Teach Yourself Logic, #7. A bit of deviance
There’s a new version of the self-help Guide downloadable from the Teach Yourself Logic page. Heavens this is time consuming, but having (as it now seems, foolishly) started, I guess I should do the best job on this that I can. Anyway, there are new sections on extensions of classical logic (second order, plural, free) and deviations from the classical paradigm (intuitionism, relevance logics). There also is a major structural change to the Guide. It is now going to be in two big chapters, one on the basics and one on more advanced stuff. Partly this is to make it all look less daunting (the idea is that any grad student working in logic-relevant areas ought to know the sort of stuff that is in Ch. 1, and then the enthusiasts for this or that area can pursue the relevant sections of Ch. 2). And partly this is to acknowledge the fact more advanced work in one area can often presuppose familiarity the basics in other areas.
All suggestions for improvement welcome as always. I’d welcome in particular any additional introductory suggestions on Second-Order Logic, and on Intuitionistic Logic. At the moment, on Second-Order Logic, I start by mentioning the article
Herbert Enderton, ‘Second-order and Higher-order Logic’, Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/log...
And suggest following that up with
John L. Bell, David DeVidi and Graham Solomon’s Logical Options: An Introduction to Classical and Alternative Logics (Broadview Press 2001), §3.3.
But now what? Stewart Shapiro, Foundations without Foundationalism: A Case for Second-Order Logic, Oxford Logic Guides 17 (Clarendon Press, 1991) is very accessible — but is there something less weighty to read beforehand?
And on Intuitionist Logic, I suggest starting with
John L. Bell, David DeVidi and Graham Solomon’s Logical Options §§5.2, 5.3., which give an elementary explanation of the contructivist motivation for intuitionist logic, and then explains a tree-based proof system for both propositional and predicate logic.
Graham Priest, An Introduction to Non-Classical Logic (CUP, much expanded 2nd edition 2008), Chs. 6, 20. These chapters of course flow on naturally from Priest’s treatment in that book of modal logics, first propositional and then pred icate.
Then, up a notch in mathematical sophistication (but manageable if you have tackled earlier chapters in this book, so you are familiar with the style), there is Dirk van Dalen, Logic and Structure (Springer, 4th edition 2004), §§5.1–5.3.
We will return in Ch. 2 to some further explorations of intuitionism where we’ll mention e.g. Dummett’s book. But what about other more introductory level material?
