A Justly Neglected Argument

Detail from title page of Robinson's Infidelity Answered

Leafing through Robert Patterson’s The Errors of Evolution (third edition, 1893), I noticed a really silly argument in a footnote. To be fair, it isn’t Patterson’s argument; it occurs in the editorial preface to the second edition, due to H. L. Hastings (1831–1899), a Boston-based evangelist and publisher. But it isn’t Hastings’s argument, either; he credits it to J. B. Robinson’s Infidelity Answered. The full title of Robinson’s book turns out to be Infidelity Answered by the Father-God and His Family (1875), and Robinson himself is identified on its title page as the “Rev. John B. Robinson, A.M., President of New-Hampshire Conference Seminary and Female College,” a Methodist institution in Tilton, New Hampshire. Robinson was born in 1834 and died in 1912. Take a deep breath, because it’s about to get really silly.

In the preface to Infidelity Answered, Robinson, taking Darwin’s Origin of Species as his subject, offers the following:

It is a book of 437 pages. Each page, upon a fair average, has ten probabilities and possibilities, and each of these hypotheticals has no more than fifty per cent, or a half[,] chance of certainty. His argument is so conducted that each proposition must stand or fall upon the validity of all that precede it combined. Then with 437 pages and ten half chances on each page, if it is desirable to know the fraction in the final assertion on the last page, we have only to regard that there are 10 X 437 half chances, in other words that one half must be raised to the 4370th power. [Hastings misquotes Robinson as saying 437th power here.] The numerator, which would be one unit, would represent the only chance in Darwin’s favor, while the denominator, minus one, will represent the chances against him. But that denominator becomes overwhelming; it would require a round number of more than fourteen hundred digits to express it, and a blackboard of one hundred and twenty feet in length to write it, allowing one inch to a figure. (emphasis in original)

He concludes: “Thus does human reason, diverging but a little from the straight line of truth, finally separate from it into infinite distances of error.”

Mathematical arguments against evolution are, of course, a fixture of antievolutionism. But I don’t think that I’ve encountered a mathematical argument against the credibility of the Origin, or of any specific work propounding evolution, before! Like the usual mathematical arguments against evolution, Robinson’s limps at every turn. Granting the data of ten assertions on each of 437 pages (although the first edition of the Origin ran 490 pages, excluding the front and back matter), 0.54370 is indeed a tiny number, approximately equal to pi (as it happens) ∙ 10-1316, although I think that Robinson is a little off on the size of the denominator (the reciprocal of 0.54370): it would take a numeral of only 1315 digits to express it and a blackboard of only 110 feet in length. But these problems are insignificant in comparison to the real howlers.

Here’s the first howler. In choosing 0.5 as the probability of each of Darwin’s assertions, Robinson is applying something variously called the principle of indifference or the principle of insufficient reason: if there are n mutually exclusive and jointly exhaustive possibilities, none of which is favored by the available evidence, the probability of each ought to be regarded as 1/n. The principle is at best contentious, but in any case Robinson is misapplying it by tacitly presupposing that there is no evidence that bears on the credibility of the assertions in the Origin. And that’s a false presupposition. For when Darwin asserts that he was on board HMS Beagle as naturalist—the first assertion in the Origin—it is not as though there is no available evidence that bears on his credibility. And so on, mutatis mutandis, throughout the book.

Robinson’s assumption that “each proposition must stand or fall upon the validity of all that precede it combined” is the second howler. True, in the final chapter of the Origin, Darwin described “this whole volume” as “one long argument” (a phrase that provided the title of Ernst Mayr’s 1993 book on Darwin). But the argument is certainly not presented in so tightly cumulative a fashion. Darwin asserts on the same page of chapter 1 of the Origin that cats with blue eyes are invariably deaf and that pigeons with short beaks have small feet; the latter is not a consequence of the former, and Darwin did not regard it as such. Indeed, I think that it would be practically impossible to write a book in a way that conforms to Robinson’s assumption, except perhaps in mathematics, and even then it would be difficult to write or read.

Beyond these problems, which are as it were internal to the argument, there’s also the problem that the argument, if sound, would prove way too much. For there’s nothing distinctive about the Origin required for the success of the argument: any book containing a large number of assertions of fact advanced in the service of a thesis would be shown to be incredible by the same line of reasoning—including, a mischievous critic might suggest, Infidelity Answered itself. (Consider it suggested.) Perhaps, then, it’s not surprising that, even considering the tendencies of antievolution writers to borrow their arguments wholesale from earlier writers and to revel in the piling up of exponent upon exponent in mathematical arguments, only Hastings seems to have repeated Robinson’s justly neglected argument.

Glenn Branch
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Glenn Branch is Deputy Director of NCSE.

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