Literature, Logic and Mathematics in the Fourteenth Century

This thesis assesses the extent to which fourteenth-century Middle English poets were interested in, and influenced by, traditions of thinking about logic and mathematics. It attempts to demonstrate the imaginative appeal of the logical problems called sophismata, which postulate absurd situations while making use of a stable but evolving, and distinctly recognisable, pool of examples. Logic and mathematics were linked. The ‘puzzle-based’ approach of late-medieval logic stemmed in part from earlier arithmetical puzzle collections. The fourteenth-century application of the ‘sophismatic’ method to problems concerned with what might now be called ‘Physics’ or ‘Mechanics’ sustained the symbiotic relationship of the two disciplines. An awareness of the importance of this tradition is perhaps indicated by the prominence of logical and mathematical tropes and scenarios in the works of three authors in particular: Geoffrey Chaucer, John Gower and the Gawain-poet. It is argued that, in the poetry of all three, what may loosely be called ‘sophismatic tropes’ are used to present concerns that the poets share with the logical and mathematical thought of their time. Certain themes recur, including the following: problematic promises; problematic reference to non-existent things; problems associated with divisibility, limits and the idea of a continuum; and, most importantly, problems focused on the contingency, or otherwise, of the future. The debate over future contingency was one of the fiercest scholastic controversies of the fourteenth century, with profound implications for both logical and theological thought. It is suggested here that the scholastic debate about future contingency has a visible impact on Chauntecleer’s prophetic dream in the Nun’s Priest’s Tale, Troilus’s apparent determinism in Troilus and Criseyde, Gower’s presentation of causation in the Confessio Amantis, and the Gawain-poet’s treatment of covenants. The conclusion reached is that fourteenth-century logical and mathematical texts had a significantly wider cultural effect than is generally recognised

Vagueness and Its Boundaries: A Peircean Theory of Vagueness

Indiana University-Purdue University Indianapolis (IUPUI)Many theories of vagueness employ question-begging assumptions about the semantic boundaries between truth and falsity. This thesis defends a theory of vagueness put forward by Charles S. Peirce and argues for a novel solution to the sorites paradox based upon his work. Contrary to widespread opinion, I argue that Peirce distinguished borderline vagueness from other related forms of indeterminacy, e.g. indefiniteness, generality, unspecificity, uninformativity, etc. By clarifying Peirce’s conception of borderline vagueness, I argue for a solution to the sorites paradox based upon his logical semantics. In addition, I argue for this theory against the epistemic theory of vagueness, which makes controversial claims concerning the sharp semantic boundary between truth and falsity, and against the supervaluationist theory of vagueness, which is committed to the in principle impossibility of sharp semantics boundaries for propositions with vague terms

Language is a complex adaptive system

The ASLAN labex - Advanced studies on language complexity - brings together a unique set of expertise and varied points of view on language. In this volume, we employ three main sections showcasing diverse empirical work to illustrate how language within human interaction is a complex and adaptive system. The first section – epistemological views on complexity – pleads for epistemological plurality, an end to dichotomies, and proposes different ways to connect and translate between frameworks. The second section – complexity, pragmatics and discourse – focuses on discourse practices at different levels of description. Other semiotic systems, in addition to language are mobilized, but also interlocutors’ perception, memory and understanding of culture. The third section – complexity, interaction, and multimodality – employs different disciplinary frameworks to weave between micro, meso, and macro levels of analyses. Our specific contributions include adding elements to and extending the field of application of the models proposed by others through new examples of emergence, interplay of heterogeneous elements, intrinsic diversity, feedback, novelty, self-organization, adaptation, multi-dimensionality, indeterminism, and collective control with distributed emergence. Finally, we argue for a change in vantage point regarding the search for linguistic universals

The Liar Paradox: A Consistent and Semantically Closed Solution

This thesis develops a new approach to the formal de nition of a truth predicate that allows a consistent, semantically closed defiition within classical logic. The approach is built on an analysis of structural properties of languages that make Liar Sentences and the paradoxical argument possible. By focusing on these conditions, standard formal dfinitions of semantics are shown to impose systematic limitations on the definition of formal truth predicates. The alternative approach to the formal definition of truth is developed by analysing our intuitive procedure for evaluating the truth value of sentences like "P is true". It is observed that the standard procedure breaks down in the case of the Liar Paradox as a side effect of the patterns of naming or reference necessary to the definition of Truth as a predicate. This means there are two ways in which a sentence like "P is true" can be not true, which requires that the T-Schema be modified for such sentences. By modifying the T-Schema, and taking seriously the effects of the patterns of naming/ reference on truth values, the new approach to the definition of truth is developed. Formal truth definitions within classical logic are constructed that provide an explicit and adequate truth definition for their own language, every sentence within the languages has a truth value, and there is no Strengthened Liar Paradox. This approach to solving the Liar Paradox can be easily applied to a very wide range of languages, including natural languages

Metaphors of travel in the language of hymns: 1650–1800

This dissertation concentrates on the role of the conceptual metaphor LIFE IS A JOURNEY in English hymns of the 17th and 18th centuries, addressing the following research questions: 1) To what extent and in which contexts have elements of the lexical category of travel, applied metaphorically, been used in English spiritual language and literature in the period 1650–1800? 2) How has metaphorical extension affected the semantic development of this category? This dissertation discusses the use of travel metaphors as structural schemata for complete hymns, and analyzes the use of individual elements of travel-related terminology across a historical textual corpus. The analyses in this dissertation are undertaken in light of recent trends in semantics, and with the aim of contributing to the development of Cognitive Metaphor Theory as a tool for historical linguistic analysis and literary criticism