The two estates; or both worlds mathematically considered. London, 1855, small (pp. 16).
The author has published mathematical works with his name. The present tract is intended to illustrate mathematically a point which may be guessed from the title. But the symbols do very little in the way of illustration: thus, x being the _present value_ of the future estate (eternal happiness), and a of all that this world can give, the author impresses it on the mathematician that, x being infinitely greater than a, x + a = x, so that a need not be considered. This will not act much more powerfully on a mathematician by virtue of the symbols than if those same symbols had been dispensed with: even though, as the author adds, "It was this method of neglecting infinitely small quantities that Sir Isaac Newton was indebted to for his greatest discoveries."
There has been a moderate quantity of well-meant attempt to enforce, sometimes motive, sometimes doctrine, by arguments drawn from mathematics, the proponents being persons unskilled in that science for the most part. The ground is very dangerous: for the illustration often turns the other way with greater power, in a manner which requires only a little more knowledge to see. I have, in my life, heard from the pulpit or read, at least a dozen times, that all sin is infinitely great, proved as follows. The greater the being, the greater the sin of any offence against him: therefore the offence committed against an infinite being is infinitely great. Now the mathematician, of which the proposers of this argument are not aware, is perfectly familiar with quantities which increase together, and never cease increasing, but so that one of them remains finite when {71} the other becomes infinite. In fact, the argument is a perfect _non sequitur_.[152] Those who propose it have in their minds, though in a cloudy and indefinite form, the idea of the increase of guilt being _proportionate_ to the increase of greatness in the being offended. But this it would never do to state: for by such statement not only would the argument lose all that it has of the picturesque, but the asserted premise would have no strong air of exact truth. How could any one undertake to appeal to conscience to declare that an offence against a being 4-7/10 times as great as another is exactly, no more and no less, 4-7/10 times as great an offence against the other?
The infinite character of the offence against an infinite being is laid down in Dryden's _Religio Laici_,[153] and is, no doubt, an old argument:
"For, granting we have sinned, and that th' offence Of man is made against Omnipotence, Some price that bears proportion must be paid, And infinite with infinite be weighed. See then the Deist lost; remorse for vice Not paid; or, paid, inadequate in price."
Dryden, in the words "bears proportion" is in verse more accurate than most of the recent repeaters in prose. And this is not the only case of the kind in his argumentative poetry.
My old friend, the late Dr. Olinthus Gregory,[154] who was a sound and learned mathematician, adopted this dangerous kind of illustration in his _Letters on the Christian Religion_. {72} He argued, by parallel, from what he supposed to be the necessarily mysterious nature of the _impossible_ quantity of algebra to the necessarily mysterious nature of certain doctrines of his system of Christianity. But all the difficulty and mystery of the impossible quantity is now cleared away by the advance of algebraical thought: and yet Dr. Gregory's book continues to be sold, and no doubt the illustration is still accepted as appropriate.
The mode of argument used by the author of the tract above named has a striking defect. He talks of reducing this world and the next to "present value," as an actuary does with successive lives or next presentations. Does value make interest? and if not, why? And if it do, then the present value of an eternity is _not_ infinitely great. Who is ignorant that a perpetual annuity at five per cent is worth only twenty years' purchase? This point ought to be discussed by a person who treats heaven as a deferred perpetual annuity. I do not ask him to do so, and would rather he did not; but if he _will_ do it, he must either deal with the question of discount, or be asked the reason why.
When a very young man, I was frequently exhorted to one or another view of religion by pastors and others who thought that a mathematical argument would be irresistible. And I heard the following more than once, and have since seen it in print, I forget where. Since eternal happiness belonged to the particular views in question, a benefit infinitely great, then, even if the probability of their arguments were small, or even infinitely small, yet the product of the chance and benefit, according to the usual rule, might give a result which no one ought in prudence to pass over. They did not see that this applied to all systems as well as their own. I take this argument to be the most perverse of all the perversions I have heard or read on the subject: there is some high authority for it, whom I forget.
The moral of all this is, that such things as the preceding should be kept out of the way of those who are not {73} mathematicians, because they do not understand the argument; and of those who are, because they do.
[The high authority referred to above is Pascal, an early cultivator of mathematical probability, and obviously too much enamoured of his new pursuit. But he conceives himself bound to wager on one side or the other. To the argument (_Pensees_, ch. 7)[155] that "le juste est de ne point parier," he answers, "Oui: mais il faut parier: vous etes embarque; et ne parier point que Dieu est, c'est parier qu'il n'est pas."[156] Leaving Pascal's argument to make its way with a person who, _being a sceptic_, is yet positive that the issue is salvation or perdition, if a God there be,--for the case as put by Pascal requires this,--I shall merely observe that a person who elects to believe in God, as the best chance of gain, is not one who, according to Pascal's creed, or any other worth naming, will really secure that gain. I wonder whether Pascal's curious imagination ever presented to him in sleep his convert, in the future state, shaken out of a red-hot dice-box upon a red-hot hazard-table, as perhaps he might have been, if Dante had been the later of the two. The original idea is due to the elder Arnobius,[157] who, as cited by Bayle,[158] speaks thus:
"Sed et ipse [Christus] quae pollicetur, non probat. Ita est. Nulla enim, ut dixi, futurorum potest existere comprobatio. Cum ergo haec sit conditio futurorum, ut teneri et comprehendi nullius possint anticipationis attactu; nonne {74} purior ratio est, ex duobus incertis, et in ambigua expectatione pendentibus, id potius credere, quod aliquas spes ferat, quam omnino quod nullas? In illo enim periculi nihil est, si quod dicitur imminere, cassum fiat et vacuum: in hoc damnum est maximum, id est salutis amissio, si cum tempus advenerit aperiatur non fuisse mendacium."[159]
Really Arnobius seems to have got as much out of the notion, in the third century, as if he had been fourteen centuries later, with the arithmetic of chances to help him.]
