Introduction to Philosophy/Logic/Preface
Why this work needs to be written and read
There is not, as far as I know, a really nice logic introduction available either on line or in print. So it is time to try to write one. I learned bits and pieces from here and there, and then struggled a bit when I went to a postgraduate logic class. For me, this book review is a journey of discovery, to write it I need to know exactly how all the pieces fit together, and it is fun to identify gaps in my knowledge and then see how they can be filled.
I do not have the solution to all the world's problems, but believe that people will be better equipped to handle them if they know just a bit about the reasoning process. If this book review helps a few people do that, I would be delighted. Of course, knowledge and learning can be used to build more lethal weapons and more oppressive tyrannies, but it can also be used to stop such things. I put my faith in reason and in human kindness, since if these are false gods, there isn't much hope for us anyway.
Wiki and Myself
I have put most of the effort into this so far, and see that this will remain the case for some time, so I consider it to be 'my' work, warts and all. I have seen this introduction to logic grow from a red link going nowhere to the state it is today. However wiki is a collective effort, so some would say that it would be unfair to call the work 'mine'. The genitive case is fraught with ambiguity. If you want to chip in, please do. There are at the moment places where results are stated but proofs need to be written out, for example.
I use the word 'I' alot. This keeps the style informal and accessible whereas using the passive voice would not. Anyway, to make a brave philosophical assertion, speakerless propositions are a myth, so there is always a first person even if this is not made explicit. (Well, we could talk about the status of computer-generated messages, or of stones on the beach just happening to arrange themselves into a well-formed sentence.)
Logic and Mathematics
When doing maths, the issue of whether propositions have speakers might not be so important as when we are talking about other things. Logic needs to develop beyond the (relatively) safe domain of mathematics to deal with propositions which may be empirical, moral, emotional, aesthetic, etc. My background however is in this mathematical tradition, and this is what I feel most competent to write about. Further, the idea of a logic wikibook is revolutionary enough - a logic wikibook introduction which did not deal with the traditional math-centred core of logic would be just too revolutionary to be accepted.
Logicians sometimes try to mathematize reason, and sometimes they try to reason about mathematics. Both are worthy aims, but we should remember that the latter aim is limited in its scope. It can lead to difficulties when people do try to apply the principles which work so well within mathematics to things outside. For example: the use of quantifiers to put differential and integral calculus on a sound conceptual footing is a rather neat achievement, while the use of quantifiers in Russell's theory of descriptions can appear to be rather clumsy by contrast, though Russell is to be commended for making the attempt.
Work That Needs Doing
There are whole chapters up for grabs. I'm just working on the propositional calculus at the moment. When I have done that I could write the predicate calculus chapter, but if you think you are up to this task, feel free. Or you could start a new chapter, to go after the predicate calculus chapter, which proves Gödel's incompleteness theorem, and then discusses the far-reaching purported implications of this result. If you wait long enough, I might do this myself, but I may find myself working right at the horizon of my abilities.
I would be delighted if anyone could take on the responsibility of writing about tense logic, modal logic, or any other kind of logical calculus, and will be one of your first readers. Also classical logic needs to be written about, so far it tersely says what needs to be said before the exposition of propositional calculus can start.
This is an introduction, so I assume as little as possible. I try not to produce a wall of opaque jargon, and explain terms as I go along. English may not be the first language of all readers, the writing therefore has to be plain but precise. As a large part of what we are doing could be described as producing a mathematical model of the reasoning process, some mathematical ability will be needed. If you can add, subtract, multiply and divide then you have enough. If you know who Euclid was, so much the better.
Thanks to the Wikimedia Foundation for providing the infrastructure which makes this work possible.
--publunch 18:40, 18 Nov 2004 (UTC)