Reddit Reddit reviews An Introduction to Non-Classical Logic, Second Edition: From If to Is (Cambridge Introductions to Philosophy)

We found 7 Reddit comments about An Introduction to Non-Classical Logic, Second Edition: From If to Is (Cambridge Introductions to Philosophy). Here are the top ones, ranked by their Reddit score.

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An Introduction to Non-Classical Logic, Second Edition: From If to Is (Cambridge Introductions to Philosophy)
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7 Reddit comments about An Introduction to Non-Classical Logic, Second Edition: From If to Is (Cambridge Introductions to Philosophy):

u/[deleted] · 6 pointsr/AcademicPhilosophy

Priest's introduction to non-classical logic. Goes through all the next steps (modal, intuitionist, fuzzy logics etc.). The formating may take a while to get used to. But a good book.

Edit: It is perfect for finding the logics you find interesting and then you can go more in depth with other books. Also, I think, it is a perfect reference book for logics that I do not know too well (but I do not know if everyone could do this due to have the chapters are arranged and so forth).

Edit2: I would also recommend the following book for nonmonotonic logic, if that floats your boat

u/crundar · 3 pointsr/logic

If inconsistent, paraconsistent, and otherwise Brazilian logics aren't already your bag, my usual recommendation is Priest's Introduction to Non-Classical Logic.

I would, of course, love to hear others' suggestions.

u/pgsr · 3 pointsr/askphilosophy

This is a difficult topic because the subject matter of logic is contestable. For instance, is logic about the laws of thought or is it about language or is it about reality? If it is about language, then classical logic is highly dubious. In ordinary language, A does not characteristically imply A or B. Nor does A and not A characteristically imply B in ordinary language.

In answer to your question, it depends on what the subject matter of logic is, and what logic is under consideration. If you want to know more, I recommend studying classical logic (propositional and predicate logic) and then reading Graham Priest's An Introduction to Non-Classical Logic. http://www.amazon.com/Introduction-Non-Classical-Logic-Introductions-Philosophy/dp/0521670268

u/topoi · 3 pointsr/askphilosophy

It depends what you're trying to get out of it.

There are literally hundreds of introductory texts for first-order logic. Other posters can cover them. There's so much variety here that I would feel a bit silly recommending one.

For formal tools for philosophy, I would say David Papineau's Philosophical Devices. There's also Ted Sider's Logic for Philosophy but something about his style when it comes to formalism rubs me the wrong way, personally.

For a more mathematical approach to first-order logic, Peter Hinman's Fundamentals of Mathematical Logic springs to mind.

For a semi-mathematical text that is intermediate rather than introductory, Boolos, Burgess, and Jeffrey's Computability and Logic is the gold standard.

Finally, if you want to see some different ways of doing things, check out Graham Priest's An Introduction to Non-Classical Logic.

u/c3261d3b8d1565dda639 · 2 pointsr/books

If you want a strong mathematical approach, check out Peter Smith's Teach Yourself Logic Guide. If you don't want to take as heavy of an approach, you can use the suggestions as a roadmap and pick-and-choose from the suggestions. Even the introductory logic book suggestions in that guide might be too math heavy, but you might at least read their reviews on Amazon. A lot of reviewers tend to link to books on either side: easier and harder approaches.

For what it's worth, while I was in University we used Computability and Logic in the second logic course, which is after the introductory course teaching basic propositional and predicate logic. It's not a book for learning logic, but it's an awesome book for tying together a lot of what you initially learn with computability, model and proof theory. In another course we used An Introduction to Non-Classical Logic. I really enjoyed both of these books, and they're relatively cheap, but as I said they are not introductory logic books.

I'll be happy to reply again if you have any further questions.

u/ADefiniteDescription · 2 pointsr/askphilosophy

> I guess I thought that modus ponens could be derived from the three laws I mentioned.

How is modus ponens derived from identity, LNC or LEM?

None of those even allow you to derive anything, let alone modus ponens. They're just statements. Without some background rules governing derivability they're useless.

I can't state this enough: this whole picture of their being some set of laws like the ones you say is constantly baffling to me. It's completely antithetical to the modern (post-Boole) way of doing logic. It is almost completely backwards! According to proper logic, LEM, LNC and identity are logical truths which hold because they're always derivable. That is, their fundamentality is completely derivative of the rules of derivability.

There is a certain sense in which they're special, but it has nothing to do with being foundational. Rather it's because they are often taken to have some sort of metaphysical import: for example, Dummettians often claim that LEM is a determinacy principle; it only holds of domains which are determinate.

> How many independently axiomatic logical foundations are there?

I'm not sure exactly what you mean by this. Most philosophers and logicians wouldn't phrase things this way and don't think of logic in terms of "axiomatic logical foundations". They might think of which particular logical system they're working in, so that may be what you have in mind. For example, the most popular (historically) logics to work in/with are classical logic and intuitionistic logic.

As to how many logics are there are: I don't know. It's well-known (from some lesser known work of Gödel's) that there are at least continuum many logics. I don't know if there's any reason for thinking there's a larger cardinality of logics than that; I suspect not.

Most of those logics have never been used and will never be. There are probably a handful - maybe a couple dozen - logics which have been continuously used and developed over the past century. The standard text to see most of these is Priest's An Introduction to Non-Classical Logic.

> And how do you know which ones to exclude?

I'm not exactly sure what you mean by this. You might be asking how do we know which logic(s) is the "right one". That's a really hard question. People write entire books and dissertations on that question. I should know - I'm one of them!

In general people start with some phenomena that you're interested in or some problem, and try to figure out which logic best accommodates that. Implicitly there's an understanding that the starting point is classical logic, and we work our way down (in terms of logical strength) from there to some non-classical logic(s) or another.

To give you a concrete case: take intuitionistic logic. LEJ Brouwer, the founder of modern topology, was concerned with the use of infinity in mathematics as it developed around the turn of the century under Cantor, Hilbert and others. To combat this, he developed a new school of mathematics: a form of constructive mathematics called intuitionism. Intuitionism is a complicated subject worth its own thread. But one of the things they deny is the Law of Excluded Middle, because it's tied up with infinity, determinacy and impredicativity. Brouwer's student Heyting developed intuitionistic logic based on these ideals, and since then it's been used for a variety of philosophical reasons, most notably in the debate over semantic realism/anti-realism.

I've linked a half dozen SEP articles above which include days worth of info that you might find interesting.

u/hell_books · 1 pointr/askphilosophy

Really? Nolt's Logics? Besides the numerous errors, it's telling that the book has not come out in a second edition.

I think Quine's Methods of Logic remains a fantastic text, if it is a bit dated and filled with Quinean quirks. A more recent text, Ted Siders' Logic for Philosophy is also very good, although the exercises are sometimes quite difficult. I would combine Sider's text with a book on metalogic, since he skips over some of that. Kleene's Mathematical Logic is a classic text by a real giant in the history of 20th century logic. Those should keep someone busy for a good year of study. If you want to branch out, Graham Priest's Introduction to Non-classical Logics will get you started in modal, tense, epistemic, paraconsistent and dialethic logics, also by a contemporary giant in the field.

After that, I would go on to set theory, and stop when I had a grasp of forcing.