Book picks similar to
Philosophy of Mathematics: Selected Readings by Paul Benacerraf
philosophy
mathematics
math
philosophy-of-mathematics
The Elements of Statistical Learning: Data Mining, Inference, and Prediction
Trevor Hastie - 2001
With it has come vast amounts of data in a variety of fields such as medicine, biology, finance, and marketing. The challenge of understanding these data has led to the development of new tools in the field of statistics, and spawned new areas such as data mining, machine learning, and bioinformatics. Many of these tools have common underpinnings but are often expressed with different terminology. This book describes the important ideas in these areas in a common conceptual framework. While the approach is statistical, the emphasis is on concepts rather than mathematics. Many examples are given, with a liberal use of color graphics. It should be a valuable resource for statisticians and anyone interested in data mining in science or industry. The book's coverage is broad, from supervised learning (prediction) to unsupervised learning. The many topics include neural networks, support vector machines, classification trees and boosting—the first comprehensive treatment of this topic in any book. Trevor Hastie, Robert Tibshirani, and Jerome Friedman are professors of statistics at Stanford University. They are prominent researchers in this area: Hastie and Tibshirani developed generalized additive models and wrote a popular book of that title. Hastie wrote much of the statistical modeling software in S-PLUS and invented principal curves and surfaces. Tibshirani proposed the Lasso and is co-author of the very successful An Introduction to the Bootstrap. Friedman is the co-inventor of many data-mining tools including CART, MARS, and projection pursuit.
Nietzsche and Philosophy
Gilles Deleuze - 1962
It is also one of the best introductions to Deleuze's thought, establishing many of his central philosophical positions.In Nietzsche and Philosophy, Deleuze identifies and explores three crucial concepts in Nietzschean thought-multiplicity, becoming, and affirmation-and clarifies Nietzsche's views regarding the will to power, eternal return, nihilism, and difference. For Deleuze, Nietzsche challenged conventional philosophical ideas and provided a means of escape from Hegel's dialectical thinking, which had come to dominate French philosophy. He also offered a path toward a politics of difference. In this new edition, Michael Hardt's foreword examines the profound influence of Deleuze's provocative interpretations on the study of Nietzsche, which opened a whole new avenue in postwar thought.
Introduction to Graph Theory
Richard J. Trudeau - 1994
This book leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. Includes exercises. 1976 edition.
A Concise Introduction to Logic [with CD-ROM]
Patrick J. Hurley - 1972
Inside: Logic Resource CD-ROM
Truth: A Guide
Simon Blackburn - 1999
Now Blackburn offers a tour de force exploration of what he calls the most exciting and engaging issue in the whole of philosophy--the age-old war over truth.The front lines of this war are well defined. On one side are those who believe in plain, unvarnished facts, rock-solid truths that can be found through reason and objectivity--that science leads to truth, for instance. Their opponents mock this idea. They see the dark forces of language, culture, power, gender, class, ideology and desire--all subverting our perceptions of the world, and clouding our judgement with false notions of absolute truth. Beginning with an early skirmish in the war--when Socrates confronted the sophists in ancient Athens--Blackburn offers a penetrating look at the longstanding battle these two groups have waged, examining the philosophical battles fought by Plato, Protagoras, William James, David Hume, Hans-Georg Gadamer, Jacques Derrida, Michel Foucault, Richard Rorty, and many others, with a particularly fascinating look at Nietzsche. Among the questions Blackburn considers are: is science mere opinion, can historians understand another historical period, and indeed can one culture ever truly understand another.Blackburn concludes that both sides have merit, and that neither has exclusive ownership of truth. What is important is that, whichever side we embrace, we should know where we stand and what is to be said for our opponents.
Wholeness and the Implicate Order
David Bohm - 1980
Although deeply influenced by Einstein, he was also, more unusually for a scientist, inspired by mysticism. Indeed, in the 1970s and 1980s he made contact with both J. Krishnamurti and the Dalai Lama whose teachings helped shape his work. In both science and philosophy, Bohm's main concern was with understanding the nature of reality in general and of consciousness in particular. In this classic work he develops a theory of quantum physics which treats the totality of existence as an unbroken whole. Writing clearly and without technical jargon, he makes complex ideas accessible to anyone interested in the nature of reality.
Irrationality: A History of the Dark Side of Reason
Justin E.H. Smith - 2019
Once, humans were benighted by superstition and irrationality, but then the Greeks invented reason. Later, the Enlightenment enshrined rationality as the supreme value. Discovering that reason is the defining feature of our species, we named ourselves the "rational animal." But is this flattering story itself rational? In this sweeping account of irrationality from antiquity to today--from the fifth-century BC murder of Hippasus for revealing the existence of irrational numbers to the rise of Twitter mobs and the election of Donald Trump—Justin Smith says the evidence suggests the opposite. From sex and music to religion and war, irrationality makes up the greater part of human life and history.Rich and ambitious, Irrationality ranges across philosophy, politics, and current events. Challenging conventional thinking about logic, natural reason, dreams, art and science, pseudoscience, the Enlightenment, the internet, jokes and lies, and death, the book shows how history reveals that any triumph of reason is temporary and reversible, and that rational schemes, notably including many from Silicon Valley, often result in their polar opposite. The problem is that the rational gives birth to the irrational and vice versa in an endless cycle, and any effort to permanently set things in order sooner or later ends in an explosion of unreason. Because of this, it is irrational to try to eliminate irrationality. For better or worse, it is an ineradicable feature of life.Illuminating unreason at a moment when the world appears to have gone mad again, Irrationality is fascinating, provocative, and timely.
Philosophical Hermeneutics
Hans-Georg Gadamer - 1976
Gadamer applies hermeneutical analysis to Heidegger and Husserl's phenomenology, an approach that proves critical and instructive.
Structure and Interpretation of Computer Programs
Harold Abelson - 1984
This long-awaited revision contains changes throughout the text. There are new implementations of most of the major programming systems in the book, including the interpreters and compilers, and the authors have incorporated many small changes that reflect their experience teaching the course at MIT since the first edition was published. A new theme has been introduced that emphasizes the central role played by different approaches to dealing with time in computational models: objects with state, concurrent programming, functional programming and lazy evaluation, and nondeterministic programming. There are new example sections on higher-order procedures in graphics and on applications of stream processing in numerical programming, and many new exercises. In addition, all the programs have been reworked to run in any Scheme implementation that adheres to the IEEE standard.
Unknown Quantity: A Real and Imaginary History of Algebra
John Derbyshire - 2006
As he did so masterfully in Prime Obsession, Derbyshire brings the evolution of mathematical thinking to dramatic life by focusing on the key historical players. Unknown Quantity begins in the time of Abraham and Isaac and moves from Abel's proof to the higher levels of abstraction developed by Galois through modern-day advances. Derbyshire explains how a simple turn of thought from this plus this equals this to this plus what equals this? gave birth to a whole new way of perceiving the world. With a historian's narrative authority and a beloved teacher's clarity and passion, Derbyshire leads readers on an intellectually satisfying and pleasantly challenging historical and mathematical journey.
Essays on the Theory of Numbers
Richard Dedekind - 1901
W. R. Dedekind. The first presents Dedekind's theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had been used on an intuitive basis since Greek times. This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis.The second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers. It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction.The contents of these essays belong to the foundations of mathematics and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the elements of our number system. As a major work of an important mathematician, the book deserves a place in the personal library of every practicing mathematician and every teacher and historian of mathematics. Authorized translations by "Vooster " V. Beman.
Every Thing Must Go: Metaphysics Naturalized
James Ladyman - 2007
In addition to showing how recent metaphysics has drifted away from connection with all other serious scholarly inquiry as a result of not heeding this restriction, they demonstrate how to build a metaphysics compatible with current fundamental phsyics ("ontic structural realism"), which, when combined with their metaphysics of the special sciences ("rainforest realism"), can be used to unify physics with the other sciences without reducing these sciences to physics intself. Taking science metaphysically seriously, Ladyman and Ross argue, means that metaphysicians must abandon the picture of the world as composed of self-subsistent individual objects, and the paradigm of causation as the collision of such objects. Every Thing Must Go also assesses the role of information theory and complex systems theory in attempts to explain the relationship between the special sciences and physics, treading a middle road between the grand synthesis of thermodynamics and information, and eliminativism about information. The consequences of the author's metaphysical theory for central issues in the philosophy of science are explored, including the implications for the realism vs. empiricism debate, the role of causation in scientific explanations, the nature of causation and laws, the status of abstract and virtual objects, and the objective reality of natural kinds
Mathematics: Is God Silent?
James Nickel - 2001
The addition of this book is a must for all upper-level Christian school curricula and for college students and adults interested in math or related fields of science and religion. It will serve as a solid refutation for the claim, often made in court, that mathematics is one subject, which cannot be taught from a distinctively Biblical perspective.
Language, Proof and Logic: Text and CD
Jon Barwise - 1999
The unique on-line grading services instantly grades solutions to hundred of computer exercises. It is specially devised to be used by philosophy instructors in a way that is useful to undergraduates of philosophy, computer science, mathematics, and linguistics.The book is a completely rewritten and much improved version of The Language of First-order Logic. Introductory material is presented in a more systematic and accessible fashion. Advanced chapters include proofs of soundness and completeness for propositional and predicate logic, as well as an accessible sketch of Godel's first incompleteness theorem. The book is appropriate for a wide range of courses, from first logic courses for undergraduates (philosophy, mathematics, and computer science) to a first graduate logic course.The package includes four pieces of software:Tarski's World 5.0, a new version of the popular program that teaches the basic first-order language and its semantics; Fitch, a natural deduction proof environment for giving and checking first-order proofs;Boole, a program that facilitates the construction and checking of truth tables and related notions (tautology, tautological consequence, etc.);Submit, a program that allows students to submit exercises done with the above programs to the Grade Grinder, the automatic grading service.Grade reports are returned to the student and, if requested, to the student's instructor, eliminating the need for tedious checking of homework. All programs are available for Windows, Macintosh and Linux systems.Instructors do not need to use the programs themselves in order to be able to take advantage of their pedagogical value. More about the software can be found at lpl.stanford.edu.The price of a new text/software package includes one Registration ID, which must be used each time work is submitted to the grading service. Once activated, the Registration ID is not transferable.
Economic Philosophy
Joan Robinson - 1962
It limps along with one foot in untested hypotheses and the other in untestable slogans. Here our task is to sort out as best we may this mixture of ideology and science.- With these provocative words, Joan Robinson introduces this lively and iconoclastic book. -In what follows, - she says, -this theme is illustrated by reference to one or two of the leading ideas of the economists from Adam Smith onwards, not in a learned manner, tracing the development of thought, nor historically, to show how ideas arose out of the problems of each age, but rather an attempt to puzzle out the mysterious way that metaphysical propositions, without any logical content, can yet be a powerful influence on thought and action.- Robinson is responsible for some of the most austerely professional contributions to economic theory, but here in effect she takes the reader behind the scenes and cheerfully exposes the dogmatic content of economic orthodoxy. In its place, she offers the possibility that with obsolete metaphysics cleared out of the way economics can make a substantial advance toward science. .