It was his feeling that a proper analysis of the use of language would clarify concepts and lead to the solution of (what seem to be) philosophical problems.Sometimes, Wittgenstein's expository method is pre-Socratic: a flow of disconnected statements, not unlike Heraclitean fragments, that range from clear aphorisms to cryptic oracles. Elsewhere, there are brief Socratic dialogues with imaginary persons, opponents of equally severe seriousness, representatives of the other half of Wittgenstein strove for total clarity of language as a means of solving philosophical problems, but some of his most meaningful statements here are expressed suggestively, subjectively, poetically.

    Written by two of the best-known names in categorical logic, Conceptual Mathematics is the first book to apply categories to the most elementary mathematics. It thus serves two purposes: first, to provide a key to mathematics for the general reader or beginning student; and second, to furnish an easy introduction to categories for computer scientists, logicians, physicists, and linguists who want to gain some familiarity with the categorical method without initially committing themselves to extended study.

    With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos.In Infinitesimal, the award-winning historian Amir Alexander exposes the deep-seated reasons behind the rulings of the Jesuits and shows how the doctrine persisted, becoming the foundation of calculus and much of modern mathematics and technology. Indeed, not everyone agreed with the Jesuits. Philosophers, scientists, and mathematicians across Europe embraced infinitesimals as the key to scientific progress, freedom of thought, and a more tolerant society. As Alexander reveals, it wasn't long before the two camps set off on a war that pitted Europe's forces of hierarchy and order against those of pluralism and change.The story takes us from the bloody battlefields of Europe's religious wars and the English Civil War and into the lives of the greatest mathematicians and philosophers of the day, including Galileo and Isaac Newton, Cardinal Bellarmine and Thomas Hobbes, and Christopher Clavius and John Wallis. In Italy, the defeat of the infinitely small signaled an end to that land's reign as the cultural heart of Europe, and in England, the triumph of infinitesimals helped launch the island nation on a course that would make it the world's first modern state.From the imperial cities of Germany to the green hills of Surrey, from the papal palace in Rome to the halls of the Royal Society of London, Alexander demonstrates how a disagreement over a mathematical concept became a contest over the heavens and the earth. The legitimacy of popes and kings, as well as our beliefs in human liberty and progressive science, were at stake-the soul of the modern world hinged on the infinitesimal.

    - predicted the reappearance of a lost planet, - discovered basic properties of magnetic forces, - invented a surveying tool used by professionals until the invention of lasers. Based on extensive research of original and secondary sources, this historical narrative will inspire young readers and even curious adults with its touching story of personal achievement.

    Using playing cards, a newspaper, the back of an envelope, a Sudoku, some pennies and of course a pair of socks, Rob Eastaway shows how maths can demonstrate its secret beauties in even the most mundane of everyday objects. Among the many fascinating curiosities in these pages, you will discover the strange link between limericks and rabbits, an apparently 'fair' coin game where the odds are massively in your favour, why tourist boards can't agree on where the centre of Britain is, and how simple paper folding can lead to a Jurassic Park monster. With plenty of ideas you'll want to test out for yourself, this engaging and refreshing look at mathematics is for everyone.