Book Notes on Logic and the Philosophy of Mathematics

Over the years, I have written over a hundred short notes (or occasionally rather long) notes on a variety of books, either as posts on the blog or as entries to the Appendix to the Study Guide; some are perhaps interesting enough to be worth listing here. So this page in fact has two lists. The first one contains links to webpages on the books that appear in that Appendix so these books are, roughly speaking, wider-ranging texts on mathematical logic (a PDF version of the complete Appendix, differently ordered,  can also be downloaded here). The second list contains links mostly to blog posts on a variety of other logic books or books on the philosophy of mathematics.

Some wider-ranging mathematical logic books

  1. Avigad, Mathematical Logic and Computation, 2023.
  2. Chiswell & Hodges, Mathematical Logic, 2007.
  3. Ebbinghaus, Flum & Thomas, Mathematical Logic, 1978, 2021.
  4. Enderton, A Mathematical Introduction to Logic, 1972, 2002.
  5. Forster, Logic, Induction and Sets, 2003.
  6. Goldstern & Judah, The Incompleteness Phenomenon: A New Course in Mathematical Logic, 1995.
  7. Hedman, A First Course in Logic, 2004.
  8. Hinman, Fundamentals of Mathematical Logic, 2005.
  9. Hodel, An Introduction to Mathematical Logic, 1995.
  10. Johnstone, Notes on Logic and Set Theory, 1987.
  11. Kleene, Introduction to Metamathematics, 1952.
  12. Kleene, Mathematical Logic, 1967.
  13. Kossak, Mathematical Logic, 2018.
  14. Leary & Kristiansen, A Friendly Introduction to Mathematical Logic, 2015.
  15. Mendelson, Introduction to Mathematical Logic, 1964, 2015.
  16. Mileti, Modern Mathematical Logic, 2023.
  17. O’Leary, A First Course in Mathematical Logic and Set Theory, 2016.
  18. Prestel & Delzell, Mathematical Logic and Model Theory, 1986, 2011.
  19. Rautenberg, A Concise Introduction to Mathematical Logic, 1995, 2010.
  20. Robbin, Mathematical Logic: A First Course, 1969.
  21. Shoenfield, Mathematical Logic, 1967.
  22. Srivastava, A Course on Mathematical Logic, 2008, 2013.
  23. Van Dalen, Logic and Structure, 1980, 2012.

Other books on logic, the philosophy of mathematics, etc.

  1. Baaz et al. (eds), Kurt Gödel and the Foundations of Mathematics: Horizons of Truth, 2011. See also the earlier blog posts.
  2. Beall, Glanzberg & Ripley, Formal Theories of Truth, 2018.
  3. Berto, There’s Something About Gödel, 2009.
  4. Bridge, Beginning Model Theory, 1977.
  5. Burgess, Set Theory, 2022.
  6. Buechner, Gödel, Putnam, and Functionalism, 2007.
  7. Csirmaz & Gyenis, Mathematical Logic: Exercises and Solutions, 2022.
  8. Colyvan, An Introduction to the Philosophy of Mathematics, 2012.
  9. Falkenstein, Stapleford & Kao, Logic Works: A Rigorous Introduction to Formal Logic, 2021.
  10. Florio & Linnebo, The One and The Many: A Philosophical Study of Plural Logic, 2021.
  11. Franks, The Autonomy of Mathematical Knowledge, 2009.
  12. Halbach, Axiomatic Theories of Truth, 2011.
  13. Hellman & Shapiro, Mathematical Structuralism, 2018.
  14. Hilbert, Lectures on the Foundations of Arithmetic and Logic 1917-1933 (Ewald & Sieg, eds), 2013
  15. Hills & Loeser, A First Journey through Logic, 2019.
  16. Horsten, The Tarskian Turn: Deflationism and Axiomatic Truth, 2011.
  17. Incurvati, Conceptions of Set and the Foundations of Mathematics, 2020.
  18. Jacquette, Frege: A Philosophical Biography, 2019.
  19. Kirby, An Invitation to Model Theory, 2019.
  20. Kossak, Model Theory for Beginners: 15 Lectures, 2021.
  21. Krömer, Tool and Object: A History and Philosophy of Category Theory, 2007.
  22. Landry, E. (ed) Categories for the Working Philosopher, 2017.
  23. Maddy, Defending the Axioms: On the Philosophical Foundations of Set Theory, 2011 (with Luca Incurvati).
  24. Mancosu, Galvan & Zach, An Introduction to Proof Theory, 2021.
  25. Manzano, Model Theory, 1999.
  26. Moore, Gödel’s Theorem: A Very Short Introduction, 2022.
  27. Olszewski et al. (eds) Church’s Thesis after 70 Years, 2006.
  28. Parsons, Mathematical Thought and Its Objects, 2008. Much longer (52 page!) review notes.
  29. Pollard, A Mathematical Prelude to the Philosophy of Mathematics, 2014.
  30. Prince, The Annotated Gödel, 2022.
  31. Rayo & Uzquiano (eds) Absolute Generality, 2006. Also see a long series of blog posts.
  32. Restall & Standefer, Logical Methods, 2022.
  33. Restall, Proofs and Models in Philosophical Logic, 2022.
  34. Rush, The Metaphysics of Logic, 2014.
  35. Shapiro, Varieties of Logic, 2014.
  36. Sider, Logic for Philosophy, 2012.
  37. Smith, N., Logic: The Laws of Truth, 2012.
  38. Robert Trueman, Properties and Propositions, 2021.
  39. Weingartner & Leeb, Kreisel’s Interests: On the Foundations of Logic and Mathematics, 2020.
  40. Weir, A Truth Through Proof, 2010.  Also see a series of blog posts.
  41. Zach, et al. Open Logic Text, 2015. [Due for update!]
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