The Myth of Occam's Razor
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.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
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 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 (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. 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, 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:  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.
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. 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
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. This discovery ought to operate as a salutary check upon dogmatism, and the tendency to turn logical rules into ontological principles.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
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.
- Coke's Reports: I., 8, 167 (Earl of Cumberland's case): and I., 9 (Sir G. Reynal's case). See also Coke's Institutes, Part I. (on Littleton) for the application of this maxim to feudal tenure.
- "The Understanding makes Nature, but does not create" (the material out of which it is made). See T.H. Green, Prolegomena to Ethics, §11, first published in Mind of January, 1882, p.9. It occurs also in his Lectures on Kant: Works, vol. ii., p.86 (§74).
- Further, we may note, there is no mention of the common formula (or any other) in the Philosophia Nominalium Vindicata of Jean Salabert, published at Paris so late as 1651.
- See end of Appendix.
- Regula I. (in the Third and last of the author's editions), corresponds with Hypoth. I. on p. 402 of the First Edition (1687). The change of name from Hypothesis to Regula, and the words "Dicunt etc.," prefixed to the original comment: "Natura enim simplex est et rerum causis superfluis non luxuriat": first appeared on p. 357 of the Second Edition (1713). In the First, the paging leaps from 383 to 400: 386 thus becoming 402.
- Thomasius says obscurely of "Entia non etc." (loc. cit.): "Quod a Ferrariensibus discimus, frequentissime Nominalea usurpasse". But I cannot find any mention of collaborate Ferrarienses (like the Salmanticenses and Conimbricenses) in any work of reference. Brucker (Hist. Phil., III., 866) classifies Hieronymus Fantonus (or Fontanus) de Ferrariis O.P. (+1532) as a Nominalis, but this Grand Inquisitor's Repertorium Scoti (or Loci Communes) contains no allusion to the Law of Parcimony in any form. Franciscus Sylvester Ferrariensis O.P. (+1526) cites 'Frustra fit etc.' (in substance), and ascribes its origin to Aristotle, in his Questions on the Physica: I., Q. 9, p. 35b. He says there: "Quod potest fieri per pauciora, superfluum est, si fiat por plura": and (a few lines lower), "Natura non agit per plura, quod fieri per pauciora potest". The latter seems to be borrowed from Averroes: Comment. de Physico Auditu (Aristotelis). N. 50, on p. 31b of the Latin translation by Jacob Mantinus (Venice, 1574). See also NN. 40 (27c) and 41 (26a).
- Cf. Prof. F. Soddy in Nature, Nos. 2490 and 2491 (1917, 12th and 13th June).