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Handbook of functional connectivity Magnetic Resonance Imaging methods in CONN
This handbook describes methods for processing and analyzing functional connectivity Magnetic Resonance Imaging (fcMRI) data using the CONN toolbox, a popular freely-available functional connectivity analysis software. Content description [excerpt from introduction] The first section (fMRI minimal preprocessing pipeline) describes standard and advanced preprocessing steps in fcMRI. These steps are aimed at correcting or minimizing the influence of well-known factors affecting the quality of functional and anatomical MRI data, including effects arising from subject motion within the scanner, temporal and spatial image distortions due to the sequential nature of the scanning acquisition protoc...
Hilbert’s Program
Hilbert's Program was founded on a concern for the phenomenon of paradox in mathematics. To Hilbert, the paradoxes, which are at once both absurd and irresistible, revealed a deep philosophical truth: namely, that there is a discrepancy between the laws accord ing to which the mind of homo mathematicus works, and the laws governing objective mathematical fact. Mathematical epistemology is, therefore, to be seen as a struggle between a mind that naturally works in one way and a reality that works in another. Knowledge occurs when the two cooperate. Conceived in this way, there are two basic alternatives for mathematical epistemology: a skeptical position which maintains either that mind and r...
Hilbert's Programs and Beyond
David Hilbert was one of the great mathematicians who expounded the centrality of their subject in human thought. In this collection of essays, Wilfried Sieg frames Hilbert's foundational work, from 1890 to 1939, in a comprehensive way and integrates it with modern proof theoretic investigations.
Philosophy of Physics
This book deals with some of the current issues in the philosophy, methodology and foundations of physics. Some such problems are: - Do mathematical formalisms interpret themselves or is it necessary to adjoin them interpretation assumptions, and if so how are these as sumptions to be framed? - What are physical theories about: physical systems or laboratory operations or both or neither? - How are the basic concepts of a theory to be introduced: by ref erence to measurements or by explicit definition or axiomatically? - What is the use ofaxiomatics in physics? - How are the various physical theories inter-related: like Chinese boxes or in more complex ways? - What is the role of analogy in ...
Functional Analysis I
The twentieth-century view of the analysis of functions is dominated by the study of classes of functions. This volume of the Encyclopaedia covers the origins, development and applications of linear functional analysis, explaining along the way how one is led naturally to the modern approach.
Perceiving the World
This volumes collects new essays by top philosophers, all on the theme of perception while also making connections between perception and other philosophical areas like epistemology, metaphysics, and philosophy of action. Perception has become a major area of philosophical interest, with a number of important collections and monographs appearing recently. This may partly be due to the growing use of empirical and neuroscientific data by philosophers of mind. The contributors in this volume represent the high quality of current scholars (many OUP authors) working in the area, among them Jesse Prinz, Fred Dretske, Susanna Siegel, and Benj Hellie. Some of the questions they raise include, What ...
Proof Theory
hiS volume in the Synthese Library Series is the result of a conference T held at the University of Roskilde, Denmark, October 31st-November 1st, 1997. The aim was to provide a forum within which philosophers, math ematicians, logicians and historians of mathematics could exchange ideas pertaining to the historical and philosophical development of proof theory. Hence the conference was called Proof Theory: History and Philosophical Significance. To quote from the conference abstract: Proof theory was developed as part of Hilberts Programme. According to Hilberts Programme one could provide mathematics with a firm and se cure foundation by formalizing all of mathematics and subsequently prove...
Foundations of Mathematics and Physics One Century After Hilbert
This book explores the rich and deep interplay between mathematics and physics one century after David Hilbert’s works from 1891 to 1933, published by Springer in six volumes. The most prominent scientists in various domains of these disciplines contribute to this volume providing insight to their works, and analyzing the impact of the breakthrough and the perspectives of their own contributions. The result is a broad journey through the most recent developments in mathematical physics, such as string theory, quantum gravity, noncommutative geometry, twistor theory, Gauge and Quantum fields theories, just to mention a few. The reader, accompanied on this journey by some of the fathers of t...
Logic from Russell to Church
This volume is number five in the 11-volume Handbook of the History of Logic. It covers the first 50 years of the development of mathematical logic in the 20th century, and concentrates on the achievements of the great names of the period--Russell, Post, Gödel, Tarski, Church, and the like. This was the period in which mathematical logic gave mature expression to its four main parts: set theory, model theory, proof theory and recursion theory. Collectively, this work ranks as one of the greatest achievements of our intellectual history. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, and artificial intelligence, for whom the historical background of his or her work is a salient consideration.• The entire range of modal logic is covered• Serves as a singular contribution to the intellectual history of the 20th century• Contains the latest scholarly discoveries and interpretative insights
