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CANTOR, THE KABBALIST SEFYROTIC SYSTEM,
AND SPINOZISM
Prof. PhD. Jacques J. ROZENBERG!
National Centre for Scientific Research (CNRS),
FRANCE
https://cnrs.academia.edu/JacquesRozenberg
ABSTRACT
This article explores the influence of Kabbalah on the philosophical systems of
Spinoza, Leibniz, Bruno, and Cantor, with a focus on some structural and conceptual
parallels. Scholars have noted that Spinoza’s Ethics exhibits a framework akin to the
Kabbalistic sefyrotic system. Their studies highlight some correspondences between
Kabbalistic notions—such as sefirot (divine emanations), attributes, and parguf
(face)—and Spinozist concepts like attributes, modes, and state powers. The article
discusses how Cantor, through his use of the symbol aleph (8) and his conception of the
absolute infinite, reflects a Kabbalistic worldview. Then it will analyze the Spinozist
interpretation that Adolphe Jellinek proposed of the kabbalist theory of R. Azriel of
Gerona. I will then examine the abstract status of numbers in Jewish commentators
such as R. Ibn Ezra and the Gaon of Wilna, who posited the equivalence between the
notions of number and sefyrah. Finally, I will analyze the post-Cantorian theory of
naming, showing that it agrees, on the one hand, with the negative theology of
Maimonides, and on the other hand, with the semantics of Saul Kripke.
Keywords: R. Abraham Ibn Ezra; R. Azriel of Gerona; R. Mosheh Cordovero; R.
Abraham Cohen Herrera; Eyn Sof; infinite; sefyrot, Spinoza; Leibniz; Cantor;
naming; Kripke
INTRODUCTION
Several scholars have argued that Kabbalah provided Spinoza with the components
of a theoretical and structural model that appear to have influenced the formation of his
Ethics. More generally, it is possible to establish the historical relations between Giordano
Bruno, Spinoza, Leibniz and Cantor as well as their relations to Kabbalah. Adolph Jellinek,
as I will analyze in detail in this article, has suggested that the structure of Ethics is entirely
similar to the sefyrotic system (sefvrot: divine emanations).”? Alexandre Matheron described
in terms of transformational structures of sefyrot, several Propositions of the Ethics, and the
' T would like to thank Avishai Bar-Asher, Sarah Glaz, Larry M. Lesser and Henri Volken for their helpful
comments on previous versions of this article.
All the translations in English are mine, unless otherwise indicated. Regarding the transliteration of Hebrew, I
have generally followed the system of Ch. L. Echols and Th. Legrand Transliteration of Hebrew Consonants,
Vowels, and Accents, etc. Academia.edu.
https://www.academia.edu/5388085/Transliteration_of Hebrew_Consonants Vowels _and_ Accents etc
2 A, Jellinek, Beitrdige zu Geschichte der Kabbalah, Erstes Heft. Leipzig. 1852, pp.62-66
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different types of powers of the Spinozist state.? Finally, Alessandro Guetta has related the
notion of sefyrah with the Spinozist notion of attribute, and the notion of parguf (face) with
that of mode.*
Concerning Leibniz, let us remember that he used the expression cabbala vera in
connection with the universal characteristic (De numeris Characteristicis ad linguam
universalem constituendam). > Leibniz seems to have taken over from Bruno the notion of the
monad. He explicitly referred this notion to the Kabbalah of the Hebrews and to their
conception of the sefyrot, as expressions or attributes of the infinite.° Like the sefyrot, the
monads are "the true Atoms of Nature and, in a word, the Elements of things." ’ The monad,
like the simple substance, is a living mirror that reflects the universe in an infinite number of
ways.® Monadic perception is described on the model of the mirror where the global is
reflected in the local.? Concerning Cantor, it should be noted that the Leibnizian notions of
reflection and monad were taken up by Cantor and by set theory.!° In addition, in positing the
transcendence of the absolute infinite, Cantor was very close to the Jewish Kabbalah, as
shown by his choice of the Hebrew letter aleph (8) to designate transfinite cardinal numbers.
1. THE CANTORIAN ALEPHS AND THE EYN SOF
In order to theorize transfinite sequences, Cantor first chose, in 1883, the Greek
letter © (omega), which designated the ordinal number of the sequence of natural numbers.!!
Louis Couturat emphasizes that the w, as an ordinal number, is not "the /ast of all finite
numbers, but it is the first after them, that is to say, the first of the infinite numbers." Since no
number can represent the entire sequence of finite numbers, a transfinite number must be
3 A. Matheron, Individu et communauté chez Spinoza. Paris, Minuit, 1968, pp.616-622. Cf. G. G. Scholem,
Major trends in Jewish Mysticism. p.214.
4 A. Guetta, Kabbalah and Rationalism in the Works of Mosheh Hayyim Luzzatto. In G. Veltri (Ed.), /talian
Jewry in the Early Modern Era: Essays in Intellectual History. Boston, Academic Studies Press, 2014, pp.218-
219.
5 Leibniz, Gerhardt, Die philosophischen Schriften, vol. VII, pp. 184-189.
® G. Bruno, De monade numero et figura liber consequens quinque de minimo magno & mensura: item: De
innumerabilibus, immenso & infigurabili; seu De universo & mundis libri octo. Francofurti, Apud Ioan.
Vvechelum & Petrvm Fischerum Consortes, 1591, pp.61-62 and p.134. A. P. Coudert reports the opinions of E.
Thouverez and M. Bréhier, according to which Leibniz borrowed the term monad from G. Bruno. A.P. Coudert,
Leibniz and the Kabbalah. Dordrecht, Kluwer Academic, 1995, p.185 note 234. However, M. R. Antognazza
has suggested that Leibniz's adoption of the term monad seems to have preceded his reading of Bruno's work,
but he may have borrowed it from authors influenced by Neoplatonism and Kabbalah, such as Ralph Cudworth,
Henry More, Christian Knorr von Rosenroth, Anne Viscountess Conway, and Franciscus van Helmont. M. R.
Antognazza, Leibniz: An Intellectual Biography. Cambridge: Cambridge University Press, 2009, p.352.
7 Leibniz, Monadology, § 3
8 Leibniz to Rémond, July 1714. GP III, 623
°M. Serres, Le systéme de Leibniz et ses modéles mathématiques : étoiles, schémas, points. Paris, PUF, 1968,
p.154 et p.180
10 Cf. A. Newstead, Cantor on Infinity in Nature, Number, and the Divine Mind. American Catholic
Philosophical Quarterly. 83, 4, 2009, p.351; W. N. Reinhardt, Remarks on reflection principles, large cardinals,
and elementary embeddings, Axiomatic Set Theory. In Thomas J. Jech (Ed.), Proceedings of Symposia in Pure
Mathematics. Providence RI: American Mathematical Society, vol. 13, bk. I, 1974, pp. 189-205. On the
importance of the Leibnizian notion of reflection in G. Cantor and K. Gédel, cf. M. van Atten, Monads and Sets.
On Gédel, Leibniz, and the Reflection Principle. in G. Primiero and S. Rahman (Eds.) Judgement and
Knowledge. Papers in Honour of B.G. Sundholm. London, College Publications, 2009, pp. 3-33.
'! G. Cantor, Uber unendliche lineare Punktmannigfaltigkeiten, 5. Grundlagen einer allgemeinen
Mannigfaltigkeitslehre. Ein mathematisch-philosophischer Versuch in der Lehre des Unendlichen 1883, In
Gesammelte Abhandlungen mathematischen und philosophischen Inhalts. Springer, Berlin, 1932, pp. 165-208.
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created, which can be described as "transcendent."'” In 1893, to designate the transfinite
cardinals, Cantor adopted the Hebrew letter aleph (&), and he named ki: the transfinite
cardinal of the first class of natural numbers. However, in 1895, he decided to name this first
class Xo, Xi the cardinality of the second class of transfinite ordinal numbers, and x2 the
cardinality of the third class of transfinite numbers, etc. Finally, Cantor names the set of all &
by the last letter of the Hebrew alphabet taw (n), while continuing to denote by @ the set of
transfinite ordinal numbers.'? Cantor was then able to construct the increasing sequence of
alephs, by extending that of the natural numbers: Xo in particular (@ is the ordinal of N)
constitutes the cardinal number immediately superior to all the xv.!* However, in his letter to
Hilbert of October 2, 1897, Cantor had warned that while the totality of all alephs can be
defined, it cannot be "completely defined (fertig definiert), inasmuch as the totality of all
alephs cannot be comprehended as a definite well-defined and also finished set.”!*
The reason for the choice of the letter &, to name infinite sets, has been explained by
the Marrano origin of Cantor. Indeed, he wrote to Paul Tannery in 1896 that his paternal
grandparents were part of the Portuguese Jewish Community of Copenhagen.!® Being of a
Marrano, like Spinoza, Cantor devoted the second part of his habilitation thesis to this
philosopher. and he shared with him, but for opposite reasons, a deep interest in Judaism.
This interest can be seen in the privately published pamphlet, in 1905, in which he mentioned
three first names, two of which were Hebrew: Georg Jacob Aaron.!’ It seems that Cantor
retained the letter 8, because it designates, in the Kabbalist tradition, the Eyn Sof, the divine
infinity. He thus constructed a theoretical model in which & express the infinite sequence of
worlds, as the Jewish kabbalists had described them.'* However, it should be stressed that the
sefyrot are metaphysical and symbolic entities, while the transfinite are formal mathematical
constructions. Their nature and objectives are then fundamentally different. Nevertheless, I
propose to reveal the theoretical convergences between these two apparently heterogeneous
notions and fields of research.
2. INFINITY AND THE EYN SOF
It should be noted that before Cantor's distinction between the absolute infinite and
the transfinite, the Jewish kabbalists had differentiated between the divine essence ( ‘agmut),
" L. Couturat, De l'infini mathématique. Reedition, Paris, Blanchard, 1973, pp.638-640
‘3G. Cantor, Beitrége zur Begriindung der transfiniten Mengenlehre (1895). Gesammelte Abhandlungen
mathematischen und philosophischen Inhalts. Cantor, 1932, pp.282-351; Cantor explains this choice in his letter
to Felix Klein of 30 April 1895, cf. J. W. Dauben, Georg Cantor. His Mathematics and Philosophy of the
infinite. Princeton, Princeton University Press, 1990, pp.179-183.
‘4H. G. W. Burchard, Georg Cantor's Ordinals, Absolute Infinity & Transparent Proof of the Well-Ordering
Theorem. Philosophy Study. 9, 8, 2019, pp.441-442
'S H. Meschkowski, W. Nilson (Eds.) Georg Cantor Briefe. Berlin: Springer-Verlag, 1991, p.388; W. Purkert &
H. J. Ilgauds, Georg Cantor 1845-1918, Birkhauser, Basel et al. 1987, pp.226—227; D. E. Rowe, On the Origins
of Cantor's Paradox: What Hilbert Left Unsaid at the 1900 ICM in Paris. The Mathematical Intelligence. 46, 2,
2023, p.107
‘6 P. Tannery, Mémoires Scientifiques 13. Correspondance. Paris, Gauthier-Villars, 1934, p.306
G. Cantor, Ex oriente lux. Gesprdche eines Meisters mit seinem Schiller iiber wesentliche Punkte des
urkundlichen Christentums. Berichtet von Schiller selbst Georg Jacob Aaron, cand. sacr. theol. Erstes Gesprach.
Privately published by Georg Cantor. Halle, 1905, cf. Y. Rav, Georg Cantor, 1845-1918, par Walter Purkert et
Hans-Joachim Ilgauds. Revue d'histoire des sciences. 43, 2-3, 1990, p.327.
'8 A.D. Aczel, The mystery of the aleph. Mathematics, the Kabbalah and the Search of the Infinity. New York,
Barnes and Noble, 2005, pp.145-148
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expressed by the Eyn Sof, the absolute infinity of which is not accessible to man, and the
infinity of the sefyrot in which the Absolute comes to manifest Itself. !”
The term unlimited appears in the Kabbalist texts, especially in the Sefer Ye¢yrah, in
connection with the notion of sefyrot, which are themselves described as "devoid of any end
('Eyn lahem sof),""° as 1 will specify later. As Sandra S. Valabregue-Perry has shown, the
Sefer Yegyrah is at the origin of the Theosophical notion of infinity.2! According to Gershom
Scholem, the utterance 'Eyn Sof is a compression of ‘ad 'Eyn Sof (to infinity), in the form of
the nominal form ‘Eyn Sof (infinite). It appears as such with R. Itshaq the Blind (R. Sagy
Nahor, 1160-1235).?? Shalom Rosenberg clarified that the term 'Eyn Sof is specific to
Kabbalist language, whereas Medieval Jewish philosophers used the expression bilty ba'al
taklyt (without end).?? However, R. Abraham Cohen Herrera (1570-1635), both a kabbalist
and a philosopher, used these two expressions as well.”*4 Scholars generally agree on the
probable influence on Spinoza of the works of R. Abraham Cohen Herrera, Casa de la
Divinidad and Puerta del Cielo, 7> both written in Spanish. They were then translated into
Hebrew, and published in Amsterdam in 1655, by R. Itshaq 'Abuav,”° who participated, the
following year, in Spinoza’s Herem (exclusion) from the Portuguese Jewish Community.
These works, while referring largely to the Neoplatonism of Pico, Ficino, and Leo the
Hebrew,’ present a certain parallel with the theological-mathematical approach of Nicholas
of Cusa.** They constitute first of all a synthesis of the Lurianic Kabbalah, which R.
Abraham Cohen Herrera knew in Dubrovnik, through the teaching of R. Israel Sarug (or
Saruq), one of the students of R. Itshaq Luria Ashkenazi (1534-1572, designated by the
'9 J. Golding, Atzmut and Sefirot: a new approach. In S. Lebens, D. Rabinowitz & A. Segal (Eds), Jewish
Philosophy in an Analytic Age. Oxford, Oxford University Press, 2019, pp.243-244
20 Sefer Yecyrah, V. The expression 'Eyn ledavar sof (a thing that has no end) is found in Mishnah Yoma I, 1.
The Midrash Tanhuma, Tazry'a, XVI, uses the expression mah she'Eyn sof to refer to "innumerable ways." On
the literature on the notion of Eyn Sof, cf. S. Valabregue-Perry, The Concept of Infinity (Eyn-sof) and the Rise
of Theosophical Kabbalah. The Jewish Quarterly Review. 102, 3, 2012, p.410, notes 16-21.
21 §. Valabregue-Perry, The Concept of Infinity (Eyn-sof) and the Rise of Theosophical Kabbalah. The Jewish
Quarterly Review. 102, 3, 2012, p. 405
22 G. Scholem, The Origins of the Kabbalah, Engl. transl. Princeton, N.J., Princeton University Press and the
Jewish Publication Society, 1987, pp.266-267
3S, Rosenberg, Mi-Anaximandros we'ad Levinas. LeToldot musag ha-'Eyn Sof. Daat, 30, 1993, pp.90-91
24 R. Abraham Cohen Herrera, Sha'ar Ha-Shamaym. Reprint, Warsaw, Kelter, Spoeki, 1864, I, 7, pp.4a-b; III, 8,
17a-18b. This author quotes a passage from the Zohar (Ytro, 7), specifying that the Divine Presence extends to
the Eyn Sof (‘ad 'Eyn Sof) in the higher worlds, and endless (‘ad ’Eyn Taklyt) in the lower worlds. Ibid., p.18a.
25 M. Beltran, The Influence of Abraham Cohen de Herrera's Kabbalah on Spinoza's Metaphysics. Leiden, Brill,
2016, pp.41-44
26 It should be noted that these two works, written in Spanish, were not published in their original language at
the time, and that their Hebrew translation, on which the Latin translation of C. Knorr von Rosenroth was based
(in his work Kabbala Denudata, Sluzbach 1678, and Frankfurt 1684), is sometimes imprecise and not always
complete. Cf. Y. Kaplan, Fylosof lury'any mitequfat ha-B’aroq. Pe’amym. 70, 1992, p.129.
27 Cf. A. Altmann, Lurianic Kabbala in a Platonic Key: Abraham Cohen Herrera's Puerta del Cielo. Hebrew
Union College Annual. 53, 1982, pp. 317-355; R. Pinto de Brito & G. Aratjo Gomes, Leo the Hebrew and a
Kabbalistic Reading of Plato’s Timaeus. Prometeus: Filosofia em Revista. 40, 2022, pp.119-129
28 G. Necker, Circle, Point and Line. A Lurianic Myth in the Puerta del Cielo. In R. Elior and P. Schafer (Eds),
Creation and Re-Creation in Jewish Thought. Tiibingen, Mohr Siebeck, 2005, p.200. Konstantin Burmistrov
reports that Reuchlin was referring to Nicholas of Cusa when he mentioned the question of the inscrutability of
the Eyn Sof. K. Burmistrov, Christian Orthodoxy and Jewish Kabbalah: Russian mystics in the search for
perennial wisdom. Leiden, Brill, 2007, p.53, note 26.
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acronym: Arizal).? According to Saccaro Battisti Del Buffa, the Spinozist distinction,
presented in Ethics I, Definition VI, Explanation, between absolute infinity of the substance
and infinity in its kind of the attribute, would proceed from that proposed by R. Abraham
Cohen Herrera, between the absolute Infinite and the infinity of the sefvrot.*° Concerning this
distinction, Harry A. Wolfson refers to the work of R. Yosef 'Albo (1380-1444), Sefer ha-
Tygqarym, which Spinoza had certainly read, expounding the notion of 'Eyn Sof as an
expression of the infinity of divine perfection.*!
The distinction between the two forms of infinity is already clearly made by several
pre-Lurianic kabbalists, such as R. M’eyr Ibn Gabay (1480-1540). He stressed that creation
took place by means of the ten sefyrot emanating from the Eyn Sof, always remains
transcendent to the sefyrot.** This precision seems to contradict the comparison of the
distinction between, on the one hand, the Eyn Sofand the sefvrot, and, on the other hand, the
Spinozist distinction between the absolute infinity of substance and the infinity in its kind of
attribute. Indeed, the Spinozist attributes constitute the infinite substance (Ethics, I,
Definition VI), while the Eyn Sof and the sefvrot remain entirely incommensurable. In fact, it
is the theory of the contraction (Zsimtsum) of the light of the Eyn Sof that determines the
radical incommensurability between the Infinity of the divine light and the finitude of its
emanations. This theory, as I will explain later, had already been formulated by R. ‘Azry’el
of Girona (1160-1238), who speaks of abstention from influx (himan‘a ha-shef‘a),*> by
Nachmanides (1194-1270), using the expression "contracted the substance of Glory (¢ym¢em
‘egem ha-Kavod),"** by R. Yosef K'aro (1488-1575),°> and by R. Mosheh Cordovero (1522-
2° The theory of R. Itshaq Luria Askenazi, interpreted by R. Israel Sarug, had been presented, among others, by
R. Yosef Shlomo Delmedigo, Mag¢ref LaHokmah (Ta'alumot Hokmah), Basel 1629, a work that Spinoza
possessed, and in the book by R. Naftaly Hyr¢ Bakrak, 'Emeq ha-Melek, published in Amsterdam in 1648. It has
been noted that through the work of C. Knorr von Rosenroth, Kabbala denudate, who had translated several
texts by R. Abraham Cohen Herrera, it was finally the teaching of R. Israel Sarug that determined the influence
of the Lurianic Kabbalah in Europe. P. Franks, The Midrashic Background of the Doctrine of Divine
Contraction: Against Gershom Scholem on Tsimtsum. In A. Bielik-Robson, D. H. Weiss (Eds), Tsimtsum and
Modernity: Lurianic Heritage in Modern Philosophy and Theology. Perspectives on Jewish Texts and Contexts.
Berlin, De Gruyter, 2021, p.43.
3° G, S. Battisti, Abraham Cohen Herrera et le jeune Spinoza, entre Kabbale et scolastique- 4 propos de la
création ex nihilo. Archives de Philosophie, 51, 1988, pp.55-74; G. S. Battisti Del Buffa, Alle origini del
panteismo: genesi dell'Ethica di Spinoza e delle sue forme di argomentazione. Milano, Franco Angeli, 2004,
pp.370-379.
31H. A. Wolfson, The philosophy of Spinoza: Unfolding the latent processes of his reasoning. Cambridge,
Harvard University Press, 1934, I pp. 116-119; R. Y. 'Albo, Sefer ha-'Tyqarym, Il, 25.
32 A. M’eyr ibn Gabay, Derek 'Emunah. Reed, Warsaw, 1890, p.12. On the theory of emanation in the Kabbalah
of the thirteenth century, cf. M. Ehrenpreis. Die Entwickelung der Emanationslehre in der Kabbala des XIII.
Jahrhunderts. Frankfurt am Main, Kauffmann, 1895.
33 R. ‘Azry’el Migyronah, By'iur 'Eser Sefyrot. Reed. Jerusalem, Makon Pithey Megadym, 1997, p.30
34 Nahmanides, Commentary on the beginning of the Sefer Yegyrah. This commentary is not found in the
classical editions of this work, where the commentary generally attributed to Nachmanides was in fact written
by R. 'Azry'el Migyronah, as noted by R. Shem Tov Ibn G'aon. Cf. G. Scholem, Ha-perush ha-'amity shel ha-
Ramban leSefer Yegyrah we-drivrey qabalah ha-'aherym ha-mityyahasym 'elayw. In M. Idel - Y. ben Shomo
(Eds.) Mehqarey Qabalah. Tel Aviv, 'Am 'Oved, 1998, p.74. M. Idel has underlined the impact of this comment
on the revival of the notion of Tsimtsum by R. Itshaq Luria. M. Idel, ‘al Toldot musag "ha-Tsimtsum"
beQabalah u-bemehqar. Mehqarey Yerushalaym beMahshevet Israel. 10, 1992, p.60.
35 This text is reported by R. Moshe Cordovero, Pardes Rimonym, V, 3, Reedition Korec, 1780, and it has been
extensively commented on by R. Shabtay Shaptal Horovy¢ (1566-1619), Shef‘a Tal, V, 1, Reedition Jerusalem,
Yaryd ha-Sefarym, 2005, pp.277-281.
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1570)°°, to finally be presented, in a completed form, by R. Itshaq Luria Ashkenazi.*” Since
in Hebrew the term number (myspar) derives from the same root as that of sefyrah (the
singular of sefyrot), it appears that mutatis mutandis, as Jorge Luis Borges has suggested,
mutatis mutandis, the distinction between the infinity of the sefvrot and the Absolute Infinite
is isomorphic to Cantor's distinction, between the mathematical infinite and the Absolute
Infinite.**
More precisely, the fact that each sefyrah includes itself ten sefyrot (kelulah
mi‘eser), and this ad infinitum,*’ anticipates Richard Dedekind's definition of an infinite
system as being equivalent to one of its parts.*° Cantor will then attest such an equivalence of
an infinite set to one of its subsets.*! In 1877, in a letter to Richard Dedekind, Cantor proved
that for any positive integer n, there exists a one-to-one correspondence between the points
on the unit line segment and the points in an N-dimensional space. The proof involves
presenting each point on a square with a pair of decimal coordinates.*? Let us recall that in
this letter, regarding the subject of the power of sets, he wrote: "I see it, but I don't believe
it!" thus showing, by this expression written in French,** that Cantor was surprised by the fact
that sets of different dimension could have the same cardinality.4 Although the Sefer
Ye¢yrah does not refer to sefyrot in strictly mathematical terms,*> nevertheless, it can be
shown that each sefyrah, itself containing ten sefvrot, each of which also includes ten sefyrot,
and this ad infinitum, thus represents a subset equal to its parts. This is calling into question,
as Cantor would do, Euclid's fifth Common Notion, according to which the whole is greater
than its parts.*° The idea of correlation between a set and its subsets, discovered by Cantor, is
already present in the numerical interpretation of the sefyrot by R. Saadia Gaon: "
establishing a correspondence (muwazat) between these Ten and Ten Things that have no end
(nihaya), he intended (to show) thereby that, whereas from the human (point of view
according to men) there is no end to what may be put together from the numbers by
36 R. Mosheh Cordovero, Pardes Rimonym, XXIII, 13; cf. B. Zak, Torat ha-Tsimtsum shel Raby Mosheh
Cordovero. Tarbiz, 58, 2, 1989, pp.207-238.
37 A. Hayym Wyt'al, Sefer 'E¢ Hayym. Drush 'Igulym we-yosher. Reedition Jerusalem, 1963, pp.11la-12a
38 J. L. Borges, El Aleph. Republished Madrid, Penguin Random House Grupo Editorial Espafia, 2011. Cf. G.
Martinez, Borges y la Matematica. Editorial Universitaria de Buenos Aires, 2003, p.15; S. Mualem, Borges and
Kabbalistic Infinity: Ein Sof and the Holy Book. In R. Walsh and J. Twomey (Eds). Borges and the Bible.
Sheffield, Sheffield Phoenix Press, 2015, pp.81-98.
3°? R. Mosheh Cordovero, Pardes Rimonym, I, 5, p.3b
40 R. Dedekind, Essays on the Theory of Numbers. English translation, Reedition, New York, Dover, 1963,
p.105
41 P_ E. Johnson, The early beginnings of set theory. The Mathematics Teacher, 63, 8, 1970, p.691
#2 J. W. Dauben, Georg Cantor and the Origins of Transfinite Set Theory. Scientific American. 248, 6, 1983,
p.126
43 Cf. J. Cavaillés, Avertissement 4 la Correspondance Cantor-Dedekind. In Philosophie Mathématique. Paris,
Hermann, 1962, p.179; J. W. Dauben, Georg Cantor and the Origins of Transfinite Set Theory. Scientific
American. 248, 6, 1983, p.126; H. Volken, « Je le vois, mais je ne le crois pas... ». Preuves et vérités dans les
sciences formelles. Revue européenne des sciences sociales. XLI-128, 2003, p.146-148.
4 Cf. F. Q. Gouvéa, Was Cantor Surprised? The American Mathematical Monthly. 118, 3, 2011, pp.198-209
4 Cf. Y. Liebes, Torat ha-vegyrah shel Sefer Yegyrah. Jerusalem, Tel Aviv, Shoken, 2011, p.13
46 Cf. T. L. Heath, The Thirteen Books of the Elements. Dover Publications, Newburyport, 2012, I, p.155; K.
Robering, The whole is greater than the part. Mereology in Euclid's Elements. Logic and Logical Philosophy.
25, 2016, pp. 371-409
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themselves, they are finite (tatanaha) from the Creator's (point of view of the Creator)."*” It
can thus be shown that the system of ten sefyrot can be thought of as the abstract concept of
enumeration that is incorporated into the concept of one-to-one correspondence.*® Let G be
the set of all the general sefyrot (Keter, Hokmah, Binah etc.), each of which includes itself ten
sefyrot, it is then possible to form the subset P of the particular sefyrot (Keter of Keter,
Hokmah of Keter, Binah of Keter... Keter of Hokmah, Hokmah of Hokmah, Binah of Hokmah
etc...). And there is thus a bijective relationship, that is to say both injective and surjective,
between each element of these two sets.*? Indeed, this map is injective, since any element of
its ending set P (the particular sefyrot) has at most one antecedent in the starting set G (the
general sefvrot). This correspondence is also surjective, because every element of the end set
P has at least one antecedent in the starting set G. Because of this bijective correspondence,
the two sets have the same cardinality, i.e., they are equipotent.*’ In this sense, it has been
suggested that, mutatis mutandis, the sephyrotic system rejoins the idea of Georg Cantor
according to which there exists an infinite sequence of mathematical infinities: No< N1< &
Fag
3. SPINOZA AND THE NOTION OF SEFYRAH
Christian Ginsburg has translated into English the Spinozist interpretation that
Adolphe Jellinek proposed of the work By‘iur ‘Eser Sefyrot by R. Azariel ben Menachem de
Girona (1160-1238). He began by affirming that, according to the Kabbalah, the universe
constitutes the garment of God. Such a garment would be woven from the divine substance
itself, and this is how Spinoza was able to affirm the immanence of God in the world.** It
should be noted, however, that the Kabbalist notion of garment (/ebush) does not designate a
part of the divine substance. Indeed, as R. Abraham Cohen Herrera points out, it is the sefyrot
that are the garments of the Eyn Sof (malbushey Eyn Sof). Just as the clothes cover the body,
but are entirely distinct from it, so the sefyrot are not to be confused with the real essence
(‘egem ha- ‘agmut) of the Eyn Sof: Although the sefyrot are not separated from it, they are of a
different nature (mitev ‘a’aher).* If the notion of emanation (‘a¢ylut) applies to the sefvrah, it
should also be emphasized that the sefyrot exist uniquely after the Tsimsum (contraction),
471 am using here the English translation, from the Arabic text, by Shlomo Pines. Points of Similarity between
the Exposition of the Doctrine of the 'Sefirot' in the 'Sefer Yezira' and a Text of the Pseudo-Clementine
"Homilies'. [srael Academy of Sciences and Humanities, Jerusalem, 1989, pp.116-117.
48S. Glaz, Mathematics in the Poetry of Sefer Yetzirah. Bridges Conference Proceedings, 2021, p.43
# P. J. Eccles, An Introduction to Mathematical Reasoning. Numbers, Sets and Functions. Manchester,
University of Manchester Press, 1998, p.103
*° Tn correspondence, Sarah Glaz underlined that G, being the general sefyrot set, seems to be the collection of
the ten sefyrot with each sefyrah including ten sefyrot, and the process continuing ad infimum. This is a
description of the natural numbers. At every stage we can increase the number of sefyrot by a power of 10, and
the most we could get is the entire natural numbers (all the numbers at every stage are a finite set of whole and
positive numbers). Therefore, the cardinality of G is aleph 0, and there will be subsets of the same cardinality,
for example the even numbers, but no other form of infinity is involved.
5! L. M. Lesser, Book of Numbers: Exploring Jewish Mathematics and Culture at a Jewish High School. The
Journal of Mathematics and Culture. 2006, VI, 1, 2006, p.18
*? Christian Ginsburg, The Kabbalah, Its Doctrines, Development, and Literature. London, Routledge, 1920,
p.108, p.178. On Adolf Jellinek and Kabbalah, cf. M. Idel, Aharon Jellinek we-ha-Kabbalah. Pe'amim. 100,
2007, pp.15-22
*3.R. Abraham Cohen Herrera, Sha ‘ar Ha-Shamaym. Reedition, Warsaw, Kelter, Spoeki, 1864, VII, 9, p.65
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which vas applied only to a glimmer of the Eyn Sof (ha-'erat Eyn Sof), and not to the Eyn Sof
Itself?
It should be remembered that R. ‘Azary’el Girona, who was a pupil of R. Isaac the
Blind (1160-1235), and the master R. Moses Nachmanides (1194-1270), wrote, in the form
of questions and answers, The Commentary on the Ten Sefyrot.>° 1 will now examine the six
propositions that Adolf Jellinek has reformulated in a more geometrico way, on the model of
Ethics, trying then to assess the relevance of such a comparison. I will retain only the
essential elements of this analysis, trying to confront them with the Kabbalist theses in
general, and with those of R. ‘Azary‘el in particular. I will thus emphasize the fundamental
differences between these theses and the essential notions of De Deo.
Definition I, presenting God as Governor (manhyg), is thus supposed to be parallel
to the first definition of the De Deo. However, R. ‘Azry‘el's text does not first introduce the
notion of cause, and even less that of causa sui (Ethics I, 1), but that of Ruler of all things,
presented according to a historical perspective that is totally absent from the Ethics. It is only
then that R. ‘Azry‘el clarifies, from a point of view that has been described as super-Esse,
according to Erigena's expression,°° or meta-ontological.>’ Indeed, the Infinite Being is the
source of all that exists, because it is the reason of all reasons (‘ylah ha- ‘ylot) and the cause
of all causes (sybah ha-sybot).** As R. Yosef 'Ang'let (14th century) points out, the Infinite
Being always remains transcendent to the sefyrot it produces (’eyn ha-ma’agyl ... beklal 'eser
sefyrot), and therefore it does not belong to their immanent series.°’ Thus, the first principle
laid down by R. ‘Azry‘el is opposed in advance to the Spinozist conception of God, as a
purely natural and immanent cause of beings, who in no way directs the world in a
providential way.®° Let us recall that, in the Short Treatise, V, 2, Spinoza has preserved the
notions of Providence (Voorzienigheid), both general and particular, but that he has emptied
them of all religious content. The first concerns only the laws of nature, and the second the
effort (conatus) of each individual to maintain its own being. For Spinoza, God remains
indifferent to human actions: "God, strictly speaking, loves no one and hates no one (Deus
proprie loquendo neminem amat neque odio habet)."*' It is only indirectly that "God, in so
far as He loves Himself, loves men (quod Deus quatenus seipsum amat, homines amat)."
However, R. ‘Azry’el underlines that anyone who says that the world has no governor is
called a heretic (kofer).™
Definition II introduced by Jellinek concerns the notion of sefyra, while Definition I
of De Deo deals with the finite thing in its kind (in suo genere finita). The sefyrot refer to the
*4R. Walkovsky, Torat Ma'asey B’ereshyt. Kedahnen, 1934, I, p.36
5 R. ‘Azry’el MiGyronah, By'iur ‘Eser Sefyrot. I refer to the edition by R. M. Shatz, Jerusalem, M. Pithey
Megadym, 1997. This edition also includes R. Meyr Gab'ay's work detailing the ten sefyrot, Derek 'Emunah.
%° G, Scholem, The Origins of Kabbaila. English translation, Princeton, Princeton University Press, 1987, p.423
57 E. R. Wolfson, Mystery of Infinity, Malxut deAdam Qadmon, and the Myth of Simsum: Engendering Alterity
in the Theosophy of Nehemiah Hiyya Hayyon. E/ Prezente. 16-17, 2022-2023, p.24
38R. ‘Azry’el MiGyronah, By'iur ‘Eser Sefvrot. First answer, pp.29
» R. Yosef 'Ang'let, Livnat ha-Sapyr. Jerusalem, 1913, p.40a
6 R. Mosheh Hayym Luzzatto (1707-1746) specifies that the Eyn Sof rules the worlds by means of the sefyrot,
each of which represents a particular dimension (‘ehat min ha-midot) among all the dimensions of the Eyn Sof,
each in a given time (bezman ha-hu'). R. Mosheh Hayym Luzzatto, Qla”h Pithey Hokmah. Reedition, Bney
Braq, R. H. Friedlander (Ed.), 1992, VI, p.18
6! Spinoza, Ethics V, 17, Corollary
® Spinoza, Ethics V, 36, Corollary
6 R, ‘Azry‘el, Derek ha-'Emunah we-derek ha-kfyrah. In G. Scholem (Ed.), Srydym hadashym miKitvey R.
‘Azry‘el MiGyronah, In Sefer Zikaron le-A.Golaq we-le-S. Klein, Jerusalem, 1942, p.207
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divine powers that Gershom Scholem describes as "living numerical beings." R. ‘Azry’el
clarified that God is the Infinite (Eyn Sof), and that His completeness is free from all lack
(Shlemut bly hysaron). However, because of this completeness, He does not lack the capacity
for limitation, which itself remains unlimited (yesh lo koah begevul mibly gevul). Without
such an ability, then His perfection would be defective. This paradox can be explained by the
fact that the first production of the Eyn Sof concerns the sefyrot which are the receptacles
(kelym) of His influx. They constitute the forces that are both complete and incomplete (koah
ha- shalem we-koah ha-haser) and this, depending on the nature of the actions that the sefyrot
must perform. They are constantly modulated by antagonistic determinations, which
themselves express the reception of the divine influx (kash-hem meqablym min ha-shef‘a)
and the restriction of this influx (himan'‘a ha-shef'a). But such a differentiation concerns only
the sefyrot and not the Eyn Sof Who is perfect (shalem).° R. ‘Azry’el calls this power:
"limiting force" (koah ha-gevul), and R. Itshaq Luria Ashkenazi will formulate such power in
terms of Tsimtsum (concentration). The essence of the sefyrah concerns the synthesis of
everything and its opposite (mahut ha-sefyrah shaveh lekol davar u-lekol temurah).© It
should be noted that the sefyrot, while endowed with a restricting force, are themselves
limitless (ha-gvul mibly gvul).°’ They constitute a numerical infinite power, in which the
absolute infinity of the Eyn Sof is expressed.°* As Elliot R. Wolfson remarks, given that all
things that can be measured should be regarded as being corporeal, it is possible and
necessary to talk about the sefvrot as the spiritual body that represents the immeasurable
infinite beyond all representation.” R. Mosheh Cordovero emphasizes that the sefvrot as
emanated are infinite, but the actions they produce are limited (hen po ‘alym pe‘ulah taklytyt),
because they relate to singular objects and to particular situations.’? While proceeding from
the unity of the Eyn Sof, the multiplicity of sefvrot expresses only His actions and never His
essence. !
Even if, according to Miquel Beltran, the notion of sefyrah, as developed by R.
‘Azry‘el, would have influenced the Spinozist theory of attributes,’? Spinoza could not accept
the notion of 7simtsum, introduced by R. Azriel. Indeed, he rejected the idea that infinite
substance could generate any lack, such as the 7zimtsum produces in the form of an empty
64 G. Scholem, The origins of Kabbalah, p.28
6 C, Third answer, p.30
6° R. 'Azry'el MiGyronah, By'iur 'Eser Sefyrot. Ninth answer, p.33. I reproduce here the English translation by
Joseph Dan, The Early Kabbalah. English transl. Mahwah, Paulist Press International, 1986, p.94
67 R, Meyr Ibn Gabay, Mar'ot 'Elohym. Venice, 1567, Heleq ha-Yhud, VIII, p.13a
68 S, Valabregue-Perry, The Concept of Infinity (Eyn-sof) and the Rise of Theosophical Kabbalah. The Jewish
Quarterly Review. 102, 3, 2012, pp.412-413
6 FE. R. Wolfson, Language, Eros, Being: Kabbalistic Hermeneutics and Poetic Imagination. New York,
Fordham University Press, 2005, p.200
7 R. Mosheh Cordovero, Pardes Rimonym, II, 7, p.9b; R. Moshe Cordovero, Sefer Shy ‘iur Qomah. Reprint,
Warsaw, 1883 p.49b.
™ R. D. Messser Leon, Magen David. This work has not been published. Hirschfeld (ms. no. 290); Ephraim
Gottlieb has reproduced some excerpts from the manuscript: E. Gottlieb, Mehgarym besifrut ha-Qabalah. Tel
Aviv University, 1976, pp. 403-422; H. Tirosh-Rothschild, Sefyrot as the Essence of God in the Writings of
David Messer Leon. AJS Review, 7/8, 1982/1983, p.421.
Mz. Beltran, The Influence of Abraham Cohen de Herrera's Kabbalah on Spinoza's Metaphysics. Leiden, Brill,
2016, p.24. Joseph Dan has specified that if the notion of sefyrah has been compared to the philosophical notion
of divine attribute, however, as shown in the Sefer Ha-Bahyr, the system of sefyrot is historically prior to the
philosophical formulation of attributes. J. Dan, Gershom Scholem's Reconstruction of Early Kabbalah. Modern
Judaism. 5, 1, 1985, p.45.
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space. According to the Explanation of Definition VI of De Deo, the essence of that which is
absolutely infinite "does not envelop any negation" (negationem nullam involvit),” and this is
the reason of Spinoza's inability to deduce the finite from the infinite. ”4
In Proposition III, A. Jellinek specifies that there are ten sefyrot. The number ten,
which implies multiplicity, does not contradict the absolute unity of the Eyn Sof from which
the sefvrot emanate. Indeed, the One (’Ehad) is the foundation (vesod) of all numbers, as I
will specify later, and therefore the plurality always proceeds from unity. Before the One,
which is of a divine nature (yesh bo ’Elohut) there is no number (‘evn mispar lifney 'ehad).™
The One is not itself a number, but constitutes the premises of all numbers (r’eshyt kol ha-
misparym).’° As R. Itshaq ben Shmu’el Mi‘Ako (13th—14th century) puts it, the origin of all
realizations does not himself belong to the realm of his realizations (‘evn ha-mamcy’ beklall
ha-nime’aym).’’ The One is not included in the digital series, but it is at the origin of this
series since the origin always remains transcendent to its products.
On the contrary, for Spinoza, the one cannot be the premises of all numbers. In
Letter 50 to Jarig Jellesz, he emphasizes: "I establish that God can only be very improperly
called one and unique (Deum non, nisi valde improprie, unum, vel unicum dici posse) with
regard to essence, but it can be said with all rigor with regard to existence." For Spinoza, the
one does not differ from the numbers that follow it, for generally speaking, it is only by
referring to the common genus (commune genus), which is of an imaginary nature, that we
arrive at the idea of exemplars of an existing thing, and thereby acquire the idea of number.
This is why, "one thing cannot be said to be one and unique before another thing has been
conceived having the same definition (as they say) as the first" (nullam rem unam, aut
unicam nominari, nisi postquam alia res concepta fuit, quae (ut dictum est) ea convenit)."®
Thus, holding together a penny and a shield allows the number two to be used, provided that
they are classified under the same denomination, namely a coin.”
From a metaphysical point of view, by grouping things together for the purpose of
counting, we remove the modes from their original order within the substance.*° By making
number an auxiliary of the imagination, Spinoza is in fact opposed to the Kabbalists, for
whom number is a divine production.*! In the Ethics, Spinoza posits that there is a single
substance (unicam substantiam existere),*? and Martial Gueroult concludes that finally
Spinoza grants substance the uniqueness of the "metaphysical one, which has nothing to do
with numerical unity."*° I do not think that conclusion is correct. In fact, in Letter 50 to
® Spinoza, Ethics I, Definition VI, Explanation
™ Cf. J. J. Rozenberg, Spinoza, le Spinozisme et les fondements de la sécularisation. Amazon, 2023, pp.221-224
BR. ‘Azry’el, Perush leSefer Yegyrah (commentary attributed to Nachmanides), I, 7, p.28b. According to G.
Scholem, this commentary was written by R. ‘Azr’el or by his brother R. ‘Ezr’a. G. Scholem, Perush ha-’amity
shel ha-Ramban leSefer Yecyrah we-divrey Qabalah 'aherym ha-mityyahesym 'elav. In Y. Ben Shlomo, M. Idel
(Eds), Mehqarey Qabalah. 1, 1998, p.67. On the different opinions concerning the author of this commentary,
cf. J. Weiss, Perush Sefer Ycyrah ha-meyuhas le-Itshaq Sagy Nahor. R’ayot le’iyshush qadmuto, m‘amado
beqerev ha-maqubalym beme'ah ha-13 u-le-mehymanut yyhuso le-Itshaq Sagy Nahor. Tarbiz, 88, 4, 2022,
p.625 note 50.
7 R. Abraham Abulafya, Gan ‘Eden Ganuz. Jerusalem, 2000, p.42
TR, Itshaq ben Shmu’el Mi’ Ako, R. H. A. Erlanger (Ed.) Me’iyrat ‘Eynaym. Jerusalem, 1993, p.93
78 Spinoza, Letter 50 to Jarig Jellesz, G. IV, 239
™ M. Gueroult, Spinoza. I, Dieu. Paris, Aubier Montaigne, 1968, p.198, p.221 note 1 and p.581.
8°-Y_ Y. Melamed, The Exact Science of Non-Beings: Spinoza's View of Mathematics’. [yyun, 47, 2000, p.10
8! R. M. Kasher, Ha-tequfah ha-gedolah. Il, Jerusalem, 2001, p.598
8 Spinoza, Ethics I, 8, scholium; Ethics I, 10, scholium.
83 M. Gueroult, Spinoza. I, p.158
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Jellesz, Spinoza had made it clear that it is only from the point of view of existence that God
can be said to be One and Unique, whereas according to essence, substance can only be said
to be one in an improper way. Now, in the Ethics, the demonstration relates only to the
unique existence of substance (unicam substantiam existere), and not to its essence.** This
suggests that Spinoza here refers to the numerical unity, and not to the metaphysical unity,
which he never mentions in the Ethics. Proposition IV states that the sefyrot emanate
(ne'ecelot) from the Eyn Sof, and they are not created (/’o nivr‘aot), because all creatures
being limited, they are always subject to change (kol mugbal mishtaneh).®° On the contrary,
the sefvrot are emanated and therefore are immaterial and perfect. They constitute the first
manifestations of the 'Eyn Sof (lehimag'a mi-'Eyn Sof), which make it possible to organize
(mashpy'iym) the created worlds according to some specific determinations. This is why
Sefyrotic productions can be both complete and defective (be-hashlamah u-behysaron),
depending on their material realizations (gashmut) which are always differentiated. Against
this perspective, which accounts for the forms of production of real, Spinoza tried to deduce
the production of finite modes from infinite modes. However, unlike the sefyrot that are
emanated, the infinite modes, both immediate and mediate, belong to the natured nature and
not to the naturing nature,*° thus leaving open the question of their infinite divine origin. In
this sense, Alain Badiou qualifies as "enigmatic" the fact that, on the one hand, the infinite
produces the infinite, and on the other hand, that the finite produces the finite, without any
intersection between them.*’
Proposition V describes the actions (pe‘ulot) of the sefyrot that determine the
different realms of reality, from the mineral to the human, leading to the psychic and spiritual
world. This is made possible by the fact that the sefyrot are both active and passive (magbyl
u-mitqabel), that is to say, everything, proceeding from the unity of the Eyn Sof, is in charge
of receiving from their predecessor and giving to their successor. The sefyrah which is of a
higher level encompasses and surrounds (magqyf we-sovev), that which is inferior to it.8° As R.
Menachem ‘Azaryah MiPanu (1548-1620) points out, the first three sefyrot correspond to the
intellectual domain (muskal); the three intermediate sefvrot determine the sensory domain
(murgash); and the last four constitute the natural domain that comes to actualize the content
of all previous sefyrot. The latter sefyrot then unveils all the actions (/egalot ha-pe ‘ulot)
carried out in the previous areas in order to concretize them.*? The sefyrot thus ensure the
ontological unity of reality, through a progressive realization from the intellectual to the
material domain. The Kabbalists have given a primordial role to the Keter (Crown),
identified with the thought of divine origin (mahshavah ’Elohyt),° which remains
inaccessible to human thought (’eyn ha-mahshavh tofeset bah).?! Indeed, the Keter, often
identified with the Eyn Sof (ha-Keter hu’ ha-’Eyn Sof),”” has its root in the Eyn Sof, which
84 Spinoza, Ethics I, 10, scholium
85 R. ‘Azry’el Migyronah, By'‘iur 'Eser Sefyrot, p.36
86 Spinoza, Ethics I, 29, scholium
87 A. Badiou, L ’infini, Aristote, Spinoza, Hegel. Le Séminaire 1984-1985. Paris, Fayard, 2016, p.170
88 R. ‘Azry’el Migyronah, By'iur 'Eser Sefvrot, p.35 and note 1
89 R. Menachem 'Azariah MiPanu, Pelah ha-Rimon. Koreg, 1786, VIII, 2, p.21a
°° A. Bar-Asher, Dimyon we-meg’yut beheger r’eshyt ha-qabalah: Perush "Sefer Yecyrah" ha-meyuhas le-
R.Ytshaq Sagey Nahor we-toldotayv beqabalah u-bemehgqar. Tarbiz, 86, 2-3, 2019, pp.233-234
°! R. Shem Tov Even Shem Tov (I) (1390-1430), Sefer ’“Emunot. Ferrera, 1557, p.33a
°2 R. Mosheh Cordovero, Pardes Rimonym, VI, 8, p.29a, Adolf Jellinek, p.19, note 6, showed that R. Abraham
Abulafya already identifies the Keter with the Eyn Sof. A. Jellinek, Ginzey hokmat ha-qabalah. Reedition,
Jerusalem, Magor, 1969, p.19, note 6.
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designates the reason of all reasons (‘ylat ha- ‘ylot).”* On the contrary, the Spinozist notion of
parallelism between thought and extension, the mental and the physical, which are supposed
to be identical, remains problematic. For if the order and connection of ideas are the same as
the order and connection of things (Ordo et connexio idearum idem est ac ordo et connexio
rerum), yet such an equivalence is no longer valid with regard to the relation between the
idea and the idea of the idea (both of which are modes of the attribute of thought), for the
idea of a thing and the idea of the idea of that thing possess different ideata.> Thus, on a
reflexive level, the modes of thought no longer correspond to the modes of extension: the
"idea of the idea" cannot correspond to "a thing of a thing."’° Moreover, the modes of
extension are temporally connected, while the ideas proper to the intellect—itself the infinite
mode of thought—are ordered according to an eternal order.”’
Proposition VI gives the list of the ten sefyrot. The first sephirah is called
Inscrutable Height (Rom M‘alah), generally referred to by the Crown (Keter); the second,
Wisdom (Hokmah); the third, /ntellect Binah); the fourth, Generosity (Hesed); the fifth,
Strengh ( Pahad or Gevurah); the sixth, Beauty (Tif eret), the seventh, Victory (Necah); the
eighth, Splendor (Hod); the ninth, Foundation of the World (Yesod); and the tenth, called
Righteousness (cedeq) by R. ‘Azry’el,”® and was later named Kingship (Malkut).””
4. INFINITY AND THE NOTION OF UNITY
The Eyn Sof is expressed only through the sefyrot, the first of which, Keter (Crown),
constitutes the primordial thought (mahshavah qedumah) in which all subsequent
determinations are anchored since thought is the root (ky ha-mahshavah hy’ shoresh).'° R.
Mosheh Cordovero emphasizes that the Emanator (Ha-Ma’acyl) thus gives vitality to all
existing beings (mehayeh kol ha-nimc’aot).'°' He states as follows:
"The chain (hishtalshelut) from existing to existent, from the Eyn Sof to the Sefvrah
Keter (Crown) is not to be found in the Eyn Sof Himself, God forbid, since He is not subject
to any chaining. The chain is found only in (from) the existence of the Keter."' This sefyrah
constitutes the first effect of the process of chaining or emanation, of which the Eyn Sof is
indeed the origin, but the Eyn Sof is by no means reduced to this sefvrah. This one mediates
between the infinity of the Eyn Sof and the finite worlds, and all this is made possible because
the Keter is both infinite, like the Eyn Sof, thus being qualified as "nothingness" (’Eyn),'° but
it is also subject to finite determinations. As Rolland Goetschel points out, if the Keter is co-
eternal with the Eyn Sof, this does not mean that they are identical.'!°* This conceptuality
°R. Abraham ben Aleksander mi-Cologne (XIII th century), Keter Shem Tov. Reedition, Amsterdam, 1816,
p.6a
4 Spinoza, Ethics, Il, 7
°° A. Matheron, Idée, idée d’idée et certitude dans le Tractatus de intellectus emendatione et dans |’Ethique. Jn
Etudes sur Spinoza et les philosophies de |’4ge classique. Lyon, ENS Editions, 2022, pp.532-533
°° C. R. Bowman, Spinoza's Idea of the Body. Jdealistic Studies. 1, 3, 1971, p.263. This author (p. 264) also
refers to Stuart Hampshire, remarking that the passage from an illogical association of ideas to a coherent form
has no equivalent in the world of extension. S. Hampshire, Spinoza. Baltimore, Penguin Books, 1965, p.126.
°7L. C. Rice, Paradoxes of Parallelism in Spinoza. Iyyun, 48,1999, pp.48-49
8 R. ‘Azry’el Migyronah, By‘iur 'Eser Sefvrot, pp.40-43
»° Cf. R. Yosef Gikatilla, Sefer Sha'arey ’Orah, Sha'ar II. Reedition Warsaw, 1842, p.46
100 R. ‘Azry’el, Y. Tishby (Ed.), Perush ’Agadot, Jerusalem, 1945 p.82
101 R. Mosheh Cordovero, Sefer Shy ‘iur Qomah. Reedition, Warsaw, 1883, p.49b
102 R. Moshe Cordovero, ‘Eylymah Rabaty. Reedition, Jerusalem, 1974, p.52b
103 Ha-Gra, Yahel ’Or. Wilna, 1882, p.12
104 R. Goetschel, Meir Ibn Gabbay, Le discours de la Kabbale Espagnole. Louvain, Peeters, 1981 p.125
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allows to establish the genetic links, original and persistent, between the divine Infinite,
which always remains transcendent, and the finite worlds. It shows how the manifestation of
the Eyn Sof in the sefvrot answers the question of how the infinite can produce the finite.!°
As I pointed out earlier, Spinoza was never able to deduce the finite from infinity. He posited
that finite modes are produced by infinite substance, but he did not explain how it produces
them.!°
In fact, in line with Emmanuel Levinas' distinction between infinity and totality,!°’
Gilah Kletenik has shown that it is the assimilation of the infinite to the totality that allows
Spinoza to establish immanence and consequently to forbid all transcendence. Contrary to the
traditional conception of God, which derives the infinite from the One, Spinoza's immanence
maintains that the divine substance being infinite, it cannot then be one. Although Spinozism
is generally referred to as monism,!” unity for Spinoza is always contingent. In the Cogitata
Metaphysica V1, Spinoza criticizes the so-called transcendental terms, which are taken by
almost all metaphysicians as the “most general affections of the being" (generalissimis Entis
Affectionibus).'°° The first of these expressions is the "One" (Uno) and the "Unity"
(Unitatem) which designate nothing real outside the intellect. They are only "modes of
thinking" (modum cogitanti), allowing one thing to be separated from other similar things.!!°
As I mentioned earlier, according to Spinoza, God cannot be called One insofar as by such a
numbering we posit Him as similar to other beings. And it is only to avoid thinking that
“there can be more than one being of the same nature, that God is then called unique”
(concipimus ejusdem naturae plures esse non posse, unicum vocari).''' In fact, this
devaluation of the One and the Unity is a consequence of Spinozist immanentism. If reality is
conceived as the product of a Being who is One, and posited as being separated, then this
Being is absolutely above the totality of other beings. This conception necessarily establishes
a hierarchical relationship, which then implies the transcendence of God.''”
Spinoza has often been considered an intransigent supporter of unity and therefore
close to the Kabbalah. Thus, according to Friedrich Heinrich Jacobi (1743-1819), Spinoza
replaced the emanating notion of Eyn Sof (infinite) with the immanent notion of causa sui,'!3
by describing Kabbalah as "undeveloped or newly confused Spinozism."!'* Solomon
Maimon (1743-1800) corrected this qualification, specifying that Kabbalah is in fact "nothing
other than an extension of Spinozism."'!> Spinoza seems to have known the theory of the
sefyrot from the commentary on the Torah by R. Menachem Recanati (1223-1290) that he
% T. Lévy, Figures de l’infini. Les mathématiques au miroir des cultures. Paris, Seuil, 1987, pp.184-185
° M. Gueroult, Spinoza I, p.327
°7 B, Levinas, Totality and Infinity: An Essay on Exteriority, Alphonso Lingis, Pittsburgh: Duquesne University
Press, 1969, pp.21-22
8 Cf. P. Goff (Ed.), Spinoza on Monism. Houndmills, Basingstoke, Hampshire, Palgrave-Macmillan, 2011
9 Spinoza, Cogitata Metaphysica, VI, G. 1. 245
10 Spinoza, Cogitata Metaphysica, VI, G. 1. 245
"| Spinoza, Cogitata Metaphysica, V1, G. 1. 246
Gilah Kletenik, To Infinity, Not Beyond: Spinoza's Ontology of the Not One. In G. Dynner, S. Heschel, and
S. Magid (Eds), New paths in Jewish and religious studies: essays in honor of Professor Elliot R. Wolfson. West
Lafayette, Indiana: Purdue University Press, 2024, pp. 419-440.
3 F. H. Jacobi, The Main Philosophical Writings and the Novel Allwill, G. di Giovanni (Ed. and trans.),
Montreal and Kingston, McGill-Queen's University Press, 1994, p.188
'4 BH. Jacobi, The Main Philosophical Writing and the Novel Allwill, p.234
15 §. Maimon, Autobiography. Y. Y. Melamed and A. Socher (Eds) translated by Paul Reitter. Princeton,
Princeton University Press, 2018, p.58
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owned,!!® as well as from the work of R. Yosef Shlomo Delmedigo, Macref Lahokmah,''’
which he also owned. However, against the tradition that links the infinite to the One,
Spinoza maintains that it is precisely because substance is infinite that it is not one. This
devaluation of uniqueness extends to the realm of finite modes, so that not only naturing
nature not one, but natured nature remains multiple.'!* In fact, Spinoza's inability to deduce
the finite from infinity stems from the identification of naturing nature with natured nature,
although he sought to distinguish between them. As Martial Guéroult maintains, it is the
same nature which is qualified as “naturing” and “natured,” according to the active and
passive forms of the verb naturare. The modes, which cannot be conceived without God, are
ultimately God Himself, for all that is in God, which are the modes, is God.'!? This is why
these two natures are the two sides of the same coin,'”° and according to Marx W. Wartofsky,
substance is ultimately identical with the infinity of its modes, because this infinity remains
dependent on its finite modes. !”!
5. SEFYROT AND NUMBERS
The Sefer Ye¢gyrah posits that the world was created through three sefarym: sefer
(book), sfar (number) and sypur (word).'”? It specifies that the sefyrot are ten, in relation to
man’s ten fingers, five regarding five (hamesh keneged hamesh). '*? Finally, it indicates that
the ten sefyrot are meaningless (bly mah), and that they are infinite (’eyn lahem sof).'** The
Sefer Yecyrah associates the ten sefvrot with the twenty-two letters of the Hebrew alphabet,
in order to present the thirty-two wonderful paths of Wisdom (shloshym we-shtaym netyvot
pely’ot hokmah).'*> The twenty-two letters will admit an almost infinite number of
combinations and arrangements, thus representing all possible conceptions of the mind, and
of the words.'”° The numerological interpretation of the notion of sefvrah has been adopted
by many commentators.!?” As Ithamar Gruenwald points out, the term sefyrot is only a
variant of the term sefurot, (those counted).'** This is why the ten sefyrot constitute the
"fundamental numbers" (ha-misparym ha-yesodyym),'”? and the term sefyrot can then be
'6R. Menachem Recanati, Bi’yur ‘al ha-Torah. Second Edition, Venice 1545, p.172b
'TR. Yosef Shlomo Delmedigo, Macref Lahokmah. In Ta ‘alumot Hokmah, Basel, 1629, p.6a
'8 G. Kletenik, To Infinity, Not Beyond: Spinoza's Ontology of the Not One. In G. Dynner, S. Heschel, and S.
Magid (Eds), New paths in Jewish and religious studies: essays in honor of Professor Elliot R. Wolfson, p.434
'°M. Gueroult, Spinoza I, p.345
20M. Gueroult, Spinoza I, p.267
21M. W. Wartofsky, Nature, number and individuals: Motive and method in Spinoza's philosophy, Inquiry. 20,
1-4, 1977, p.460
2 Sefer Yecyrah I, 1
3 Sefer Yecyrah I, 3
4 Sefer Yecyrah I, 5
25 Sefer Yecyrah I, 1
26 P. Mordell, The origin of letters and numerals according to the Sefer Yetzirah. Philadelphia, P. Mordell, H.
Fleischmann, 1914, p.12
7 Giulio Busi refers to Lazarus Goldschmidt, Philipp Bloch, Leo Baeck, Philip Merlan, Ithamar Gruenwald
and Shlomo Pines, among others. However, Giulio Busi proposes to interpret the notion of sefvrah as an "act of
writing". G. Busi, Engraved, Hewed, Sealed. Sefirot and Divine Writing in the Sefer Yetzirah. In Mehqarey
Yerushalaym beMahshevet Israel, 21, 2007, pp.3-4.
'28 1. Gruenwald, Some Critical Notes on the First Part of Séfer Yezira. Revue des Etudes Juives, 132, 4, 1973,
p/484
129 Y. Liebes, Sefer Yecyrah ’ecel R. Shlomo ’Eben Gabyrol u-perush ha-shyr "'ahavatyk". Mehqarey
Yerushalym Bemahshevet Israel. 1, 3-4, 1983, p.95
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translated as numbers.'*° From an arithmetic point of view, Jewish thinkers have given the
number One, represented by the letter aleph (&), a special status. According to R. Abraham
Ibn Ezra (1089-1167), the One is the cause of all numbers and that is why it is not itself a
number (hyot ha-’ehad sibat kol ha-mispar we-’eynneno mispar). Therefore, referring to the
Sefer Yegyrah, R. Abraham Ibn Ezra adds that the number ten, which is the equivalent of the
One for decimals, is also not a number. While initiating the series of decimals, the number
ten is called "bly mah," that is what it is devoid of numerical determination, but it always
implies the numbers that follow it (raq ‘aher ‘imo).'3' In this sense, the One, and therefore
also the ten, counts itself and no other number can count it (ha-’ehad sofer ‘agmo we-’eyn
‘aher sofro).'** Therefore the One resembles substance (ha-’ehad domeh la-‘ecem),'** and R.
Abraham ibn Ezra has given it an absolute character. !*4
The Gaon of Wilna (Ha-Gaon Rabeynu 'Elyahu, 1720-1797), who wrote a treatise
on trigonometry,!*> emphasizes that the One does not belong to numeration (hu' had we-l'o
behushban'a),'*® because it is the root of number (shoresh ha-mispar).'*’ Contrary to
Spinoza, and before Frege, the Gaon of Wilna emphasizes the purely abstract characteristic
of number: "apart from number there is no other thing found solely in thought" (‘evn davar
ba ‘olam she yhye bemahshavah_levad raq ha-mispar). He specifies, as R. Abraham Ibn Ezra
did, and as I have reported above, that the One, designated by the letter aleph (x), is not a
number. Indeed, all numeration begins with the number two, while the & is numbered only
after it has been included in the two. He also notes that, on the one hand, numeration
concerns only the sequence of numbers beginning with the number two (kehaknys bemispar
raq davar sheyesh lo sheny). But on the other hand, he explains the question of the Sefer
Yecyrah: "Before the One, what can you count?" (Lifney ’ehad mah ’atah sofer?), by the fact
that the One, while not itself a number, nevertheless associates itself (shituf) with the number
two. The antecedent of the One refers to the purely spiritual world called Primordial Adam
(‘Adam qadmon), which is entirely transcendent to any process of numeration.'** The One
remains insensitive to multiplication and division (’eyno mitrabeh we’eyno mithaleq).
Number is purely conceptual and knows no end (queg¢) or limit (taklyt), but it is endowed
with a differentiating power. It is through it that it is possible to distinguish one thing from
another thing (devar ha-nispar nivdal ’ehad mihavero), and numerical differentiation exists
only in thought (ha-mispar ’eyn hevdel nykar ’el’a bemahshavah). The number is totally
infinite (ha-mispar 'eyn lo ge¢ we-taklyt le ‘olam).
3°, Kalisch, Sefer Yetzirah. A book of Creation. The Jewish metaphysics of remote antiquity. New York, I. H.
Frank & Co., 1877, p.6
31. R. Abraham Ibn Ezra, Sefer Ha-shem. Fiirth, D. I. Ziirndorff, 1834, pp.5a-5b. Sefer Yecyrah, 1, 2. In his
mathematical work, Sefer ha-mispar, R. Abraham Ibn Ezra also refers to the ten sefvrot of the Sefer Yegyrah. R.
Abraham Eben Ezra, Sefer ha-mispar. Berlin, M. Zilberberg, 1895, p.1.
32. R. Abraham Ibn Ezra, Sefer ha-’ehad. Odessa, S. Pinsker (Ed.), 1867, p.1; Y. T. Langermann and S.
Simonson, The Hebrew Mathematical Tradition. In H. Selin (Ed.), Mathematics Across Cultures The History of
Non-Western Mathematics. Vol. 2, Dordrecht, Kluwer, 2000, p.168.
33. R. Abraham Ibn Ezra, Sefer ha-’ehad. p.5, note 7
34M. Olitzki, Die Zahlen Symbolik des Abraham ibn Ezra. In E. Hildesheimer and D. Hoffman (Eds.).
Jubelschrift zum siebzigsten Geburtstag des Dr. Israel Hildesheimer. Berlin 1890 p.102
35 Ha-Gr'a miWilna, Sefer ’Ayl meshulash. Wilna, 1833
36 By’ur Ha-Gr'a ‘al Tyquney Ha-Zohar. Wilna, 1867, p.138a
37 By’ur Ha-Gr'a ‘al Tyquney Ha-Zohar, p.3b
38 Perush Ha-Gra ‘al Sefer Yecyrah, VII, 8, and Perush Pery Itshaq ad locum. Reedition, Jerusalem, 1965, p 10a
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In the same way, the sefyrot are called numbers (/ashon mispar), and they belong
only to thought (raq bemahshavah).'*? As I mentioned, the sefyrot remain meaningless (bly
mah),'*° that is, they are properly indeterminate, because the meaning or nature (mahut) of a
thing always implies a differential and determinate relation to other things (ky ha-mahut
nivdal ’ehad mihavero). Numbers and sefvrot do not differ in their essence (’eynam nivdalym
be‘egem), but only by the objects and situations to which they refer. Regarding specifically
the number, the Gaon of Wilna stressed that it should not be confused with the numbered
things. When the number and the thing numbered become separated, the number assigned to
them at the time of the numbering is no longer identifiable as such (kash-ytpardu ’eyno nykar
my hu’). The number is itself unlimited because it is always possible to count to infinity
(lispor ‘ad ’eyn sof), and the infinite itself does not have any part (heleq) since the part is
finite.'4! The sefyrot are also devoid of end and limit (’eyn lahem sof we-taklyt), since they
also exist only in thought.!*? According to Phineas Mordell, the expression characterizing the
sefvrot as "nothing" (bly mah), implies that originally the text must have had ‘Eser sefvrot u-
bly mah: ten digits and zero, which explains the fact that the ten sefyrot are capable of
expressing all numbers.'*? This enables to identify the different levels of infinite spiritual
worlds, in a stratified way, which allows a continuity between the infinite origin and its finite
productions.
It is only through the notion of Tsimtsum that it is possible to distinguish God from
the universe.'*4 In Cantorian terms, the Tsimtsum enables to differentiate between the
absolute Infinite and the transfinite, distinguishing between the realms of infinity that are
humanly accessible, and those that are not.'4? Therefore, no inquiry can be made into the
essence of Eyn Sof,'*° and no thought can relate to it (‘eyn lahshov bo klal), for the divine
unity cannot be the object of any qualification (’asur lekanot bo).'*’ Thus, the Zohar states:
"You are One but outside of all account (’ant had we-l’o behushban)."'*® Similarly, for
Maimonides, the divine Unity, expressed by the term One (’Ehad), does not in any way
denote a species that would contain many individuals (ke myn sheu’ kolel ‘ahadym harbeh),
nor the unity of an organism (guf) that would bring together a multiplicity of parts, but it
refers to a unification (iyhud), which remains ontologically heterogeneous to any created
unity.'4? R. Yosef ’Albo notes that complete Unity (ha-’ahdut ha-gmurah) concerns only
God, the type of unity of which is entirely different from that of number, for nothing can be
associated with God, or compared to Him.'°® This is why R. Mosheh Cordovero and the
39 Ha-Gr'a miWilna, Yahel 'Or, 6b
40 Sefer Yeyrah, I, 2, p.Sa
41 Ha-Gr'a miWilna, Liqutey Ha-Gr’a. In Sifr’a Digny’ut’a. Wilna, 1912, p.38 a,
# Ha-Gr'a miWilna, Yahel 'Or, 6b
*® P. Mordell, The origin of letters and numerals according to the Sefer Yetzirah. p.21
44 J. J. Rozenberg, Spinoza and Kabbalah: convergences, Divergences, and their Theoretical Implications.
Journal of Religion and Theology, 6. 11. 2024, pp.59-80
45 N. Horwitz, Reality in the Name of God. Scotts Valley, CreateSpace, 2012 pp.102-104 and p.106; S. Glaz,
Mathematics in the Poetry of Sefer Yetzirah. Bridges Conference Proceedings, 2021, p.40.
46 R. ‘Azry’el, Derek ha-’Emunah we-derek ha-kfyrah. In G. Scholem (Ed.), Srydym hadashym miKitvey R.
‘Azy’el MiGyronah, p.207
47 Ha-Gr'a miWilna, Liqutey Ha-Gr’a. In Sifr’a Digny’ut’a. p.38 b
48 Petah ‘Elyahu, ha-mevo’ar. Beyt Shemesh, Mif‘al ha-Zohar ha-‘olamy, 2011, p.3
Maimonides, Hilhot Yesodey Ha-Torah, 1, 7. Leibniz took up Maimonides' thesis of the non-numerical unity
of God. AK, VI, IH, 477. Cf. O. Nachtomy & T. Levanon, On Oneness and Substance in Leibniz's Middle
Years. The Leibniz Review. 24, 2014, pp.69-91.
°R. Yosef 'Albo, Sefer ha- ‘iyqarym, Il, 10
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Maharal of Prague have both specified that the divine unity is in no way like the cardinal one
(ke’ehad ha-manuy), which would necessarily imply a numerical sequence: "He is One and
has no second (hu’ ’Ehad we ’eyn sheny lo)." The divine unity is purely spiritual because it
belongs to the higher world (‘olam ha-‘elyon), whereas the number concerns only the world
of the multiple and of separation (‘olam ha-pyrud).'*! Unlike Spinoza, who posited the divine
attributes as being "really distinct (realiter distincta),"!** Maimonides opposed the real
distinction of attributes, as being properly incompatible with the notion of divine simplicity:
the person who would believe that that He is One (’Ehad), but at the same time possesses
many attributes (ba’al te’arym mispar), would express by his word that He is One, but in
thought he would believe Him to be multiple.!* As R. Itshaq Abrabanel's commentary on
this passage from Maimonides points out, the idea of multiplicity of attributes necessarily
implies the notions of materiality and corporeality, which are incompatible with the notion of
divine Unity.'** This is the reason why, Spinoza admits that he does not "understand why
matter would be unworthy of the divine nature (cur [materia] divina natura indigna esset),"
since it is granted eternity and infinity.'°° That is why he posits: Deus est res extensa.'*° Such
a determination, which in fact constitutes the only alternative to the idea of creation, and to
that of Tsimtsum (contraction) that it implies, makes necessary, within the framework of
Spinozism, the corporeality of God, as being in conformity with the pantheistic affirmation:
quicquid est, in Deo est.'>'
It should also be noted that the 7’simtsum, by allowing the emergence of the finite,
also determines the relationship of otherness that is expressed in the ontological difference
between the transcendent Creator and His creatures, which Spinoza's immanentism had
sought to suppress. This distance of otherness, which makes language itself possible,
according to Lacan,'** also initiates the process of naming the divine.'*?
6. THE NAMING OF THE EYN SOF
If the name Eyn Sof may evoke the idea of infinity, its real reference remains
unassignable, although this name aims to make it accessible to man.'®’ As R. Me’yr Ibn
Gabay quotes, the "root of all roots" does not itself have a name (shoresh kol ha-shorashym
‘eyn lo shum shem)."°! In this sense, R. Mosheh Cordovero specified that the term infinite
'S!_R. Moshe Cordovero, Sefer Pardes Rimonym, IV, 5; Maharal, Hydushey ’agadot, Sotah 7b. As Louis
Couturat points out, cardinal numbers derive from ordinal numbers; they likewise imply the idea of relativity
between sets. L. Couturat, Sur une definition logique du nombre. Revue de Métaphysique et de Morale. 8, 1,
1900, pp.26-27.
>? Spinoza, Ethics I, 10, scholium
3 Maimonides, Guide, I, 50, Hilkot Yesodey ha-Torah, 1, 12
4 R. Itshag Abrabanel, Perush ‘al Moreh Nevukym, I, 50. Reedition, Jerusalem, 1960, p.70
>> Spinoza, Ethics I, 15, scholium
© Spinoza, Ethics II, 2
57 Spinoza, Ethics I, 15 ; P. Macherey, Introduction a l’Ethique de Spinoza. La premiere partie, la nature des
choses. Paris, PUF, 2001, p.127
8 J, Lacan, L’éthique de la psychanalyse. Paris, Le Seuil, 1986, p. 84
°° J. J. Rozenberg, Ethique, langage et abstraction selon la tradition hébraique. Revue de Métaphysique et de
Morale. 90, 3, 1985, pp. 362-376
60 J, Zacklad, Pour une Ethique I. De Dieu. Lagrasse, Verdier, 1979, pp.39-41. The term Name (Shem) comes
to designate, in the Pentateuch, the Tetragrammaton, cf. Leviticus 24:11.
6! A. Me’yr Ibn Gabay, ‘Avodat ha-Qodesh. Reedition Lemberg, 1857, p.10a. On the status of the notion of
Eyn Sof in this kabbalist, cf. A. Bar-Asher, Beqadmut ’Eyn Sof: Pyrush ‘Eser sefyrot le-R.David Ha-Kohen
talmyd ha-Rashb’a. Daat, 82, 2016, pp.151-153.
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remains a simple appellation, for lack of a better means of expression: "He is called Infinite
(God) (’Eyn Sof), because all existents have an end whereas He has no end (kol hanimc'aym
sof we-Hu’ ’Eyn lo sof)."'°
In fact, we can conceive naming in a way that is not reductive regarding to the
named being to whom we refer. Such an approach seems to have been first envisaged, in a
mathematical context, by Henri Lebesgue, who introduced, in 1904-1905, the notion of the
"named set,"'® in relation to Cantorian infinity. He then distinguished between existence,
which is logically deduced from non-measurable sets, and the possibility of naming them by
means of finite expressions in order to be able to describe these two different types.
However, this notion of naming gave rise, among several Russian mathematicians of the
early twentieth century, such as Nikolai Lusin and Dmitri Egorov, to a confusion responsible,
on the one hand for a pantheistic drift consisting in identifying God with his Name, and on
the other hand for a polytheistic shift, since His Names are multiple. The proponents of
"Name Worshipping" (Imiaslavia in Russian) found in Lebesgue the idea of "naming" God,
without however defining Him.’ Let us note that Lebesgue had indeed used the term
naming as a synonym for definition, but then in opposition to a reductionist approach to the
divine.'®
Saul Kripke introduced a similar distinction, by separating the proper name, which
designates an individual in all possible worlds, from his or her definite description, which is
always subject to some variations according to circumstances. When we fix the reference of a
proper name, we do not determine, by any limitation, the properties of its reference.' It
emerges from the approaches of Lebesgue and Kripke that the Name may well constitute a
divine attribute, while remaining radically distinct from the Infinite Being that this Name
comes to name.!®’ In this sense, God's designation remains unitary, since it expresses God's
unity without ever reducing it to His Name.!® For Maimonides, the Tetragrammatic Name
refers to the essence of the divine, thus adopting a non-representative approach to reference,
which anticipated the theories of Hilary Putnam and Saul Kripke.'® Indeed, the
Tetragrammatic Name can be understood as the rigid designator of an invariable reference,
allowing us to conceive God in a purely abstract way, without ever perceiving Him
sensorially.'”° These reminders allow us to understand that Spinoza's error consisted in
wanting to identify the essence of God, of an intensional order, with His Name, of an
® R. M. Cordovero, ‘Eylymah Rabaty, p.2b
3H. Lebesgue, Sur les fonctions représentables analytiquement. @uvres scientifiques. Paris, Gauthiers-Villars,
1972, Tome III, p. 16
64 L. Graham & J-M. Kantor, Naming Infinity: A True Story of Religious Mysticism and Mathematical
Creativity. Cambridge Mass. London, The Belknap Press of Harvard University Press, 2009, pp.15-17
65 H. Gispert, La théorie des ensembles en France avant la crise de 1905: Baire, Borel, Lebesgue. . . et tous les
autres. Revue d’histoire des mathématiques. 1, 1995, p.63
6° S, Kripke, Naming and necessity. Cambridge, MA. Harvard University Press. 1980, pp.58-59
67 N. Horwitz, Reality in the Name of God, New York, Punctum Books, 2012, p.73 and pp.166-167
68 M. T. Miller, The Name of God in Jewish Thought: A philosophical analysis of Mystical Traditions from
Apocalyptic to Kabbalah. London, New York, 2016, p.105
6° Maimonides, Guide, I, 61. Cf. E. Z. Benor, Meaning and Reference in Maimonides' Negative Theology. The
Harvard Theological Review, 88, 3, 1995, p.347, note 28.
7 Y. Gellman, Names and Divine Names: Kripke and Gikatilla. In M. Koppel and E. Merzbach (Eds), Sefer
Higayon, Studies in rabbinic logic. Alon Shevut, Zomet, 1995, pp.52-54; S. Kripke, Naming and Necessity,
p.l1; R. Yosef Gikatilla, Gynat ’Egoz. Reedition Jerusalem, Ha-Hayym we-ha-Shalom, 1989, pp.19-28.
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extensional order.'”! Indeed, Spinoza equates Nature with is one of God’s Derived Names:
'Elohym, whose numerical value is the same as the term "the nature" (ha-tev'a). He was most
certainly familiar with this correspondence, as well as with the commentaries of R. Ibn Ezra
and Maimonides on this topic.'”” By reducing the absolute ontological referent to one of Its
Derived Name, he did also reduce the natura naturans to the natura naturata. Then, at the
same time Spinoza corporealized the divine as being a res extensa,'” thus following the
example of Zoroastrianism, which divinized space as an expression of a fusional relationship
with the natural divine.'”4
Another type of encounter between Cantor and the Jewish tradition concerns a
distinction, already proposed by Bolzano, between the notion of equivalence, which can be
applied to infinite sets, and that of equality, which must be reserved for finite domains.'’> The
Talmud explains that the Biblical injunction to follow the ways of the Tetragrammaton ("thou
shalt walk in His ways," (Deuteronomy 28:9) does not concern a relationship of equality
between finite creatures and the infinite Creator, but it implies a relationship of emulation.'”°
According to Maimonides, such an emulation (imitatio Dei) constitutes the only legitimate
framework for expressing, from a human point of view, the divine attributes. What does it
mean to follow His ways? Just as He is called "Compassionate (Hanun)," man should be
compassionate toward his neighbor. Just as He is called "Merciful (Rahum)," each one should
be merciful to the other. Just as He is called "Holy" (Qadosh), every individual should aspire
to holiness.'’” For Gersonides the notion of imitatio Dei must stimulate everyone’s desire to
perfect others, which constitutes the greatest of perfections.!”*
For Maimonides, the notion of emulation allowed the prophets of Israel to describe
divine actions in order to set out the rules of behavior by which man must imitate God,
without ever pronouncing on His essence.'!” This is why, beyond the tension between the
infinity of the divine intellect and the finitude of the human intellect,'®° man’s cognition
remains capable of knowing the Names of God that designate His actions in the world. This
suggests the impossibility of accessing, as Spinoza claimed, the domain sub specie
ceternitatis,'*! because such an attempt always uses a language that necessarily remains
temporal in nature and then contradicts this claim.'®”
This is precisely what Cantor sought to establish when he pointed out that there is no
Genus supremum of the actual infinite, because that which surpasses the finite and the
™ On the importance of the notions of intension and extension in the formation of Spinozism, see J. J.
Rozenberg, Spinoza, Spinozism and the Foundations of Secularization. pp. 38-39.
?W. Z. Harvey, Idel on Spinoza. Journal for the Study of Religions and Ideologies. V1, 18, 2007, p.90
® Spinoza, Ethics Il, 2
™ J. A. Montgomery, "The Place" as an Appellation of Deity. Journal of Biblical Literature. 24, 1, 1905,
pp.21-22
8 Cf. A. Koyré, Etudes d'histoire de la pensée philosophique. Paris, Gallimard, 1971, pp.26-28
% Deuteronomy 13:5; Shabat 133b; Sotah 14a; Syfry ‘Eqev 49.
™ Maimonides, Hilkot de ‘ot, 1, 6; Hilkot ‘avadym, IX, 8; Hilkot Megylah, Il, 17; Hilkot tumat ’ohalym, XVI,
12.
78 Gersonides, Commentary on the Song of Songs, I, 2; cf. M. Kellner, Gersonides on Imitatio Dei and the
Dissemination of Scientific Knowledge. The Jewish Quarterly Review, New Series, 85, 3/4, 1995, pp.284-285.
Gersonides thus expressed an idea developed by the Kabbalists, of the purpose of creation as concern for the
good of the other. Cf. R. Moshe Cordovero, Me’or Moshe ‘al Sefer Shomer Ha-Pardes. Bney Braq, 1996, p.213.
Rambam, Hilkot de’ot, I, 5-6
180. Kreisel, Imitatio Dei in Maimonides' "Guide of the Perplexed". AJS Review, 19, 2, 1994, p.180
'81 Spinoza, Ethics V, 23, scholium
182 A Kojéve, Introduction a la lecture de Hegel. Paris, Gallimard, 1947, pp.351-354
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transfinite cannot be described in terms of genus. The absolute infinite constitutes a singular
unity totally inaccessible to man; he is the Actus Purissimus which is called God.'™
CONCLUSION
This article has sought to understand the nature of the relationship between, on the
one hand, the Cantorian notions of absolute infinity and the transfinite, and on the other hand,
the Kabbalist notions of Eyn Sof and sefyrot, by confronting them with the Spinozist
concepts. The notions of substance and infinite attributes have often been associated with
these Kabbalist notions. I have analyzed the significance of Adolph Jellinek's project, to
present the essential notions of R. ‘Azry’el of Gerona’s Kabbalah, in the more geometrico
form which is specific to Spinoza's Ethics. I then showed the fundamental differences
between these two approaches, particularly concerning the notions of infinity and divine
unity. I then examined the abstract status of number in Jewish commentators such as R. Ibn
Ezra and the Gaon of Wilna, who posited the equivalence between the notions of number and
sefyrah., Finally, I analyzed the post-Cantorian theory of naming, showing that it agrees, on
the one hand, with the negative theology of Maimonides, and on the other hand with the
semantics of Saul Kripke.
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CANTOR, THE KABBALIST SEFYROTIC SYSTEM, AND SPINOZISM
Jacques J. Rozenberg