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How to Prove It
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
Foundations for Moral Relativism
In this new edition of Foundations for Moral Relativism a distinguished moral philosopher tames a bugbear of current debate about cultural difference. J. David Velleman shows that different communities can indeed be subject to incompatible moralities, because their local mores are rationally binding. At the same time, he explains why the mores of different communities, even when incompatible, are still variations on the same moral themes. The book thus maps out a universe of many moral worlds without, as Velleman puts it, "moral black holes”. The six self-standing chapters discuss such diverse topics as online avatars and virtual worlds, lying in Russian and truth-telling in Quechua, the pleasure of solitude and the fear of absurdity. Accessibly written, this book presupposes no prior training in philosophy.
Beyond Price
In nine lively essays, bioethicist J. David Velleman challenges the prevailing consensus about assisted suicide and reproductive technology, articulating an original approach to the ethics of creating and ending human lives. He argues that assistance in dying is appropriate only at the point where talk of suicide is not, and he raises moral objections to anonymous donor conception. In their place, Velleman champions a morality of valuing personhood over happiness in making end-of-life decisions, and respecting the personhood of future children in making decisions about procreation. These controversial views are defended with philosophical rigor while remaining accessible to the general reader. Written over Velleman's 30 years of undergraduate teaching in bioethics, the essays have never before been collected and made available to a non-academic audience. They will open new lines of debate on issues of intense public interest.
Self to Self
This collection of essays by philosopher J. David Velleman on personal identity, autonomy, and moral emotions is united by an overarching thesis that there is no single entity denoted by 'the self', as well as themes from Kantian ethics and Velleman's work in the philosophy of action.
Calculus: A Rigorous First Course
Designed for undergraduate mathematics majors, this rigorous and rewarding treatment covers the usual topics of first-year calculus: limits, derivatives, integrals, and infinite series. Author Daniel J. Velleman focuses on calculus as a tool for problem solving rather than the subject's theoretical foundations. Stressing a fundamental understanding of the concepts of calculus instead of memorized procedures, this volume teaches problem solving by reasoning, not just calculation. The goal of the text is an understanding of calculus that is deep enough to allow the student to not only find answers to problems, but also achieve certainty of the answers' correctness. No background in calculus is necessary. Prerequisites include proficiency in basic algebra and trigonometry, and a concise review of both areas provides sufficient background. Extensive problem material appears throughout the text and includes selected answers. Complete solutions are available to instructors.
Philosophies of Mathematics
This book provides an accessible, critical introduction to the three main approaches that dominated work in the philosophy of mathematics during the twentieth century: logicism, intuitionism and formalism.
How We Get Along
Philosopher David Velleman compares our social interactions to the interactions among improvisational actors on stage.
On Being Me
"In being me, a philosopher reflects in everyday language on what it is like to be a person, arriving at unexpected conclusions about the self and its future, time and mortality, free will and personal efficacy, regret and love. These topics are explored in brief sections titled "Wanting to go on", "Running out of time", "Regretting what might have been", "Aspiring to Authorship", "Making things happen", and "Wanting to be loved". Written in the first person, the text shows how reflecting on ordinary human concerns can lead anyone to profound puzzles that only philosophy can solve. Familiar examples and an artist's illustrations make each train of thought accessible to readers having no prior acquaintance with philosophy"--
How to Prove It
This new edition of Daniel J. Velleman's successful textbook contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software.
Practical Reflection
"What do you see when you look at your face in the mirror?" asks J. David Velleman in introducing his philosophical theory of action. The face that you see is doing two things - trying to see itself and presenting itself to be seen. Velleman takes this simple act of self-scrutiny as a model for the reflective reasoning of rational agents: our efforts to understand our conduct are aided by our reciprocal efforts to make it intelligible. He then argues that this reflective reasoning is what constitutes practical reasoning, the reasoning by which we figure out what to do. The thing to do, he claims, is the thing that would make sense, in that it would be intelligible. By applying this conception of practical reasoning, Velleman develops philosophical accounts of intention, free will, and the foundations of values and morals. --
