When I was little and Christmas time was approaching, we children knew that there would be two kinds of presents: the soft packages that contained useful but unexciting clothes, and the hard boxes that contained gorgeous new toys. I learned later that the same formula repeats itself often in life, and even in logic. There are the discussions about first principles: what rests on what, what comes first in the end of all analyses, and what it all means – and these are the useful but relatively unexciting soft packages. Then there is the box that is really interesting to open, and that is what I call the deductive machinery of logic – how it all actually works. Others have called it the inferential engine. I believe that logic should not be presented to us just in those soft packages – the hard box has to be there to be opened as well, so that we can find out how logical arguments function. It is a hands-on kind of learning in which one tries and retries things by oneself until the machinery runs smoothly. Then it is the time to discuss the nature of the first principles.

The book begins with a linear form of proofs that I learned from Dag Prawitz' Swedish compendium ABC i Symbolisk Logik. Little did I think, back in 1973 when using that text for the first time, that my teaching of elementary logic would one day grow into a comprehensive presentation in the form of a book.