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Mathematical Logic: An Introduction is a textbook that uses mathematical tools to investigate mathematics itself. In particular, the concepts of proof and truth are examined. The book presents the fundamental topics in mathematical logic and presents clear and complete proofs throughout the text. Such proofs are used to develop the language of propositional logic and the language of first-order logic, including the notion of a formal deduction. The text also covers Tarski’s definition of truth and the computability concept. It also provides coherent proofs of Godel’s completeness and incompleteness theorems. Moreover, the text was written with the student in mind and thus, it provides an accessible introduction to mathematical logic. In particular, the text explicitly shows the reader how to prove the basic theorems and presents detailed proofs throughout the book. Most undergraduate books on mathematical logic are written for a reader who is well-versed in logical notation and mathematical proof. This textbook is written to attract a wider audience, including students who are not yet experts in the art of mathematical proof.

Mathematical logic, logic of the first order, logic of the second order, deductive reasoning.

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"In this book the philosophers Steve Nadler and Lawrence Shapiro will explain why bad thinking happens to good people. Why is it, they ask, that so large a segment of public can go so wrong in both how they come to form the opinions they do and how they fail to appreciate the moral consequences of acting on them. Their diagnosis of the current state of affairs in America, at least, is this: a significant proportion of the population is stupid. They intend this not as mere name-calling, but a diagnosis of a problem that we neglect at our peril. By "stupid" they do not mean lacking intelligence, knowledge, education, skill or savvy. Stupidity, as they understand it, is a character flaw deserving of blame. Unlike ignorance or lack of intelligence-and bearing in mind that even very smart people can be stupid-it is generally avoidable. Stupid people do not have to be stupid. But they typically refuse to take the steps that would cure them of their condition. This book is our effort to illuminate the various dimensions of stupidity so that it might be more easily recognized and treated. The philosophical subjects of epistemology, which addresses what knowledge is and how to distinguish knowing something from merely believing it, and ethics, the study of the moral principles that ought to govern our behavior, can help us understand the difficult and perilous situation in which we now find ourselves. As philosophers, Nadler and Shapiro will aim to offer a way forward through the tools of philosophy-its questions, its methods and even its millennia-old history of recommendations for how to lead a good and rational life. As they will show, the most potent antidote to stupidity is the wisdom and insights, as well as the practical skills provided by philosophy and its history"-- "Why the tools of philosophy offer a powerful antidote to today's epidemic of irrationalityThere is an epidemic of bad thinking in the world today. An alarming number of people are embracing crazy, even dangerous, ideas. They believe that vaccinations cause autism. They reject the scientific consensus on climate change as a "hoax." And they blame the spread of COVID-19 on the 5G network or a Chinese cabal. Worse, bad thinking drives bad acting-it even inspired a mob to storm the U.S. Capitol. In this book, Steven Nadler and Lawrence Shapiro argue that the best antidote for bad thinking and acting is the wisdom, insights, and practical skills of philosophy. When Bad Thinking Happens to Good People provides an engaging tour through the basic principles of logic, argument, evidence, and probability that can make all of us more reasonable and responsible citizens.When Bad Thinking Happens to Good People shows how we can more readily spot and avoid flawed arguments and unreliable information; determine whether evidence supports or contradicts an idea; distinguish between merely believing something and knowing it; and much more. In doing so, the book reveals how epistemology, which addresses the nature of belief and knowledge, and ethics, the study of moral principles that should govern our behavior, can reduce bad thinking and bad action. Moreover, the book shows why philosophy's millennia-old advice about how to lead a good, rational, and examined life is essential for escaping our current predicament.In a world in which irrationality has exploded to deadly effect, When Bad Thinking Happens to Good People is a timely and essential guide for a return to reason"--

Thought and thinking. --- Fallacies (Logic) --- Abductive reasoning. --- Admonition. --- Akrasia. --- Aphorism. --- Apology (Plato). --- Baruch Spinoza. --- Base rate fallacy. --- Base rate. --- Causality. --- Certainty. --- Climate change. --- Confirmation bias. --- Consideration. --- Conspiracy theory. --- Copyright. --- Cover-up. --- Decision-making. --- Deductive reasoning. --- Deed. --- Deliberation. --- Discretion. --- Disgust. --- Disjunctive syllogism. --- Embarrassment. --- Epistemology. --- Ethics. --- Eudaimonia. --- Euthyphro (prophet). --- Euthyphro. --- Evidentialism. --- Existence of God. --- Explanation. --- Fallacy. --- Feeling. --- Good and evil. --- Gun control. --- Hoax. --- Hypothesis. --- Idiot. --- Inductive reasoning. --- Inference. --- Instance (computer science). --- Irrationality. --- Laziness. --- Literature. --- Logic. --- Mathematician. --- Meditations on First Philosophy. --- Morality. --- Nicomachean Ethics. --- Objectivity (philosophy). --- Observation. --- Of Education. --- Phenomenon. --- Philosopher. --- Philosophy of science. --- Philosophy. --- Phronesis. --- Piety. --- Plato. --- Police officer. --- Politician. --- Practical reason. --- Pre-Socratic philosophy. --- Prejudice. --- Premise. --- Premises. --- Principle. --- Probability. --- Psychologist. --- Quantity. --- Racism. --- Rationality. --- Reason. --- Reasonable person. --- Requirement. --- Result. --- Science. --- Scientific method. --- Scientist. --- Security guard. --- Self-control. --- Shame. --- Skepticism. --- Slippery slope. --- Soundness. --- State of affairs (sociology). --- Stupidity. --- Suffering. --- Suggestion. --- The Philosopher. --- The unexamined life is not worth living. --- Theft. --- Theory of justification. --- Theory. --- Thought. --- Truism. --- Uncertainty. --- Vaccination. --- Validity.

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A firm grasp of Islamic fundamentalism has often eluded Western political observers, many of whom view it in relation to social and economic upheaval or explain it away as an irrational reaction to modernity. Here Roxanne Euben makes new sense of this belief system by revealing it as a critique of and rebuttal to rationalist discourse and post-Enlightenment political theories. Euben draws on political, postmodernist, and critical theory, as well as Middle Eastern studies, Islamic thought, comparative politics, and anthropology, to situate Islamic fundamentalist thought within a transcultural theoretical context. In so doing, she illuminates an unexplored dimension of the Islamist movement and holds a mirror up to anxieties within contemporary Western political thought about the nature and limits of modern rationalism--anxieties common to Christian fundamentalists, postmodernists, conservatives, and communitarians. A comparison between Islamic fundamentalism and various Western critiques of rationalism yields formerly uncharted connections between Western and Islamic political thought, allowing the author to reclaim an understanding of political theory as inherently comparative. Her arguments bear on broad questions about the methods Westerners employ to understand movements and ideas that presuppose nonrational, transcendent truths. Euben finds that first, political theory can play a crucial role in understanding concrete political phenomena often considered beyond its jurisdiction; second, the study of such phenomena tests the scope of Western rationalist categories; and finally, that Western political theory can be enriched by exploring non-Western perspectives on fundamental debates about coexistence.

Islamic fundamentalism --- Rationalism --- Islamic countries --- Politics and government --- Islamic fundamentalism. --- Rationalism. --- #SBIB:031.IO --- #SBIB:321H91 --- #SBIB:316.331H330 --- Knowledge, Theory of --- Religion --- Belief and doubt --- Deism --- Free thought --- Realism --- Fundamentalism, Islamic --- Islamism --- Islam --- Religious fundamentalism --- Niet-specifieke politieke en sociale theorieën vanaf de 19e eeuw: islam, Arabisch nationalisme --- Godsdienst en politiek: algemeen --- -Muslim countries --- Politics and government. --- Islamic countries - Politics and government --- Alterity. --- Ambiguity. --- Anachronism. --- Anathema. --- Anthropomorphism. --- Anti-Oedipus. --- Anti-Western sentiment. --- Anti-imperialism. --- Antinomy. --- Apologetics. --- Assassination. --- Authoritarianism. --- Clash of Civilizations. --- Communitarianism. --- Criticism. --- Critique of ideology. --- Critique. --- Deductive reasoning. --- Deism. --- Demagogue. --- Despotism. --- Dialectical materialism. --- Dichotomy. --- Dictatorship. --- Disadvantage. --- Disenchantment. --- Emotivism. --- End of history. --- Ethnocentrism. --- Excommunication. --- False consciousness. --- False god. --- God. --- Great Satan. --- Hannah Arendt. --- Heresy. --- Heterodoxy. --- Hostility. --- Hypocrisy. --- Ideology. --- Idolatry. --- Impediment (canon law). --- Imperialism. --- Infidel. --- Injunction. --- Inner-worldly asceticism. --- Irrationality. --- Irreligion. --- Islam. --- Islamic extremism. --- Islamism. --- Islamization of knowledge. --- Jamal ad-Din al-Afghani. --- Jihadism. --- Legitimation crisis. --- Manichaeism. --- Materialism. --- Militarism. --- Modernity. --- Nihilism. --- Obscurantism. --- Oppression. --- Orientalism. --- Overreaction. --- Paradox. --- Political Order in Changing Societies. --- Political alienation. --- Political aspects of Islam. --- Political decay. --- Political philosophy. --- Political prisoner. --- Politics. --- Postmodern philosophy. --- Postmodernism. --- Prejudice. --- Protest vote. --- Qutb. --- Radicalism (historical). --- Radicalization. --- Rashid Rida. --- Reactionary. --- Rebuttal. --- Reformism. --- Religion. --- Seditious conspiracy. --- Separate spheres. --- Separation of church and state. --- Sharia. --- Skepticism. --- Social criticism. --- Sovereignty. --- Spiritual crisis. --- Superstition. --- The End of Ideology. --- Truism. --- Vagueness. --- Vulnerability. --- Wahhabism. --- Yellow Peril.

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What is life? What is water? What is sound? In Sounding the Limits of Life, anthropologist Stefan Helmreich investigates how contemporary scientists-biologists, oceanographers, and audio engineers-are redefining these crucial concepts. Life, water, and sound are phenomena at once empirical and abstract, material and formal, scientific and social. In the age of synthetic biology, rising sea levels, and new technologies of listening, these phenomena stretch toward their conceptual snapping points, breaching the boundaries between the natural, cultural, and virtual.Through examinations of the computational life sciences, marine biology, astrobiology, acoustics, and more, Helmreich follows scientists to the limits of these categories. Along the way, he offers critical accounts of such other-than-human entities as digital life forms, microbes, coral reefs, whales, seawater, extraterrestrials, tsunamis, seashells, and bionic cochlea. He develops a new notion of "sounding"-as investigating, fathoming, listening-to describe the form of inquiry appropriate for tracking meanings and practices of the biological, aquatic, and sonic in a time of global change and climate crisis.Sounding the Limits of Life shows that life, water, and sound no longer mean what they once did, and that what count as their essential natures are under dynamic revision.

Physical anthropology. --- Human biology. --- Life sciences. --- Ethnology. --- Cultural anthropology --- Ethnography --- Races of man --- Social anthropology --- Anthropology --- Human beings --- Biosciences --- Sciences, Life --- Science --- Biology --- Physical anthropology --- Biological anthropology --- Somatology --- Human biology --- Life sciences --- Ethnology --- 781.1 --- 7.01 --- Sound studies --- Antropologie --- Geluidskunst --- Kunst ; theorie, filosofie, --- Artificial Intelligence. --- Artificial Life. --- Century's End. --- Charles Sanders Peirce. --- Cold War. --- DNA. --- Deaf studies. --- Donna Haraway. --- Earth. --- Florian Hecker. --- Google Earth. --- Google Ocean. --- Hillel Schwartz. --- India. --- Indian Ocean tsunami. --- Peter Galison. --- Raymond Williams. --- Rudolph Bodmer. --- Satish Singh. --- The Culture of the Copy. --- abductive reasoning. --- analog whale. --- anthropology. --- aquatic. --- artificial life form. --- astrobiology. --- auditory chimeras. --- auditory chimerism. --- biological. --- biology. --- chimeric composition. --- chimeric listening. --- cognition. --- computational life sciences. --- computer simulations. --- coral reef science. --- coral reefs. --- culture. --- cyborg sound. --- deaf futurists. --- deafness. --- deductive reasoning. --- digital life forms. --- digital media. --- digital whale. --- ethno-conchology. --- experimental music. --- extraterrestrial intelligence. --- extraterrestrial life. --- feminist science studies. --- fiberglass whale. --- genealogies. --- geological time. --- global ocean. --- global warming. --- globalization. --- hearing. --- human microbiome. --- icons. --- indexes. --- inductive reasoning. --- knowledge. --- life form. --- life. --- limit biologies. --- listening. --- marine biology. --- marine microbiology. --- microbes. --- microbial life. --- migration. --- modernism. --- modernity. --- natural philosophers. --- nature. --- ocean time. --- ocean. --- oceanization. --- oceanographic conference. --- popular science. --- race. --- scientific research. --- scientists. --- sea lions. --- seashell sound. --- seashells. --- seawater. --- sex. --- signification. --- silence. --- simulated whale. --- social theory. --- sonic. --- sound recordings. --- sound studies. --- sound. --- species. --- speech. --- symbols. --- theory machine. --- theory. --- time. --- underwater archaeology. --- underwater music. --- water. --- whale fall. --- whales.

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The present book contains the 24 total articles accepted and published in the Special Issue “Fuzzy Sets, Fuzzy Logic and Their Applications, 2020” of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of fuzzy sets and systems of fuzzy logic and their extensions/generalizations. These topics include, among others, elements from fuzzy graphs; fuzzy numbers; fuzzy equations; fuzzy linear spaces; intuitionistic fuzzy sets; soft sets; type-2 fuzzy sets, bipolar fuzzy sets, plithogenic sets, fuzzy decision making, fuzzy governance, fuzzy models in mathematics of finance, a philosophical treatise on the connection of the scientific reasoning with fuzzy logic, etc. It is hoped that the book will be interesting and useful for those working in the area of fuzzy sets, fuzzy systems and fuzzy logic, as well as for those with the proper mathematical background and willing to become familiar with recent advances in fuzzy mathematics, which has become prevalent in almost all sectors of the human life and activity.

Research & information: general --- Mathematics & science --- bipolar gradation of openness --- bipolar gradation of closedness --- bipolar fuzzy topology --- bipolar gradation preserving map --- fuzzy collaborative forecasting --- dynamic random access memory --- partial consensus --- fuzzy intersection --- fuzzy linear system --- fuzzy number --- fuzzy number vector --- embedding method --- inductive and deductive reasoning --- fuzzy logic (FL) --- scientific method --- probability and statistics --- Bayesian probabilities --- fuzzy implication --- ordering property --- least fuzzy negation --- t-conditionality --- neutrosophic set --- plithogenic set --- fuzzy set --- entropy --- similarity measure --- information measure --- Hyers-Ulam stability --- pexider type functional equation --- intuitionistic fuzzy normed spaces --- alternative fixed point theorem --- interval-valued fuzzy competition graph --- interval-valued fuzzy p competition graph --- interval-valued fuzzy neighbourhood graph --- interval-valued m-step fuzzy competition graph --- homomorphism of graph products --- max-min algebra --- fuzzy max-T algebra --- Łukasiewicz triangular norm --- max-Łukasiewicz algebra --- parametric solvability --- soft set --- fuzzy soft set --- multi-fuzzy set --- multi-fuzzy soft set --- ℒℳℱ?? --- similarity measure of ℒℳℱ?? --- site selection --- shopping mall site selection --- linguistic terms for fuzzy variable --- fuzzy AHP --- fuzzy TOPSIS --- octahedron set --- i-octahedron subgroupoid --- i-octahedron ideal --- i-sup-property, i-octahedron subgroup --- i-octahedron subring --- interval matrix --- interval eigenvector --- strong interval eigenvector --- fuzzy nonlinear systems --- fuzzy arithmetic --- fuzzy calculus --- multidimensional fuzzy arithmetic --- RDM fuzzy arithmetic --- fuzzy parametric form --- fuzzy measures --- monotone measures --- product spaces --- Schauder fixed point theorem --- fuzzy normed linear space --- t-norm --- measure of non-compactness --- fuzzy logic connectives --- law of importation --- α-migrativity --- distance measure --- fuzzy differential equations --- fuzzy difference equations --- mixed continuous-discrete model --- strongly generalized Hukuhara differentiability --- time value of money --- GEFS --- SEFS --- fuzzy relations: fuzzy sets --- max–min composition --- min–max composition --- monotone statistical parameters --- fuzzy statistics --- FAHP --- FTOPSIS --- FCOPRAS --- hexagonal fuzzy number --- governance --- fuzzy logic --- management system --- type-2 fuzzy set --- fuzzification --- type-reduction --- defuzzification --- B-spline surface model function