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_.