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Recommendations of math and physics texts for philosophy students wanting to study philosophy of physics

Brian Leiter

A reader writes (a propos this):  

I wonder whether you could use your platform to ask professional philosophers of physics for a self-study guide to the literature. Long term I would find it wonderful if students and enthusiastic laymen had something similar at hand as Peter Smith’s “Beginning Mathematical Logic: A Study Guide”. Smith has over the years compiled his various thoughts and reviews on logic textbooks resulting in an extremely helpful booklet that details a path from absolute beginner in logic to that of a very competent reader of technically advanced literature. If you could ask your readers for reading suggestions for both maths and physics textbooks, in sum amounting to a semi-detailed reading list, I am sure lots of people would appreciate it! I ask specifically for the opinion of philosophers (especially for the physics books) as lots of physics books often lack conceptual clarity or flatly misrepresent some finer points relevant to the philosophy. Jenann Ismael’s SEP entry for quantum mechanics includes a very helpful short guide and I would hope we could expand on that and gather something similar for other areas of the philosophy of physics.

I am unfortunately not very tech-savvy, so I hope that one of your readers will eventually take the task upon himself to continue this project and migrate it to his own site but I would be very willing to provide feedback over time from the perspective of the average student and his opinion on the didactical merits of some of the books.

A final list (in the far future) ideally would consist of three areas:

One for the mathematics needed (linear algebra, analysis, differential geometry, topology…), one for the physics needed, and one actually consisting of the philosophical literature (various introductions to the philosophy of physics, loci classici, etc.) with each of them ordered in terms of difficulty.

Let me make the easy start/ provide an example of what I mean:

For the mathematics needed:

In my opinion the best introduction to mathematical reasoning is Daniel Velleman’s “How to Prove It: A Structured Approach”. It assumes no knowledge beyond high school mathematics (even less so) and introduces gently the logical structure of proofs and the various proof strategies an undergraduate in mathematics ought to know. Lots of exercises, some with detailed answers. Various online blogs are out there to compare one’s own solutions to that of others.

For a start in linear algebra:

Serge Lang: Introduction to Linear Algebra

Gentle undergraduate introduction to proof-based linear algebra that assumes no knowledge of analysis. Contains exercises and solutions are easily found online. Treats the usual basics up to determinants and eigenvectors/eigenvalues.

Serge Lang: Linear Algebra

Covers the roughly same ground as the slightly shorter Introduction by Lang at a higher pace, leaves out some topics such as Gauss elimination and also touches upon other topics such as polynomials and symmetric, Hermitian and Unitary Operators. Intended as the next step after Lang’s “Introduction to Linear Algebra”

And so on.

Comments are open for reading suggestions.   Please use your full name or at least identify yourself by description (e.g., "graduate student in philosophy of physics"; "mathematician interested in physics" etc.).

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14 responses to “Recommendations of math and physics texts for philosophy students wanting to study philosophy of physics”

  1. Michael B

    If you plan to study on your own I think you could do a lot worse, and maybe not much better, than searching your favourite secondhand marketplaces for undergraduates texts on mathematics and physics from the Open University in the UK. As you are not tech savvy, here is a link to their honours degree in mathematics and physics:

    https://www.open.ac.uk/courses/maths/degrees/bsc-mathematics-and-physics-q77

    You could look at the pages for straight physics or straight mathematics degrees to get a wider range of texts.

    From what you wrote, try searching any of the following course codes along with "Open University" and see what suits you: MU123, MST124, MST125, MST224, SM123, S217. The initial number in the course code refers to the 1st, 2nd or 3rd year of the honours degree. So e.g. S217 is a 2nd year course in physics.

    It may be relevant to your decision to know that the Open University is exclusively distance learning at undergraduate level and has been for 50-odd years. So it has much experience in writing materials for students who study alone. Also, being open, it has written the materials without assuming the traditional background of A-level [high school] maths or physics. They start slow and then ramp up. Happily, every exercise – and there are a lot – has answers, usually fairly detailed. These almost always follow worked examples.

    Source: I am finishing off a degree in statistics with them having done a degree and MA in philosophy in other places. Over the many years I have been with them, many mature students, with mathematics/physics degrees from all the top departments here in the UK, comment on the clarity and user-friendliness of the materials. I only know the OU's stuff so make of this anecdote what you will.

    Reply
  2. Siddharth Muthukrishnan

    David Wallace has detailed reading lists on his website for the three main subtopics of philosophy of physics (statistical/thermal physics, spacetime, and quantum physics). The lists also include relevant physics textbooks and some remarks on how to use these lists.

    You can find them here: https://sites.pitt.edu/~dmw121/resources.html

    Reply
  3. Paul Weithman

    Within the last year or so, I had occasion to search for an introductory book on topology. I looked at quite a few and thought the best — by far — was Robert Conover's A FIRST COURSE IN TOPOLOGY. It is too elementary for anyone with much of any mathematical background, but for someone who knows no more than a bit of calculus and a smattering of real analysis, it's useful, clear and does a good job motivating the subject.

    For linear algebra: the UCLA mathematician Terence Tao posted course materials — including partial solutions to problem sets — many years ago, but I have never done more than glance at it. You can do the same here: https://www.math.ucla.edu/~tao/resource/general/115a.3.02f/

    Reply
  4. Anon

    These days, youtube is often the best place to learn math. Ted Shifrin's videos on multivariable calc and linear algebra are excellent and cover through advanced topics (e.g. differential forms). Steve Brunton's channel is also fantastic for math for engineering and physics.

    Reply
  5. Peter

    Hi!

    I am the reader who asked for help. Thanks to all who answered and to Professor Leiter for posting my question.

    @Michael B

    The Open University has watered its curriculum massively in recent years. I am very sceptical that it will be of much help. Anyway, thank you!

    @Paul Weithman

    Tao is an exceptionally clear writer and didact. Unfortunately important links on his webpage (like that linking to the lecture notes) do not seem to work.

    I should add that with the internet at hand, it is very easy to download almost any book (library genesis, *cough*). People like me do not struggle with accessibility of material but are overwhelmed by the resources. I was wondering for example whether I should read Feynman's lectures in toto as I lack a background in physics. Reading through Wallace's guide, thank you Siddarth, it does not look like it. But I have had conversations who pointed to Leonard Susskind's Theoretical minimum series. Unfortunately, time is short and I hope that one can skip considerable parts of the average physics curriculum without compromising on understanding the philosophical issues discussed in the literature.

    Reply
  6. Richard Baron

    Another Youtube recommendation, the channel called The Bright Side of Mathematics:
    https://www.youtube.com/@brightsideofmaths

    Reply
  7. Curtis Franks (poet interested in physics)

    "… and one actually consisting of the philosophical literature"

    Just on this point, I can highly recommend Roberto Torretti's /The Philosophy of Physics/. It is the sort of philosophy book that you can work through. I read pathologically slowly and for that reason am selective about what I pick up, but I read this thing cover to cover three times. It's just great: straightforward with the math, deriving everything carefully and explicitly, historically sound about the introduction of concepts and how to interpret things. So much philosophy of physics (rightly) jumps right in to abstract indices for differential geometry, category theoretic frameworks for expressing symmetries, and suchlike. It can be alienating to the non-expert. This book shows you how much you can understand with some basic nuts and bolts, and in doing so keeps close to the context of discovery.

    Reply
  8. Marius Stan

    Books that have helped me much better than others.

    For linear algebra: Strang's two textbooks, elementary and advanced. Also, he teaches it at MIT, and videos of his lectures are available there for free.

    For Calc III: Marsden and Tromba, "Vector Calculus." Unrivalled.

    For differential geometry: M.P. do Carmo, "Differential Geometry of Curves and Surfaces."

    All-in-one resources: R. Courant, "Methods of Mathematical Physics," 2 vols.

    For classical mechanics:

    Elementary expositions. A.P. French, "Newtonian Mechanics."
    Mid-level presentations. Of analytic mechanics: O. O'Reilly, "Engineering Dynamics." L.A. Pars, "Intro to Dynamics. Of continuum theory: M. Gurtin, "An Intro to Continuum Mechanics."
    Advanced textbooks. On analytic mechanics: treatises by Neimark & Fufaev, and by Gantmacher, respectively. L.A. Pars, "A Treatise on Analytical Dynamics." On continuous systems: Gurtin, Fried & Anand, "The Mechanics and Thermodynamics of Continua."

    Ambitious surveys. Goldstein, "Classical mechanics." Truesdell & Noll, "The Classical Field Theories of Mechanics." (And another volume on non-linear theories.) G. Hamel, "Theoretische Mechanik."

    Reply
  9. Charles Sebens

    My recommendations for readings appear in the syllabi for my introduction to the philosophy of physics (with a focus on electromagnetism) and my philosophy of quantum mechanics course, both of which are available on my personal website: https://sites.google.com/site/csebens/

    Reply
  10. David Wallace

    Siddharth was already kind enough to link my first-order suggestions. In lieu of that, here's a second-order comment.

    I think philosophers of physics, and would-be philosophers of physics, hope that there's some way to extract the conceptual core of a physics theory from all its tedious applications and calculational techniques, and indeed to clean up various infelicities on the way. I don't want to pick on the OP, whose requests is entirely understandable, but when I see comments like "lots of physics books often lack conceptual clarity or flatly misrepresent some finer points relevant to the philosophy" or "time is short and I hope that one can skip considerable parts of the average physics curriculum without compromising on understanding the philosophical issues discussed in the literature" I worry.

    A lot of the content of a physics theory is contained in its applications and calculational methodology rather than its explicit axioms (which, as Kuhn and others taught us, don't always reflect the actual theory as used), and the questions of how to present a physics theory with conceptual clarity and how to identify which fine points are misrepresented are contested within philosophy of physics and can't be presupposed before you start doing it. I strongly believe that to understand physics you need to spend at least some time learning the subject the way physicists learn it: applications, calculational techniques, conceptual infelicities, and all.

    Once you've got that you can ask philosophical questions about what is and is not central, and in due course you can take shortcuts in learning new material, but you can't entirely bypass the messy details.

    Reply
  11. Nick

    I was in a similar position not long ago (PhD student without prior technical background learning similar subjects, for career change), and I highly recommend using 3blue1brown as your guide: https://www.3blue1brown.com/

    His book recommendations: https://www.3blue1brown.com/blog/recommendations
    (The Hubbard and Hubbard linear algebra/calculus book is the first book you should get, I think.)

    Essence of linear algebra: https://www.3blue1brown.com/topics/linear-algebra
    Essence of calculus: https://www.3blue1brown.com/topics/calculus

    Some physics videos: https://www.3blue1brown.com/topics/physics

    Once you have a basic familiarity with linear algebra, this is a very cool book: https://www.cambridge.org/core/books/picturing-quantum-processes/1119568B3101F3A685BE832FEEC53E52

    Reply
  12. Peter

    Thanks for the answer, Professor Wallace.

    My worry is exactly that I skip relevant parts for a sound understanding and that is why I do not want to skip the tedious parts such as calculations. However, time is a constraint and not all physics curricula are equal (my local university has devoted a huge part of its curriculum to biophysics and astrophysics, and I was and still do not know whether I should seriously devote time studying these areas).
    Personally I lean towards comprehensiveness and I seriously think about working through all three parts of the Feynman lectures/Susskind's introductory books for foundations. What is your advise? Is Feynman outdated, do you prefer other books for laying a foundation?

    Reply
  13. V. Alan White

    I have downloaded Wallace's short introduction–what an excellent little book.

    For my part, I worked in philosophy of time/relativity exclusively, mostly defending Einstein's views against critics of SRT in several pubs. As Wallace says, the only way I could do this is learning the math behind SRT and even GRT, to see how the two connect (the math is necessary to understand even basic stuff like how co- and contravariant spacetime diagrams work). So I'd say if one wishes to work in one sub-field of philosophy of physics, do learn the math. It gets harder with quantum stuff, as my own inroads on those realms disclosed to me, so Wallace has my respect.

    Reply
  14. Walther Robert Ellis, Jr.

    Feynman's lectures (3 books plus some lectures published elsewhere) were meant for a freshman physics sequence required of all undergraduate students at Caltech decades ago. These lecture notes are probably too advanced for an average student to learn basic physics without a lot of additional assistance. In any event, they are quite inadequate for someone intending to do physics-related research. Physics is not a spectator sport–be prepared to work through lots of problems, otherwise you will not really understand the material.

    Along with the physics, you will need to devote time to learning more math than what is covered in a year-long calculus sequence. James Nearing's "Mathematical Tools for Physics" (an inexpensive Dover text) offers a good overview of the math needed to get through most undergraduate physics texts written for sophomore-junior courses, as well as introductory quantum mechanics.

    I also recommend Sean Carroll's book on general relativity.

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