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I am a student in a French university in pure mathematics. I recently came across modal logic and more particularly doxastic logic. But, the only masters of logic offered are reserved for students of the philosophy department.

So I wondered what was the best way to learn about this field of philosophy outside of a university degree. The ultimate goal would be to publish a (serious) article on the subject, as a kind of personal reward.

I have already looked at the SEP article and at Carneades.org's video series but I am a bit lost on how to progress towards the state of the art.

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    There are many textbooks on ML. Jan 19, 2020 at 16:39
  • Applications of mathematics to specific domains generally are part of the domain in question, rather than part of mathematics. Otherwise, we would get to claim huge chunks of all kinds of things -- all the hard part of computing and half of theoretical physics, for instance. Even a degree in applied logic is not about applications, but about determining what kind of general methods to apply. If you are pursuing a philosophical topic, what is wrong with doing so in a philosophy department? Jan 20, 2020 at 4:48
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    If you are looking for self-study resources the recent Introduction to Logics of Knowledge and Belief looks accessible. The problem of logical omniscience is an active research topic in this area, see Jago, Problem of Rational Knowledge and Rönnedal, Doxastic logic. But if you really want to write a research paper you'll need an advisor to direct your efforts. Much of it is mathematical logic, so it could be a mathematician.
    – Conifold
    Jan 20, 2020 at 5:59
  • I claim absolutely nothing and hold philosophy in high esteem! It is simply too late to change departments. I'm a second-year college student.
    – user36437
    Jan 20, 2020 at 7:20
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    Nino B. Cocchiarella & Max A. Freund, Modal Logic: An Introduction to its Syntax and Semantics (Oxford UP, 2008) Jan 20, 2020 at 11:01

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I'd like to add an addition to A.K.'s otherwise very good answer to address the topic of progressing to the "state of the art." A.K.'s reading list will get you the basics. That will be very doable on your own. By contrast, it's very difficult to progress to the state of the art without a mentor or PhD advisor, simply because you won't have any orientation or understanding of the basic trends. If there are any logicians at your university's philosophy department, even if you cannot study under them formally, I would recommend meeting with them and seeing if they'd be willing to give you any guidance.

In any case, after you read Fitting and Mendelsohn and get a basic grasp on modal logic, I would recommend reading Holliday's work on epistemic and doxastic logic as an excellent guide to the state of the art today: Cf. https://philosophy.berkeley.edu/file/856/EC-EL-1.pdf

Beyond that, you will need to get to a level where you can read and understand the significance of the articles published in top logic journals. I would recommend places like The Review of Symbolic Logic, the Journal of Philosophical Logic, Studia Logica, The Notre Dame Review of Formal Logic.

I would definitely not recommend reading Kripke and Lewis if your goal is to understand the state current epistemic/doxastic modal logic. That will send you very far astray from the problems that logicians work on, and into territory that is resolutely philosophical.

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  • That's exactly the kind of advice I was looking for, I'm listing all your recommendations, thank you so much.
    – user36437
    Jan 20, 2020 at 18:48
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One way would be to follow along a syllabus for a relevant course at the MA or PhD level. I know for a fact that this is a good course, but I'm sure there are many others.

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  • That's definitely a good idea to start with!
    – user36437
    Jan 19, 2020 at 17:17
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if you'd like to teach yourself through reading, I'd sincerely recommend the following books. the prerequisite is familiarity with propositional logic and first-order logic. and I suppose you've met this requirement as a math student.

  1. First-Order Modal Logic By M. Fitting & Richard L. Mendelsohn.
    I learnt modal logic by reading this book. its exposition is friendly and clear, which posits no threshold for neither philosophy nor math students.
  2. A New Introduction to Modal Logic By M.J. Cresswell & G.E. Hughes.
    Many friends of mine who also study modal logic in philosophy department recommend this book to me, saying it's also friendly to newcomers. I myself only looked through it, finding the symbols are somewhat different from that in Fitting's book.
  3. An Introduction to Non-Classical Logic By Graham Priest.
    I recommend this book for its introduction to some philosophical explanations and discussions on Normal Modal Logic's semantics, i.e. possible worlds. though it's obvious that a deeper understanding of its philosophical aspects requires more reading of recent papers. and I have to say that Priest's expositions are super-clear with his special notations, but it could also seem over-simplistic from my perspective.

Digression: I suppose what you want to systematically learn is Normal Modal Logic, i.e. logic concerning necessity and possibility of propositions. and as you've already known, there are other types of modal logic such as doxastic logic, epistemic logic. and I think it would be better to start with Normal Modal logic.

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    That's a great answer, thank you very much! However, I was wondering one last thing. What is the next step between reading this book and academic literature? It seems to me to be an abyss. All in all, thank you very much again.
    – user36437
    Jan 20, 2020 at 16:49
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    @Blincer you're welcome! I would suggest reading papers listed in the bibliography of the sep article first. also, I'd like to recommend the PhilPapers portal of modal logic. you can start with texts listed in the "Introduction" part. and I also recommend two prominent books on possible world semantics: 1. Naming and Necessity by Kripke; 2. On the Plurality of Worlds by Lewis. these two books are representative works on two different positions toward possible worlds - possibilism and actualism.
    – user42653
    Jan 20, 2020 at 17:53

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