Foundations of Mathematics and Other Logical Essays

by F.P. Ramsey

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

Genres: Mathematics, Philosophy, Logic

312 pages, Kindle Edition

First published January 24, 2001

About the author

Frank Plumpton Ramsey (B.A. (Senior Wrangler), Mathematics, Trinity College, Cambridge, 1923) was a philosopher, mathematician, economist, and a member of the Cambridge Apostles, the secret intellectual society.

Reviews

[Lucille Nguyen · Rating 4 out of 5]

A classic of analytic philosophy. Advances a philosophy of mathematics from the logicist approach (I admit to having come from the Formalist school, particularly proto-structuralism a la Haskell Curry). As such, I found the defenses of the law of the excluded middle, the objections to Keynes's probability, and the logical treatment of probability wanting. A classic, for sure, but not one without shortcomings or things found objectionable with what we know now.

[(_____) (____) · Rating 5 out of 5]

I am not exactly sure how this book is on Goodreads, but as it is, it requires a review. It is somewhat presumptuous to review one of the classics of analytic philosophy, nonetheless, so I'll focus mainly on broad details that a prospective reader should know.
Firstly, this is probably the best collection of Ramsey's philosophical papers, although it contains none of his work on economics or mathematics. There is a slightly more complete collection: "Philosophical Papers", edited by D. H., Mellor, which contains his excellent paper "Universals of Law and of Fact" as well as another paper called "Law and Causality", neither of which are in this collection. However, "Philosophical Papers" is approximately twice as expensive as this books, and as the manuscript of "Universals of Law and of Fact" is available online, this collection is probably more worthwhile. Ramsey's handwriting is atrocious, but it's still possible to decipher the manuscript.
One really ought to read Russell and Wittgenstein before reading this book, for several reasons. Firstly, Wittgenstein greatly influenced Ramsey, and also the book contains Ramsey's review of Wittgenstein's "Tractatus Logico-Philosophicus", which introduced the color-exclusion objection. Secondly, Ramsey is something of a philosopher's philosopher, despite being a pragmatist, and generally assumes his reader to be very familiar with the sorts of styles and ideas prevalent in analytic philosophy during his time.
Despite being entitled "The Foundations of Mathematics and Other Logical Essays", this book does not contain an inordinate amount of symbolic logic. That is fortunate, as Ramsey uses Russell's justly-rejected and rather obnoxious notation. The most technical essays are "Theories" and "On a Problem of Formal Logic", which are quite honestly unreadable. The other essays don't require overmuch grappling with notation, and the editor provides a helpful guide to the symbolism. Ramsey is also very good at explaining what he means without symbolism when he wants to be, which means that it is technically possible to read "The Foundations of Mathematics" and mostly skim over the more complicated notation (though surely not recommended).
Ramsey generally writes either very long or very short papers. Some are only two to three pages long; others, like the titular essay, are more like short monographs. There are a few exceptions, however.
Finally, many of the papers, especially the more philosophical ones (as opposed to those concentrating chiefly on mathematical logic) are unfinished. Some are really more like personal notes than essays.
A comparison might be drawn with Kafka in the above two respects.