1. From the middle of the Nineteenth Century, nearly every modern book on Logic has contained the words:
Entia non sunt multiplicanda, præter necessitatem:
quoted as if they were the words of William of Ockham. But nobody gives
a particular reference to any work of the Singular and Invincible
Doctor: sometimes also, as on the title-page of his
De Sacramento Altaris (1513), described as the
Venerabilis Inceptor (of "Terminism" ?). We turn in vain even to Sir William Hamilton,
facile princeps
(among English writers) in philosophical learning; or to his nearest
rival, his disciple Dean Mansel. And my own fruitless inquisition for
the formula, in those works of Ockham which have been printed, has led
me to disbelieve that he ever used it to express his Critique of
Entities.
2. This disbelief is further justified by what I find, and cannot
find, in laborious recent histories of Medieval philosophy. Haureau (in
his
Philosophie Scholastique, vol. ii, chap. xxviii., pp. 438, 443, 446): Erdmann (in his
History of Philosophy, vol. i., §216); and De Wulf (in his
Medieval Philosophy,
§368); all concur in giving another set of words, as those usually
employed by Ockham: "Pluralitas non est ponenda (or Non est ponenda
pluralitas) sine necessitate". They do not even mention the common form
of the
Novaculum Nominalium. Nor does Prantl, in his large collection of citations (
Geschichte der Logik,
iii., pp. 327-420); though one of them (Note 758) contains: "Nunquam
ponenda est pluralitas sine necessitate". Nor does Stockl, in his very
full
Geschichte der Philosophie des Mittelalters,
§§259-266, pp. 986-1021 in the second volume. He selects: "Frustra fit
per plura, quod potest fieri per pauciora": as distinctive of Ockham in
this connexion. So did the earlier historian Tenneman:
Geschichte der Philosophie, p. 851 in band viii. (1810). In England this phrase even became a legal maxim: as we may see in Wingate's
Maxims of Reason (1658), no. 177. And it was judicially applied by Lord Chancellor Ellesmere
[1]
in 1610 and 1612. But it seems likely that Ockham's most famous phrase
in his own day was the: "Sufficiunt singularia, et ita tales
res universalia omnino frustra ponitur": from which
he
probably became known as the Singular Doctor. It must not, however, be
supposed that Albertus Magnus was called the Universal Doctor, for a
similar though opposite reason. He, like Aristotle and Francis Bacon,
"took all knowledge to be his province".
3. Ueberweg indeed, whose
History of Philosophy was first published in 1863 (ten years after the revised edition of Hamilton's
Discussions
in 1853), said in §16 of his second volume (§104 of the English
translation by Morris and Porter): "William of Occam founds his
rejection of Realism on the principle;
Entia non sunt multplicanda præter necessitatem. He combats the realising and hypostatising of abstractions (
Sufficiunt Singularia, etc.)":
p. 462 in the first volume of the English translation by Morris (1872),
and §36 page 307 of theil ii., in the new German edition of 1898. No
reference is given; and Ueberweg cannot always be trusted, even when he
does give a reference. On the previous page (461) of §104, he refers to
the Scotis Petrus Aureolus (†1322, Archbishop of Aix): In SS., ii., D.
12, Q. 1, for an assertion that: "He (P.A.) enounced the principle
subequently known as the Law of Parcimony:
Non est Philosophicum, pluralitatem rerum ponere sine causa; frustra enim fit per plura, quod fieri potest per pauciora". But there are no such clauses in the
locus
indicated; and the Index gives no clue to their presence anywhere else.
It is indeed possible that he has written them somewhere; because the
words had previously been used by his master Duns Scotus: a fact, with
which Ueberweg does not seem to have been acquainted. Aureolus actually
says (
In SS., i., D. 3, on p. 164 of vol. i.), referring to Aristotle's
Physica (i.): "In principiis debet tanta paucitas, quanta sufficit ad salvandum ea, quæ sunt in natura necessaria".
4. My note of April, 1915, asking for references to Ockham from readers of
Mind,
had the same fate as Prof. W. R. Sorley's inquiry in July, 1904 (p.
456), for the source of T.H. Green's fictitious quotation from Kant
[2]
(so long beloved of Oxford examiners): "Macht zwar der Verstand die
Natur, aber er schafft sie nicht". There was no response; and, I venture
to think, for the same reason. The earliest use of the popular phrase,
which I had then lighted upon, occurs in an Inaugural Dissertation by
Leibnitz in 1670:
De Stylo Philosophico Marii Nizolii, §28 (De Secta Nominalium). He does not, however, profess to quote, but says in
oratio obliqua:
"Generalis autem Regula est, quo Nominales passim untuntur, Entia non
esse multiplicanda præter necessitatem". The words do not appear in the
only philosophical work of Mario Nizzoli:
De veris principiis et vera ratione philosophandi: published at Parma in 1553. Another editition was published at Frankfurt in 1674, under the new title
Anti-barbarus Philosophicus;
with the dissertation by Leibnitz prefixed as in Introduction. In Hurter's
Nomenclator
(iii., 8), Nizolius is described as: "Philosophiæ scholasticæ acer
adversarius, Occami Nominalismi assecla". But he is better known through
the many editions of his
Ciceronian Concordance (
Thesaurus Ciceronis).
5. I have since found in Clauberg's
Elementa Philosophiæ seu Ontosophia
(Groningen, 1647), part ii., §169, p. 74: "Entia non sunt temere (sine
necessitate) multiplicanda". And again on page 174 (part iii., §121): in
both cases without quotation-marks, or any reference to Nominalism, to
Ockham, or to any source whatever. Possibly he regarded the phrase as a
proverb, needing no sponsor. But I cannot find any such proverb in those
vast collections of mediæval and earlier phrases: the
Adagia of Erasmus, and the
Polyanthes of Mirabellius. The common formula is exactly given in Clauberg's
Logica Vetus et Nova (1654), page 320, under Definition; but not as a quotation, nor with any reference.
6. De Wulf in §335 accuses Duns Scotus of: "creating fictitious,
misleading, and superfluous beaconlights, - in defiance of a precept
which he himself pretended to approve of:
entia non sunt multiplicanda præter necessitatem".
But he gives no reference, and I cannot find the formula anywhere in
the text of the Subtle Doctor's writings. It appears substantially
indeed in Wadding's edition (1639), tom. vii., p. 723 (27): but only in a
new Franciscan Commentary on the
Opus Oxon., iii., D. 34, Q. 1,
Scholium 4. Wadding's chief collaborator, John Ponce of Cork, there
mentions "illud axioma vulgare, quo tam frequenter utuntur Scholastici;
non sunt multiplicanda entia sine necessitate". He does not, however, name any of these
Scholastici;
and I can merely affirm (with almost mathematical certainty) that they
do not include Ockham, Scotus, or Aquinas; and the axiom does not occur
in the two most popular textbooks of the Middle Ages, the
Sentences of Peter Lombard (Bishop of Paris, †1164), and the
Summulæ Logicales
of Petrus Hispanus (†1277, as Pope John XXI.). I may add, with
sufficient moral certainty, Abelard, Hales, Albert, Bonaventura, and
Durand. Ockham's disciples, Gabriel Biel of Tuebingen (†1495), and John
Major of Haddington and St. Andrews (†1540), each of whom has been
called, "The Last of the Schoolmen," are satisfied with their Master's
Pluralitas or
Frustra fit.
[3] Reference may be made for the German, to his
In Sententias, iii., D. 3, Q. 2, N. 4 (
Conclusio 1), or (for applications) to i., D. 26, Q. 1, A. 1 (
Conclusio 3). And for the Scot, to his
Logica (1516),
Tractatus Primus Summularum, folio 28, col. 4.
7. On the other hand, De Wulf might have said with perfect accuracy,
that Scotus, no less than Ockham, accepts and systematically applies the
Law of Parcimony; whose origin he ascribes to Aristotle's
Physica and
De Anima, especially the first Book of
the former (cc. 5 and 7). Two (if not more) equivalent phrases are common to Ockham and Scotus:
Pluralitas, etc., and
Frustra fit, etc.
- (a) "Nunquam est ponenda pluralitas sine necessitate," appears in the Scotian Commentary In Metaphysica (Aristotelis): i., Q. 4, Scholium 3, p. 532 (10) of Wadding's tom. iv.
- (b) "Pluralitas non est ponenda, nisi ubi est necessitas": Opus Oxon., i., D. 3, Q. 6, Scholium 5, p. 525 (12) of tom. v.
- (c) "Ista opinio ponit pluralitatem sine necessitate, quod est contra doctrinam Philosophorum": Opus Oxon., iv., D.1, QQ. 4 and 5, Scholium 3, p. 84 (7) of tom. viii.
- (d) And in the next Scholium (4) he declares: "Sicut sequenti
rationem naturalem, non sunt ponenda plura, nisi quae ratio naturalis
concludit, ita sequenti fidem non sunt ponenda plura quam veritas fidei
requirat": p. 90 (9) of tom. viii.
- (e) A peculiar variant occurs on page 737 (4) of tom. iv.: In Metaphysica, viii., Q. 1, Scholium 2: "Positio plurium semper debet dicere necessitatem manifestam".
- (f) "Frustra fit per plura, quod potest fieri per pauciora:" is found on page 30 (3) of tom. ii.: In Physica (Aristotelis), i., Q. 8.
- (g) This is expanded into: "Generale enim principium est, quod si
aliquid potest aeque bene fieri per pauciora, sicut per plura, nullo
modo talis pluralitas debet poni": De Rerum Principio, Q. 1, art. 2, Scholium on page 92 (9) of tom. iii.
- (h) Another peculiar Scotian variant is given in the Reportata Parisiensia, ii., D. 15, Q. 1, Scholium 5, on page 348 of tom. xi.: "Paucitas est ponenda, ubi pluralitas non est necessaria".
8. The Metaphysical (or Methodological) Law of Parcimony (or Logical
Frugality), indicated but not very distinctly expressed by Aristotle,
[4]
was fully and finally established, not by Ockham (†1347), but by his
teacher Duns Scotus (†1308): the greatest mind of the later Middle Ages,
so unhappily cut off when he was only beginning to pass from the
critical to the constructive stage. According to some biographers he
died at thirty-four. Though unintelligently described by Leibnitz and
others as an Extreme Realist, his Universal was only an
Ens Rationis; a Brain-tool having a merely metaphorical entity. "Ens (Reale seu Naturale) est concretum," he said in his
Tractatus de Modis Significandis,
i., c. 25 (12): page 58b in tom. i. "Ens est duplex, naturae et
rationis ... Ens Rationis ... cujusmodi sunt Genus, Species, Definitio:"
in his [[
In Elenchorum LL. , Q. 1, page 224 (2) in tom. i. "Est enim Species tenuis similitudo Singularium": in his
Super Universalia Porphyrii,
Q. 4, page 90 (4) in tom. i. The "Formalism" of the Most Subtle Doctor
looks like the tentative and temporary device of a public teacher in
Holy Orders; who did not wish to break openly with the dominant
tradition of Realism; but was feeling his way to the "Terminism" boldly
professed by his independent contemporary Bishop Durand of Meaux
(†1332), and
afterwards
completely worked out by his pupil William of Ockham. It has lately
been stigmatized by the modern semi-Scotist Professor Pohle of Breslau,
as: "an inconceivable hybrid, which excludes every attempt of the mind
to grasp it": p. 153 of
The Essence and Attributes of God: vol. i. of his
Dogmatic Theology,
translated by Arthur Preuss. Both the Oxford Fransciscans (Ockham and
Scotus) used indifferently the two formulas: "Pluralitas non est ponenda
sine necessitate": and, "Frustra fit per plura, quod potest fieri per
pauciora"; while a former very similar to the latter was used by the
Most Resolute Doctor, the great Dominican Nominalist Durand; "Frustra
ponuntur plura, ubi unum sufficit":
In Sententias, ii., D. 3, Q.
5, N. 4. Occam's main contribution to the Doctrine was a special
application to the Logic of Universals, in his characteristic formula:
"Sufficiunt Singularia, et ita tales
res universales omnino frustra ponuntur":
In SS.,
i., D. 2, Q. 4 (top of col. 18). Few or no competent critics will
question Mansel's judgment of Ockham, on page 40 of his Introduction to
the
Rudimenta of Aldrich: "The ablest writer on Logic whom the Schools have produced.... The
Summa Totius Logicæ of Occam is the most valuable contribution of the Middle Ages to the
Logica Docens. His editor, Mark of Beneventum, said that, if the Gods used Logic, it would be the Logic of Ockham."
9. The doctrine was first completely applied to Physics by Sir Isaac
Newton in 1713. He quotes the very words of Scotus and Ockham in the
brief annotation of his first
Regula Philosophandi:
[5] which is itself a very similar statement of the principle. In the Third Edition (1726) of the
Principia Mathematica (
De Mundi Systemate,
lib. iii., p. 387, the Rule runs: "Causas rerum naturalium non plures
admitti debere, quam quae et verae sint et earum phenomenis explicandis
sufficient". Newton then subjoins: "Dicunt utique philosophi: Natura
nihil agit frustra, et frustra fit per plura quod fieri potest per
pauciora": a comment not found in the First Edition (1687). There is,
however, no mention of Ockham or Nominalism in the
Principia. The term
Novaculum Nominalium was quite unknown in the seventeenth century, as the international learned translation of Condillac's Gallic wit:
Rasoir des Nominaux, in a note on page 214 of his
Origine des Connasissances Humaines
(1746): Section V. (Des Abstractions), chap. i., §5. The English
variant (Occam's Razor) is a century younger; having made its first
appearance in
Sir William Hamilton's
Discussions (1852), page 590 (
On Causality).
In the second edition (1853) it is used on pages 616 and 629. In the
latter place it is for the first time distinctly associated with the
current form.
10. The following Conclusions I call Provisional, mainly because
there is still a possibility that they may be upset by German
investigators of Ockham's unpublished manuscripts. These have lain idle
for nearly six centuries at Ingolstadt or Munich; still uncopied, and
probably unread, by any Englishman; much to the discredit of Merton
College and the University of Oxford. Many of his cardinal works have
never been printed: including his Commentaries on the Second, Third, and
Fourth Books of the Lombard Sentences. The Commentary on the First Book
(printed in 1495) is very full; but the appended comments on the other
Books are only slender bundles of selected Questions, occupying together
only one-third of the volume.
Provisional Conclusions
A. "Occam's Razor" is a modern myth. There is nothing mediaeval in it, except the general sense of the post-mediaeval formula:
Entia non sunt multiplicanda praeter necessitatem.
This myth has come to full maturity and secured general assent, within
the lifetime of many philosophers of the present day; though it is a
matter of purely intellectual interest, without any impulse or
reinforcement from commercial greed, family-pride, national vanity,
sectarian zeal, or political party-spirit.
B. The age of the English title is not yet three-score years and ten: dating from the publication of Sir William Hamilton's
Discussions (1852).
C. The Latin title,
Novaculum Nominalium, is little (if at all) more than a century older: being a translation of the French title,
Rasoir des Nominaux, bestowed upon the current formula by Condillac in 1746.
D. (1) The current formula was unknown to Ockham and the other Schoolmen.
- (2) It was invented in 1639, substantially in its present wording, by the Scotist Commentator, John Ponce of Cork: a little-known man of great abilities and very independent disposition.
-
- (3) It first appeared in its present exact order of words, in the Logica Vetus et Nova of John Clauberg of Groningen in 1654.
-
- (4) It was first formally associated with Nominalism by Leibnitz in
1670; and this connexion seems to have been generally accepted from the
beginning of the eighteenth century. The reason of the connexion was
indicated in 1676, by Jakob Thomasius (father of the celebrated jurisprudent Christian T.), in his Oration De Doctoribus Scholasticus Latinis
to the University of Leipzig: "Hoc principium: Non esse absque
necessitate multiplicanda entia. Hinc enim ipsi (Nominales) Realibus ut
prodigis rerum
multiplicioribus invidiam fecerunt, suam vero philosophiam frugalitatis
nomine extulerunt. Reales vicissim qui principium illud, mirum entium
avaritiam quam tamen natura non amet, in Scholas importasse, simulque;
multas interemisse veritates dictitarent, Nominalibus avaritiam probi
loco objecerunt." It is possible that Leibnitz, who was only twenty-four
in 1670, may have got the notion of connecting Parcimony (or Logical
Frugality) with Nominalism, from some earlier expression of opinion by
the elder Thomasius.[6] Some of the very words of Thomasius appear in Morhof's Polyhistor (1688), Tom. II. (1), c. 13, p. 75: which is followed in Brucker's History of Philosophy (1766), Tom. III., p. 904, §27.
- (5) Still, even then, nobody connected Ockham in particular, with
the newly-accepted Scotist-Nominal formula. That connexion may be dated
apparently from 1812; when Tennemann in his Grundriss der Geschichte der Philosophie
(§271), wrote of Ockham as following the Rule: Entia non sunt
multiplicanda praeter necessitatem: without expressly ascribing to him
the actual use of the very words. They had not been mentioned in his
previous larger History (1810), which had quoted "Frustra fit" in a note
on page 851 of band viii. Tennemann's loose anachronistic use of the
post-mediaeval formula seems to have misled Ueberweg; and had previously
caused misunderstanding in Britain. His
Manual had been translated in 1832 by Rev. Arthur Johnson, from the
posthumous edition of 1829 as revised by Wendt. Hamilton never noticed
the anachronism, though he reviewed Johnson's translation very severely
in the
Edinburgh Review
of October, 1832. He indeed tacitly adopted it in 1853, after inventing
the label Occam's Razor. That label was at first (in 1852) applied by
him to the Law of Parcimony in general. Hamilton, moreover, seems to
have previously devised that very title, Parcimony, in place of the
older Frugality. So far as I can find, it first appeared in his edition
of Reid's
Works (1846), in a note to Reid's First
Essay on the Intellectual Powers (chap. iii., p. 236), and in his Supplementary Note A, §2, p. 751.
The unfortunate carelessness of Tennemann and Hamilton has engendered
a very serious philosophic corruption. For, it has turned a sound rule
of Methodology into a Metaphysical dogma. As
J.S. Mill pointed out in his
Examination of Hamilton (ch. 24, p. 542 in 4th edition): "The
Law of Parcimony
... is a purely logical precept". It is folly, to complicate research
by multiplying the objects of inquiry; but we know too little of the
ultimate constitution of the Universe, to assume that it cannot be far
more complex than it seems, or than we have any actual reason to
suppose. The value of this warning has just now received signal
illustration from the very recent discovery of Chemical
Isotopes; which has proved (
e.g.), that what had previously been simply called "lead" is infinitely complex in its composition.
[7]
This discovery ought to operate as a salutary check upon dogmatism, and
the tendency to turn logical rules into ontological principles.
Appendix
Some readers of
Mind,
and other students of Philosophy, to whom the rare works of Ockham are
not readily accessible, may be glad to have the following list of
seventeen relevant quotations at hand for ready reference: -
A. "Pluralitas non est ponenda sine necessitate." (1) In
Sententias (Petri Lombardi), lib. i.,
Distinctio i., QQ. 1 and 2. (2)
In SS., i., D. 7, Q. 2. (3)
Quodlibeta, i., Q. 3. (4) Do., iii., Q. 2. (5) Do., iv., Q. 15. (6) Do., v., Q. 5 (lines 3 and 4).
B. "Non est ponenda pluralitas sine necessitate."
In SS., ii., Q. 15 (second column): Utrum Angelus superior intelligat per pauciores species quam inferior?
C. "Nunquam ponenda est pluralitas sine necessitate."
In SS., i., D. 27, Q. 2 (section K, not J as given by Prantl in his Note 758). The matter discussed is
Species Intelligibilis.
D. "Talis species (intelligibus) non est ponenda propter superfluitatem."
Expositio Aurea: Perierm., Proem. See Prantl, N. 757.
E. "Si duae res sufficiunt ad ejus veritatem, superfluum est ponere aliam (tertiam) rem": (1)
Quodlibeta, iv., Q. 19; (Prantl, N. 768). (2) Do., iv., Q. 24; (Haureau, ii., 459).
F. "Sufficiunt singularia, et ita tales
res universales omnino frustra ponuntur."
In SS., i., D. 2, Q. 4 (top of column 18).
G. "Frustra fit per plura, quod potest fieri per pauciora."
- (1) Summa Tot. Log., Pars. i., cap. 12, f. 6, r. A.: referring to Intentio prima and secunda.
- (2) In SS., i., D. 31, Q. 1 (middle of first column): Utrum Identitas, Similitudo, et Equalitas in divinis sint relationes reales?
- (3) In SS., ii., Q. 15, sections O and Q: referring to Species Intelligibilis.
- (4) Philosophia Naturalis (Summulæ in Physicorum LL.), Quarta Pars,
cap. 1, p. 86b of the Roman edition (1637). In this he denies the
reality of an Instant of Time; showing some anticipation of the (New
Herakleitean) doctrines associated with the names of Bergson and William
James. See also page 85a (at the top). Ockham's doctrine of the Continuum (in regard to Space), as it appears in his Quodlibete, I., Q. 9: Utrum linea componatur ex punctis: has been set out and discussed by Mr. Delisle Burns in Mind of October, 1916 (pp. 506 ff.)
- (5) De Sacramento Altaris, Q. 3 (Utrum corpus quod est
quantitas set res absoluta, distincta realiter a substantia), page 41 of
the Paris (Blackletter) edition of 1513. I am indebted for this last
reference to Mr. C. Delisle Burns, in Mind,
October, 1915. Mr. Burns has shown the philosophical incongruity, and
consequent improbability of the commonly assumed use of "Entia, etc.," by Ockham. See also page 45. And compare with Scotus on the same subject (Quantity): In Physica, i., Q. 8: tom. ii., p. 30 (3). Refer to §7 (f.) supra.
Aristotle's nearest approximations to the doctrine developed by Scotus
will be found in cc. 4, 6, and 7 of the First Book of the Physica.
"Beltion de elattō kai peperasmena labein, hoper poiei Empedokles:
(Praestat autem pauciora et finita principia sumere: quod quidem
Empedocles)": cap. 4, p. 188a, lines 17-18 (Bekker). See also c.6; p. 189a, lines 12-13, 20, 26-27; and p. 189b, lines 18-19. Likewise c. 7; p. 190b, lines 35-36; and p. 191a, lines 6-7.
W. M. Thorburn.