Name: Introduction to mathematical philosophy
ISBN: 9780486277240

Introduction to mathematical philosophy

In the words of Bertrand Russell, "Because language is misleading, as well as because it is diffuse and inexact when applied to logic (for which it was never intended), logical symbolism is absolutely necessary to any exact or thorough treatment of mathematical philosophy." That assertion underlies this book, a seminal work in the field for more than 70 years. In it, Russell offers a nontechnical, undogmatic account of his philosophical criticism as it relates to arithmetic and logic. Rather than an exhaustive treatment, however, the influential philosopher and mathematician focuses on certain issues of mathematical logic that, to his mind, invalidated much traditional and contemporary philosophy. In dealing with such topics as number, order, relations, limits and continuity, propositional functions, descriptions, and classes, Russell writes in a clear, accessible manner, requiring neither a knowledge of mathematics nor an aptitude for mathematical symbolism. The result is a thought-provoking excursion into the fascinating realm where mathematics and philosophy meet — a philosophical classic that will be welcomed by any thinking person interested in this crucial area of modern thought.

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WillAdamsAug 2026

For an accessible introduction before beginning this, consider his _Introduction to Mathematical Philosophy_:

https://en.wikipedia.org/wiki/Introduction_to_Mathematical_P...

and for ease of reading see the various PDF versions at:

https://people.umass.edu/klement/imp/

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WillAdamsDec 2024

A good example of this is Bertrand Russell's _Introduction to Mathematical Philosophy_:

https://courses.umass.edu/klement/imp/

which is available in a number of sizes _and_ has the LaTeX source available showing how the various sizes are arrived at.

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anaphorSep 2021

As someone with a philosophy degree this isn't a great list. Most of the recommended readings seem like random textbooks they found. It's pretty light on actual source material, and when they do list it, it's a bit bizarre, like recommending "On Formally Undecidable Propositions of Principia Mathematica and Related Systems" for philosophy of mathematics (Not that I think it's not worth reading, but not as your introduction to philos of math!), or recommending Kuhn as a supplemental reading, but not Popper, Bacon, Hume, etc.

FWIW, for philosophy of mathematics, I'd recommend reading "Introduction To Mathematical Philosophy" by Bertrand Russell. The recommendation of The Frege Reader is actually good, but I'd recommend watching some lectures or something as well, otherwise it'll be a difficult read.

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anaphorDec 2019

Most of mine are going to be books by philosophers or scientists (about philosophy or other things).

- The Conquest of Happiness by Bertrand Russell was a pretty good one. He has a lot of ideas that were ahead of their time (positive psychology, etc). You can see a lot of parallels between his ideas and modern Stoicism (although Russell criticized it elsewhere, I think he came to some of the same conclusions).

- Introduction To Mathematical Philosophy by Bertrand Russell. Another Russell one. I think this is probably the clearest and easiest to understand explanation I've ever read of the underpinnings of mathematical foundations. It's written in a style that should be accessible to almost anyone with a high school education. He wrote it while he was in prison (for refusing to be drafted) during WW1. Apparently he left a copy of it to the prison warden.

- An Enquiry Concerning Human Understanding by David Hume. This is worth reading because it is the motivation for basically all of modern philosophy of science (at least in the west). It's also pretty easy to read and if you read it you'll be able to more easily understand other books and papers that are responses to it.

- Turing's Cathedral by George Dyson. This book should be required reading for every programmer or aspiring programmer IMO. I learned so much about the history of computing that I didn't know before reading this. You will not regret buying this one.

- I Am A Strange Loop by Douglas Hofstadter. Obviously everyone knows about GEB, but he also wrote a shorter follow up that in my opinion expresses his ideas much more clearly. I think that even if you disagree with him, it's worth reading because there are so many things you can take away from this book. For example, he talks about his wife's death, and ties that into his theory of mind and explains the unstated purposes of why we have funerals/wakes for people.

- An Introduction to Information Theory by John R. Pierce. For someone like me who doesn't really have a very strong math background, this was a very clear intro to the ideas behind information theory, and why they're important historically. I would recommend this to anyone who feels like they need a gentle intro to the ideas and motivation for them. Dover mathematics books in general are great.

- Borrow: The American Way of Debt by Louis Hyman. This is a fantastic historical overview of personal credit in the US that covers the past 120 years or so. I learned a ton from reading this that I had no clue about. Recommended to anyone who wants to understand the origins of credit cards / loans, and how society came to embrace being in debt.

https://archive.org/details/in.ernet.dli.2015.222834/page/n7

https://people.umass.edu/klement/imp/imp-ebk.pdf

https://archive.org/details/humeenquiry00humerich/page/n7

https://www.amazon.com/Turings-Cathedral-Origins-Digital-Uni...

https://www.amazon.com/Am-Strange-Loop-Douglas-Hofstadter/dp...

https://www.amazon.com/Introduction-Information-Theory-Symbo...

https://www.amazon.com/Borrow-American-Debt-Louis-Hyman/dp/0...

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chicobMay 2019

I suspect the Humanities seem to be at an advantage here. In the Arts, students learn about the basic physiology of the human eye, the Physics behind color and also some Geometry. In Sociology, surely there must be some Statistics course. In Archeology, Nuclear Physics, Plate Tectonics and Astronomy are unavoidable.

In Physics, it is almost impossible not to make use of History timelines for the sake of understanding the evolution of ideas. But that's that.

I think some course in the History of Science would be highly valuable in STEM. Philosophy of Science would also be very beneficial.

There are many writings by Bertrand Russell that would fit in Math courses and that have a lot to do with Philosophy and that are very pertinent to any math student.[1][2]

In my opinion, one of the books that better makes the bridge between the Humanities and Science is Florian Cajori's History of Mathematical Notation. No only it is a very interesting book, shedding light at the intimate relationship of our symbol lexicon, our skills at abstraction and the progress in Mathematics, but it also teaches about cuneiform writing, rhetorical Math teaching in ancient Egypt, and how fundamental the invention of typography was for the stability of Mathematical notation.

A Professor I once knew lend me his only copy just because I mentioned the topic, and after skimming through I knew I had to buy my own. (For all of those of have lent books, you must know how much of a gamble it is, specially when the person you're lending the book is some random student!)

[1] Introduction to Mathematical Philosophy (http://people.umass.edu/klement/russell-imp.html)

[2] On Denoting (http://bactra.org/Russell/denoting/)

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nyc111Oct 2018

You might like Russel's Introduction to Mathematical Philosophy https://people.umass.edu/klement/imp/imp-ebk.pdf

From the Introduction:

"And as we need two sorts of instruments, the telescope and the microscope, for the enlargement of our visual powers, so we need two sorts of instruments for the enlargement of our logical powers, one to take us forward to the higher mathematics, the other to take us backward to the logical foundations of the things that we are inclined to take for granted in mathematics."

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