The Open Logic Project
openlogicproject.org
openlogicproject.org
Mathematical Logic, Set Theory and its Logic, Methods of Logic. All three of these are by Willard van Orman Quine. If you know anything about modern logic, then that is a name that you should recognize.
A more accessible textbook is Sweet Reason by Tymoczko & Henle. They're a philosopher & mathematician pair and I like their approach. I'm currently halfway through the first edition. The errors are a bit annoying and I wish that I had waited for the second edition.
We're all nerds, here, so I understand the emphasis on mathematical logic, but you owe it to yourself to be familiar with traditional Aristotelian logic, as well. Noting the difference in mindset between traditional and modern logic is enlightening.
Being Logical, by D.Q. McInerny is a quick introduction to traditional logic. Socratic Logic by Peter Kreeft is much more involved. Be warned; Kreeft takes a strong stand against modern logic. He has some good points, but he's a bit unfair.
(Maybe I am being unfair to those jointly appointed. I am a mathematician, but not a logician, so I don't have a proper sense of what such an appointment means.)
More to the point, Mathematical Logic is a bit of a term of art referring in general to the study of formal logical systems and related objects/constructions. The term Mathematical Logic is typically used to distinguish from e.g. the sort of informal logic you might encounter in a course where one might read Aristotle and discuss informal logical fallacies.
Also, TBF, a lot of Mathematical Logic happens in analytically-inclined Philosophy departments these days. And it's not at all uncommon for a Mathematics department to have exactly zero Logicians. Just playing the odds, it's somewhat unsurprising that a group of high-quality Mathematical Logicians just happened to not include any people with a sole appointment to a Mathematics department.
Indeed, as are Antonelli and Arana. They carry joint appointments in math and philosophy, which, if I am being fair, should probably mean that their opinions should be given more, not less, weight in a book like this targeted at philosophers.
> More to the point, Mathematical Logic is a bit of a term of art referring in general to the study of formal logical systems and related objects/constructions. The term Mathematical Logic is typically used to distinguish from e.g. the sort of informal logic you might encounter in a course where one might read Aristotle and discuss informal logical fallacies.
Oh, thanks! I didn't realise this.
> Just playing the odds, it's somewhat unsurprising that a group of high-quality Mathematical Logicians just happened to not include any people with a sole appointment to a Mathematics department.
I agree that this would be unsurprising in a random selection from a random fixed department, but not so much in an institutions-spanning effort like this one. Nonetheless, as I mention, I should probably attach more, not less, weight to a joint appointment.
http://people.ucalgary.ca/~rzach/static/open-logic/open-logi...
Summary: They are going for the foundations of maths, computer science, and logic with completeness, decidability and computability on the menu. I don't know the authors, and I understand your reticence, but the contents looks really good. It's not the kind of logic a practitioner would care about, probably, but it is the big mathy results that logicians do need to learn: they actually mention that this isn't a new course for them, but rather a reference book for lessons that are already given to philosophers.
It's also clearly not written for people who are afraid of maths -- I'm more concerned about their targeted audience. Can you go through that text without an already solid interest in maths?
(Similar to how the kind of mathematics knowledge that an accountant and a physicist would need to understand would be different. Both math. One is math as it relates to the law. The other math as it relates to apples falling from trees.)
Almost definitely, but that was not what worried me—I definitely trust philosophers to pick the topics in mathematical logic that are appropriate for a student of philosophy, but would like to see a mathematician's hand somewhere on the tiller to make sure that the discussion of those topics is fully mathematically accurate.
I disagree! (I would probably say something like that logic, in its informal mathematical meaning (i.e., the meaning that would be given it by a mathematician who is not a logician), lives at the intersection at least of all the sciences.) Nonetheless, it's probably more a matter of terminology, if not even just of my ignorance of the proper domain of philosophy, than of substantive disagreement.