The role of logic

In addition to standard mathematics, the formal system most widely discussed since antiquity is logic (see page 1099). And starting with Aristotle there was in fact a long tradition of trying to use logic as a framework for drawing conclusions about nature. In the early 1600s the experimental method was suggested as a better alternative. And after mathematics began to show extensive success in describing nature in the late 1600s no further large-scale efforts to do this on the basis of logic appear to have been made. It is conceivable that Gottfried Leibniz might have tried in the late 1600s, but when his work was followed up in the late 1800s by Gottlob Frege and others the emphasis was on building up mathematics, not natural science, from logic (see page 1149). And indeed by this point logic was viewed mostly as a possible representation of human thought—and not as a formal system relevant to nature. So when computers arose it was their numerical and mathematical rather than logical capabilities that were normally assumed relevant for natural science. But in the early 1980s the cellular automata that I studied I often characterized as being based on logical rules, rather than traditional mathematical ones. However, as we will see on page 806, traditional logic is in fact in many ways very narrow compared to the whole range of rules based on simple programs that I actually consider in this book.