"The study of mathematics is apt to commence in disappointment."

"One of the causes of the apparent triviality of much of elementary algebra is the preoccupation of the textbooks with the solutions of equations."

In discussing Descartes' coordinate geometry, Whitehead states, "Philosophers, when they have possessed a thorough knowledge of mathematics, have been among those who have enriched the science with some of its best ideas. On the other hand, it must be said that, with hardly an exception, all remarks on mathematics made by those philosophers who have possessed but a slight or hasty and late-acquired knowledge of it, are entirely worthless, being either trivial or wrong."

"Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle - they are strictly limited in number, they require fresh horses, and must only be made at decisive moments."

"The really profound changes in human life have all had their ultimate origin in knowledge pursued for its own sake."

Alfred North Whitehead, a remarkable British mathematician and philosopher, enlivens his look at the fundamental ideas underlying mathematics with provocative observations. Nonetheless, Whitehead does not avoid mathematics while trying to explain mathematics. While this book is clearly for the layman, it may occasionally require some effort. "An Introduction to Mathematics" is delightful, insightful, and intellectually stimulating.

Whitehead argues that mathematics is an abstract science that is primarily concerned with generality, not specificity. In trying to master the techniques and mechanics of arithmetic, algebra, and geometry, many students fail to recognize the fundamental ideas. They become lost in a murky fog of details.

I found myself surprised by Whitehead's insightful explanations of familiar topics like variables, constants, and simple algebraic equations. I know math. But I now recognize that I had not really given sufficient thought to some very basic concepts. Just a few pages into this little book I was actually looking at some familiar concepts from a very different perspective.

Later discussions on mathematical symbolism, imaginary numbers, conic sections, trigonometry, and infinite series move more slowly and may require rereading. But the insights gained will more than offset any additional effort.

Whitehead occasionally digresses to discuss the act of mathematical creation. He agrees with the poet Shelley who compared the discovery of "some great truth" to the slow snowflake by snowflake accumulation that leads to an avalanche. While not discounting the role of genius, Whitehead sees breakthroughs in mathematical thought, often as unexpected as an avalanche, the natural result of the accumulation of knowledge through the centuries.

I am not a teacher, but I would like to use this book as a basis for a short class or tutorial for high school students or undergraduates, for science, math, and humanities majors alike. "An Introduction to Mathematics" would serve as an effective counterbalance to standard textbooks that focus too much on technique, manipulation, and mechanics. I rate this book 5-star. It is well-worth the price.

This is an expertly written book by a brilliant man, filled with valuable insights and impressive prose. I picked it up as a tool to re-familiarize myself with the fundamental ideas of mathematics and found it more than satisfactory to that end. In 150 or so pages, Whitehead takes the reader step by step through the evolution of mathematical thought, pointing out each new discovery, the circumstances surrounding the breakthrough and why it was so important. This is NOT a textbook -- no sample problems to work on or anything like that -- and it will be difficult to fully grasp the concepts unless the reader has had some math experience (ie. high school education). It is rather a philosopher's math book, full of insights, enjoyable anecdotes and beautiful prose.

Whitehead's text is a masterful study in the art of clear and precise writing. Introduction to Mathematics brilliantly revels to those of us with little or no mathematical skill or background the fascinating allure of mathematical thought. Whitehead's exploration of the basic central themes of math is made concrete through his frequent use of simple mathematical examples yet the text never bogs down in pedantic detail. Moreover, while the book is introductory in character, and therefore focused on fundamental rather than advanced areas of mathematical study, it is anything but small minded or condescending. Rather, Whitehead electrifies the reader's mind by illuminating for him the profound insights behind even the simplest of mathematical operations. Written with razor sharp clarity, this little gem of a volume is required reading for all those fuzzy-headed intellectuals who never understood math in school or how anyone could find the subject even remotely interesting. If only Professor Whitehead had blessed us with a whole series of such volumes taking us by the hand and walking us in detail through the wondrous intellectual word of math

For the reader looking for a way into the thought of Alfred North Whitehead, this short volume is the best place to begin. In six lectures delivered toward the end of his career, Whitehead provides a non-technical sketch of the metaphysics and cosmology he had earlier presented in extended and highly technical form in his magnum opus, Process and Reality.

Modes of Thought is not an easy book--for it is highly compressed and sometimes reads like a series of aphorisms. But while this book will likely leave most readers wondering how all these aphorisms hold together, they are individually nearly crystaline in clarity and are wonderfully provocative. Even if one never reads further in Whitehead, engaging this short volume will set one pondering productively. And, if nothing else, one will come away armed with some wonderful philosophical one-liners.

If reading Modes of Thought makes one want to read on, the good way to proceed would be to read Science and the Modern World next followed by Adventures of Ideas and then (and only then) Process and Reality.

Whitehead wrote clearly and simply about some of the most difficult philosophical ideas. This brief book is perfect for anyone who has ever wondered "How do I know what I know?" It is filled with gems such as "The notion of a mere fact is the triumph of the abstractive intellect"; "The whole understanding of the world consists in the analysis of process in terms of the identities and diversities of the individuals involved." Today we know a lot more about the machinery of the mind and the nature of human cognition than he did. But like Darwin who didn't really know how "genes" work, Whitehead saw things that most of us miss. You have to think "on your toes" to read him. But the reward is worth the effort. No one who claims to be an educated person should make such a claim without "reading their Whitehead."

In his other books, and especially in Process and Reality, Whitehead's prose can be so dense as to discourage all but the most determined readers. But Religion in the Making, while occasionally technical, is Whitehead at his simplest and most elegant. Reading this book, written just three years before P&R, will show people who have been exposed to "process theology" that Whitehead's own beliefs about God were really much more simple and poetic. The great Cambridge-Harvard philosopher's spirituality boils down to a single sentence in the midst of Religion in the Making: "Expression is the one fundamental sacrament."

It's good to have this work of Whitehead back in print. This is an excellent contribution to our understanding of religion. Judith Jones gives a fine introductory essay showing the metaphysical roots of Whitehead's concept of religion.

After a long and enjoyable relationship with all of Whitehead's works, I am well aware of the very real problems of interpreting his thought. I remain convinced of two things: (1) Whitehead was the equal to Heidegger and Wittgenstein in every way, and ranks with them in the triumvirate of original and brilliant philsophers of this century, and (2) he is under-read mainly because of the difficulty one encounters in understanding his thought, oddly enough much like Heidegger and Wittgenstein. Heidegger has long been the patron saint of contemporary continental thought, and analytic thinkers still read and teach Wittgenstein, though they have trouble with some of the mystical elements that keep creeping in and spoiling a good syllogism. By and large, no one reads Whitehead with any consistency, except theologians (and not all, or even most, of them). More's the pity, since his thought, like that of Kant or Plato, always brings new things to the discussion each time it is encountered.

This little book could do its small part in changing all that, though I doubt it. I envision philosophers world over reading the book and saying, "Oh, THAT'S what he meant!" Whitehead studies will take the fore, and we usher in a new age of creative speculation in philososphy. Until that happens (and I am not holding my breath), read this book so that you'll be ahead of the game. Because, I assure you, if you are new reader of Whitehead or an old hand, you too will have at least one "So THAT'S what he meant" moment in the course of reading this book.

If you are a student looking for textbooks, buy this one if you are reading Whitehead, and read this book before (long before, actually) you try to plow into Process and Reality. Hosinski will not steer you wrong, and, unless your prof read this book too, you might actually understand better than she does. You have probably come across Sherburne's Key to Process and Reality. That is the standard intro, but I actually like Hosinski's better. He explains the concepts, the "why," of Whitehead, and once you have that, you don't need a "key." Once you have figured out Whitehead's language, like that of Hegel or Heidegger or Derrida, reading him is a joy and actually not that difficult. Like all good philosophy, it is poetry; it has its own language, and you have to know how to read it.

If you are a professor teaching Whitehead and have not read this book, shame on you. If you are a professor not teaching Whitehead because you think you know what Whitehead was all about ("oh, he was the last metaphysician, a ultra-modernist system builder like Hegel without Hegel's staying power), maybe you should read it again. Then read any of the play-ful postmodern or even deconstructionist philosophers, and see if Whitehead's event-ontology (like Heidegger's, its closest relative) and his "fallacy of misplaced concrescence" seem familiar. If it does, you have understood well. As this book makes very clear, in formulating his thoughts Whitehead emphasized play, not rule; action not stasis; fallability not airtight systems; creativity not tradition (except where that tradition serves as a lure for creative transformation); objective uncertainties (to use Kierkegaard) not wretched complacency (to use Nietzsche); and above all revisability not dogmatism. Speculative philsophy is just that--imaginative construction. It must always pass the test of adequacy. After all, since Heidegger announced the death of metaphysics and Derrida buried it, speculation for the sake of speculation is useless. Whitehead's philosophy--and Hosinski's wonderful book, which I cannot recommend more highly--is useful. Read it, then use it.

Alfred North Whitehead is, without question, the most original philosopher of the twentieth century. Unfortunately, his most important work, Process and Reality: An essay in cosmology, is almost impenetrable. This is not the first attempt to make Whitehead's metaphysics more understandable, but it is the best to date. Although Whitehead's goal was to uncover the structure of reality as revealed in human experience, his insights have been laregely overlooked, in no small part because of the difficulty of his text. Hosinksi has accomplished what many may have assumed to be impossible, namely, to make Whitehead's speculation accessible. I highly recommend this book to anyone interested in metaphysics.

Although most of these essay were written over eight decades ago, I found them to be extremely timely, especially the title essay. Whitehead shoots straight. He begins by stating that most teachers transmit "inert" ideas in their practice--they teach material that has to practicable bearing on providing any meaningful help to students.

He identifies three different stages or rhythms in educational methodology that happen in tandem and in rotation (I visualize a geocentric universe filled with epicycles of rotating moons and planets to illustrate the layers and rings of motion in teaching). He bases these stages on Hegel's Thesis, Antithesis and Synthesis, but he adapts them to the classroom and human learning. He calls these rhythms Romance, Precision, and Generalization. In Romance, the teacher needs to awake the sense of wonder and curiosity in a student's mind. This will provide the impetus to pursue the learning to the next stage: Precision. In the second stage, the student studies by drill and repetition the formulae, rules, and grammars that build upon a thorough knowledge of a filed. In the third stage, Whitehead declares that the student needs to move into a realm of Generaliztion. In this rhythm, the student makes connections, applications, and full, mature usage of the material and ideas.

I wish more teachers and teachers interested in developing their pedagogical methodolgy would take the time to read this short masterful book.

This is more than a fine study of Whitehead. It show how Whitehead's metaphysics can be used to develop new approaches in ethics and other branches of philosophy. Clear, intelligent contribution to metaphysics and to the retrieval of classical American philosophy.

In Novel Theology: Nikos Kazantzakis's Encounter With Whiteheadian Process Theism, Darren Middleton employs the narrative fiction of Kazantzakis and the process thought of Alfred North Whitehead to reveal a common philosophy that shaped both Kazantzakis's and Whitehead's understanding of God through texts of their literature and theology. By comparing specific themes in the novels by Kazantzakis and the works of Whiteheadian process theologians, Middleton reveals that the literature and theology constantly deconstruct each other and suggests that this deconstructive assignment is one that is, itself, a process. Novel Theology is insightful, thought-provoking reading and highly recommended for students and scholars of literature and theology, and the non-specialist general reader with an interest in the works of Nikos Kazantzakis, the philosophy of Alfred North Whitehead, and process thought as found in theology and literature.

I must say, I am indebted to Colin Wilson for leading me to this book. I read Beyond the Outsider a few years ago, and immediately afterwards was itching to read this book. A.N Whitehead is a clear and logical thinker. A genius of the 20th century, his idea of the two modes of perception: Immediacy Perception and Causal Efficacy. Finally, I think, refutes 'successfully' Hume's theory that causation cannot be perceived.

The thought in this book is profound and enlightening, the style and language are clear enough, but I found it unbearably hard going to get through it.

There are four parts to this text: "Sociological," "Cosmological," "Philosophical," and "Civilization." The first part is a history of how ideas, especially moral ideas, have influenced the progress of civilization. Whitehead is by training mathematician and by nature a philosopher, not a historian. As a consequence, he covers a great deal of historical ground at a high level of generality which, in Whitehead's case, I consider a virtue. He has a beautiful, long-term perspective; his account of the transition from a world in which slavery was taken for granted to one in which it is no longer legitimate, and the role that the ideas of Platonism and Christianity played in that 2500 year transition, makes me quite optimistic about the long-term possibility of humane progress in the world.

I describe the first section in depth because it is among the more accessible pieces of Whitehead's writing. The remainder of the book calls upon his unique metaphysical perspective to some extent, and is thus more of a struggle for the casual reader. It, too, is beautiful and valuable for those who are willing to learn how to read Whitehead, but it is not easy. Buy the book for the first part, then if you like Whitehead's highly idiosyncratic view of reality, train yourself to read the rest of the book.

Personally, although Whitehead has fallen out of favor of academic philosophers for most of this century, I think that his work is more likely to be read 200 years from now than are most other works written this century. Whitehead is definitely thinking of the big picture with a certain serene timelessness. Far more people should be exposed to his 20th century articulation of the eternal search for the True, the Good, and the Beautiful (and the Adventure).

Whitehead was the foremost twentieth-century advocate of Process Philosophy--he called it "The Philosophy of Organism"--the conviction that reality is composed of processes rather than of substances or matter.

Students of process thought frequently focus on Whitehead's major work, _Process and Reality_, sometimes to the neglect of his other books. But Whitehead's thought was, fittingly, in continual flux; and _Adventures of Ideas_, written after _Process and Reality_, contains new themes which, some would say, provide needed correctives to some of the notions in Whitehead's earlier books. _Adventures of Ideas_ is also considerably more readable than _Process and Reality_. It should not be passed over.

I approached this book as an influence to Ken Wilber. In his book, SEX, ECOLOGY, SPIRITUALITY, he recognizes Whitehead "as one of the first great philosophers of vision-logic" (p. 191). As Editor Donald Sherburne acknowledges in the Preface to this edition, PROCESS AND REALITY "is highly technical and far from easy to understand" (p. v). In fact, Whitehead (1861-1947) makes reading Ken Wilber seem easy.

First published as a series of lectures in 1929, PROCESS AND REALITY sets forth Whitehead's philosophy of speculatve metaphysics. "Speculative Philosophy," he writes, "is the endeavor to frame a coherent, logical, necessary system of general ideas in terms of which every element of our experience can be interpreted" (p. 3). Whitehead integrates the the works of Plato, Aristotle, Descartes, Locke, Hume, and Kant (p. 39), as he looks into the nature of all things as an ongoing process. (About Plato, Whitehead says, "the safest general characterization of the whole Western philosophic tradition is that it consists of a series of footnotes to Plato.")

I do not profess to fully understand Whitehead, but his basic premise appears to be that reality is in an organic process of becoming, and is never complete. That is, he asserts the many become one and are then increased by one. So, too, God is a process of becoming. Whitehead's philosophy is revolutionary. "Philosophy never reverts to its old position after the shock of a great philosopher" (p. 11), he writes. I have given this book a four-star rating only because Whitehead's writing style is difficult and at times impenetrable, which detracts from his five-star content.

G. Merritt

A philosophical masterpiece. This is a difficult, but extraordinary articulation of Whitehead's "philosophy of organism".

It could change your life.

Early in this century American philosophy made a 'linguistic' turn that determined the direction it would take all the way to the present day. In the spirit of the times, language made its way to the forefront of philosophy, the end result being (among other things) Positivism and a scientistic approach to the Geisteswissenschaften. It is a turn many of us, looking back, wish it had never made. Because of this turn, certain philosophers and ways of doing philosophy all but stopped being considered. Among these philosophers were Dewey and James. These thinkers have in recent decades been resurrected by contemporary neopragmatists, most notably Richard Rorty, who look back at the arid desert of mid-twentieth century philosophy and wonder how far we have come after all. To quote Rorty (who is certainly no Whiteheadian), American philosophical thought 'began taking its cue from Frege rather than Locke.' Broadly considered, this meant that language rather than experience, mind rather than body, was taken to be the most serious matter for philosophy.

Whitehead stayed with Locke. Whitehead wanted to critique most Modern philosophy with what he termed the 'philosophy of organism;' that is, Whitehead insisted that experience or 'feeling' rather than disembodied thinking was the hallmark of human existence, and that all experience was subjective. Now, this does not sound like Locke. Anyone writing this side of modernity knows that Locke was the quintessential modern philosopher, with all the baggage that entails. But when Whitehead wrote in the preface to Process and Reality that 'the writer who most fully anticipated the main positions of the philosophy of organism is John Locke,' he was stressing the fact that Locke discarded metaphysics, seeking rather to look at what was actually happening, as far as he could tell.

In many ways, and though they wrote at the same time but in complete isolation from each other's thought, Whitehead and Heidegger were searching for the same thing, the thing both philosophers thought that Plato and Aristotle had known, but that had been forgotten in the intervening centuries: what it actually meant to experience something, or, as Cooper puts it, how 'to make intelligible our immediate experience so that we can discover how it is possible to have any experience of the actual world.' Rather than reading Whitehead as an elaborate and old-school metaphysician, one ought to read him as a phenomenological empiricist, if such a beast exists, and thus find an answer to the people who dismiss Whitehead as 'behind the times,' people who simply don't bother to actually read Whitehead.

It is true that thinkers still committed to a reductionist/linguistic approach to philosophy will not see Whitehead's importance as a critic of closed systems (Whitehead's is expressly open and revisable, one reason it has endured as long as it has without being widely read in philosophy departments). It is also true that American philosophy left Whitehead behind. However, the blind alleys linguistic analysis and positivism lead us into should cause us to wonder if we were led in the right directions, or if we should have left in the first place. Leaving something behind certainly does not necessarily mean progressing beyond it. Whitehead's goal was expressly NOT the goal of philosophy in America after his time, though Whitehead's goal had been an important part of James's 'Radical Empiricism,' ironically. Whitehead looked back to James and Dewey, and Bergson on the continent, hoping 'to rescue their type of thought from the charge of anti-intellectualism, which rightly or wrongly has been associated with it.' Present-day neopragmatism, noting how vapid and unsatisfying most rationalist and linguistic philosophy has become in American thought, also looks back to Dewey and James, but to the pragmatism rather than to the empiricism of these two masters. It has become axiomatic that the only way to read James and Dewey is as pragmatists, after all.

However, the axiom is not true. A 'rediscovery' of Whitehead by contemporary American philosophy might lead to another and equally valid reading of James and Dewey. James, Dewey, and Whitehead were thinkers of the same ilk. If you like any two, you should at least consider reading the third. Similarly, the relations between Heidegger and Whitehead have only recently been resurfacing, and deserve closer scrutiny. Analytic philosophy never took seriously the questions raised by Heidegger because they weren't precise enough for logical analysis. When a grandfather of the analytic movement, Wittgenstein, began distancing himself from his earlier work, his own disciples balked because, they said, he seemed to be retreating into metaphysics! It is much more likely, however, that Wittgenstein realized that life cannot be reduced to propositions and truth tables. This was also Whitehead's view. Whitehead was also not precise enough for the analytic philosophers (I always wonder who is). Whether or not the fact that he did not measure up to their standards (and still does not) should be seen as an indictment or a complement remains to be seen.

Whitehead is an immensely difficult writer. Hosinski's Stubborn Fact and Creative Advance (1993) is a brilliant introductory work, and I highly recommend it, especially if you have to read Whitehead for a class Sherburne's Key is also very helpful, though you get a lot of Sherburne, too. At issue is usually Whitehead's neologisms. To draw another analogy between Heidegger and Whitehead, however, both men were notorious for creating new words because what they wanted to explain was both so uncanny and yet so obvious that the old words didn't work. Don't let the language scare you away. Whitehead rewards hard work, and you will likely never forget what you learn from him. The ideas that we are beginning to take much more seriously these days about holistic thinking, interconnectedness, interdisciplinarity, non-dualism, commensurability between science and religion, and creativity were all covered by him seventy years ago. Don't let your professors tell you that Whitehead is an outmoded metaphysician. His 'philosophy of organism' is as inherently open-ended, properly understood, as anything passing today as postmodernism. Read Whitehead.