Daniel M. Hausman opens the introduction to his anthology The Philosophy of Economics (Cambridge University Press, 1984) with a contemptuous statement about economics quoted from a character in a novel by the satirist Thomas Love Peacock (1785-1866), Crotchet Castle. One character has just referred to “political economy, the science of sciences,” but another, the Rev. Dr. Folliott, demurs, calling it “hyperbarbarous” (there’s a word you don’t see every day!):
“Premises assumed without evidence, or in spite of it; and conclusions drawn from them so logically, that they must necessarily be erroneous.”
Peacock, of course, is just having fun: He doesn’t expect anyone to take Dr. Folliott seriously (and Hausman merely wants a hook to introduce a discussion of propositions that economists assume without evidence, like “commodities are infinitely divisible” or “individuals have perfect information”). But I found myself distracted by a nerdy thought: Dr. Folliott is clearly mistaken.
First, and most obviously, he appears to equate premises assumed without evidence with premises that are false: a confusion of logic and epistemology. You can assume something without evidence (even ignoring whatever evidence there might be), yet by pure luck hit on a proposition that happens to be true. So correct application of logical inference rules can certainly lead to a correct conclusion despite premises assumed without benefit of evidence: to say “they must necessarily be erroneous” is wildly wrong.
But there’s a second error. Although it is true that you always get true conclusions from true premises if you reason using sound inference rules, it is not true that making a false assumption will doom you to draw false conclusions. The obvious way to illustrate this is with a false premise figuring as the antecedent in a conditional. This simple argument is (counterintuitively) valid, with a true conclusion:
- If Seattle is in Oregon, then Ohio is in the Eastern time zone.
- Seattle is in Oregon.Therefore (by modus ponens),
- Ohio is in the Eastern time zone.
Premise 1 is ridiculous, and its protasis is false, but it is true under standard propositional logic, given the somewhat inadvisable but well-established tradition of treating English conditional “if” (which has a variety of uses) as expressing material implication. Treating “If P then Q ” as expressing P → Q means treating it as logically equivalent to Q ∨ ¬P = “either Q or not P,” which is true provided P isn’t.
Premise 2 is false, but it happens to do no harm to the argument: By modus ponens (the inference rule that says ‘P → Q ’ and ‘P ’ together permit us to infer ‘Q ’ for any P and Q ), we can infer 3 (a true conclusion) from 1 and 2.
So the Rev. Dr. Folliott is doubly wrong: Logical reasoning based on premises assumed without evidence will not necessarily yield erroneous conclusions, and that holds even if not all the premises are true.
Why (I hear you ask) am I musing on topics in baby logic like this? Well, it’s just that I found myself wondering whether typical undergraduates today know at least enough logic and grammar to follow the reasoning above. At one time, centuries ago, every pupil at a good high school was expected to study the three subjects that medieval scholars regarded as prerequisites to all higher learning: logic, grammar, and rhetoric. Those constituted the trivium: Only after mastering them could you go on to the upper-division subjects of the quadrivium (arithmetic, music, geometry, and astronomy). I was just wondering (not for the first time) if we could be sure today that every university graduate is well acquainted with the essentials of the subjects making up the trivium.
At St. Mary’s College in Indiana, 80 years ago, that was the expectation. One of the books on my elementary-grammar shelf is The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric, by Sister Miriam Joseph, published in 1937 and written to serve as a text for a foundational course at the college. The array of topics covered is inspiringly ambitious: the nature and function of language (in other words, some basic general linguistics); universal grammar (general concepts of morphology and syntax); propositional logic; syllogisms; fallacies; induction; rhetoric; poetry; and composition. Quite a course of study. Though I should note that the logic that Sister Miriam presents is desperately old-fashioned, and the linguistics even more so; the whole book needs radical revision (much more radical than the light revision by Marguerite McGlinn that Paul Dry Books published in 2002).
But setting aside the details, what I was wondering about was how many of the undergraduates we recently sent off with their 2016 bachelor’s degrees could say they had a good grasp of most of these topics. Not that many would be my guess. Probably far too few.
