The Infinite

by A.W. Moore

An historical study of the infinite, covering all its aspects, from the mathematical to the mystical. Moore discusses not only Aristotle and Zeno, but also Cantor, Gödel and Wittgenstein, and examines God, mortality and human finitude.

Genres: Philosophy, Nonfiction, Mathematics

268 pages, Paperback

First published January 1, 1990

About the author

Adrian William Moore (born 1956) is a Professor of Philosophy and Lecturer in Philosophy at the University of Oxford and Tutorial Fellow of St Hugh's College, Oxford.

Reviews

[Mr Siegal · Rating 5 out of 5]

30 Years in the Making

What an excellent book. In “The Infinite”, A. W. Moore takes us from Ancient Greece up to Cantor and beyond in addressing infinity. A crucial distinction in his book is metaphysical infinity which encompasses the notions of completeness, wholeness, unity, universality and so on, and mathematical infinity, which encompasses the notions of endlessness, immeasurability, eternity, endlessness and so on.

Moore has an apparent gift in finding a narrative through history. Just as in his monumental “The Evolution of Modern Metaphysics”, so here one sees a continuous development of a single idea, as well as comparisons between philosophers, most noticeably Hegel and Spinoza.

Crucial to the entire enterprise is Wittgenstein’s distinction between saying and showing. Though we cannot grasp the infinite, we are shown it in some way. Thus, the infinite becomes ungraspable in language, and Moore wishes to keep it as, amongst other reasons, it helps us come to terms with our finitude. Indeed, he concludes the third edition of this book by saying that “we shall never know how to be finite if we do not reckon properly with the infinite.

The only issue I had with this book, and I believe that it has to do with the writing style of analytic philosophy, is that it is not daring enough. In addition, it is very wide ranging and you get the feeling that it is more like different ideas where put together over time rather than one self standing piece of work. That being said, it is an excellent read.

Finally, I want to emphasise a more ‘continental’ twist to this book, especially in the new chapters. Moore has become more and more interested in the likes of Deleuze over the years, and this shows in his willingness to take such thinkers seriously rather than scoff at them. But then again, any serious philosopher manages to evaluate ideas for themselves, and does not rely on labels. Moore is a very serious philosopher and one how I hope continues to write for years to come.

[Andrew Langridge · Rating 4 out of 5]

A.W. Moore's masterly study demonstrates how a proper appreciation of the infinite is crucially important in deciding the limits of our knowledge and providing meaning for our lives. After an illuminating historical exposition of the key debates from the Ancient Greeks to the present day, Moore advances his view that our radically finite lives are aspects of an infinite whole. This is something that we are shown, not something that we can know. We cannot fully grasp the infinite (despite Cantor's best efforts), but self-conscious introspection invites us to apply a-priori Ideas of the infinite to reality. For example, continuous lines and shapes are really self-contained wholes but can be treated by mathematicians as if they were sets of infinitesimal points. What I find remarkable is that Aristotle had already solved many of these problems through advancement of the 'potential' infinite.

[Maurizio Codogno · Rating 4 out of 5]

L'infinito tra matematica e metafisica

Come forse sapete, il concetto di infinito oscilla da millenni tra la filosofia (meglio, la metafisica) e la matematica. In questo libro Moore sceglie di avvicinarsi di più alla metafisica. Questo non significa che non ci sia matematica nel testo, anzi: però il suo approccio fa entrare in gioco filosofi come Spinoza, Hegel e Nietzsche che con la parte matematica hanno ben poco a che fare. La lettura è insomma consigliata a chi vuole avere una visione a 360 gradi dei problemi che il concetto di infinito ci dà (e magari ripassare un po' di filosofia...)

[saml · Rating 4 out of 5]

i used to hold the opinion that questions about infinity were really mathematical, and that no philosophical considerations known a priori could drive us to believe there were an infinite or finite number of anything. the best way to unsettle this view (though i haven't abandoned it completely) is the kind of broad hermeneutic project moore undertakes here, not only to make sense of the history of thinking about the infinite, but to convince ourselves that there are problems to be solved (even if it turns out we won't solve them). placing the infinite at the centre of lots of other philosophical questions is thus a good strategy to convince us we always already were trying to think the infinite. moore gives a bit of a quick history in the first half, and can't quite bring the well-explained gloss on more technical material in the second half into close unity with it. but he articulates the moments of thought well, putting emphases in the right places. where this leaves us, i don't know. less confident, perhaps