Logic

"Yes, for someone who’s motivated and already has some aptitude, for example who enjoys mathematics. If you found algebra fun at school, you’re probably going to get on well with Logic Primer . My second choice is another textbook that you could use to learn logic yourself. In fact, I was given it by a maths teacher while I was at school, who thought I was getting bored in maths lessons. This is Wilfrid Hodges’ book, which is just called Logic . It’s a Penguin book and has been used by several universities as a textbook. This book sets logic more in the context of the humanities than mathematics. It’s written for someone who has an interest in the workings of language and the clever things you can do (and not do) with language. In that sense, yes, it’s still doing logic; it’s still going to be formal; it’s still going to have symbols; but it’s a much softer, gentler introduction, appealing to a different curiosity. It’s also a book that’s written in such a way that if you didn’t want to learn formal logic for the purpose of doing an exam in the subject—completing the exercises and the quizzes—but you wanted to get a really good sense of what it was like , you could read this book without having to learn all of the techniques. It has other virtues, as well. From the point of view of learning logic, I think it has the best discussion of relations. A sentence like ‘The ball is red’ has a subject (‘ball’) and what logicians call a predicate (‘is red’), which says the ball has a property. So the predicate ‘is red’ applies to one thing, or group of things like the apples in the bowl, but what it applies to is taken as a single subject. When I say ‘Mary is my daughter’, we have a relation there between two subjects. There’s my daughter and me. Then we’ve got a relation between the two, which in this example is a biological relation, a family relation. But there are lots of other relations: to the right of, larger than, smaller than. So, relations typically are parts of language that pick out not a feature of one thing or collection of things, as predicates do, but something structural holding between two or more things. Relations have their own logic. We can say, ‘If John is taller than Peter, and Peter is taller than Fred, then John is taller than Fred.’ That’s an inference in natural language and when we start using formal logic we also want to use such inferences. That would be the logic of relations. Hodges does this particularly well in his book, and of the textbooks I’ve looked at and used, I think Hodges’ account is the best. “As a form of mind-training it is very good because it forces you to pay attention to the details of exactly what is being said and exactly what is meant.” The other thing to say about this textbook in contrast to Logic Primer is it uses a different logical system. I said that Logic Primer is a natural deduction system; you start with your premises and you try to reach your conclusion, so you’re moving through steps to try to get to your conclusion. Hodges uses a different system, which is called a tree proof system. I won’t go into the details, but it’s very graphical, very visual. I talked about truth preservation and validity earlier. When trying to prove that some conclusion follows from certain premises—if you accept these premises, then you must accept this conclusion—that’s equivalent (nice logician’s term there) to saying that if you accept these premises and deny this conclusion, you’re committed to a contradiction. What a tree proof system does is it starts with the premises, denies the conclusion, and then tries to show that there’s no way of avoiding contradiction."