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… is from page 126 of Adam Smith’s essay “The Principles which Lead and Direct Philosophical Enquiries; Illustrated By the History of the Ancient Logics and Metaphysics,” as this essay appears in Liberty Fund’s 1982 collection of Smith’s Essays on Philosophical Subjects [2] (a collection originally published by Cadell and Davies, in London, 1795):
A notion of this kind, as long as it is expressed in very general language; as long as it is not much rested upon, nor attempted to be very particularly and distinctly explained, passes easily enough, through the indolent imagination, accustomed to substitute words in the room of ideas; and if the words seem to hang easily together, requiring no great precision in the ideas. It vanishes, indeed; is discovered to be altogether incomprehensible, and eludes the grasp of the imagination, upon an attentive consideration.
DBx: Smith here refers specifically to Plato’s notion of the nature of “the sensible world.” But Smith’s description of wrongheaded thinking is beautiful and general. Very often do people mistake words for the full and nuanced reality to which the words refer. People then wrongly suppose that by ‘hanging’ the words together coherently the reality to which the words refer can thus be ‘hung’ together just as easily and with all of, yet only, the perceived consequences of so ‘hanging’ the words together.
And what’s true for words is true for mathematical symbols and graphs. I can, for example, draw a supply and demand graph, and label the horizontal axis “quantity of labor hours” and label the vertical axis “hourly wage.” I can then draw a few additional lines on that graph to show that a minimum wage placed just right will raise the wages of all affected workers without causing a single one to lose his or her job. Beautiful. Elegant. And, for several reasons, almost certainly inapplicable to reality.