Presuppositions, Logic, and Dynamics of Belief

In researching presuppositions dealing with logic and dynamic of belief we distinguish two related parts. The first part refers to presuppositions and logic, which is not necessarily involved with intentional operators. We are primarily concerned with classical, free and presuppositonal logic. Here, we practice a well known Strawson’s approach to the problem of presupposition in relation to classical logic. Further on in this work, free logic is used, especially Van Fraassen’s research of the role of presupposition in supervaluations logical systems. At the end of the first part, presuppositional logic, advocated by S.K. Thomason, is taken into consideration. The second part refers to the presuppositions in relation to the logic of the dynamics of belief. Here the logic of belief change is taken into consideration and other epistemic notions with immanent mechanism for the presentation of the dynamics. Three representative and dominant approaches are evaluated. First, we deal with new, less classical, situation semantics. Besides Strawson’s theory, the second theory is the theory of the belief change, developed by Alchourron, Gärdenfors, and Makinson (AGM theory). At the end, the oldest, universal, and dominant approach is used, recognized as Hintikka’s approach to the analysis of epistemic notion

On Supervaluations, Meaning and Consequence

The problem of vagueness is motivated by consideration of a sorites series, and the supervaluationist solution is presented. It is argued that supervaluationism can be regarded as an application of the model-theoretic conception of consequence and should therefore be accepted by all. The limitations of this conception are then explored. In particular, if the theory is to provide a constitutive account of vagueness, an account of vagueness as underspecification is required. University of London Jacobsen Prize Essay 200

The implications of vagueness

Due to the character of the original source materials and the nature of batch digitization, quality control issues may be present in this document. Please report any quality issues you encounter to [email protected], referencing the URI of the item.Includes bibliographical references (leaves 29-30).If grains of sand are added, one by one, to a growing collection of sand on an otherwise empty table, there will eventually be a "heap" of sand on the table. It seems impossible, however, to specify the precise point at which the collection becomes a heap. One grain of sand is certainly not a heap of sand. Does two grains comprise a heap? Can the collection be called a heap at three grains, at 10 grains, or at 500 grains? The commonly used term "heap" is vague -- there is no clear line, which demarcates the heaps from the non-heaps. The difficulty presented by this vagueness becomes clear when we examine the sorites paradox, a very old philosophical problem, which is centered around the premise that the term "heap" has no precise definition. If it is impossible to specify exactly which objects are heaps and which objects are not heaps, how do we continue to use the term with such impunity? Is it possible for a system of logic to model the use of vague terms, if their application is often "neither true nor false," or, "only a matter of interpretation?" How are we to understand the role of vagueness within language

Free Higher-Order Logic - Notion, Definition and Embedding in HOL

Free logics are a family of logics that are free of any existential assumptions. This family can roughly be divided into positive, negative, neutral and supervaluational free logic whose semantics differ in the way how nondenoting terms are treated. While there has been remarkable work done concerning the definition of free first-order logic, free higher-order logic has not been addressed thoroughly so far. The purpose of this thesis is, firstly, to give a notion and definition of free higher-order logic based on simple type theory and, secondly, to propose faithful shallow semantical embeddings of free higher-order logic into classical higher order logic found on this definition. Such embeddings can then effectively be utilized to enable the application of powerful state-of-the-art higher-order interactive and automated theorem provers for the formalization and verification and also the further development of increasingly important free logical theories

Eventuality-based interval semantics and Free Logic: what if there, like, is no future, man?

2019 Summer.Includes bibliographical references.Future contingent propositions have famously been a source of trouble for philosophers and logicians committed to any variety of indeterminism on which facts about the future are not yet fixed. One possible answer to the problem involves presupposition—namely, that propositions lack truth-value when other propositions that they presuppose are false. This paper explores the plausibility of such an answer, beginning with a brief discussion of the problem of future contingent propositions and presupposition. From there, an in-depth discussion of Free Logic lays the groundwork of logical tools for the project, exploring the motivation for Free Logic's development and examples of Free Logic semantics. Subsequently, this paper discusses the history and usefulness of events-based semantics in analyzing English sentences. Using the tools of events-based semantics and formal logic, this paper formally models this approach to sentences in English by defining a semantics which can capture both tense and aspect of such sentences and which allows for truth-valueless future contingent propositions while preserving logical truths like the law of excluded middle

Counterfactuals and Undefinedness: Homogeneity vs. Supervaluations

Theories of counterfactuals agree on appealing to a relation of comparative similarity, but disagree on the quantificational force of counterfactuals. We report on two experiments testing the predictions of three main approaches: universal theories, homogeneity theories, and single-world selection theories (plus supervaluations over selection functions). The critical cases in our experiment were constructed so as to discriminate between the three theories. Our results provide empirical support for the selectional theories, while challenging the other two approaches

Borderline vs. unknown: comparing three-valued representations of imperfect information

International audienceIn this paper we compare the expressive power of elementary representation formats for vague, incomplete or conflicting information. These include Boolean valuation pairs introduced by Lawry and González-Rodríguez, orthopairs of sets of variables, Boolean possibility and necessity measures, three-valued valuations, supervaluations. We make explicit their connections with strong Kleene logic and with Belnap logic of conflicting information. The formal similarities between 3-valued approaches to vagueness and formalisms that handle incomplete information often lead to a confusion between degrees of truth and degrees of uncertainty. Yet there are important differences that appear at the interpretive level: while truth-functional logics of vagueness are accepted by a part of the scientific community (even if questioned by supervaluationists), the truth-functionality assumption of three-valued calculi for handling incomplete information looks questionable, compared to the non-truth-functional approaches based on Boolean possibility–necessity pairs. This paper aims to clarify the similarities and differences between the two situations. We also study to what extent operations for comparing and merging information items in the form of orthopairs can be expressed by means of operations on valuation pairs, three-valued valuations and underlying possibility distributions

Dissatisfaction Theory

I propose a new theory of semantic presupposition, which I call dissatisfaction theory. I first briefly review a cluster of problems − known collectively as the proviso problem − for most extant theories of presupposition, arguing that the main pragmatic response to them faces a serious challenge. I avoid these problems by adopting two changes in perspective on presupposition. First, I propose a theory of projection according to which presuppositions project unless they are locally entailed. Second, I reject the standard assumption that presuppositions are contents which must be entailed by the input context; instead, I propose that presuppositions are contents which are marked as backgrounded. I show that, together, these commitments allow us to avoid the proviso problem altogether, and generally make plausible predictions about presupposition projection out of connectives and attitude predicates. I close by sketching a two-dimensional implementation of my theory which allows us to make further welcome predictions about attitude predicates and quantifiers

Three Essays on Substructural Approaches to Semantic Paradoxes

This thesis consists of three papers on substructural approaches to semantic paradoxes. The first paper introduces a formal system, based on a nontransitive substructural logic, which has exactly the valid and antivalid inferences of classical logic at every level of (meta)inference, but which I argue is still not classical logic. In the second essay, I introduce infinite-premise versions of several semantic paradoxes, and show that noncontractive substructural approaches do not solve these paradoxes. In the third essay, I introduce an infinite metainferential hierarchy of validity curry paradoxes, and argue that providing a uniform solution to the paradoxes in this hierarchy makes substructural approaches less appealing. Together, the three essays in this thesis illustrate a problem for substructural approaches: substructural logics simply do not do everything that we need a logic to do, and so cannot solve semantic paradoxes in every context in which they appear. A new strategy, with a broader conception of what constitutes a uniform solution, is needed