Appendix:  Logical Set Theory And The Lurianic Tarot

In the study of any mystical tradition, one is almost certain to learn of secret relationships between sets of information which superficially may seem unrelated. In encountering these relationships in study, often the student will notice a logical, coherent pattern or progression. Seldom is a mystical tradition entirely devoid of sensible correlations between set elements, even if their immediate significances cannot be immediately determined. In pursuit of the truth, one may encounter within the same mystical tradition different systems which attempt to explain these relationships differently from each other, while tending to agree regarding general understandings about the tradition. An excellent example can be cited within the realm of astrology, in which the twelve signs of the zodiac are thought to be somehow related to other duodecads (sets of twelve) such as the twelve Christian apostles, the twelve ‘lesser’ prophets of the Hebrew Scriptures, or the twelve tribes of Yisra’el (actually, the list goes on). No existing mystical traditions would denounce this as untrue, even if they cannot collectively agree on exactly how these sets are related.

Here for the student lies the daunting task of exploring the various mystical systems within a tradition (e.g., Kabbalah) to secure the most appropriate (and hopefully, verifiable) trend within that tradition to explain the relationships between various sets (e.g., four elements of m [Fire], , [Water], . [Air], / [Earth]; seven astrological planets, &c.). It is also important for the student to be able to recognise when sets are not particularly related, or when the relationship is so complex that continued study becomes counterproductive to our understanding of it. Take here for example the two previously mentioned sets, the four elements and the seven planets. Both of these sets are related to the twelve signs of the zodiac, but each in its own way, and although it is possible to correlate the seven astrological planets with the four elements, the relationship is difficult to define as a coherent or recurring pattern and is significant only within the context of the twelve astrological signs. Removing the astrological element from the equation leaves the student with fragmented bits of information which lead him/her nowhere other than a general polarity between ./? Air-Earth (1 Mercury, 2 Venus, 6 Saturn) and ,m Water-Fire (4 Mars, 5 Jupiter), with 0 Sol (m Fire) and 3 Luna (, Water) left over. Without the framework of the twelve astrological signs, we have no useful, discernible or coherent (or recurring) pattern here.

In my own kabbalistic studies, I have attempted to formulate a general understanding regarding the correlation of different information sets; a corollary, as it were, to help in explaining how known sets of information are associated, so that this same organisational method can be applied to other newer sets of information encountered later. This system of relationships is what binds all of these things together in a mystical system. If a set of information cannot be incorporated as relevant in some way within an existing system, that set of information cannot be easily added to the mystical tradition to which that system belongs. A rather far-fetched, but illustrative example can be seen in the hypothetical inclusion of a foreign mystical trend, such as the divination with cowrie shells in the African Yoruba mystical system, into the realm of Kabbalah. Even if someone were to study both systems, there is no assurance that anyone may be able to accurately and properly correlate them; they are altogether foreign to each other. This, of course, does not purport that one is ‘good’, while the other is ‘evil’; rather, it simply means that either some systems are incomplete in the information which they present (relative to others), or that the respective systems are based on different fundamentals. It’s much more far gone than trying to compare apples with oranges; it’s much more akin to comparing apples with jalapeños! Both are seed-bearing fruit, but that is about the extent of their similarity.

The most important tenet in my whole philosophy is almost affable in its presentation: Keep It (as) Simple (as Possible!). I have encountered students of mystical systems who did everything mortally possible to complicate their study (generally lacking in consistency), only to laugh when it is suggested that simplicity should be their key. Here are some secondary understandings which have proven very helpful in my grasp of Kabbalah:

  1. Part of ‘keeping it simple’ is grasping for logic when trying to unlock the relationships in a mystical system. People often believe that mystical relationships are inscrutable in their complexity, quickly forgetting that the mystical traditions were created by Man for Man, not by God or for God. Logic is an integral part of mystical study, as it serves as the secret foundation for all of human understanding. Why then should logic be thrown out the window when someone opens oneself to mystical study? Grasp Logic!
  2. Don’t wait for an epiphany to happen along and knock you upside-the-head to catch your attention. Mystical study is not about chasing down epiphanies; certainly, one encounters them throughout mystical study, regardless of tradition, but they should not be the sole reason for engaging in such studies. Our attention turns to the Divine Commandments to love God with all we are and with everything we have, and also to love and help each other. It is difficult to see how sequestering oneself in a study and hiding in a book or a scroll might help us fulfill either of these two greatest of commandments, but as we become better students, we prepare ourselves for the day when the younger generation comes to us with questions about spiritual matters. It is the pursuit of these same studies which allows us to solidify our own convictions regarding the Divine Mysteries whose understanding we crave, enabling us to more capably and confidently answer our children when they ask probing questions regarding God’s relationship with them or with mankind in general. Don’t engage in mystical study for its own sake; rather, pursue its understanding to empower you spiritually for the time when you are called as a teacher or counselor.
  3. Prayer vs. Meditation. Some have difficulty separating these two activities; I believe this may be due to the failure of our society to accurately define the difference between them. Prayer is a vital factor in the life of any believer, and certainly moreso in the life of a student of the Faith, but meditation is a much more valuable activity for purposes of ‘probing the æthyr’, as some may prefer to call it. I prefer to think of the meditative experience as less of an incursion into the ‘astral plane’ [sic], and as more of a detachment from oneself and attachment to the Creator. Additionally, while methods of prayer generally tend to be established more or less with influence from spiritual leaders, meditation is a much more private and personal thing, and there are perhaps as many meditative techniques as there are people meditating. Prayer serves us as a method of exocentric communication with the Creator, but meditation is really more of a method of endocentric communication with the Creator through oneself. I cannot stress the value of engaging in meditative activity; it provides for some an excellent technique for self-examination, provided the individual can be honest with oneself, and this is the key to unlocking the secret of one’s place and purpose. This text does not expound on meditative techniques, neither does it uphold any particular method; it is only mentioned here as a vital element in mystical study.

As a result of my own kabbalistic studies, I have encountered various traditions within the system of Kabbalah which present much the same information, but formatted differently and/or with different esoteric correlations between data sets. An excellent example of different traditions within the same system is brought to light in the examination of the interrelation between the twelve Yisra’eli tribes and the twelve signs of the zodiac. Most mystical traditions will agree that the two sets are somehow esoterically related, although few would agree on the actual associations between them: the Masonic organisations accept one particular order of associations, while an hermetic order may uphold an entirely different order of associations. A kabbalist may disagree with both of these understandings, having formulated yet a different set of meaningful associations. Which of the three is ‘correct’? More importantly, how does one defend what one believes to be an accurate understanding of such relationships? This text will approach such relationships from a logical, analytical point of view. The reader would also do well to remember that in cases where a particular system embraces an understanding without deviation, that understanding should be upheld more frequently than it is questioned: the presumption is that if an entire system agrees on an article of faith or in a point of exegetical or homiletical study, then the unity of that system usually validates such a tradition.

It is this search for Truth among the many and varied mystical trends within the kabbalistic tradition which results in one particular trend being identified as ‘correct’ above the other contending trends. In fact, one may wonder how a singular tradition could be responsible for so many different trends concerning associated information sets. Keep in mind, however, that these different trends were usually formulated by the popular school(s) of thought, each in a certain part of the world and active during a particular generation or generations, and although today we enjoy a vast network for sharing information, these mystical relationships were guarded as secret (and may still be, even today) and not shared abroad, even between students of different schools within the same basic tradition. This lack of publication generally means that unless different trends have a common root influence, they are likely to formulate different understandings regarding esoteric relationships. I have compiled some basic axioms regarding logical set theory (discrete math) to be used in identifying what type of correlations should or might exist between different data sets:

  1. A set is defined as a collection of elements which exists as a constituted whole (e.g., the set of the twenty-two Hebrew letters, the set of the four kerubic elements).
  2. A subset is a group of elements found in a parent set. A subset is identified with the parent set because it contains only elements found in that parent set.
  3. A set can be a subset of itself or of a larger set; a set can never be a subset of a smaller set (one which contains fewer elements).
  4. Two or more elements in a single set which are identical are actually one and the same set element (e.g., in the mathematical set of rational numbers, 1/5, 0.2, and 3/15 are mathematically equivalent and therefore would actually be a single set element and not three).
  5. The null set {Ø} is empty and contains no set elements.
  6. The union of two or more sets or subsets results in a new (larger) set which includes all elements contained in the sets prior to their union (with no duplication of set elements — see rule 4).
  7. The intersection of two or more different sets (or subsets) contains all elements common to all intersecting sets; some intersections consist of no elements (the null set).
  8. An ordinal sequence must maintain the ordinal progression/relationship throughout; ordinal refers to an arrangement of elements into a fixed linear series with respect to some natural ordering (e.g., the order of the seven ancient planetary spheres: 6 Shabbathai [Saturn], 5 Tsedeq [Jupiter], 4 Ma’adim [Mars], 0 Shemesh [Sol], 2 Nogah [Venus], 1 Kokav [Mercury], 3 Levanah [Luna]).
    1. A sequence which contains some ordinal progressions and others which are non-ordinal is classified as wholly non-ordinal (e.g., within the Hebrew alef-beth, the subset of ‘double letters’ in any arrangement is non-ordinal, since the sequence of letters includes alphabetic skips {b (Beth), g (Gimmel), d (Daleth), k (Kaf), p (Peh), r (Resh), t (Taw)}, even though the letters may be arranged alphabetically). Ergo, (b)…
    2. An ordinal subset is a subset composed of entirely sequential set elements (e.g., the series {i (Yodh), k (Kaf), l (Lamedh), m (Mem), n (Nun)} is an ordinal subset of the Hebrew alef-beth.
    3. An ordinal subset exists within any non-ordinal set which includes at least two sequential set elements.
    4. A non-ordinal set composed entirely of non-sequential set elements will never include an ordinal subset.
  9. Regarding the correlation of two or more sets of equivalent size (same number of set elements):
    1. Ordinal progression of association is non-mandatory, even non-preferred. The natural tendency is non-ordinal (e.g., the set of the seven days of the week when compared with the seven ruling planets yields a non-ordinal relationship, with respect to either the ancient/esoteric or modern/scientific ordering of the planets). An esoteric understanding of ordinal relationships between data sets should never contradict previously established relationships. Therefore, the existing esoteric relationship between the seven days of the week and their seven ruling planets is retained as valid because the relationship is derived through non-ordinal (but rather, periodic) associations.
    2. Some sets of equivalent size do share an ordinal relationship; however, these relationships are generally regarded as mundane (e.g., the twelve months of the year vis-à-vis the twelve signs of the zodiac), and are by definition non-mystical in nature.
  10. Regarding the correlation of sets of inequivalent size (different numbers of set elements):
    1. Ordinal progression of association is anticipated, even mandatory. The natural tendency is to associate sets of different sizes in a mutually-ordinal fashion, usually with an apparent repetitive pattern.
    2. e.g., the four kerubic elements m (Fire), / (Earth), . (Air), , (Water) vis-à-vis the twelve signs of the zodiac; the elemental association of the twelve astrological signs follows the repeating ordinal pattern of fire, earth, air, water, fire, earth, air, water, &c.