Marvell’s Formal Fallacy

Many decades ago, when I first taught in college, I was assigned a course in logic. Not the strictest kind of logic—the abstract and theoretical concepts of the logical positivists, the logic of such philosophers as Bertrand Russell and A. N. Whitehead and A. J. Ayer—but rather the logic we actually use in daily life. Or do not use. The aim of the course was to prepare students to be able to think more clearly, to organize their thoughts and statements effectively, and to test the validity and strength of their arguments.

In preparing the course I had to learn what I had myself never been formally taught: deductive and inductive systems. I found that I quite enjoyed learning about the mechanisms of deductive syllogisms and inductive generalizations and hypotheses. And it chastened me to realize that I had always taken for granted the rightness of my propositions and positions, my too easily assumed common sense. Now I had specific tools for examination and analysis. Now I had, for instance, the fallacy of the undistributed middle term or the false disjunctive. Now I had Ockham’s razor.

At about this same time in a literature course I taught I assigned Marvell’s “To His Coy Mistress.” I summoned up all that I had been taught about this famous poem—the carpe-diem theme and its tradition, the metrical scheme, the rich allusions, and, perhaps above all, the hypothetical syllogism that shaped the poem. I was well prepared for my class. But then I realized that Marvell had made a logical error, a formal error!

In the hypothetical syllogism you can either affirm the antecedent proposition or deny the consequent:

If it rains, then the corn will rot. It is raining. The corn will rot.

Or

If it rains, then the corn will rot. The corn did not rot. It did not rain.

Marvell says “Had we but world enough, and time, / This coyness, Lady, were no crime.” But then he denies the antecedent: “But at my back I always hear / Time’s wingèd chariot hurrying near.” That is, there is not enough time. From this his conclusion (“Now therefore . . .”) cannot logically follow. Marvell makes what is called a formal fallacy (as distinct from a material fallacy). In deductive logic (Aristotelian logic) your conclusion must be either absolutely correct or absolutely incorrect. In this great poem Marvell’s conclusion is absolutely incorrect.

At my discovery I was elated. I would write this up and present it to the world, and my young scholarly reputation would be, if not made, then at least established. A revelation of this magnitude could not be ignored, especially when the idea that the hypothetical syllogism containing Marvell’s argument in this poem was firmly established. Was firmly established then, and remains so to the present day.

But before I wrote my little paper I did scholarly due diligence. I checked wherever I could, particularly the bibliography of the mla. And there, alas, I found it in North Dakota Quarterly—Bruce E. Miller’s article “Logic in Marvell’s ‘To His Coy Mistress.’” Even before I read it, I knew instinctively what Miller had found, and I was right. In a succinct note Miller describes the fallacy and makes the additional important point: Marvell, educated at seventeenth-century Cambridge, would have studied Aristotelian logic “as a major part of the course of study.” His making a mistake of this kind would have been highly unlikely. Marvell must have done it on purpose. Miller concludes: “I doubt if Marvell intended the reader to be misled by the fine rhetoric and the specious logic. He intended rather to defend chastity by attacking it—in a way at once ingenious and false.” Given Marvell’s Puritan allegiances I think Miller could be right; but I don’t feel that Miller accounts for the pervasive richness of the poem.

I believe the poem is best read as a witty gambit, a flattering compliment. The speaker knows the woman he addresses, knows her to be quick enough to catch the fallacy of the argument, knows her...