§1. This annex begins with the most concise definition of the relation between inductive and deductive reasoning that I’ve ever read:
Induction, aided by analysis and deduction, brings together appropriate classes of facts, arranges them, analyses them and infers from them general statements or laws. Then for a while deduction plays the chief rôle: it brings some of these generalizations into association with one another, works from them tentatively to new and broader generalizations or laws and then calls on induction again to do the main share of the work in collecting, sifting and arranging these facts so as to test and “verify” the new law (p 644)
Marshall then goes on to contextualise the value of mathematics:
It is obvious that there is no room in economics for long trains of deductive reasoning: no economist, not even Ricardo, attempted them. It may indeed appear at first sight that the contrary is suggested by the frequent use of mathematical formulæ in economic studies. But on investigation it will be found that this suggestion is illusory… as [the mathematician is] often unaware how inadequate the material is to bear the strains of his powerful machinery (p 644).
§2. Marshall’s comment on money as a measure of motive opens with a delight:
If we shut our eyes to realities we may construct an edifice of pure crystal by imaginations, that will throw side lights on real problems; and might conceivably be of interest to beings who had no economic problems at all like our own. Such playful excursions are often suggestive in unexpected ways: they afford good training to the mind: and seem to be productive only of good, so long as their purpose is clearly understood.
For instance, the statement that the dominant position which money holds in economics, results rather from its being a measure of motive than an aim of endeavour, may be illustrated by the reflection that the almost exclusive use of money as a measure of motive is, so to speak, an accident, and perhaps an accident that is not found in other worlds than ours. When we want to induce a man to do anything for us we generally offer him money. It is true that we might appeal to his generosity or sense of duty; but this would be calling into action latent motives that are already in existence, rather than supplying new motives…But political services are more frequently rewarded by such honours than in any other way: so we have got into the habit of measuring them not in money but in honours.
It is quite possible that there may be worlds in which no one ever heard of private property in material things, or wealth as it is generally understood; but public honours are meted out by graduated tables as rewards for every action that is done for others’ good. If these honours can be transferred from one to another without the intervention of any external authority they may serve to measure the strength of motives just as conveniently and exactly as money does with us. In such a world there may be a treatise on economic theory very similar to the present, even though there be little mention in it of material things, and no mention at all of money.
It may seem almost trivial to insist on this, but it is not so. For a misleading association has grown up in people’s minds between that measurement of motives which is prominent in economic science, and an exclusive regard for material wealth to the neglect of other and higher objects of desire. The only conditions required in a measure for economic purposes are that it should be something definite and transferable.
I find these observations interesting for two reasons: First, economists often need to remind “civilians” that we study choices and happiness, not [typically] money, which is used as an accounting unit. (Studies of money supply, velocity, inflation, and so on do focus on money, but they are a small share of all economic studies.) Second, people are not just motivated by money: In 2005, Akerlof and Kranton argued that identity can be used as motivation. They received a lot of attention for their “discovery”, but it seems — yet again — that they have only rediscovered something Marshall wrote down 85 years earlier. (They cite Pareto 1920 but not Marshall.)
§3. Marshall ends the appendix with some notes on how some outsiders (and economists) misperceive economics as only focussed on money when there are long traditions of studying other motives, history and institutions in addition to money.
This post is part of a series in the Marshall 2020 Project, i.e., an excuse for me to read Alfred Marshall’s Principles of Economics (1890 first edition/1920 eighth edition), which dominated economic thinking until Van Neumann and Morgenstern’s Theory of Games and Economic Behaviour (1944) and Samuelson’s Foundations of Economic Analysis (1946) pivoted economics from institutional induction to mathematical deduction.