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Some Truth, Some Validity, Some Opinion: Lessons from an Old Mathematics Teacher to New Mathematics Teachers By: David A. Crothamel David A. Crothamel has taught mathematics for thirty-eight years from the seventh grade level up to calculus. Throughout his many years of teaching, he has seen many times teachers skip over proof of the techniques. Students then tend to memorize how to get an answer without knowing the methodology behind it. Crothamel would like this book to be used as a guide for students to navigate the “whys” of some of the mathematics they study.
Radical Intellectuals and the Subversion of Progressive Politics is a challenge to contemporary radical politics and political thought. This collection of essays critiques the dominant trends and figures on the left that have distorted the legacy of progressive politics, arguing that they have moved politics away from issues of class and economic power toward a preoccupation with culture and identity. The contributors discuss this new radicalism from the perspective of a more rational form of leftism capable of reviving interest in a more politically relevant form of politics.
This revised and updated edition of a standard work provides a clear and authoritative survey of the Western tradition in metaphysics and epistemology from the Presocratics to the present day. Aimed at the beginning student, it presents the ideas of the major philosophers and their schools of thought in a readable and engaging way, highlighting the central points in each contributor's doctrines and offering a lucid discussion of the next-level details that both fills out the general themes and encourages the reader to pursue the arguments still further through a detailed guide to further reading. Whether John Shand is discussing the slow separation of philosophy and theology in Augustine, Aquinas and Ockham, the rise of rationalism, British empiricism, German idealism or the new approaches opened up by Russell, Sartre and Wittgenstein, he combines succinct but insightful exposition with crisp critical comment. This new edition will continue to provide students with a valuable work of initial reference.
In an age of rising groupthink, reactionary populism, social conformity, and democratic deficit, political judgment in modern society has reached a state of crisis. In The Specter of Babel, Michael J. Thompson offers a critical reconstruction of the concept of political judgment that can help resuscitate critical citizenship and democratic life. At the center of the book are two arguments. The first is that modern practical and political philosophy has made a postmetaphysical turn that is unable to guard against the effects of social power on consciousness and the deliberative powers of citizens. The second is that an alternative path toward a critical social ontology can provide a framework for a new theory of ethics and politics. This critical social ontology looks at human sociality not as mere intersubjectivity or communication, but rather as constituted by the shapes that our social-relational structures take as well as the kinds of purposes and ends toward which our social lives are organized. Only by calling these into question, Thompson boldly argues, can we once again attempt to revitalize social critique and democratic politics.
Over the last several decades, questions about practical reason have come to occupy the center stage in ethics and metaethics. The Routledge Handbook of Practical Reason is an outstanding reference source to this exciting and distinctive subject area and is the first volume of its kind. Comprising thirty-six chapters by an international team of contributors, the Handbook provides a comprehensive overview of the field and is divided into five parts: Foundational Matters Practical Reason in the History of Philosophy Philosophy of Practical Reason as Action Theory and Moral Psychology Philosophy of Practical Reason as Theory of Practical Normativity The Philosophy of Practical Reason as the Theory of Practical Rationality The Handbook also includes two chapters by the late Derek Parfit, ‘Objectivism about Reasons’ and ‘Normative Non-Naturalism.’ The Routledge Handbook of Practical Reason is essential reading for philosophy students and researchers in metaethics, philosophy of action, action theory, ethics, and the history of philosophy.
An international journal of general philosophy.
"Sets [Lessing's] life and work in the context of the intellectual, social, and cultural background of eighteenth-century Europe."--Provided by publisher.
Beginning with the origins of Western philosophy, the profound creation of the Hellenic genius, Reale presents an appreciation of the Naturalists, the Sophists, Socrates, and the Minor Socratics. Special attention is paid to the Eleatics because their problems decisively mark Platonic and Aristotelian philosophy. Interpretation of the Sophists benefits from the recent reevaluation of their thought. Socrates himself would be inconceivable without the Sophists since he is one of them. Socrates is given major prominence. Plato, Aristotle, and all of Hellenistic philosophy are deeply impregnated with his words and spirit. The teachings of the Minor Socratics are interpreted as one-sided reductions of the pluralistic values of Socratic thought and as anticipations of some issues that explode later in the Hellenistic Age. There are two appendices. The first concerns Orphism and contains a series of documents indispensable for the comprehension of some aspects of pre-Socratic and Platonic thought. The second explains the key to understanding the message of the Greeks--the message of "theorein".
The first interdisciplinary textbook to introduce students to three critical areas in applied logic Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic Treats traditional logic in a modern format Presents relevance logic with applications Provides an ideal text for a variety of one-semester upper-level undergraduate courses
This is a book about the one objective truth of existence, and the countless subjective falsehoods accepted as true by the vast majority of humanity. This book focuses especially on New Age guru Ken Wilber's fallacious system, known as Integral Theory, his "theory of everything", where he attempts to place a wide diversity of mystical theories and the teachings of various gurus into a single framework that supposedly explains everything. Wilber's system is best summed up in his statement, "I have one major rule: Everybody is right. More specifically, everybody – including me – has some important pieces of truth, and all of those pieces need to be honored, cherished, and included in a more gracious, spacious, and compassionate embrace." It is exactly this sentiment that underlies the New Age hegemony of relativism and subjectivism, of everyone having their own experiences, their own path, their own truth. In such a system, it becomes impossible for people to reach the one, absolute, objective truth of existence which grounds everything. In order to reach the Truth, the task is not to pretend to people that they are all right, but to show where they have gone wrong, where they have strayed from reason and logic, where they have succumbed to irrationalism via emotionalism, sensory empiricism, faith, and mysticism. Wilber adopts a fully irrationalist stance when he claims that the "enlightened" are what he calls "trans-rational", i.e. they have somehow transcended reason and logic and thus reached the zone, according to Wilber, where they can apprehend Absolute Reality. In fact, Absolute Reality, insofar as it is intelligible, is nothing but the expression of the Principle of Sufficient Reason and its corollary, Occam's razor. How do we eliminate the infinite wrong answers to existence and reach the one, infallible right answer to existence? It's simplicity itself. The answer to existence is the simplest and most rational possible. Any answer that is not rational is irrational, hence false. Any answer that is not the simplest is wrong because reality would never privilege complexity over simplicity. Reality necessarily follows the path of least resistance, the most economic path. It does not know how to introduce superfluous, needless and pointless complexity. You will never understand the answer to existence if the "answer" you support is against rationalism and against rational simplicity.