Infinity is a profoundly counter-intuitive and brain-twisting subject that has inspired some great thinkers – and provoked and shocked others. The ancient Greeks were so horrified by the implications of an endless number that they drowned the man who gave away the secret. And a German mathematician was driven mad by the repercussions of his discovery of transfinite numbers. Brian Clegg and Oliver Pugh’s brilliant graphic tour of infinity features a cast of characters ranging from Archimedes and Pythagoras to al-Khwarizmi, Fibonacci, Galileo, Newton, Leibniz, Cantor, Venn, Gödel and Mandelbrot, and shows how infinity has challenged the finest minds of science and mathematics. Prepare to enter a world of paradox.
What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.
Infinity is a Spiritual product line developed by Author Melissa Davidson. She is a Clairvoyant, Angelic Medium and is also a Spiritual Healer. She works on the Physical Pain Healing with her products. "I'm not a Miracle Worker, but I work with the Divine, and I have a very special Archangel, and many Divine Healers that love to help me, help you." If you have blockages from past traumas, low energies, low confidence, and need help on your path, Infinity products are simply made to help you. Sessions with Melissa will benefit your daily path to be on your intended journey. This is a short product descriptive booklet about Infinity's history.
INTRODUCING guide to the history and theory of still controversial 'speaking cure'. The ideas of psychoanalysis have permeated Western culture. It is the dominant paradigm through which we understand our emotional lives, and Freud still finds himself an iconic figure. Yet despite the constant stream of anti-Freud literature, little is known about contemporary psychoanalysis. Introducing Psychoanalysis redresses the balance. It introduces psychoanalysis as a unified 'theory of the unconscious' with a variety of different theoretical and therapeutic approaches, explains some of the strange ways in which psychoanalysts think about the mind, and is one of the few books to connect psychoanalysis to everyday life and common understanding of the world. How do psychoanalysts conceptualize the mind? Why was Freud so interested in sex? Is psychoanalysis a science? How does analysis work? In answering these questions, this book offers new insights into the nature of psychoanalytic theory and original ways of describing therapeutic practice. The theory comes alive through Oscar Zarate's insightful and daring illustrations, which enlighten the text. In demystifying and explaining psychoanalysis, this book will be of interest to students, teachers and the general public.
"Introducing Plato" begins by explaining how philosophers like Socrates and Pythagoras influenced Plato's thought. It provides a clear account of Plato's puzzling theory of knowledge, and explains how this theory then directed his provocative views on politics, ethics and individual liberty. It offers detailed critical commentaries on all of the key doctrines of Platonism, especially the very odd theory of Forms, and concludes by revealing how Plato's philosophy stimulated the work of important modern thinkers such as Karl Popper, Martha Nussbaum, and Jacques Derrida.
As we find ourselves at the cusp of an economic downturn, there has been a clear reinvigoration of Keynesian economics as governments are attempting to stimulate the market through public funds. Forming his economic theories in the wake of the Great Depression, John Maynard Keynes argued that a healthy economy depended on the total spending of consumers, business investors and, most importantly, governments too. Keynes formulated that governments should take control of the economy in the short term, rather than relying on the market, because, as he eloquently put it 'in the long run, we are all dead'. This graphic guide is the ideal introduction to one of the most influential economists of the 20th century, at a time when his theories may be crucial to our economic survival. Through a deft mixture of words and images, "Introducing Keynes" is a timely, accessible and enjoyable read.
Paolo Mancosu provides an original investigation of historical and systematic aspects of the notions of abstraction and infinity and their interaction. A familiar way of introducing concepts in mathematics rests on so-called definitions by abstraction. An example of this is Hume's Principle, which introduces the concept of number by stating that two concepts have the same number if and only if the objects falling under each one of them can be put in one-one correspondence. This principle is at the core of neo-logicism. In the first two chapters of the book, Mancosu provides a historical analysis of the mathematical uses and foundational discussion of definitions by abstraction up to Frege, Peano, and Russell. Chapter one shows that abstraction principles were quite widespread in the mathematical practice that preceded Frege's discussion of them and the second chapter provides the first contextual analysis of Frege's discussion of abstraction principles in section 64 of the Grundlagen. In the second part of the book, Mancosu discusses a novel approach to measuring the size of infinite sets known as the theory of numerosities and shows how this new development leads to deep mathematical, historical, and philosophical problems. The final chapter of the book explore how this theory of numerosities can be exploited to provide surprisingly novel perspectives on neo-logicism.
Epigenetics is the most exciting field in biology today, developing our understanding of how and why we inherit certain traits, develop diseases and age, and evolve as a species. This non-fiction comic book introduces us to genetics, cell biology and the fascinating science of epigenetics, which is rapidly filling in the gaps in our knowledge, allowing us to make huge advances in medicine. We’ll look at what identical twins can teach us about the epigenetic effects of our environment and experiences, why certain genes are 'switched on' or off at various stages of embryonic development, and how scientists have reversed the specialization of cells to clone frogs from a single gut cell. In Introducing Epigenetics, Cath Ennis and Oliver Pugh pull apart the double helix, examining how the epigenetic building blocks and messengers that interpret and edit our genes help to make us, well, us.
How can the infinite, a subject so remote from our finite experience, be an everyday working tool for the working mathematician? Blending history, philosophy, mathematics and logic, Shaughan Lavine answers this question with clarity. An account of the origins of the modern mathematical theory of the infinite, his book is also a defense against the attacks and misconceptions that have dogged this theory since its introduction in the late 19th century.
Release on 2002-10-23 | by Vladimir Dybin,Sergei M. Grudsky
Author: Vladimir Dybin,Sergei M. Grudsky
Pubpsher: Springer Science & Business Media
We offer the reader of this book some specimens of "infinity" that we seized from the "mathematical jungle" and trapped within the solid cage of analysis The creation of the theory of singular integral equations in the mid 20th century is associated with the names of N.1. Muskhelishvili, F.D. Gakhov, N.P. Vekua and their numerous students and followers and is marked by the fact that it relied principally on methods of complex analysis. In the early 1960s, the development of this theory received a powerful impulse from the ideas and methods of functional analysis that were then brought into the picture. Its modern architecture is due to a constellation of brilliant mathemati cians and the scientific collectives that they produced (S.G. Mikhlin, M.G. Krein, B.V. Khvedelidze, 1. Gohberg, LB. Simonenko, A. Devinatz, H. Widom, R.G. Dou glas, D. Sarason, A.P. Calderon, S. Prossdorf, B. Silbermann, and others). In the ensuing period, the Fredholm theory of singular integral operators with a finite index was completed in its main aspects in wide classes of Banach and Frechet spaces.