Logic: A Study Guide

The Teach Yourself Logic study guide has, as I said a couple of posts ago, grown over the years in a really rather haphazard and disorganized way. Looking at it again, more carefully,  the guide really need to be rewriten from the ground up. And, to add to the guide’s usefulness, it would be very good to begin each chapter/major section with a short essay (up to half a dozen pages, say) giving some orientation, briefly surveying the relevant area of logic.

So all that is what I plan to do. And it should be fun to put it together. However, it will be really quite time-consuming, writing the essays and revisiting the large literature to re-assess my various current recommendations. So I intend to work on TYL’s planned descendant — Logic: A Study Guide — in intermittent stages over the coming months, posting the new chapters for comments as I go along.

I’ve made a start. And now will be a very good time to make suggestions for improvement for the early chapters on the more elementary material (i.e. the core math logic topics covered in what are now Chapters 4 and 5). TYL is downloaded a great deal: so tell me what what you think!  — all comments and advice will, as always, be very gratefully received.

7 thoughts on “Logic: A Study Guide”

  1. Beginning each topic with an essay on what the general ideas to be learned are is a suggestion I was thinking of making and fully support. I think for people who are self studying, having a guide which stresses the main ideas and topics they should take away from the books in order to build their knowledge of a subject is key.

    I have one other suggestion, regarding different domains of logic. To me, logic is the study of (without being too circular) logical consequence, both semantic and syntactic. We build formal systems, we prove meta properties about those systems, but more importantly, we use those systems to study other domains such as mathematics, computation, linguistics, and philosophy. And I think those four areas, mathematical logic, computational logic, linguistical logic, and philosophical logic, all deserve mention in a guide such as this.

    Linguistical logic may be the outlier here, I’m mostly thinking of the use of lambda calculi and automata theory in generative grammar, Davidsonian truth conditions and the Freagean principle of compositionality in generative semantics, etc. in formal linguistics, things that are covered in Partee, ter Meulen, Wall for example. But putting that aside since it isn’t as fleshed out of a ‘-al logic’ field as the others, I think it would be nice for the guide to make a clear demarcation between mathematical logic, i.e. using the tools of formal logic to study mathematics and metamathematics, philosophical logic, i.e. using the tools of logic to study problems in the philosophy of language, science, epistemology, metaphysics, etc., and computational logic, i.e. using the tools of logic to study topics in complexity theory, computability theory, programming language theory, finite model theory, automated theorem proving, etc., since these are all areas in which the main tools of formal logic are used and indeed were even developed for.

    A thorough expansion of the guide to cover all four of these areas, or even just mathematical and philosophical logic, would add a considerable work load on top of writing out discursive essays outlining each area of the guide, I am sure, so perhaps doing all of this isn’t realistic. Still, in addition to full support for the introductory essays, my suggestion would be to at least relegate a section at the end of the guide to “logic outside of metamathematics” where you might touch upon general topics in philosophical logic and the use of logic in theoretical computer science. Tim Button and Sean Walsh’s excellent Philosophy and Model Theory is the kind of book I’m thinking would be nice to include in a section of philosophical logic, for example. It would also make a nice section to discuss non-classical logics of all different kinds and books on topics like possible world semantics without feeling a need to shoehorn them in as an afterthought to other tangential topics.

    I believe adding such sections would greatly round out the guide as a true guide to teaching oneself logic, as opposed to just mathematical logic.

  2. I agree with peter f suggestions .i have started using the guide around 6months a go and as a person without any academic background regarding logic I personally learned a lot even if i would attend academically logic courses i wouldn’t learn more .it goes without saying it is the best among it’s peers.lack of chapters for logic domains evidently felt in the guide.which is big deal for students like me studying engineering and physics. after all we started logic studies to work on its applications .but anyways the guide is great and prepare u for all domains but it is good addition to specify chapters for such domains.

  3. As someone interested in the theory of programming languages and theorem proving, I would really appreciate to see chapters devoted to type theory, the lambda calculus and category theory/categorical logic. Throughout the recent months, I tried to get a grasp of the field through many books and articles, and I found that these fields have a long history (at least compared to other fields of computer science), and notorioulsy, different terminology for the same concepts. I believe that a structured guide would benefit many people who are in my shoes as well. Also, the last few years saw many interesting developments like HoTT and Cubical Type Theory so there is plenty of new stuff to cover.

  4. I agree with Peter F’s suggestion of organizing the guide into separate parts for “mathematical logic” and “philosophical logic.” For example, the “mathematical logic” part could include most of the material from chapters 4,5,7,8 (proof theory, model theory, computability theory, set theory.) The “philosophical logic” part could include chapter 6 and some other material.

  5. A self-study guide should in my opinion also include as many links as possible to (correct) solutions. Sometimes these get posted on various forums but then the danger is that the internet is not forever and these sites vanish. Hodges and Leary do provide some solutions but the text books for beginning set theory do not (Goldrei is the exception).

    Perhaps ask some retired math lecturers you know and who have used in their teaching some of the books you recommend, if they have saved the solutions to some exercises as pdf files? Or ask your followers if they can search the web for you! I would do my duty for this wonderful project.

  6. In addition to the suggestions by Peter F, I would add that some roadmaps for those interested in further research on the philsophical foundations of mathematics would come in handy. Sometimes one gets the impression that it all ended with Gödel’s Incompleteness Theorems. But, being a philosophy major myself, I know nothing is ever really, finally settled. I’m sure the debate continues! However, in which areas or research programs of mathematical logic are these debates taking place? After Gödel, what has been left unresolved, if anything?

    As fascinating as the study of logic is in itself (and TYL has been a great help for me in this!), I’m largely driven by the Big Questions in the philosophy of mathematics. And sometimes one misses the forest for the trees. A reminder of what the full picture is would be very useful!

  7. I don’t quite agree with the sort of division between mathematical logic and philosophical logic that some comments above seem to have in mind.

    Mathematical logic is largely just first-order logic, its syntax, semantics (model theory), and ways of doing proofs. It’s a natural next step beyond an elementary introduction, and it provides a foundation for understanding and working with other logics. Once you have the idea of models for propositional and first-order logic, for example, you have a framework for understanding possible-worlds semantics for modal logics.

    Mathematical logic also brings in topics of considerable philosophical interest such as incompleteness and the Löwenheim–Skolem theorems.

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