Saturday, April 19, 2014

Logic Books: what to read and what to avoid

Not so long ago I tried to get head first into Aristotle's Organon starting backwards with the Topics  and, oh, it is so tough.

I blame his style for being so convoluted. It is still chock full of goodies, but much effort is needed to  unearth the gems. I decided that what was needed to get the info was either : a) sterling willpower and pen & paper; b) a guided tour;  or  c) the indirect route. I chose the latter by retaking symbolic logic, the same I should have learned from high school. Looking around, I found some books that I wanted to mention.

(What follows refers mostly to college level intro logic)

Sherlock's Logic

This is divided into two parts. The first one is a detective story involving a murder and the Templars. The story itself is good and a quick read. The second part introduces concepts of symbolic logic, one at a time, matching each with a chapter from the preceding story. Explanations are very condensed, which requires the reader to really exert herself to grasp each concept. In general, it is a survey of logic all right, but leaves out great many unexplored areas, has too few exercises (and those without answers), is unsystematic, steep,  and in the end, unsatisfying.

Introduction to Symbolic Logic by Karl J Smith

If you are on the run and need only a refresher, this is the book for you. Concepts are quickly explained and exercises for each chapter, with answers at the end of the book provided.

Schaum's Outlines: Logic 2nd by Nolt

Nolt's is just like Smith's but on steroids. You know the series. I came to this one for the solved exercises (which once you get to them are like meh), but stayed for the concise explanations which shine. This one covers the whole spectrum and a bit more. Inexpensive and readily available.

Logic: a Modular Approach by Facione & Scherer

Now we enter into those of textbook calibre. This one starts from naught and begins building from there, first with language and then with the usual logic programme. Each concept is clearly delineated and referenced to previous ones. As said the system is built upon itself through modules which correspond to subchapters in the usual sense. There are 46 modules in total. A fair amount of exercises are also to be found at the end of each module with answers to about half of the problems. Four cumulative tests are also included. This is an old book (the Disco font on the cover betrays its age), but still feels current and can still be purchased new. Compared to Copi's, this book is easier (yet not dumbed down) and its content more thoroughly explained. It unfortunately has also some long stretches of mind-numbing expositions. Its biggest faults however are that it only has a couple of modules on inductive reasoning and doesn't get into predicate calculus.

Introduction to Logic by Copi & Cohen

This appears to be the standard on logic textbooks. Notwithstanding, it is unnecessarily dense.   Answers to just 1 out of 5 exercises. I would skip this one altogether since, despite its many editions, it still needs moderate to heavy streamlining. It is also expensive.

Symbolic Logic by Copi

Tough and stingy with explanations, yet it is well worth a look to affirm and expand the basics.  Definitely not a first course. The hardest exercises are to be found here though this one too has too few solutions. Peter Suber and someone else on the net have solutions up to chapter 5.

Symbolic Logic: A First Course by Gary M. Hardegree

This one is the best on translation to symbolic (formalization) I've seen bar none. Goes up to polyadic predicate. It doesn't rush things and looks at every nook and cranny without losing the thread. Can take a while to make through the relevant chapters, but you end with the feeling of really knowing the stuff. Dozens of exercises are also provided with answers. Regrettably, identity is not covered.

Logic: Analysing and Appraising Arguments by Gensler

This one is an extensive attempt but is relatively light on explanations. Of all the books mentioned it is the only one which takes a look at modal logic in some length though. It has been superseded by a newer book by the same author. 

A Concise Introduction to Logic by Hurley

As with the first Copi, this is an inexplicably expensive book.  This one also carries about the same usual logic topics. Includes predicate logic calculus. Of all, this one felt best at expounding inductive logic and probably the best overall. Once more, answers to just a few exercises.

Logic by Paul Tomassi

In this one the author tries to make intro logic accessible to students who struggle with it once and for all. I'm not sure he succeeds in this, but the book might come in handy as a backup as it goes deeper than the rest on some philosophical aspects. As of late, the more I look at it, the more I like it.

Logic With Trees by Howson

A showcase of the Truth-Trees. The author takes a deep look into them which has the unfortunate effect of placing the book beyond the scope of first time delvers. Unless you really have to know about the inner-workings of Trees, you are better off with Tomassi's book or with Nolt's which look at their immediate, mechanical aspect in a more practical, concise manner. Howson's book could serve as a first course, but it wouldn't be my first choice, nor my second, nor my third, etc. Some solved exercises. Can be skipped safely.

First Course in Mathematical Logic by Suppes

This one too starts from the ground up, but shifts the focus from language to mathematical expressions. The author appears to be going somewhere with the focus on number expressions, but its the same logic from the other books with just different symbols. Worth a look if you're math oriented, have interest in logic in general or if it's the only one you can lay your hands on. If language or philosophy, however, is your interest, you might be better served  by one of the others. While strong on propositional,  for predicate it shrinks from Existential Instantiation/Elimination rules entirely. Note that set theory is also not covered. No answers to the exercises. Wah! Oh wait, Frederick Binford has those.

Lógica Clásica de Primer Orden by Falguera

The most dense of the ones here, idiosyncratic, out of print and in another language. All the same, it has great many substitution rules with proofs for predicate logic. Also has a couple hundreds of exercises with solutions on an accompanying booklet.

In closing, here's something completely different:

Logicomix by Doxiadis et al.

This is one is a graphic novel based on Bertrand Russell's search of Truth & certainty in logic. An easy read, places many of the concepts in their historical context and serves as a good appetizer for Gleick's The Information of which we'll talk next week.


syd barret said...

ah atlast i found this stuck with paul tomassi book logic... as per me, im not liking it thinking to quit..please need your thoughts on it..which book should i read ?

Carl05 said...

Try Facione or Hurley to get some traction as I find them the most down-to-earth (but with the reservations pointed above). Be sure to check Hardegree (free text online) in any case for the translations (the calculus rules however I find them odd). You can always come back to Tomassi later for the philosophy extras.

Bangladeshi Green Baron said...

Are there any answers for the exercises in Tomassi's book that you are aware of? I already have an answer sheet for Chapter 2 but what about 3 and 5?

It's kind of frustrating that I can't check my answers.

Carl05 said...

BGB: Checked, but it seems I've got nothing. On some exercises, though, you can tell you've got the right answer by the usual proof methods (you've proved that the argument is correct or that it isn't). Truth trees would be my choice for quick checks as it is easy and straightforward.

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