The Open Logic Project(openlogicproject.org)
openlogicproject.org
The Open Logic Project
http://openlogicproject.org/
3 comments
Looks like a great start. But I didn't find any intention to add some exercises. No textbook is complete without exercises!
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I'm a little disconcerted by the fact that no-one involved in this is a mathematician, full stop. At least three of those involved seem to have joint appointments in math and philosophy (Antonelli, Arana, and Avigad). While the aim of the text to be suitable for non-mathematician philosophy majors means that a heavy bias towards philosophers is probably both inevitable and correct, I would like to see at least one just-mathematician to make sure that it really deserves its description as mathematical logic.
(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.)
(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.)
Just from purusing the author's personal websites: Avigad's Ph.D. is in Mathematics (from Berkeley) and he is a professor in a mathematics department.
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.
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.
> Avigad's Ph.D. is in Mathematics (from Berkeley) and he is a professor in 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.
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.
Have you looked at the table of contents?
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?
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?
I was worried not about the list of topics, but rather about whether or not their coverage is mathematically accurate, which I would like to see a mathematician 'on staff' to ensure. To be sure, the best way to test the validity of that concern would have been to read the content, not to play credential checking.
Is there a difference between the sort of logic that a mathematician would need to know and the kind that would be appropriate for a philosopher?
(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.)
(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.)
> Is there a difference between the sort of logic that a mathematician would need to know and the kind that would be appropriate for a philosopher?
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.
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.
Sorry: the parent comment (which is mine) was well meant, but is not nearly as constructive as winestock (https://news.ycombinator.com/item?id=9964680 )'s, which is currently lower on the page. Please read that one instead!
Well logic is a sub-category of philosophy, not mathematics. Logic and math are similar in some ways, but logic != math. Both contain lots of symbols and formal methods of getting from a to b, however the content is quite different. There is overlap however in mathematical logic, but again, logic systems != math.
> Well logic is a sub-category of philosophy, not mathematics.
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.
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.
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.