CHAPTER 3: FOUNDATIONS
Historically, foundations and science itself emerge at the end of centuries of practical application. A logical place for foundations in textbooks is the beginning. So it was with Halliday and Resnick on physics, which began with Newton’s kinetics (motion in time and space) and then this three laws. Only in the last chapter did the authors remind us that Einstein later put two of these three into question, and even the kinetics. Halliday and Resnick reasoned, correctly | think, that we sometimes learn more efficiently by learning something slightly wrong first and fixing it later. | will do that, in a sense, by reasoning first through free growth theory as if the Y=C + ] equation were true, and then again with the two corrections. The sometimes
counterintuitive logic of teaching and learning, including that, is “heuristics”.
Building on explicit axioms was common in economics throughout the classical period running from Petty in the 17" century through Mill in the 19th. Then came the major shift in focus, beginning in 1871, called the marginalist revolution. What mattered was less our goals, and more the market mechanisms that aligned supply, demand and price. The meeting point was the margin. Axioms about goals disappeared, including the usual one of prioritizing survival and reproduction, and axioms kept were usually left implicit. The implicit ones, essential to marginalism in my view, included convergent tastes and predictions. I will make those two and
others explicit, and eventually add back the goals.
This book on the whole is about second-guessing what is taught. This chapter is different. The nearest thing to a surprise in itis the idea that economics needs explicit foundations in the sense of axioms and basic definitions and equations. All the ones | choose are well accepted. Why | pick which should seem obvious in hindsight. But some mini-surprises will accumulate. Why do I take such pains to prove every feature of what everyone accepts already? Why all the boilerplate and bulletproofing? I need them because I will later try to shoot down other beliefs
everyone accepts. We must know what is sound to find what is not.
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