3 of 3 people found the following review helpful
A new realm of beauty,
This review is from: Logic (Paperback)
I had begun to read Grayling's An Introduction to Philosophical Logic, but it soon became apparent that I would need more than the hazy logic I had picked up over my years in software development to make genuine headway. It would thus seem a detour into formal logic was in order. Hodges' book had been sitting on my shelf for some years, since an earlier fraternisation with the subject that had petered out. This time I persisted, managing to read the thing in about half a dozen sittings.
The book is divided into many short chapters, each on a distinct topic, which are bought together at two key points, the first to introduce propositional logic, and finally, at the end, first order predicate calculus. There are exercises throughout each chapter, and since to learn logic one has to do it, it is necessary to engage with these exercises if genuine comprehension is to be acquired. Most of the chapters are trivially easy, and Hodges' friendly and informal style makes them a pleasure to read. There are a handful of places where an idea is introduced, and one would really like to be able to clarify one's understanding with the author, or where, despite immediate understanding, it has implications later on which do not seem obvious. Nonetheless, it is possible to go with these questions and still get to the end having comprehended the broad structure and most of the detail of the subject. The exercises vary from trivially easy to rather opaque. Indeed, there are a few places where one is grateful that comprehensive answers to the exercises are given, so that rather than doing the exercises, one is able to follow the working out of the answers as an amplification or clarification of the main text.
I estimate that by the end of the book I had an 80% understanding of what was going on. Which is to say that, in the final critical chapter where everything comes together, while I didn't feel confident to do most of the exercise questions, I was able to follow their answers and understand most of what was happening. Furthermore, I was able to precisely identify the points where my understanding broke down, leaving me with a succinct list of would-be questions rather than a general sense of bafflement. So, is that my fault or Hodges'? I'm pretty confident that I could read the book a second time around and come out with 90-95% comprehension. As it happens though, I probably won't be doing that, because I have since got going with Smith's excellent An Introduction to Formal Logic, which largely covers the same ground but with different emphases, and with which I am proceeding very comfortably. I can't really know how difficult I would have found Smith if I had not read Hodges first. What I can say though is that, having read Hodges first, I am completely at home with the core material in Smith, and am thus able to concentrate more directly on the more subtle aspects of the subject that Smith attempts to introduce. Thus, if asked, I would say read Hodges, but don't get hung up on any details that don't at first seem clear, then read Smith.
I undertook this 'detour' into formal logic to enable me to make progress with philosophical logic, and I am gratified to find that I am now able to read Grayling with far more ready comprehension. But what I did not anticipate was that I would come to a revelatory appreciation of formal logic in its own right. There is an aesthetic dimension to the subject that I was quite unprepared for, and I feel I have been given a glimpse into an abstract world of beauty that I wish to form a deeper acquaintance with. I realise that I am probably a long way from being the first of Mr Hodges' many readers to have been granted this dawning awareness, and find myself harbouring a deep sense of gratitude towards him. Thank you Mr Hodges.