Felipe Fernandez

The discovery that the DNA of chimpanzees and humans is incredibly similar, sharing 98% of the same code, suggests that there is very little different--or special--about the human animal. Likewise, advances in artificial intelligence mean that humans no longer have exclusive access to reason, consciousness and imagination. Indeed, the harder we cling to the concept of humanity, the more slippery it becomes. But if it breaks down altogether, what will this mean for human values, human rights, and the defense of human dignity? In a book of breathtaking range, Felipe Fernandez-Armesto takes us on an enlightening journey through the history of humankind, a narrative tour de force that challenges our most fundamental belief--that we are, and have always been, human. Humankind confronts the problem from a historical perspective, showing how our current understanding of what it means to be human has been shaken by new discoveries from science and philosophy. The author shows how our concept of humankind has changed over time, tracing its faltering expansion to its present limits and arguing that these limits are neither fixed or scientifically verifiable. Controversially, he proposes that we have further to go in developing our concept of humankind and that we need to rethink it as a matter of urgency. One of the most imaginative historians writing today, Felipe Fernandez-Armesto here combines astonishing breadth with passionate and exciting storytelling. For the intellectually curious, for those interested in history, philosophy, science and culture, and for anyone who has ever wondered about what makes us human, Humankind offers an exhilarating new perspective.

Mind out of matter: the imaginative animal -- Gathering thoughts: thinking before agriculture -- Settled minds: early "civilized" thinking -- The great sages: the first named thinkers -- Thinking faiths: ideas in a religious age -- Rebirth: thinking through plague and cold -- Global enlightenments: joined-up thinking in a joined-up world -- The climacteric of progress: nineteenth-century certainties -- The revenge of chaos: unpicking certainty -- The age of uncertainty: twentieth-century hesitancies -- The end of ideas.

You think you're human. But what does that mean? How can humanity be defined? Felipe Fernandez-Armesto takes us on an enlightening and provocative journey through the history of humankind to reveal the challenges to our most fundamental belief - that we are, and have always been, human. Fernandez-Armesto investigates advances in artificial intelligence and genetics, and asks what these mean for the future of human values, human rights, and the defence of human dignity. The book illustrates how our concept of humankind has changed over time and how our current understanding of this has been shaken by new challenges from science and philosophy.

The progress of Mathematics during the nineteenth century was characterised both by an enormous acquisition of new knowledge and by the attempts to introduce rigour in reasoning patterns and mathematical writing. Cauchy’s presentation of Mathematical Analysis was not immediately accepted, and many writers, though aware of that new style, did not use it in their own mathematical production. This paper is devoted to an episode of this sort that took place in Spain during the first half of the century: It deals with the presentation of a method for numerically solving algebraic equations by José Mariano Vallejo, a late Spanish follower of the Enlightenment ideas, politician, writer, and mathematician who published it in the fourth (1840) edition of his book Compendio de Matemáticas Puras y Mistas, claiming to have discovered it on his own. Vallejo’s main achievement was to write down the whole procedure in a very careful way taking into account the different types of roots, although he paid little attention to questions such as convergence checks and the fulfilment of the hypotheses of Rolle’s Theorem. For sure this lack of mathematical care prevented Vallejo to occupy a place among the forerunners of Computational Algebra.

In this paper we study the axiomatic system proposed by Bourbaki for the Theory of Sets in the Éléments de Mathématique. We begin by examining the role played by the sign \(\uptau \) in the framework of its formal logical theory and then we show that the system of axioms for set theory is equivalent to Zermelo–Fraenkel system with the axiom of choice but without the axiom of foundation. Moreover, we study Grothendieck’s proposal of adding to Bourbaki’s system the axiom of universes for the purpose of considering the theory of categories. In this regard, we make some historical and epistemological remarks that could explain the conservative attitude of the Group.

_"A stimulating history of how the imagination interacted with its sibling psychological faculties—emotion, perception and reason—to shape the history of human mental life."—_The __Wall Street Journal__ To imagine—to see what is not there—is the startling ability that has fueled human development and innovation through the centuries. As a species we stand alone in our remarkable capacity to refashion the world after the picture in our minds. Traversing the realms of science, politics, religion, culture, philosophy, and history, Felipe Fernández-Armesto reveals the thrilling and disquieting tales of our imaginative leaps—from the first _Homo sapiens_ to the present day. Through groundbreaking insights in cognitive science, Fernández-Armesto explores how and why we have ideas in the first place, providing a tantalizing glimpse into who we are and what we might yet accomplish. Unearthing historical evidence, he begins by reconstructing the thoughts of our Paleolithic ancestors to reveal the subtlety and profundity of the thinking of early humans. A masterful paean to the human imagination from a wonderfully elegant thinker, _Out of Our Minds_ shows that bad ideas are often more influential than good ones; that the oldest recoverable thoughts include some of the best; that ideas of Western origin often issued from exchanges with the wider world; and that the pace of innovative thinking is under threat.

The way we live - our manners, morals, habits, experiences, relationships, technology, values - are changing ever faster and faster than ever. The effects can be dislocating, baffling, sometimes terrifying. Why? How can we get off the whirligig? Felipe Fernández-Armesto explores the evidence and offers answers. Combining insights from history, biology, anthropology, archaeology, philosophy, sociology, ethology, zoology, primatology, psychology, linguistics cognitive sciences, and even business studies, he argues that culture is exempt from evolution. No environmental conditions, no genetic legacy, no predictable patterns, no scientific laws determine our behaviour. We can make and remake our world in the freedom of unconstrained imaginations.