The Textbook Blog

This is a location for discussion of Symbolic Logic. Comments may range from general review and evaluation of the text, to details of presentation. We can discuss substantive questions about logic too. You may submit a post of your own or add comments to another. If you require special symbols, \LaTeX code may be inserted between the markers [latex] . . . [/latex] — to start with this, see LaTeX Typing (you see the compiled result only when posted).

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change log 2021

Substantive changes in this period include,

  • 2/13/21: Clean up treatment of defined operators in “Conditions for Definition.”
  • 2/7/21: Clean up “legitimacy” adjunct to T13.13.
  • 2/1/21: T13.73 updated to distinguish cases for \mathcal t equal to Sx and to Sy (x distinct from y).
  • 1/25/21: Repair definition of \mathit{sub}_n in 13.5.3 to set up \mathit{Prvpa}[\![\mathcal{P}]\!]^x_t. Corresponding changes in rest of section.
  • 1/5/21: \Sigma_{\!\star} definition in 13.5.2 clarified to make variables distinct.

For prior changes, see change log 2020. T.R.

textbook commentary

It is surprising to me that the initiation of this textbook blog seems to have reduced, rather than expanded, commentary on SL (which I used to receive regularly by e-mail). It is not the case that fewer people are using the text. Perhaps the public nature the forum discourages participation? Or maybe nobody wants to be “the first”? If you have an explanation, I would love to hear. For now, I can only encourage you that I welcome comments, and that the public nature of the forum lets your discussion benefit others (and email is still fine). T.R.

SLAPP: Symbolic Logic APP

For what it is worth, I am embarked on a (long-term) project to produce an open-source computer application that would be a context for creation, submission, and correction of exercises for Symbolic Logic. If you are contemplating study of Symbolic Logic, do not “wait for it,” it will be a long time coming. However over the next years I do hope to release the program bit by bit. Among goals are,

  • Exercises are cleaner and easier (more fun) in SLAPP than on paper. (This is not trivially true – see many existing web apps.)
  • Provides contextual feedback and checking, with goal that students always complete exercises correctly – or at least know that and where they have problems.
  • Runs on as many platforms as possible – but primarily on laptop / desktop.

Quite generally, logic software is beset by a problem of resources: The market is not large enough to support full-scale commercial development (as for mathematics), and instructors may have neither the time nor training to develop full-fledged software projects on their own. I hope to overcome at least the time problem by the magic of “retirement”! T.R.

change log 2020

Substantive changes in this period include,

  • 12/20/20: Repair for T13.57j,m. Includes new theorems in chapter 13 (and consequent renumbering of others).
  • 11/29/20: Small chapter 11 changes to clarify that sets of sentences and classes of models are language-relative.
  • 11/18/20: Clean up T11.15.
  • 11/15/20: Simplification and strengthening of T10.5 (and deletion of corresponding proof exercise).
  • 11/13/20: Reorganization and revision to T13.12–13.14 (again, sigh).
  • 11/9/20: Cleanup and fix to T11.31.
  • 11/3/20: Fix chapter 7 statement for definition by (abv).
  • 11/2/20: Revision of T13.13 case for (o). I keep fighting with this.
  • 10/30/20: E8.16 is new (with renumbering of subsequent chapter 8 exercises).
  • 10/28/20: Reorganization and cleanup of 13.6.2 reasoning that Godel’s second theorem implies Lob’s theorem.
  • 10/21/20: Clean up formulas vs sentences, especially in chapter 11.
  • 10/17/20: Formulation of T12.23 and T14.6 reflects restriction to languages extending \mathcal{L_{\mathrm{\scriptscriptstyle{NT}}}}.
  • 10/16/20: Reasoning for T12.20 accounts for theorems that are not sentences.
  • 10/16/20: log start date.


version updates

3/1/20: The SL version is updated from 8.2 to 8.3.  Small changes, new cover by my wife!  Adopted Creative Commons License and posted to the Merlot textbook repository.

9/10/19: The SL version number is updated from 8.1 to 8.2.  Main structure remains the same.  But there are enough changes to mark this as a substantive improvement over previous versions.

4/29/19: The SL version number is incremented from 8.0 to 8.1. Changes to the main body are minor. The primary update is that Answers to Selected Exercises are moved online. This permits large pages and so improved formatting.


jolly good

As a retired engineer, I decided to get back to my passion of understanding ethics. Most of the works were clearly woolly and very soon I realized that I needed to enhance my skills in logic to make any headway in this direction. Most of the recent books in logic were loaded in formal mathematics and appeared way beyond my reach. It was then that Prof Roy’s book on the Internet came as a pleasant surprise. Two years later, I managed to complete most of the exercises in his book and understand the principles. It is to Prof Roy’s credit that someone like me with little training in formal mathematics can learn such a difficult subject and all along keep my interest in it without being daunted by the complexity of the subject. During this journey, Prof Roy gave his time unstintingly to respond to my queries. Nuggets of Russelian wit, veiled challenges to the daredevils, and his love for his family are sprinkled in every chapter in this book. What attracted me most were the problems at the end of each chapter; in every chapter you invariably find one which asks the student to draft a short note explaining the main ideas in the chapter in a language his teenage daughter can understand. It is well known that, if you understand something well, you ought to be able to communicate that to the non-initiated. And, equally if you teach someone what you learnt, your concepts become even clearer. As the Tamil poet says, knowledge is rare commodity that grows by giving. To recognize this and challenge the reader to try his hands at this, Prof Roy shows great intuition in the art of teaching.

As an old man living in the UK, I cannot say his book is cool, but perhaps I could say it is jolly good.  R.V.

answers to exercises

I have complete answers to nearly all the exercises in the text (and am working on the rest). It is easy to move answers in or out of the Selected Answers at the back of the book. Short of including them all, if you think some answer(s) should or should not be included among the Selected Answers, let me know. T.R.