, the theory of the TRL is widely regarded to suffer from several fundamental problems. In this paper we propose several new TRL semantics, each with differing degrees of success. This leads up to our final semantics, which is a cross between the TRL and supervaluationism. We discuss the notions of truth, validity and semantic consequence which result from our final semantics, and demonstrate some of its pleasing results. This account, we believe, answers themain objection in the literature, and thus places the TRL on the same level as any other competing semantics for future contingents

A unified theory of truth and reference

The truthmaker theory rests on the thesis that the link between a true judgment and that in the world to which it corresponds is not a one-to-one but rather a one-to-many relation. An analogous thesis in relation to the link between a singular term and that in the world to which it refers is already widely accepted. This is the thesis to the effect that singular reference is marked by vagueness of a sort that is best understood in supervaluationist terms. In what follows we show that the supervaluationist approach to singular reference, when wedded to the truthmaker idea, yields a framework of surprising power, which offers a uniform set of solutions to a range of problems regarding identity, reference and knowledge, problems which have hitherto been dealt with on an ad hoc basis

Probability and nonclassical logic

Classical tautologies have probability. Classical contradictions have probability. These familiar features reflect a connection between standard probability theory and classical logic. In contexts in which classical logic is questioned—to deal with the paradoxes of self-reference, or vague propositions, for the purposes of scientific theory or metaphysical anti-realism—we must equally question standard probability theory. Section 1 covers the intended interpretation of ‘nonclassical logic’ and ‘probability’. Section 2 reviews the connection between classical logic and classical probability. Section 3 briefly reviews salient aspects of nonclassical logic, laying out a couple of simple examples to fix ideas. Section 4 explores modifications of probability theory. The variations laid down will be motivated initially by formal analogies to the classical setting. In section 5, however, we look at two foundational justifications for the presentations of ‘nonclassical probabilities’ that are arrived at. Sections 6-7 describe extensions of the nonclassical framework: to conditionalization and decision theory in particular. Section 8 will consider some alternative approaches, and section 9 evaluates progress

Fara's formula and the Supervaluational Thin Red Line

Este artículo se centra en un argumento presentado por Fara (2010) en contra del supervaluacionismo en el contexto de la vaguedad. Muestro cómo dicho argumento es igualmente aplicable al supervaluacionismo de tiempo ramificado (presentado por primera vez por Thomason 1970), pero no a la semántica 'STRL' de Malpass y Wawer (2012), que está estrechamente relacionada

Groundedness - Its Logic and Metaphysics

In philosophical logic, a certain family of model constructions has received particular attention. Prominent examples are the cumulative hierarchy of well-founded sets, and Kripke's least fixed point models of grounded truth. I develop a general formal theory of groundedness and explain how the well-founded sets, Cantor's extended number-sequence and Kripke's concepts of semantic groundedness are all instances of the general concept, and how the general framework illuminates these cases. Then, I develop a new approach to a grounded theory of proper classes. However, the general concept of groundedness does not account for the philosophical significance of its paradigm instances. Instead, I argue, the philosophical content of the cumulative hierarchy of sets is best understood in terms of a primitive notion of ontological priority. Then, I develop an analogous account of Kripke's models. I show that they exemplify the in-virtue-of relation much discussed in contemporary metaphysics, and thus are philosophically significant. I defend my proposal against a challenge from Kripke's “ghost of the hierarchy”

Noncomparabilities & Non Standard Logics

Many normative theories set forth in the welfare economics, distributive justice and cognate literatures posit noncomparabilities or incommensurabilities between magnitudes of various kinds. In some cases these gaps are predicated on metaphysical claims, in others upon epistemic claims, and in still others upon political-moral claims. I show that in all such cases they are best given formal expression in nonstandard logics that reject bivalence, excluded middle, or both. I do so by reference to an illustrative case study: a contradiction known to beset John Rawls\u27s selection and characterization of primary goods as the proper distribuendum in any distributively just society. The contradiction is avoided only by reformulating Rawls\u27s claims in a nonstandard form, which form happens also to cohere quite attractively with Rawls\u27s intuitive argumentation on behalf of his claims

Groundedness

In philosophical logic, a certain family of model constructions has received particular attention. Prominent examples are the cumulative hierarchy of well-founded sets, and Kripke’s least fixed point models of grounded truth. I develop a general formal theory of groundedness and explain how the well-founded sets, Cantor’s extended numbersequence and Kripke’s concepts of semantic groundedness are all instances of the general concept, and how the general framework illuminates these cases. Then, I develop a new approach to a grounded theory of proper classes. However, the general concept of groundedness does not account for the philosophical significance of its paradigm instances. Instead, I argue, the philosophical content of the cumulative hierarchy of sets is best understood in terms of a primitive notion of ontological priority. Then, I develop an analogous account of Kripke’s models. I show that they exemplify the in-virtue-of relation much discussed in contemporary metaphysics, and thus are philosophically significant. I defend my proposal against a challenge from Kripke’s “ghost of the hierarchy”

Modes of Truth

The aim of this volume is to open up new perspectives and to raise new research questions about a unified approach to truth, modalities, and propositional attitudes. The volume’s essays are grouped thematically around different research questions. The first theme concerns the tension between the theoretical role of the truth predicate in semantics and its expressive function in language. The second theme of the volume concerns the interaction of truth with modal and doxastic notions. The third theme covers higher-order solutions to the semantic and modal paradoxes, providing an alternative to first-order solutions embraced in the first two themes. This book will be of interest to researchers working in epistemology, logic, philosophy of logic, philosophy of language, philosophy of mathematics, and semantics