The Sentinel, vol. ix. no. 27. London, Saturday, May 26, 1855.
This is the first London number of an Irish paper, Protestant in politics. It opens with "Suggestions on the subject of a _Novum Organum Moralium_," which is the application of algebra and the differential calculus to morals, socials, and politics. There is also a leading article on the subject, and some applications in notes to other articles. A separate publication was afterwards made, with the addition of a long Preface; the author being a clergyman who I presume must have been the editor of the _Sentinel_.
Suggestions as to the employment of a _Novum Organum Moralium_. Or, thoughts on the nature of the Differential Calculus, and on the application of its principles to metaphysics, with a view to the attainment of demonstration and certainty in moral, {75} political and ecclesiastical affairs. By Tresham Dames Gregg,[160] Chaplain of St. Mary's, within the church of St. Nicholas intra muros, Dublin. London, 1859, 8vo. (pp. xl + 32).
I have a personal interest in this system, as will appear from the following extract from the newspaper:
"We were subsequently referred to De Morgan's _Formal Logic_ and Boole's _Laws of Thought_[161] both very elaborate works, and greatly in the direction taken by ourselves. That the writers amazingly surpass us in learning we most willingly admit, but we venture to pronounce of both their learned treatises, that they deal with the subject in a mode that is scholastic to an excess.... That their works have been for a considerable space of time before the world and effected nothing, would argue that they have overlooked the vital nature of the theme.... On the whole, the writings of De Morgan and Boole go to the full justification of our principle without in any wise so trenching upon our ground as to render us open to reproach in claiming our Calculus as a great discovery.... But we renounce any paltry jealousy as to a matter so vast. If De Morgan and Boole have had a priority in the case, to them we cheerfully shall resign the glory and honor. If such be the truth, they have neither done justice to the discovery, nor to themselves [quite true]. They have, under the circumstances, acted like 'the foolish man, who roasteth not that which he taketh {76} in hunting.... It will be sufficient for us, however, to be the Columbus of these great Americi, and popularize what they found, _if_ they found it. We, as from the mountain top, will then become _their_ trumpeters, and cry glory to De Morgan and glory to Boole, under Him who is the source of all glory, the only good and wise, to Whom be glory for ever! _If_ they be our predecessors in this matter, they have, under Him, taken moral questions out of the category of probabilities, and rendered them perfectly certain. In that case, let their books be read by those who may doubt the principles this day laid before the world as a great discovery, by our newspaper. Our cry shall be [Greek: eurekasi]![162] Let us hope that they will join us, and henceforth keep their light [_sic_] from under their bushel."
For myself, and for my old friend Mr. Boole, who I am sure would join me, I disclaim both priority, simultaneity, and posteriority, and request that nothing may be trumpeted from the mountain top except our abjuration of all community of thought or operation with this _Novum Organum_.
To such community we can make no more claim than Americus could make to being the forerunner of Columbus who popularized his discoveries. We do not wish for any [Greek: eurekasi] and not even for [Greek: heurekasi]. For self and Boole, I point out what would have convinced either of us that this house is divided against itself.
[Alpha] being an apostolic element, [delta] the doctrinal element, and [Chi] the body of the faithful, the church is [Alpha] [delta] [Chi], we are told. Also, that if [Alpha] become negative, or the Apostolicity become Diabolicity [my words]; or if [delta] become negative, and doctrine become heresy; or if [Chi] become negative, that is, if the faithful become unfaithful; the church becomes negative, "the very opposite to what it ought to be." For self and Boole, I admit this. But--which is not noticed--if [Alpha] and [delta] should _both_ become negative, diabolical origin {77} and heretical doctrine, then the church, [Alpha] [delta] [Chi], is still positive, what it ought to be, unless [Chi] be also negative, or the people unfaithful to it, in which case it is a bad church. Now, self and Boole--though I admit I have not asked my partner--are of opinion that a diabolical church with false doctrine does harm when the people are faithful, and can do good only when the people are unfaithful. We may be wrong, but this is what we _do_ think. Accordingly, we have caught nothing, and can therefore roast nothing of our own: I content myself with roasting a joint of Mr. Gregg's larder.
These mathematical vagaries have uses which will justify a large amount of quotation: and in a score of years this may perhaps be the only attainable record. I therefore proceed.
After observing that by this calculus juries (heaven help them! say I) can calculate damages "almost to a nicety," and further that it is made abundantly evident that c e x is "the general expression for an individual," it is noted that the number of the Beast is not given in the Revelation in words at length, but as [Greek: chxw'].[163] On this the following remark is made:
"Can it be possible that we have in this case a specimen given to us of the arithmetic of heaven, and an expression revealed, which indicates by its function of addibility, the name of the church in question, and of each member of it; and by its function of multiplicability the doctrine, the mission, and the members of the great Synagogue of Apostacy? We merely propound these questions;--we do not pretend to solve them."
After a translation in blank verse--a very pretty one--of the 18th Psalm, the author proceeds as follows, to render it into differential calculus:
{78}
"And the whole tells us just this, that David did what he could. He augmented those elements of his constitution which were (_exceptis excipiendis_)[164] subject to himself, and the Almighty then augmented his personal qualities, and his vocational _status_. Otherwise, to throw the matter into the expression of our notation, the variable e was augmented, and c x rose proportionally. The law of the variation, according to our theory, would be thus expressed. The resultant was David the king c e x [c = r?] (who had been David the shepherd boy), and from the conditions of the theorem we have
du/de = ce(dx/de) + ex(dc/de)x + cx
which, in the terms of ordinary language, just means, the increase of David's educational excellence or qualities--his piety, his prayerfulness, his humility, obedience, etc.--was so great, that when multiplied by his original talent and position, it produced a product so great as to be equal in its amount to royalty, honor, wealth, and power, etc.: in short, to all the attributes of majesty."[165]
The "solution of the family problem" is of high interest. It is to determine the effect on the family in general from a change [of conduct] in one of them. The person chosen is one of the maid-servants.
"Let c e x be the father; c_1e_1x_1 the mother, etc. The family then consists of the maid's master, her mistress, her young master, her young mistress, and fellow servant. Now the master's calling (or c) is to exercise his share of control over this servant, and mind the rest of his business: call this remainder a, and let his calling generally, or all his affairs, be to his maid-servant as m : y, i.e., y = (mz/c); ... {79} and this expression will represent his relation to the servant. Consequently,
c e x = (a + mz/c)e x; otherwise (a + mz/c)e x
is the expression for the father when viewed as the girl's master."
I have no objection to repeat so far; but I will not give the formula for the maid's relation to her young master; for I am not quite sure that all young masters are to be trusted with it. Suffice it that the son will be affected directly as his influence over her, and inversely as his vocational power: if then he should have some influence and no vocational power, the effect on him would be infinite. This is dismal to think of. Further, the formula brings out that if one servant improve, the other must deteriorate, and _vice versa_. This is not the experience of most families: and the author remarks as follows:
"That is, we should venture to say, a very beautiful result, and we may say it yielded us no little astonishment. What our calculation might lead to we never dreamt of; that it should educe a conclusion so recondite that our unassisted power never could have attained to, and which, if we could have conjectured it, would have been at best the most distant probability, that conclusion being itself, as it would appear, the quintessence of truth, afforded us a measure of satisfaction that was not slight."
That the writings of Mr. Boole and myself "go to the full justification of" this "principle," is only true in the sense in which the Scotch use, or did use, the word _justification_.
