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A survey of the most important axiomatizations of truth, exploring their properties and how the logical results impinge on philosophical topics.
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This volume covers a wide range of topics in the most recent debates in the philosophy of mathematics, and is dedicated to how semantic, epistemological, ontological and logical issues interact in the attempt to give a satisfactory picture of mathematical knowledge. The essays collected here explore the semantic and epistemic problems raised by different kinds of mathematical objects, by their characterization in terms of axiomatic theories, and by the objectivity of both pure and applied mathematics. They investigate controversial aspects of contemporary theories such as neo-logicist abstractionism, structuralism, or multiversism about sets, by discussing different conceptions of mathematic...
This volume contains the proceedings of the Logic at Harvard conference in honor of W. Hugh Woodin's 60th birthday, held March 27–29, 2015, at Harvard University. It presents a collection of papers related to the work of Woodin, who has been one of the leading figures in set theory since the early 1980s. The topics cover many of the areas central to Woodin's work, including large cardinals, determinacy, descriptive set theory and the continuum problem, as well as connections between set theory and Banach spaces, recursion theory, and philosophy, each reflecting a period of Woodin's career. Other topics covered are forcing axioms, inner model theory, the partition calculus, and the theory of ultrafilters. This volume should make a suitable introduction to Woodin's work and the concerns which motivate it. The papers should be of interest to graduate students and researchers in both mathematics and philosophy of mathematics, particularly in set theory, foundations and related areas.
This volume honours the life and work of Solomon Feferman, one of the most prominent mathematical logicians of the latter half of the 20th century. In the collection of essays presented here, researchers examine Feferman’s work on mathematical as well as specific methodological and philosophical issues that tie into mathematics. Feferman’s work was largely based in mathematical logic (namely model theory, set theory, proof theory and computability theory), but also branched out into methodological and philosophical issues, making it well known beyond the borders of the mathematics community. With regard to methodological issues, Feferman supported concrete projects. On the one hand, thes...
Logical consequence is the relation that obtains between premises and conclusion(s) in a valid argument. Orthodoxy has it that valid arguments are necessarily truth-preserving, but this platitude only raises a number of further questions, such as: how does the truth of premises guarantee the truth of a conclusion, and what constraints does validity impose on rational belief? This volume presents thirteen essays by some of the most important scholars in the field of philosophical logic. The essays offer ground-breaking new insights into the nature of logical consequence; the relation between logic and inference; how the semantics and pragmatics of natural language bear on logic; the relativity of logic; and the structural properties of the consequence relation.
This book is a printed edition of the Special Issue "Atherosclerosis and Vascular Imaging 2016" that was published in IJMS
“Contradiction” is a core concept in the humanities and the social sciences. Beside the classical ideas of logical or dialectical contradiction, instances of “lived” contradiction and strategies of coping with it are objects of this study. Contradiction Studies discuss the many ways in which explicit or implicit contradictions are negotiated in different political or cultural settings. This volume collects articles that tackle the concept of contradiction, practices of contradicting and lived contradictions from a number of relevant perspectives and assembles contributions from linguistics, literary studies, philosophy, political science, and media studies.
Tissue fibrosis may occur for unknown causes or be the consequence of many pathological conditions including chronic inflammatory or infectious diseases, autoimmune disorders, graft rejection, or malignancy. On the other hand, malignant tumors have been identified in fibrotic tissues decades ago, and now accumulating evidence suggests that fibrotic lesions enhance the risk of cancer in several organs such as liver, lungs, and breast. Disruption of an organ parenchymal cells and of its normal structural scaffold during tissue fibrogenesis appears to induce loss of cell polarity, promoting uncontrolled cell proliferation that may eventually lead to cancer development. Many cellular and molecul...