Introduction Modal Logic with emphasis on metaphysics - free will particularly - and also mathematical logic

Question

I'm reading Timothy O'Connor's 'Persons & Causes The metaphysics of free will' and the first chapter briefly goes into (though without introduction) the application of modal logic and counterexamples to non-sufficiently refined explications of the Consequence Argument.

Now, I am actually a mathematics and philosophy student so have studied both 'baby first order logic' in maths, and also Peter Smith's intro to formal logic (seen here) http://www.amazon.co.uk/Introduction-Formal-Logic-Peter-Smith/dp/0521008042 and will be working through Hodges and Chiswell's mathematical logic.

What route - or what material - in modal logic do you think is both sufficient for me to tackle the modal arguments in O'Connor yet at the same time be basic enough to progress from my present understanding of first-order / baby logic?

I would also be interested, on a related note, if someone with experience in the mathematics of philosophy could give some recommendations of - roughly - what kind of suitable progression one may take with a set of logical or mathematical philosophical books of their choosing from someone with not any real exposure to mathematical philosophy.

I bought Russell's Principles of Mathematics but I don't really think this is going to be an enjoyable read on the account of both suitability and introductory considerations.

Answer 1

Hodges and Chiswell's mathematical logic may not help much with modal logic, which is more like an extension to predicate logic. I'm not familiar with Peter Smith's book, but Amazon's index indicates that he already introduced the universal and existential quantifiers ∀ and ∃, respectively. Modal logic simply adds to these with the possible and necessary modal operators □ and ◇, respectively.

The textbook I was taught with was Brian Chellas's Modal Logic: An Introduction. It's fairly concise, with good examples, if a little dry. You might also try Modal Logic for Philosophers by Garson. I haven't read it myself, but the review on the book seems like it may be just what you're looking for.

As for the philosophy of mathematics, I think most people would recommend a university course, rather than just a book. mario's suggestions look sound enough for a start.

Answer 2

The best introductory text for modal logic, in my opinion, is Fitting and Mendelsohn, First Order Modal Logic, Synthese Library, 1999. It is quite important to get the full first-order treatment of modal logic for contemporary metaphysics, because you need some of the important devices (like predicate abstraction) that don't standardly get introduced in books that just treat the propositional modal logic, like Hughes and Creswell. I really like the tableau proof system in M&F too!

Answer 3

for the Phil of Math part, give a look at Philosophy of Mathematics: Selected Readings 2nd Edition by Paul Benacerraf (Editor), Hilary Putnam (Editor) and to The Philosophy of Mathematics (Oxford Readings in Philosophy) 1st Edition by W. D. Hart (Editor)

I can not post more than two links, but look for books by Charles Parsons and Stewart Shapiro too.