The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it.
Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer?
How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God.
Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.
Being a winner means more than just picking a lucky lottery ticket, it means that you have improved yourself and your environment to ensure that your luck is good and your chances of success are high.
Being a winner does not mean that you are better than somebody is, it means that you have achieved your goals; you have won the path to your destiny. Sounds too good to be true? Well, it is not. You can be a winner, take a gamble on yourself, and find out how lucky you can be in your own life.
Stop wishing for things to happen your way, and work towards it.
A New York Times Notable Book.
The Babylonians invented it, the Greeks banned it, the Hindus worshiped it, and the Church used it to fend off heretics. Now it threatens the foundations of modern physics. For centuries the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. For zero, infinity's twin, is not like other numbers. It is both nothing and everything.
In Zero, Science Journalist Charles Seife follows this innocent-looking number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe, its rise and transcendence in the West, and its ever-present threat to modern physics. Here are the legendary thinkers—from Pythagoras to Newton to Heisenberg, from the Kabalists to today's astrophysicists—who have tried to understand it and whose clashes shook the foundations of philosophy, science, mathematics, and religion. Zero has pitted East against West and faith against reason, and its intransigence persists in the dark core of a black hole and the brilliant flash of the Big Bang. Today, zero lies at the heart of one of the biggest scientific controversies of all time: the quest for a theory of everything.
The antidote to fuzzy thinking, with furry animals!
Have you read (or stumbled into) one too many irrational online debates? Ali Almossawi certainly had, so he wrote An Illustrated Book of Bad Arguments! This handy guide is here to bring the internet age a much-needed dose of old-school logic (really old-school, a la Aristotle).
Here are cogent explanations of the straw man fallacy, the slippery slope argument, the ad hominem attack, and other common attempts at reasoning that actually fall short—plus a beautifully drawn menagerie of animals who (adorably) commit every logical faux pas. Rabbit thinks a strange light in the sky must be a UFO because no one can prove otherwise (the appeal to ignorance). And Lion doesn’t believe that gas emissions harm the planet because, if that were true, he wouldn’t like the result (the argument from consequences).
Once you learn to recognize these abuses of reason, they start to crop up everywhere from congressional debate to YouTube comments—which makes this geek-chic book a must for anyone in the habit of holding opinions.
Considered to be one of the most important philosophical works of all time, the History of Western Philosophy is a dazzlingly unique exploration of the ideologies of significant philosophers throughout the ages—from Plato and Aristotle through to Spinoza, Kant and the twentieth century. Written by a man who changed the history of philosophy himself, this is an account that has never been rivaled since its first publication over sixty years ago.
Since its first publication in 1945, Lord Russell’s A History of Western Philosophy is still unparalleled in its comprehensiveness, its clarity, its erudition, its grace, and its wit. In seventy-six chapters he traces philosophy from the rise of Greek civilization to the emergence of logical analysis in the twentieth century.
Among the philosophers considered are: Pythagoras, Heraclitus, Parmenides, Empedocles, Anaxagoras, the Atomists, Protagoras, Socrates, Plato, Aristotle, the Cynics, the Sceptics, the Epicureans, the Stoics, Plotinus, Ambrose, Jerome, Augustine, Benedict, Gregory the Great, John the Scot, Aquinas, Duns Scotus, William of Occam, Machiavelli, Erasmus, More, Bacon, Hobbes, Descartes, Spinoza, Leibniz, Locke, Berkeley, Hume, Rousseau, Kant, Hegel, Schopenhauer, Nietzsche, the Utilitarians, Marx, Bergson, James, Dewey, and lastly the philosophers with whom Lord Russell himself is most closely associated—Cantor, Frege, and Whitehead, coauthor with Russell of the monumental Principia Mathematica.
Logically Fallacious is one of the most comprehensive collections of logical fallacies with all original examples and easy to understand descriptions, perfect for educators, debaters, or anyone who wants to improve his or her reasoning skills.
"Expose an irrational belief, keep a person rational for a day. Expose irrational thinking, keep a person rational for a lifetime." - Bo Bennett
From Socrates to Sartre presents a rousing and readable introduction to the lives, and times of the great philosophers. This thought-provoking book takes us from the inception of Western society in Plato’s Athens to today when the commanding power of Marxism has captured one third of the world. T. Z. Lavine, Elton Professor of Philosophy at George Washington University, makes philosophy come alive with astonishing clarity to give us a deeper, more meaningful understanding of ourselves and our times.
From Socrates to Sartre discusses Western philosophers in terms of the historical and intellectual environment which influenced them, and it connects their lasting ideas to the public and private choices we face in America today.
From Socrates to Sartre formed the basis of from the PBS television series of the same name.
From the Paperback edition.
Winner of the 2011 National Book Award for Non-Fiction One of the world's most celebrated scholars, Stephen Greenblatt has crafted both an innovative work of history and a thrilling story of discovery, in which one manuscript, plucked from a thousand years of neglect, changed the course of human thought and made possible the world as we know it.
Nearly six hundred years ago, a short, genial, cannily alert man in his late thirties took a very old manuscript off a library shelf, saw with excitement what he had discovered, and ordered that it be copied. That book was the last surviving manuscript of an ancient Roman philosophical epic, On the Nature of Things, by Lucretius—a beautiful poem of the most dangerous ideas: that the universe functioned without the aid of gods, that religious fear was damaging to human life, and that matter was made up of very small particles in eternal motion, colliding and swerving in new directions.
The copying and translation of this ancient book-the greatest discovery of the greatest book-hunter of his age-fueled the Renaissance, inspiring artists such as Botticelli and thinkers such as Giordano Bruno; shaped the thought of Galileo and Freud, Darwin and Einstein; and had a revolutionary influence on writers such as Montaigne and Shakespeare and even Thomas Jefferson.
With their accessible compendium of philosophy and social progress, the Durants take us on a journey through history, exploring the possibilities and limitations of humanity over time. Juxtaposing the great lives, ideas, and accomplishments with cycles of war and conquest, the Durants reveal the towering themes of history and give meaning to our own.
Eric Steinhart provides lucid explanations of the basic mathematical concepts and sets out most commonly used notational conventions. Furthermore, he demonstrates how mathematics applies to many fundamental issues in branches of philosophy such as metaphysics, philosophy of language, epistemology, and ethics.
And now, you can read Daniel Klein's further musings on life and philosophy in Travels with Epicurus and Every Time I Find the Meaning of Life, They Change it.
From the Trade Paperback edition.
Did Newton “unweave the rainbow” by reducing it to its prismatic colors, as Keats contended? Did he, in other words, diminish beauty? Far from it, says acclaimed scientist Richard Dawkins; Newton’s unweaving is the key too much of modern astronomy and to the breathtaking poetry of modern cosmology. Mysteries don’t lose their poetry because they are solved: the solution often is more beautiful than the puzzle, uncovering deeper mysteries. With the wit, insight, and spellbinding prose that have made him a bestselling author, Dawkins takes up the most important and compelling topics in modern science, from astronomy and genetics to language and virtual reality, combining them in a landmark statement of the human appetite for wonder.
This is the book Richard Dawkins was meant to write: a brilliant assessment of what science is (and isn’t), a tribute to science not because it is useful but because it is uplifting.
“A love letter to science, an attempt to counter the perception that science is cold and devoid of aesthetic sensibility . . . Rich with metaphor, passionate arguments, wry humor, colorful examples, and unexpected connections, Dawkins’ prose can be mesmerizing.” —San Francisco Chronicle
“Brilliance and wit.” —The New Yorker
When young Joseph Banks stepped onto a Tahitian beach in 1769, he hoped to discover Paradise. Inspired by the scientific ferment sweeping through Britain, the botanist had sailed with Captain Cook in search of new worlds. Other voyages of discovery—astronomical, chemical, poetical, philosophical—swiftly follow in Richard Holmes's thrilling evocation of the second scientific revolution. Through the lives of William Herschel and his sister Caroline, who forever changed the public conception of the solar system; of Humphry Davy, whose near-suicidal gas experiments revolutionized chemistry; and of the great Romantic writers, from Mary Shelley to Coleridge and Keats, who were inspired by the scientific breakthroughs of their day, Holmes brings to life the era in which we first realized both the awe-inspiring and the frightening possibilities of science—an era whose consequences are with us still.
BONUS MATERIAL: This ebook edition includes an excerpt from Richard Holmes's Falling Upwards.
Utilizing real questions submitted to his popular website ReasonableFaith.org, Dr. Craig models well-reasoned, skillful, and biblically informed interaction with his inquirers. A Reasonable Response goes beyond merely talking about apologetics; it shows it in action. With cowriter Joseph E. Gorra, this book also offers advice about envisioning and practicing the ministry of answering people’s questions through the local church, workplace, and in online environments.
Whether you're struggling to respond to tough objections or looking for answers to your own intellectual questions, A Reasonable Response will equip you with sound reasoning and biblical truth.
From the Trade Paperback edition.
Lively, clever, and thought-provoking, The Pig That Wants to Be Eaten is a portable feast for the mind that is sure to satisfy any intellectual appetite.
The two-part selection of puzzles and paradoxes begins with examinations of the nature of infinity and some curious systems related to Gödel's theorem. The first three chapters of Part II contain generalized Gödel theorems. Symbolic logic is deferred until the last three chapters, which give explanations and examples of first-order arithmetic, Peano arithmetic, and a complete proof of Gödel's celebrated result involving statements that cannot be proved or disproved. The book also includes a lively look at decision theory, better known as recursion theory, which plays a vital role in computer science.
Ideas are the cogs that drive history, and in explaining the most complex and influential ones in laymen's terms, Ideas that Matter will help every engaged citizen better understand it.
For anyone tackling philosophical logic and critical thinking for the first time, Critical Thinking: An Introduction to Reasoning Well provides a practical guide to the skills required to think critically. From the basics of good reasoning to the difference between claims, evidence and arguments, Robert Arp and Jamie Carlin Watson cover the topics found in an introductory course.
Now revised and fully updated, this Second Edition features a glossary, chapter summaries, more student-friendly exercises, study questions, diagrams, and suggestions for further reading. Topics include:
the structure, formation, analysis and recognition of arguments
deductive validity and soundness
inductive strength and cogency
inference to the best explanation
tools for argument assessment
informal and formal fallacies
With real life examples, advice on graduate school entrance exams and an expanded companion website packed with additional exercises, an answer key and help with real life examples, this easy-to-follow introduction is a complete beginner's tool set to good reasoning, analyzing and arguing. Ideal for students in basic reasoning courses and students preparing for graduate school.
Game theory shows that in order to coordinate its actions, a group of people must form "common knowledge." Each person wants to participate only if others also participate. Members must have knowledge of each other, knowledge of that knowledge, knowledge of the knowledge of that knowledge, and so on. Michael Chwe applies this insight, with striking erudition, to analyze a range of rituals across history and cultures. He shows that public ceremonies are powerful not simply because they transmit meaning from a central source to each audience member but because they let audience members know what other members know. For instance, people watching the Super Bowl know that many others are seeing precisely what they see and that those people know in turn that many others are also watching. This creates common knowledge, and advertisers selling products that depend on consensus are willing to pay large sums to gain access to it. Remarkably, a great variety of rituals and ceremonies, such as formal inaugurations, work in much the same way.
By using a rational-choice argument to explain diverse cultural practices, Chwe argues for a close reciprocal relationship between the perspectives of rationality and culture. He illustrates how game theory can be applied to an unexpectedly broad spectrum of problems, while showing in an admirably clear way what game theory might hold for scholars in the social sciences and humanities who are not yet acquainted with it.
In a new afterword, Chwe delves into new applications of common knowledge, both in the real world and in experiments, and considers how generating common knowledge has become easier in the digital age.
Logic is synonymous with reason, judgment, sense, wisdom, and sanity. Being logical is the ability to create concise and reasoned arguments—arguments that build from given premises, using evidence, to a genuine conclusion. But mastering logical thinking also requires studying and understanding illogical thinking, both to sharpen one’s own skills and to protect against incoherent, or deliberately misleading, reasoning.
Elegant, pithy, and precise, Being Logical breaks logic down to its essentials through clear analysis, accessible examples, and focused insights. D. Q. McInerney covers the sources of illogical thinking, from naïve optimism to narrow-mindedness, before dissecting the various tactics—red herrings, diversions, and simplistic reasoning—the illogical use in place of effective reasoning.
An indispensable guide to using logic to advantage in everyday life, this is a concise, crisply readable book. Written explicitly for the layperson, McInerny’s Being Logical promises to take its place beside Strunk and White’s The Elements of Style as a classic of lucid, invaluable advice.
Praise for Being Logical
“Highly readable . . . D. Q. McInerny offers an introduction to symbolic logic in plain English, so you can finally be clear on what is deductive reasoning and what is inductive. And you’ll see how deductive arguments are constructed.”—Detroit Free Press
“McInerny’s explanatory outline of sound thinking will be eminently beneficial to expository writers, debaters, and public speakers.”—Booklist
“Given the shortage of logical thinking,
And the fact that mankind is adrift, if not sinking,
It is vital that all of us learn to think straight.
And this small book by D.Q. McInerny is great.
It follows therefore since we so badly need it,
Everybody should not only but it, but read it.”
With zest and rigor, Bertrand Russell applies twentieth-century thinking to age-old philosophy, from the works of Plato and Aristotle to those of René Descartes and John Locke. In The Problems of Philosophy, he reviews the Western canon’s most influential ideas and thought experiments, offering a comprehensive and enlightening text for curious and seasoned philosophy readers alike. Infused with Russell’s own observations and critiques, this study offers reviews of topics such as idealism, knowledge, and the natures of truth, reality, and existence. Including the author’s prominent thinking on knowledge by acquaintance versus knowledge by description, The Problems of Philosophy is a critical look at the major philosophical accomplishments spanning from classical Greece to the twentieth century.
This ebook has been professionally proofread to ensure accuracy and readability on all devices.
This new edition features a revised text that supplants all previous versions, English translations of the many passages in foreign languages, a new foreword in which Berlin biographer Michael Ignatieff explains the enduring appeal of Berlin's essay, and a new appendix that provides rich context, including excerpts from reviews and Berlin's letters, as well as a startling new interpretation of Archilochus's epigram.
Perhaps the most readable and accessible of the great works of scientific inquiry, The Origin of Species sold out its first printing on the very day it was published in 1859. Theologians quickly labeled Charles Darwin the most dangerous man in England and, as the Saturday Review noted, the uproar over the book quickly “passed beyond the bounds of the study and lecture-room into the drawing-room and the public street.” Based largely on Darwin’s experience as a naturalist while on a five-year voyage aboard H. M. S. Beagle, The Origin of Species set forth a theory of evolution and natural selection that challenged contemporary beliefs about divine providence and the immutability of species. This Modern Library edition includes a Foreword by the Pulitzer Prize–winning science historian Edward J. Larson, an introductory historical sketch, and a glossary Darwin later added to the original text.
Hannah Arendt’s insightful observations of the modern world, based on a profound knowledge of the past, constitute an impassioned contribution to political philosophy. In Between Past and Future Arendt describes the perplexing crises modern society faces as a result of the loss of meaning of the traditional key words of politics: justice, reason, responsibility, virtue, and glory. Through a series of eight exercises, she shows how we can redistill the vital essence of these concepts and use them to regain a frame of reference for the future. To participate in these exercises is to associate, in action, with one of the most original and fruitful minds of the twentieth century.
"Why are Christians so intolerant?"
"Why can't we just coexist?"
In an age in which preference has replaced morality, many people find it difficult to speak the truth, afraid of the reactions they will receive if they say something is right or wrong. Using engaging stories and personal experience, Edward Sri helps us understand the classical view of morality and equips us to engage relativism, appealing to both the head and the heart. Learn how Catholic morality is all about love, why making a judgment is not judging a person's soul, and why, in the words of Pope Francis, "relativism wounds people." Topics include:
• Real Freedom, Real Love
• Sharing truth with compassion
• Why "I disagree" doesn't mean "I hate you"
An instructor’s website is available with solutions to all the exercises in the text, including the many new exercises which have been added to this new edition.
The book emphasizes the relationship between models and the traditional goal of logic, the evaluation of arguments, and critically examines apparatus and assumptions that often are taken for granted. Philosophical Logic provides an unusually thorough treatment of conditional logic, unifying probabilistic and model-theoretic approaches. It underscores the variety of approaches that have been taken to relevantistic and related logics, and it stresses the problem of connecting formal systems to the motivating ideas behind intuitionistic mathematics. Each chapter ends with a brief guide to further reading.
Philosophical Logic addresses students new to logic, philosophers working in other areas, and specialists in logic, providing both a sophisticated introduction and a new synthesis.
... a first-rate edition, which supersedes all other portable Peirces.... all the Peirce most people will ever need." —Louis Menand, The New York Review of Books
Volume 2 of this convenient two-volume chronological reader’s edition provides the first comprehensive anthology of the brilliant American thinker Charles Sanders Peirce’s mature philosophy. A central focus of Volume 2 is Peirce’s evolving theory of signs and its appplication to his pragmatism.
In How We Think, Dewey shares his views on the educator’s role in training students to think well. Basing his assertions on the belief that knowledge is strictly relative to human interaction with the world, he considers the need for thought training, its use of natural resources, and its place in school conditions; inductive and deductive reasoning, interpreting facts, and concrete and abstract thinking; the functions of activity, language, and observation in thought training; and many other subjects.
John Dewey’s influence on American education and philosophy is incalculable. This volume, as fresh and inspirational today as it was upon its initial publication a century ago, is essential for anyone active in the field of teaching or about to embark on a career in education.
This is the first time both volumes have been available in paperback. They include a new introduction by Dermot Moran, placing the Investigations in historical context and bringing out their contemporary philosophical importance.
These editions include a new preface by Sir Michael Dummett.