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Education
Logic

What books would serve as a comprehensive overview of philosophical and mathematical logic?

These are very large fields, so I'm not sure a comprehensive overview is really possible. (Though there is the umpteen volume Handbook of Philosophical Logic .) That said, there is a new book out quite recently, by John Burgess, titled Philosophical Logic , that gives a good introduction to that area. For mathematical logic, I like Peter Hinman's Foundations of Mathematical Logic , as it covers a fairly wide range of material.
Education
Logic
Philosophy

I presently working through Grayling's Introduction to Philosophical Logic (Blackwell), after studying philosophy at university in the late 1960s. Can anyone recommend a follow-on text (for when I feel I have assimilated this book)? (I have seen the interesting replies to the August post about further reading on symbolic logic.) Peter

There aren't a whole lot of textbooks on this sort of thing. A more current text is John Burgess's Philosophical Logic . And, depending upon your interests, you might have a look at something like Graham Priest's Introduction to Non-classical Logic . Working through a serious textbook on modal logic would also be worth doing. The two classics are by Chellas and by Hughes and Cresswell. A quite different route would be to look into linguistic semantics. Many forms of philosophical logic—tense logic, modal logic, epistemic logic—originated as attempts to deal with some of the features of natural language that are omitted by quantification theory. But the relation between the logical treatments and natural language were always pretty obscure, and around 1960 people started to get much more serious about dealing with natural language in its own terms. Formally, much of linguistic semantics looks like philosophical logic (especially in certain traditions), but it is targeted at an empirical...
Education
Logic

I aced a basic logic class in college that covered both sentential and predicate logic. I am interested in furthering my skills in symbolic logic, but I don't know how. My school doesn't offer any upper-level logic courses. I'm thinking I would like to buy a simple textbook for a more in-depth study of the more advanced concepts (I've heard the term "modal logic" thrown around, but I don't know what that is). Can you suggest a good text or author I should investigate?

Peter might also have mentioned his book, An Introduction to Gödel's Theorems , and the similarly targeted book by George Boolos, John Burgess, and Richard Jeffrey, Computability and Logic . Both are standard texts used in intermediate logic courses.
Education
Philosophy

Hello Philosophers! I graduated college not too too long ago and have missed the intellectual discussions I used to have there. Someone alerted me to this site, and it has done more than anything else to bring back the good memories. Thanks to all of you for spending your time on this - it's like having a mini personalized philosophy class - and it's free! I was intrigued by the recent question about philosophy and improving students' characters (posted Sept. 9), responded to by Professor Louise Antony and was wondering if that discussion could be continued a little. In particular, I was unclear on whether Professor Antony was positioning herself as disagreeing with the questioner. Is she saying that it is not philosophy's purpose to improve character, or just that it is un-PC for a professor to state it as a goal of the course? Would, for example, Dr. Martin Luther King Jr., (or Socrates, as I think was the example used by the questioner) be considered presumptuous? It was my understanding that...

I'll let Louise respond on her own behalf, as far as her own position is concerned. But, if I may address the second question, in a spirit with which I think she'd agree.... Yes, of course, date rape, and hazing, and binge drinking, and the like are all serious problems. But the question is why one should suppose that philosophy classes are the right place to address them. I think it's asking a lot of philosophy—not to mention of philosophy professors—to suppose that it—and we—are in some special position to instill wisdom in our students. Certainly, if you ask me what I'm trying to teach the average student in one of my undergraduate courses—the one who's not a major or, perhaps, is but is headed to law school or the business world or what have you—I'll say I want them to learn to read and listen well, and to think and express themselves clearly. And one would certainly hope that these skills might help people live their lives better. But, however clearly I can think (and I don't even manage...
Education
Mathematics

From a philosopher's point of view, should logic be taught in grammar school or junior high in preparation for algebra, or, should algebra be taught in preparation for logic? One consideration might be that we begin learning logic as early as the first year of life, but not in an ordered or conscious way. Should we get that part of thinking straight before being introduced to its applications, or follow the usual procedure and experience the applications then be confronted with the general principles?

From any point of view, I think the question here ought to be: What way of teaching such material will make it most likely that students will learn it? But that's not a question a philosopher is well-placed to answer. Someone with expertise in education would be the right person to ask.
Education
Logic

I realize that this isn’t exactly a philosophical question but I’ve tried asking it elsewhere, to no avail. Can anyone help? I'm studying at home with two books on critical reasoning that are recommended in some philosophy introductions. I think I've done ok with most of the exercises so far, but I've really struggled with the sections on identifying implicit assumptions (context, underlying, additional reasons/ enthymemes, intermediate conclusions etc.). Is there anyone on this panel who is aware of any other resource which gives further opportunity to practice identifying implicit assumptions, and gives answers? Old law-school admission tests or something? I've gone through all the exercises in both books now, and unfortunately the answers are heavily etched into memory, so they’re no longer practice. If not then perhaps some general tips? Any help would be valuable, as it would seem to be a serious hurdle for me. I’m trying to ease back into the realms of academia after having three children and...

Unfortunately, I think the only concrete thing I can suggest is that you look for other texts on critical reasoning. (You don't say which two you have, and I'm not familiar with many, so I'm afraid I can't give more specific advice.)
Education
Philosophy

Do students of philosophy have much to gain by travel, study abroad, or cultural immersion?

How about this for an argument? Human beings have much to gain by travel, study abroad, and cultural immersion. Students of philosophy are human beings. Therefore, students of philosophy have much to gain by travel, study abroad, and cultural immersion. That'd be an instance of the valid form "Barbara", and I take it both premises are true. Oh! I see! You meant, do students of philosophy, qua students of philosophy, have much to gain by travel, study abroad, and cultural immersion! Well, that's a different question. Let me answer it from the perspective of a North American. Adjust as necessary. But the answer to it is much the same. For one thing, to some significant extent, doing philosophy involves trying to pry oneself free of one's own unnoticed preconceptions. There's nothing like exposure to other ways of living to teach one how unnoticed some of those preconceptions can be. In that sense, then, I think anything that expands one's mind, and one's conception of life...
Education
Philosophy

Is there any reason that philosophy seems not to be taught in most American high schools (I could be wrong, I'm only speaking from experience)? I'm a college student who did not discover philosophy until my sophomore year, and I really wish I had had a chance for exposure to the stuff earlier on.

One reason, I'm sure, is the same reason so many American high schools have eliminated languages, music, and the arts: A lack of money, coupled with a very narrow conception of what education is. The latter, I'd guess, is the reason so few American high schools would have offered philosophy even before the cuts in funding for public education.
Education

I am a a high school teacher working for the Los Angeles Unified School District. I have been given approval to begin teaching a Philosophy survey course for the next school year. Although I am well read and schooled in Philosophy (I think?), I am unaware of possible textbooks for the study of Philosophy. I am looking for something that might be high school student friendly. Thus the Adorno Reader might be out of sorts for my pubescent high school students. In addition, I am fielding advice on the best approach to teaching Philosophy to high schoolers. I am interested in possible methods, assignments and projects. Any advice would be welcomed. Thank you, Ramon

There are a lot of introductory textbooks, most of them collections of material on various themes: mind-body, skepticism, etc. Bratman and Perry's Introduction to Philosophy was what was used at MIT when I was a graduate student, and it seems popular, from what I can tell. But I don't know whether it would be appropriate to your needs. The American Philosophical Association has subparts that are concerned specifically with philosophy at the pre-college level. I'd try writing to them for some advice and some resources.