Four Thinkers and the Torah Codes – An essay on Prophesy
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Four Thinkers and the Torah Codes – An essay on Prophesy Professor Andre Rosenthal [email protected] School of Applied Management and Decision Sciences, Operations Research Walden University, MD USA 1/25/2010
Transcript of Four Thinkers and the Torah Codes – An essay on Prophesy
Four Thinkers and the Torah Codes – An essay on Prophesy
Professor Andre Rosenthal [email protected]
School of Applied Management and Decision Sciences, Operations Research Walden University, MD USA
1/25/2010
Abstract
The first section of this essay will be dedicated to the learning of four thinkers: Maimonides,
Spinoza, Leibniz and Kant. The choice of these four amongst the many is mostly due to the
following criteria of filtering. All these four thinkers where authors whose body of work
included ethics, theology and logic. Additionally the author spring boarded concepts that are in
use by recent researchers and scientists. To culminate, these authors’ influences and
theological treatises played a role in either the advancement or the retraction of the Judeo-
Christian values of Western societies as far as their ability to strengthen the formal methods of
reasoning for the attainment of knowledge is concerned. The aforementioned components of
this essay allowed for a practical application which will be demonstrated at the Application
component. In the Application portion, the hypothesis is presented as, contrary to half the
thinkers set’s logic, there exists a source of information that, correctly analyzed, is capable of
foretelling the future a posteriori. Here the contrast between proving and disproving lies solely
on the boundary constraints of the hypothesis, either setting as true the null-hypothesis, or
reversing the other. Regardless of the boundary constraints, it will be demonstrated that
statistical correlations do prove or not the null-hypothesis beyond a given p-value. As to
correctly enunciate the problem in its entirety, the Application portion looks as what is known
as the Torah Codes and infers the hypothesis that these codes can foretell the future by
noticing the statistical correlations of letters of certain important figures when they are
equidistantly spaced.
TABLE OF CONTENTS
Abstract ........................................................................................................................................... iv
Introduction .................................................................................................................................. 10
Rambam’s philosophy ................................................................................................................... 13
Rambam’s Theological Logic formation ............................................................................ 14
God is the Primal Cause .............................................................................................. 16
On the belief System and Aristotle ............................................................................. 18
On the notion of Prophesy .......................................................................................... 18
Spinoza’s Philosophy ..................................................................................................................... 19
Spinoza’s Theological Logic formation .............................................................................. 21
Spinoza’s Axioms ......................................................................................................... 23
On the Cartesian method and belief system .............................................................. 25
On the notion of Prophesy – Spinoza’s Hermeneutics ............................................... 26
Leibniz Philosophy......................................................................................................................... 28
Leibniz’s Theological Logic formation ............................................................................... 29
Vérités de Raison ........................................................................................................ 29
Vérités de Fait ............................................................................................................. 30
On the notion of Monad ............................................................................................. 30
On the notion of obscurity of Monads ....................................................................... 32
On the notion of Prophesy .......................................................................................... 33
Kant’s Philosophy .......................................................................................................................... 35
Kant’s Theological Logic formation ................................................................................... 36
On the notion to a priori knowledge .......................................................................... 36
On the notion to a posteriori knowledge ................................................................... 38
On Kant’s belief System .............................................................................................. 39
On the notion of Prophesy .......................................................................................... 40
Summary ....................................................................................................................................... 41
Literature Review Essay ................................................................................................................ 42
Literacy Conclusion ........................................................................................................... 44
Practical Application – WRR Algorithm in the nutshell ................................................................ 46
Preliminary Concepts ........................................................................................................ 46
Equidistant Letter System ................................................................................................. 46
ELS Definition and Nomenclature ............................................................................... 47
Compactness of an Array ............................................................................................ 51
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Domain of minimalism ................................................................................................ 52
Explanatory narrative of the Process ............................................................................................ 53
Perturbations over the Arithmetic Progression................................................................ 53
-Perturbed Distances ............................................................................................... 54
Statistical Analysis of ........................................................................................................ 55
ELS Hypothesis – encoded Text versus Monkey Text ....................................................... 56
Findings ......................................................................................................................................... 58
Calibration ......................................................................................................................... 59
Results of List one ....................................................................................................... 61
Conclusion ......................................................................................................................... 62
Author’s opinion about the Torah Codes ..................................................................................... 63
Physical Inconsistencies when compared with an epistemological viewport .................. 64
Logical inconsistencies when compared with an epistemological viewport .................... 65
REFERENCES .................................................................................................................................. 67
APPENDIX A ................................................................................................................................... 71
Gematria ........................................................................................................................... 71
The Absolute Value Algebra (Normative Value) ......................................................... 71
The Ordinal Value Algebra .......................................................................................... 73
The Reduced Value Algebra ........................................................................................ 73
The Integral Value Algebra ......................................................................................... 73
Letter Filling Algebra ................................................................................................... 74
Operations over the various algebras ............................................................................... 75
Ordinal Pairing ............................................................................................................ 75
Reflexivity Properties .................................................................................................. 77
Reflexive Pairing Properties ........................................................................................ 77
Ordinal Triple Properties ............................................................................................. 78
Reduced Reflexive Property ........................................................................................ 79
Reflexive Tuple Properties .......................................................................................... 79
APPENDIX B ................................................................................................................................... 80
Hebrew Equivalence Table................................................................................................ 80
APPENDIX C ................................................................................................................................... 81
C# Code for the ELS algorithm as defined by WRR ........................................................... 81
APPENDIX D ................................................................................................................................... 86
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APPENDIX E ................................................................................................................................... 87
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LIST OF FIGURES
Figure 1: First page of manuscript of Spinoza’s Small Treatise (Wolf, 1905) ............................... 20
Figure 2: subjective v. objective determinations (Kant, 1781) ..................................................... 39
Figure 4: Rambam's title in a cluster with skip 50 (Haralick, 2000) .............................................. 49
Figure 5: a typical cylinder (WRR, 1994) ......................................................................... 50
Figure 6: C(w,w') for calibration pair ............................................................................................ 60
Figure 7: C(w,w') for calibration pair on G and M ........................................................................ 61
Figure 8: snapshot of the ELS program running with the items of the abridged list ................... 62
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LIST OF TABLES Table 1: Hebrew Normative Values for cycle 1 ........................................................................... 73 Table 2: Gematria Tables (Ginsburgh, 2002) ............................................................................... 74
Table 3: Tuple pairing for Ordinal Pairing Operation .................................................................. 77 Table 4: Tuple Ordinal Transformation ........................................................................................ 79
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Introduction
The study of logic is defined as the art and sciences of valid inference aiming towards
the attainment of knowledge for the construction of systems of reasoning. Historians have
traced back societies and their unique systems of reasoning and different cultures produced
singular reasoning systems according to local and tribal traditions. Regardless of their origin,
the reasoning systems attained all seem to point towards a common center of mass, found at
the discourse of man’s origins and its soul’s journey through its existence.
Thales de Miletus (ca. 635 BCE) is considered the first of the Greek masters of logic, a
lineage that progressed for over 200 years until 440 BCE with the beginning of the Socratic
movement. For Thales and his followers the elements1 were the source of man’s origin
therefore detached from any supernatural deities’ authority, a thought clearly in direct
contradiction to Greek mythology. The school of philosophers that followed Thales seems to
gravitate towards that direction, viz., to further detach themselves from a divinity-centric
metaphysics and move towards a natural driven one. It was not until the next mark in the
evolutionary tree of philosophy originated by Socrates that this natural focus lost acceptance.
Socrates was born in 469 BCE and died in 399 BCE. During his long life he wrote nothing, and
most of his knowledge came as a result of Plato, his pupil, and the founder of the famous
Platonic Academy in 387 BCE. Plano said in the name of Socrates that man is obliged to do
what he thinks is right even when confronted by opposing forces, and man’s quest is the pursue
1 It is conjectured that Thales singled water as the source. There is no concrete reason to believe this is true
however, and is mainstream accepted that the elements in question were land, water, fire and air (Gonzales, 2006). 2 This KAM considers the full spectrum of Renaissance philosophy, starting at the 12
th and ending at the 19
th
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of knowledge regardless of consenting or dissenting voices. As Plano narrates in The Apology,
the discourse changes the philosophy route from a nature-bound to an epistemic-bound.
Whereas during Thales man was to find in nature the origins of his decision and being, Socrates
now shows that the origin is nothing else but a discourse on truth, belief, and ethics. As side
effect of this new Socratic origin is noted the paving of a comeback route for theology as
supporting argument for ethical divergences. Western philosophy would continue using this
symbiosis of Socratic analysis and theology support up until the advent of the Renaissance
period2 when a new wave of thinkers came about.
It is however noteworthy to mention that other styles of logic appeared on or before
the times of Thales. These styles were either theological-based or naturalist-base, and most of
them survived the Greek influence with minimal disturbance. Confucius (551 BCE) already
crafted a complex system of ethics based on ancient Chinese systems of reasoning, Buddha
(563 BCE) crafted the logic of monism, and Moses (1390 BCE) crafted the complex system of
laws and ethics known as the Torah. Furthermore it is imperative to note that the last two
protagonists were the founders of major religions, whose foundation lies heavily on logic and
philosophy. This is not to say that religion was immune to the Greek influence. In the realm of
religious philosophy, or of abstract theology, various influences combined to strengthen the
formal methods of reasoning for the attainment of knowledge and the Renaissance was a
theater arena whose protagonist were eager to show their unique influences. Out of the
luminaries of the Renaissance, this essay focuses on a particular set, carved out of the group 2 This KAM considers the full spectrum of Renaissance philosophy, starting at the 12
th and ending at the 19
th
centuries of the Common Era
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according to their influence during and continuation of ideas post Renaissance. The set in
question is formed by four luminaries on the topic of ethics, logic and theology. Their unique
approach, combine with their ability of influence school of followers, assures this essay’s ability
to demonstrate the impact of their epistemology on human knowledge and man’s desire to
predict its course. Concepts such as logic, rationalism, empiricism, knowledge, judgment and
the impact of human experience are explored from the perspective of Immanuel Kant, Baruch
de Spinoza, Moses ben Maimon – Maimonides for shorts –, and Gottlieb Leibniz, four influential
thinkers whose body of work helped understand the foundations of logical or “sound human
behavior”. To facilitate the placement of important in historical periods set the order of the
thinkers by their birth and death dates: Maimonides comes first having lived from 1135 to
1204, leaving a hiatus of 400 years until Baruch de Spinoza (1632 – 1677), Gottfried Leibniz
(1646-1716), and Immanuel Kant (1748-1804). A clever reader would notice the climax of rivalry
between these thinkers, noticing their lifelong battle trying to disprove another.
The remainder of this section will be dedicated to the learning of these four thinkers.
The choice of these four amongst the many is mostly due to the following criteria of filtering. All
these four thinkers where authors whose body of work included ethics, theology and logic.
Additionally the author spring boarded concepts that are in use by recent researchers and
scientists. To culminate, these authors influenced and theological treatises played a role in
either advancement or retraction of the Judeo-Christian values of Western societies as far as
their ability to strengthen the formal methods of reasoning for the attainment of knowledge is
concerned.
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Henceforth, Kant’s Critiques falls under all three items above as depicted by the Breadth
area of this essay. Spinoza theist vision clearly checkmarks two of them; as for third one, it is
worthwhile to note Einstein’s acceptance of Spinoza’s God in various correspondences3. As for
Leibniz, his clear confrontation with Spinoza’s theism views solidifies the checkmark of each
criterion above. Lastly, Maimonides, hereinafter called by his Rabbinical name of Rambam4, was
a Rabbi and author of a gamut of theological and logic treatises on the logic of Torah and
transcendental aspects of Kabala aiming towards the explanation of prediction of events. To
finalize it is interesting to notice that these four thinkers all share a common pillar, founded on
the theories and ideologies of Rene Descartes. This particular fact would come back at this
section when their divergent Cartesian views are explored.
Rambam’s philosophy
The Rambam was born in Spain in 1135 and died in Egypt in 1204, begun his writings in
the same fashion of his predecessors, viz., with a commentary of the Torah. Following the
footsteps of Rashi5, Rambam first published a treatise on Jewish Law, called Mishneh Torah,
where he crafted the thirteen principles of the Jewish Faith, and dedicated the remainder of its
contents to the explanation of the 613 obligations as defined by the Jewish canon. Of interest
3 I am not dedicating a large amount of supporting evidence to this fact simply because it is well known that
Einstein referred to his God as Spinoza’s God in many a correspondence. 4 Rabbinical names are derived from the first two letter of the word Rabbi, Ra, followed my their first initial ,
middle and last name letters – consequently Moses Ben Maimon yields Ra + M + B + M , or Rambam for shorts. All great Rabbis are mentioned by their rabbinical names, and a foot note will be posted to enunciate their common names whenever needed for clarification. 5 Rabbi Shlomo Yitzhaki (1040-1105) is the author of one of the most comprehensive commentaries of the torah,
and the direct linage patron of over 200 years of successive torah commentaries, both by his sons in law, and later by his grandsons.
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to this section is book number one. In there, little to no support is given to each and every law,
yielding to Scripture its validity. Not surprising, the leading rabbinical council of the date
denounced his treatise and being of little value, mostly due to the almost impossible task of
matching Rashi’s glorious work. Rambam rebutted the allegation of shallowness of this treatise,
and worked to formulate the best known book of his authorship, the Guide for the Perplexed,
where he stated ad nauseum each and every claimed left unproven by the first treatise.
Rambam’s Theological Logic formation
His first treatise is separated in books as opposed to chapters, indicating a possible
desire to publish the books separately from the treatise, and is considered a religious treatise.
Rambam writes an introduction, and proceeds to weave up the seemingly disparate set of
books into this treatise. The focus of treatise is the evisceration of the canon of Jewish Law,
found sprinkled around the Torah. Of interest to this essay’s part, is his analysis on social law,
and the notion of God. It should be noticed that Rambam’s analysis of the existence of God
follows the same metric of logic as defined by the Greeks that preceded him. The introduction
to the books states a sequence of facts that mimic the sequence given at Genesis’s 1:1 to 15:5,
but also strikes a curious resemblance with Socrates’ explanatory process, given that only facts
are to be considered, and not allegories or innuendoes. Consider the Introduction’s Rule 24
where Rambam states
The subject matter of the two Talmuds is the interpretation of the text of the Mishnah and explanation of its profoundest points and the matters that developed in the various courts from the time of Our Holy Teacher until the writing of the Talmud. From the two Talmuds, and from the Tosefta, and from the Sifra and from the Sifre, and from the
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Toseftot--from them all--are to be found what is forbidden and what is permitted, what is unclean and what is clean, what is punishable and what is not punishable, what is fit for use and what is unfit for use, according to the unbroken oral tradition from Moshe as received from Sinai. The dialectic approach is clearly visible and the supporting facts are shown to give
credence to the treatise as if citations were not a necessity. This was the utmost reason why
the treatise was outcast and deemed inappropriate: not a single explanation from Scripture is
given, leaving the interpretation process as the only support evidence of the validity of the text.
The first book states ipsis literis the law as it is found at the Torah, and provides no further
inception on Rambam’s methodology for logical conjecturing. In there, Rambam groups laws in
categories, being of interest to this essay only the Laws of the Foundations of the Torah, where
Rambam included the Ten Commandments, and derived positive and negative commandments,
being some the existence of God, the uniqueness of God, and indivisibility of God, and the
Oneness of God. He does not provide theorems that show any support for the claims, basing
their existence solely on Scriptures. It is not until he published the Guide for the Perplexed that
Rambam crafted the system of theological thought necessary for the acceptance prima facie of
the unsupported claims found in his first treatise.
It is therefore of no surprise that Rambam found obligated to prove that the premises
he aspired to communicate were undeniably established via philosophy. This assignment he
consummated through a treatise called Moreh Nebukim, loosely translated as The Guide for the
Perplexed, hereinafter The Guide, of which great devotion is included herein.
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The Guide is an Aristotelian treatise in formation, formed on the principles of denial of
Aristotle Eternal Universe and the difficulty in setting the differences between creationism as
defined by the Torah and Universal existentialism as defined by Aristotle. While the former
heavily leans towards a manicured crafted of events by God, the latter states the eternal
formation proofs govern the creation, and supersedes it by definition and cause with creation
ex nihilo. Rambam does accept prima facie almost all other principles of Aristotelian
philosophy, including the parallelism between Primum Motum and the Psalmist teachings.
At The Guide, Rambam decries the impropriety of assigning attributes to God, insofar as
they are not the original thirteen he himself crafted at Mishneh Torah. This paper now engulfs
itself in the explanation of the rejection by Rambam of these attributions.
God is the Primal Cause
A simple matter of clear derivation from the Rambam’s acceptance of the creation ex
nihilo hypothesis, it that should the world be accepted as existing ad eternum, then, in the lines
of Aristotelian thought, the Primum Motum is to be accepted prima facie. However, since
Rambam accepted the hypothesis above, only the notion of intelligent creation is left, yielding
to the Primal Cause theory, and the rejection of the Aristotelian views of the eternity of matter.
Now if there is One, should the hypothesis of oneness be violated, the second One would share
some substratum with the first One, yielding in a partial definition. Worse, the line of thought
provides a direct conclusion of the physicality of God, for in an at least binary model, a
shareable substratum would necessary exist, which would then be capable of being removed
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and existing on itself, free of the necessity of the original vessel. That yields a quantitative
attribution of God, which contradicts the Primal Cause, for the substratum would exist on itself,
theoretically before the One. Inasmuch as the movement of things was concerned, Rambam
cleverly proved the existence of God with a formulation similar to the Aristotelian Spheres,
noticing that a causation motion is necessary and sufficient for the model to operate, and once
in motion, things causes other things to move. There is therefore only one thing that causes
motion without itself being in motion, which is outside the Sphere model, thus Primal Cause in
essence.
Consequently Rambam concluded the existence and Oneness of God, without any need
for attribution of definition, for any definition of substratum yields a partial definition, and
consequently a not One thing. This conclusion would become of great curiosity when talking
about Kant’s views of the uniqueness of God.
Once the existence, uniqueness, and oneness of God established, the harder definition
of the incorporeality of God becomes of much greater debate at The Guide. Rambam carefully
chooses the context in which he sustains that any attribution of corporeality to God would
necessarily yield on a substratum capable of many sub-attributions in terms of
anthropomorphisms and essential properties. For instance, once the acceptance of corporeality
is yield, the acceptance of humanistic facades is granted prima facie, which would directly
contradict the Oneness of God, but nevertheless quite acceptable in terms of Greek mythology.
As mentioned before, only the thirteen attributes of God as it relates to his human creation are
to be accepted, and none as it relates to the Primal Cause itself.
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On the belief System and Aristotle
It is surprising to notice that Rambam goes into great efforts not to expose his
adherence to creation ex nihilo, knowing very well that the Aristotelian thought would be seen
as the doctrine of choice by The Guide. Whereas Rambam explains the creation using Genesis’
first line and purposely does not offer an explanation for the creation ex nihilo, Aristotelian
views dictate that the universe is a direct result of fixed and immutable law. Should Rambam
explain the notion of creation ex nihilo, one would be hard pressed to show support for it at
Scripture! That is, Scripture would have to contain in it some kind of fixed and immutable law,
contradicting the hypothesis. Instead, Rambam notices that creation ex nihilo is a result of
God’s desire to create the intelligent process from which the Spheres and its motion is possible,
thus capable of closing the loop without exposing the inner works for the idea.
On the notion of Prophesy
Rambam wrote on the notion of prophesy as plausible within the doctrine of creation ex
nihilo. However, the separates two distinct views of prophesy, one that is inspired by God and
entrusted to the prophet as a mission, and another that is of allegorical value. He agrees with
the current philosophical trend that prophesy is a faculty of natural men and in total
accordance with natural laws of nature, but at the same time he holds that the same faculties
that permit a man to become a prophet are influenced and under the realm of divine
intervention. Likewise, just as men can become prophets with the permission of God, God can
remove the attributes to which men uses to perform its prophetic abilities. However the
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dichotomy of the views expressed are paved in both solid fabric of theology as well as accepted
sociologically by the philosophers of time.
Spinoza’s Philosophy
Much is written about Baruch de Spinoza and his treatises, and even more is attributed
to him as far as being a pivotal philosopher and creator of theories. Whichever view one takes
on Spinoza is almost by definition a tainted one: he is consider by many the father of pantheism
and the first to cohesively stipulate the laws of Scripture without religious biased, and at the
same time considered by his coreligionaries to have missed the point, imitate Descartes, and
produce a body of work that was devoid of value and substance. Clearly one can state that
Spinoza is a Cartesian disciple and an analysis of his first treatise exposes this savoir faire in
large scale. To the degree inferred by this section of the essay, the concern is more on his Short
Treatise, his first body of work, his Treatise on the Improvement of the Understanding, his
second body of work, and culminating with The Ethics, his apotheosis.
One thing is clear, up until his first publication, never before in the history of Jewish
thinkers a person so openly expressed his admiration to Christian values as Spinoza did, so
much so by devoting an inspirational line as seen below:
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Figure 1: First page of manuscript of Spinoza’s Small Treatise (Wolf, 1905)
Whatever reasons Spinoza had to dedicate the book to Jesus Christ is unknown; it could
have been a political plot by him to gain acceptability by the house of Oranges after being
excommunicated by rabbinical degree (Wolf, 1905) – doubtful since he himself proclaimed a
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non political affiliation – or just in spite of the rabbinical degree imposed to him, the fact is that
no one really knows. However, it was not for over 150 years that his treatises would be again
touched with seriousness by the European thinkers, viz., Lessing often cited as a contributing
fact that puts the European Jewry in synch with illuminist values and simultaneously giving birth
to the Jewish Reform Movement in Bavaria, spearheaded by Friedrich Heinrich Jacobi.
Spinoza’s Theological Logic formation
Spinoza’s Short Treatise mimics Rambam’s The Guide in which the former attempts to
provide his viewpoints on the latter’s topics of choice, viz., the existence of God and its
attributes. To the dismay of the rabbinical body, including the intellectual rabbis that gravitated
by the House of Orange’s representatives at The Hague, Spinoza assumed an Aristotelian vision
of nature and God, and a Cartesian view of the essence of oneness of God. Spinoza starts by
assuming that God is nature, and by a mere reason that men think of God, it should exist, at
least insofar as men ability to formalize God is concerned. He produces a divergent opinion
from the Rambam, namely, that God has infinite attributes, and His existence can be proven by
means of inferring on the attributes, so clearly and distinctly as it is seen to belonging to nature
of a thing and with truth affirm of that thing if accepting the nature of a being that has infinite
attributes belonging to existence (Spinoza, 1653). Therefore he affirms the thing, viz., God, and
not the nature of things, viz. the attributions. A comparison is necessary here: it is well known
that Baruch studied The Guide at school, a treatise by then widely used in Jewish academic
circles. He also studied Rashi and was known to correctly cite Rashi in his explanations of the
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passages of Torah to his teachers (Wolf, 1905). Therefore it is another curiosity to notice that a
person whose formation was so grounded in Jewish thought would craft a viewpoint so
orthogonal to the value system he has espoused. Whatever motivation Spinoza had to state this
notion on God’ essence, one thing is sure: he truly believed in it; it is clear that today’s society
accepts prima facie his views, and even luminaries of the 19th century physics world applauded
and accepted Spinoza’s view on God as their own, Einstein being a notorious one. But enough
of digressions; in fact, Spinoza’s (1653) continues his observations on the oneness of God as
follows:
“From all this the second point is proved, namely, that the cause of a man s ideas is not his imagination but some external cause, which compels him to apprehend one thing sooner than another, and it is no other than this, that the things whose essentia objectiva is in his understanding exist formaliter, and are nearer to him than other things. If, then, man has the idea of God, it is clear that God must exist formaliter, though not eminenter, as there is ideas that we have must be fictions no less.” So unique was his viewpoints that he only accepted God as essentia objectiva, insofar as
its own existence is formal, not the source of generation as stated by the Bible. This on itself is
of tremendous value, for it sets precedence on the facts that God IS nature, and not the creator
of it, as stated by the Bible. Further, there is no difference in the formalities by which one
defines the attributes of God, for it contains infinite attributes as nature does. From this
definition it follows clearly the proof both a priori and a posteriori that God exists. In lines with
the Rambam, Spinoza accepts the notion of Prima Causa, but alters it sui generis as Causa Sui,
viz., that God is “the first cause of all things, and also the cause of himself.” Curiously both
Rambam and Thomas Aquinas steered away from an a priori definition of God given that would
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imply in a non-causation acceptance. In here, the notion of a priori and a posteriori were not
postulated in details as done by Kant, and one is free to accept that Spinoza did not know for
sure the true meaning of the terms used. Rather, it is more so that he aligned the terms with
“due to thinking substance” (a posteriori) and “due to substance” (a priori.) (Spinoza, 1653)
Proceeding to the Treatise of the Emendation of the Intellects, Spinoza provides a more
detailed analysis of aesthetics when he delved into the differences between men’s attributions
and God’s, being that the former is additive and compounded, and the latter is indivisible and
absolute. That treatise focused on the relations of man to man mostly, but it inked at the
rationale further used by Spinoza at the Ethics, where he delineated the essence of his
epistemology.
The Ethics is the acumen of Spinoza’s theological analysis, and provides the utmost
inner self version of his reality. This essay now devotes some lines to the axioms and their
explanatory analysis.
Spinoza’s Axioms
Spinoza’s claimed he crafted the axioms by himself, but a simple analysis of the first two
axioms demonstrates that the heavily borrowed from Rashi and Rambam’s definitions,
synthesizing them in the aforementioned treatise; the axioms were not unique, but their
explanations were indeed bona fide Spinoza’s.
Axiom 1 states that “Everything which exists, exists either in itself or in something else.”,
and axiom 2 states that “That which cannot be conceived through anything else must be
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conceived through itself”. Now Rambam concluded that God’s existence must be Prima Causa
for it is defined ex nihilo through the creation process. Therefore axiom 1 is found at Rambam’s
Moreh treatise, and further found at Rashi’s commentaries of Genesis 1:1 to 1:7 (ArtScroll
Sidur, 2009). As for axiom 2, it suffices to replace exist by conceived, and to notice that the
former is a definition a priori and the latter a definition a posteriori (see Kant’s description at
the next section.)
Proposition XI attempts to marry Rambam’s theological explanation of the existence of
God’s principles with Spinoza’s naturalistic ones. Spinoza states that:
PROP. XI. God, or substance, consisting of infinite attributes, of which each expresses eternal and infinite essentiality, necessarily exists. Insofar as proof, he provides a denial ad absurdum using proposition VIII, which states
the infiniteness of substances. But prop. VIII can only be accepted if the acceptance of axiom II
is established and accepted prima facie. Since the latter is axiomatic by definition, prop. VIII is
therefore dogmatic, which is a clear contradiction of Spinoza’s attempts to rationalize God’s
existence. Consequently Leibniz rebutted his axioms as an attempt to define a religion rather
than a philosophy, which greatly diminished Spinoza’s acceptance for a long time thereafter.
Spinoza concludes that since nature exists, God must necessarily exist, thus giving birth to the
post-Socratic pantheistic movement. Of curiosity is the fact that the Stoics firstly defined the
same notions in Greece some three centuries before, and Lao Tzu firstly introduced the concept
in China some six centuries before. It is therefore conceivable that Spinoza read and was aware
of these notions before he wrote The Ethics. As mentioned before, Leibniz rebuttal of
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pantheism is a strong factor to support the sidelining of Spinoza’s ideas, which resurfaced only
in the mid 1800’s with Lessing bedridden acceptance of Spinoza’s God. It is widely accepted
that from then on, illustrious physicist, unable to reconcile the substance’s ability to create
dilemma, accepted prima facie Spinoza’s God’s definition (Einstein, 1947).
It is also fascinating to see a correlation between the Oneness of God as defined by
Rambam and Spinoza’s prop. XIV where he attempted to equate the oneness of the substance
and God is proposed. It is of no wondering that Spinoza write ad nauseum an explanation for
proposition XIV inside prop. XV and provides the extra enunciate that
Such are the arguments I find on the subject in writers, who by them try to prove that extended substance is unworthy of the divine nature, and cannot possibly appertain thereto. However, I think an attentive reader will see that I have already answered their propositions; for all their arguments are founded on the hypothesis that extended substance is composed of parts, and such a hypothesis I have shown…
Noteworthy explanation indeed for an astute reader will clearly see a circular definition,
only plausible by the acceptance prima facie of proposition XIV. Recall that Spinoza’s prior
treatise claimed that God could only be accepted to exist formally, and not as an emitter of
byproduct substances. This is the topic of our next section.
On the Cartesian method and belief system
Spinoza is aligned in logical formulation with Rene Descartes’ viewpoints. That is evident
from the structure of The Ethics, which opens and flows more like a mathematics treatise than
a philosophical treatise. However, since Spinoza spent a good portion of his early adulthood
writing his Descartes Principles (a treatise a propos similar to Euclid’s Elements), it is of no
wonder one would find axioms, propositions and demonstrations on The Ethics. Noteworthy to
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mention is the fact that Leibniz found no issue on the flow of the book; he however thought of
“The Ethics” as an empty pretentions device.
Since established the fact that Spinoza based his logic formulations of Descartes, left to
be mentioned is his late philosophy: true to “Je pense donc je Suis” (Descartes, 1673) Spinoza
attempted to add that besides being – je Suis – one has to understand. Remarkably he stop
short of changing the Cartesian thought to “Je pense donc je compris” , which would for sure be
more appropriate than “… that is without a definition of the understanding and its power, it
follows either that the definition of the understanding must be clear in itself, or that we can
understand nothing” (Spinoza, 1677). Since Spinoza discarded the mere fact that being is
enough to justify the thinking process, a fact that for sure deserves applause, he added that a
clear understanding of the thinking process supersedes and suffices as singleton for rationality.
Unfortunately Spinoza did not finish the On the Improvement of the Understanding so no one
would never really know if a total revision of Cartesian pillars were coming this way. Suffice to
mention however that the last portion of the Improvement Spinoza attempts to discard love as
yet another thinking process, a topic which he did elope unfortunately.
On the notion of Prophesy – Spinoza’s Hermeneutics
Baruch defines at the Theologico-Politico Treatise, pages 9 through 23, the
epistemological status of Prophecy as “… Prophecy, or revelation, is the sure knowledge of
some matter revealed by God to man. A prophet is one who interprets God’s revelations to
those who cannot attain to certain knowledge of the matters revealed, and can therefore be
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convinced of them only by simple faith.” That is, Prophetic knowledge is not superior to natural
knowledge but differs only in the kind of certainty involved. The prophets “perceived God’s
revelations with the aid of the imaginative faculty alone, that is, through the medium of words
or images, either real or imaginary”. Spinoza calls this knowledge “through a sign”. Spinoza
argues that each prophet had a different style, form, and degree of clarity; the nature of the
prophecy depended on a prophet’s particular “temperament” and concludes that: 1) Prophets
“have perceived much that is beyond the limits of intellect”, 2) Prophets taught in parables and
allegories, 3) Prophecy was not common but “very rare, manifesting itself in very few men, and
infrequently even in them”, and 4) The prophets’ certainty “was not a mathematical certainty,
but only a moral certainty”.
Compare Spinoza’s lukewarm acceptance of prophesy with Rambam’s. While the former
considers the prophets as nothing more than zealous moralists, the latter sees prophesy as the
most advanced level of intellect a mind can reach.
Spinoza (1677) proclaims that prophets are neither philosophers nor theologians, and
that prophesies often contradict one another:
…Prophecy varied not only with the imagination and temperament of each prophet, but also with the beliefs in which they had brought up, and that their prophesying never made the prophets more learned…God adapted His revelations to the understanding and beliefs of the prophets, who may well have been ignorant of matters that have no bearing on charity and moral conduct but concern philosophic speculation, and were in fact ignorant of them, holding conflicting beliefs. Therefore knowledge of science and matters spiritual should by no means be expected of them. So we conclude that we must believe the prophets only with regard to the purpose and substance of the revelation.
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Spinoza concludes that prophets leverage poetry and proclaimed messages that are holy
for ethical sake, and not for the sake of metaphysics. The fact that Spinoza did not mention
anything about prophesy at The Ethics and previous treatises indicate that he did not level the
prophets as philosophers, for it indeed they would be dealt with natural reason instead of
revelation. Spinoza limits the extent of prophetic influence as means to set up some sort of
unique derivation of thought, thus demonstrating that study of metaphysics is free of the
prophets, who clearly could not be seeing as subject matter experts. To conclude, Spinoza
leaves only prophetic significance to the world of moral virtues thus dismissing any
philosophical opinions or metaphysics previously associated with prophets and prophesy.
Leibniz Philosophy
Known to be the last of Rationalists, Gottfried Wilhelm Leibniz is considered by most
opinions The Influential philosopher of reason: while both Descartes and Spinoza penciled
around the notion of reason and fact, it was Leibniz that glued together via a predecessor of
predicate calculus6 the two notions above. Moreover, he was instrumental in paving the road to
Kant in determining the true meaning of the two reasons (see Kant in a subsequent section of
this essay.) Leibniz based his philosophy on the subject-predicate postulates of primitive
predicate calculus and weaved a theory where all propositions are analytics where predicates’
concepts are embedded in its subject. This essay looks into three of his most works, La
6 Predicate Calculus was not yet formalized during Leibniz lifetime, a fact accomplished by Dedekind and Peano in
1888 and 1889, respectively.
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Monadologie (1714), Les Discours de Métaphysique (1686), and Théodicée (1710), hereinafter
called by the monikers LM, LDM, and TD.
In lines Descartes, Leibniz’s LM and LDM attempt to resolve hard philosophical topics by
referencing God. For Leibniz it is God and only God that exists by necessity having everything
else being derived from the divine. Per LM, it is only a matter of choice for God to conceive all
possible worlds —one with one monad, another with two monads, others with three, and so
forth ad infinitum. It is the God’s arbitrary decision which one to materialize. The next series of
paragraphs will delve into the notion of monads and how this arbitrarily is resolved.
Leibniz’s Theological Logic formation
It is again of no surprise that Leibniz knew Spinoza, met him on occasions and exchange
letters with him. It is however a surprising fact that Gottfried thought Spinoza missed the point
entirely when he wrote The Ethics. For Leibniz, all existential aspects and proposition are truths
of facts, not of reason. Therefore attempting to formalize a reason as a Cartesian would yields
only in more denial of the reality underneath. In his LM, Leibniz defines two kinds of true
propositions, being those truths of reason and truths of facts.
Vérités de Raison
For Leibniz, les Vérités de Raison are explicit statements of identity, or could be made
reducible via predicate calculi’s statements. Consequently these truths cannot be denied, for a
denial would yield a fallacy of the statements used, contradicting the tautology of reducibility.
The truths of reason are furthermore split in two specific kinds: les Vérités Eternes and les
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Vérités Positives, or what can be eternally proven a priori, and what can be tautologically
proven a posteriori. Of some examples are the laws of geometry, viz. the internal sums of the
angles of triangles, and the Pythagorean Theorem, respectively.
Vérités de Fait
Contrary to truths of reason, les Vérités de Fait are implicit statements of identity, or
could not be made reducible via predicate calculi’s statements. Consequently these truths can
be denied, disputed, or rejected since any attempts to reduce these to yield a tautology may
result in an infinite loop. Leibniz accepts that all moral judgments are found as truths of reason,
being therefore capable of argument in a court of law, a fact pretty predictable being Leibniz a
lawyer by formation.
On the notion of Monad
A monad, according to LM, is a complete dimensionless indivisible substance whose sole
responsibility is to act as a center of force. It is complete because it contains all its features:
past, present, and future. Furthermore it is indivisible because, per afore definition, it is
complete, and independent of everything else. Lastly it is dimensionless because these
substances are self-contained, and therefore not shareable – only shareable substances have a
collision point, and therefore, in terms of Cartesian planarian model, create a dimensional
model. To clear matters, consider as example a dog and litter: true to the monad vision, a
mommy dog has a litter, and the puppies are her offspring. However these facts are totally
independent from one another: the mommy dog might disappear or the individual puppies
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might be place somewhere else, the notion that a mommy dog had offspring is immune to
alteration. Thus Leibniz considers at LM that monads are windowless entities.
Compare the notion of Spinoza’s world of comprehensive substances or Descartes
extended matter with Leibniz nomad – whereas the formers considered a global indivisible,
though extensible substance, the latter says these are all atomic entities just coincidently living
side by side to one another without really imposing dimensionality. It is however worth to
mention that Leibniz did not craft the notion of monads. Many before him had used Monad as a
moniker to God, as to provide a means to define an incorporeal, spiritual substance. What is
unique about Leibniz is that he altered the meaning of Monad to an orthogonal new meaning:
that of a corporeal, though indivisible, substance.
Consequently monads nothing else but simple and inelastic substances, understood as a
center of force. Except by divine creation or annihilation they could neither begin nor end.
Being only able to internal activity monads suffers no physical influence by anything but
themselves. Moreover, each monad is a singleton. Leibniz’s LM goes further and claims that the
monads must possess unique qualities for "otherwise they would not even be entities". Now
heavily borrowing from Spinoza’s modes, it is clear that any given monad possesses a reflective
mode, which “reflects all other monads in such a manner that an all-seeing eye could, by
looking into one monad, observe the whole universe mirrored therein”.
Furthermore a mode differential from monad to monad is they unique reflective
property, considered as unconscious the lowest reflective mode, and as conscious the opposite.
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It is of curiosity that Leibniz openly criticized Spinoza because the latter rejected the existence
of unconscious mode.
On the notion of obscurity of Monads
Leibniz defines two diametrical opposed modes, named the obscure mode, and the
clear mode. At the lowest applicability, say a speck of dust, the obscurity mode is prevalent,
restricting the monad of the pure laws of physics. If however one considers the soul7 , named
by Leibniz as the Queen Monad, it is said it possesses the highest mode of clarity, and the
lowest mode of obscurity. Leibniz assumes the range in between to account for all kinds of
degrees of variation of the clarity mode. In addition to the clarity mode, Leibniz defines two
other essential modes: one to define the essence of materialism associated with full obscurity,
and the essence of immaterialism, associated with full clarity.
For Leibniz, there is no monad besides the soul that is immaterial: for if indeed, it would
become a dimension of the previous one, thus contradicting the postulate. However, true to
the nature of soul, Leibniz assumes the possibility that other substances possesses soul, and
therefore imposes the fact that, absent the human soul, all other souls are made of a
composition of materialism and immaterialism, being the higher degree of the latter mode
prevalent on insensible substances.
This postulate however goes against the grain of Leibniz catholic upbringing and for this
to be accepted in larger scales he would have to account for what he calls the principles of pre-
7 Leibniz calls this the human soul, as an attempt to provide a monadic separation between other possible souls.
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established harmony. Since there is no dimensionality on monads, viz. the region of boundary is
infinite, only God could make it in such as way that the order of creation of monads would be
such that, absent a boundary zone, the influence is provided by divine order. Leibniz writes that
"Bodies act as if there were no souls, and souls act as if there were no bodies; and yet both act
as if one influenced the other" (LM). The fact that Leibniz relinquishes to God the task of
homogenizing the structure is of no coincidence. Anything else would be the acceptance of
Spinoza’s viewpoints, which were already rebutted even prior to the publication of LM. Left to
be proven though is the order which souls were made. Consequently the angels, ruling on
behalf of God, created the systems of souls such that one soul is subordinated to another by
Divine Providence, and not by monadic inference. This yields the mode of architect to God, and
later of ruler and legislator. Leibniz writes that “God as architect satisfies God as legislator"
(LM), or in laymen terms, monads obey the structure defined solely by God, and from the
moment of definition, are unable to alter their modes.
On the notion of Prophesy
Being a fervent Protestant, Leibniz grew up with the belief on Scriptures, and grew old
accordingly. His TD work is a classical sample on how to correlate the imperfection of human
behavior with the perfection of God’s creation. Insofar as the depth of TD is concerned, clearly
Leibniz drew attention of coreligionists, and even became a parody on a play written by Voltaire
(Voltaire, 1759) sometime after Leibniz’s death in 1716. At TD, proposition 118, Leibniz first
introduces the trust of reason status to prophesy as stated:
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An infinite goodness having guided the Creator in the production of the world, all the characteristics of knowledge, skill, power and greatness that are displayed in his work are destined for the happiness of intelligent creatures. He wished to show forth his perfections only to the end that creatures of this kind should find their felicity in the knowledge, the admiration and the love of the Supreme Being.
The issue as debated from this part on lies on the fact, that being an eternal truth that
God created the world as best as it He see fit, from his will, and because it was written in the
book of the eternal verities, which contains the things possible before any decree of God, that
His creation would freely turn toward evil if it see fit. Consequently prophesy becomes a truth
of facts imposed by God’s involvement on the process. Proposition 276 illustrates Leibniz’s
enunciation of several instances where prophetic aptitudes, though only be allowed as truths of
facts, are nonetheless derived exclusively out of an outcome predefined by truths considered
eternal verities.
It is in his Confessio Philosophi, a treatise where Leibniz wrote in Latin, that it is found
his wiliness to admit in absoluto that a dichotomy exist between the admission of eternal
verities and prophesy, for if a prophet predicts an event and foretells such event, men is totally
free to do the exact opposite to assert their truths of fact. However, the prophet may chose to
follow God’s vision and command, which would then create yet another truth of fact, possibly
contradicting the first one. Leibniz answers the dichotomy with a clever solution: if the prophet
is a true emissary of God’s actions, he would have foretold men’s desire to do the exact
opposite, and either foretell this fact to a witness thus corroborating the fact the prophet is
indeed God’s emissary, or silently omit the original intent and tells men the right opposite thus
enforcing God’s will. Either way, God’s truth of verities will be imposed. As a conclusion, it is
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worth to notice that Leibniz’s views on prophesy are to be taken twofold: the first being in
accordance with Scriptures and therefore theological in nature, and the second being in
accordance with his logical formulation, being an eternal truth in nature.
Kant’s Philosophy
Contrary to the previous thinkers Immanuel Kant did not follow any of their Cartesian
structures. Kant addresses the need to remove oneself from the traditional epistemology and
immerse oneself with a continuation of Leibniz’s truths of reason; however Kant did not reuse
postulates from Leibniz, rather, he rejects the eternal truths and only admits that the mind
conceives only what is made causal to it, for it cannot conceive what it is not causal since the
cause imposes the a manner of thought. Kant’s work of interest to this essay can be classified as
theological and critical. From the former an analysis of metaphysical epistemology is driven,
and from the latter an analysis of cause and effect is driven. Therefore this essay analyses The
Critique of Practical Reason for ethical and theological discussions, The Critique on Judgment
for teleological discussions, and The Critique of Pure Reason for rational discussions. The other
three major works of Kant are only used as supporting arguments, being of most use The
Metaphysics of Morals. Being that Kant was so proliferate in writing, it is quite a task to
compound an essay in five pages or so that encompasses that this essay aims to debate, and
therefore a large amount of footprints would direct the attentive reader to the source or origin
of further debates.
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Kant’s Theological Logic formation
By all means Kant’s influence in Western philosophy in immeasurable. Singlehandedly
he changed the way society sees rationality and conditions possibilities, and infuses a paradigm
change that identifies pre-Kantian philosophy from Post-Kantian philosophy: the former
preoccupied with Cartesianism and the latter based on his three formulations of logic.
Beginning with a discussion on rational thought it is clear to an unbiased observer that
Kant does not continue Leibniz’s work just as Einstein did not continue Newton’s work. True to
the nature of examination, Leibniz introduces the ideas where a rationale thought is differential
from factual or causal thought, but it was not until Kant that a formalization of the differences
was proposed and accepted prima facie. The Critique of Pure Reason introduces two very
special formalizations that were mentioned ad nauseum since Plato, viz. where does the fact
originated when compared to the observation, before or after.
On the notion to a priori knowledge
Kant formulates a theory of perception based on the clear differential as defined above.
In order to clearly understand the differential factor, one is forced to differentiate between
analytical propositions as first introduced8 by Leibniz predicate calculus, and the synthetic
analysis found at Spinoza et al. For Kant, a formalization of predicate calculus provided not only
the stepping stone for the differentiability but also the orthogonality necessary for a correct
8 Indeed this is not totally accurate: analytical propositions existed much before Leibniz but it was not until then
that they followed predicate calculi notions. A curious reader would only need to visit Plato’s work and be amazed with tautological statements present in his vast work. Further, Descartes was a true believer in analytical propositions but failed to formalize them as Leibniz did.
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definition of origin and destination. Whereas analytical thought imposes the predicate to be
associated with the subject in all cases, synthetic thought permits the relaxation of the
imposition thus clearly separating the two thought processes. Likewise, if a predicate is forced
to be subjected to explanation through experience it is said to be an a priori predicate, of
simply an a priori proposition. Therefore Kant concluded that two a priori propositions must
exist, an analytical a priori proposition, and a synthetic a priori proposition. Kant’s discourse
follows that proving analytical a priori proposition is an easy task, given that one is only forced
to “… extract the predicate from the conception, according to the principle of contradiction,
and thereby at the same time become conscious of the necessity of the judgment, a necessity
which I could never learn from experience. “ (pp.40). However, Kant devoted almost entirety
The Critique of Pure Reason in proving synthetic a priori propositions. Suffice to say here that in
terms of mathematics, Kant demonstrates that all principles defined by mathematics are
synthetically a priori formulated. Consider the example Kant used, viz. the summation of two
integers. One is left without any recourse if attempted to define the summation, yet another
integer, from the sum operator of the other two integers: all concepts are analytical in their
separate ways, but totally synthetic when observed throughout the optic of a sum operator,
thus proving that arithmetical proposition are synthetic. Suffice to use induction over the set of
integers to see that all other similar propositions are also synthetic, thus proving the
hypothesis.
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On the notion to a posteriori knowledge
Of much different aspect is the notion a posteriori of both analytic and synthetic
propositions. Due to the nature of a priori analytical propositions, it follows that there exists no
possible a posteriori analytical propositions, for it so, one would find such contradiction to the
predicate, and therefore immediately remove them from their analytic status and replace them
with synthetic instead. Consequently Kant proves that analytical propositions are only a priori.
That leaves synthetic a posteriori propositions to be defined. Kant calls this by the term
Transcendental Aesthetics or simply stating, the space and time. Within space and time
mankind finds all empirical and provable causal phenomena that lie as synthetically a posteriori
propositions, including sensuous and the intellectual notions found by Leibniz’s clarity modes.
Kant discards Leibniz’s modes and replaces them with nothing else but the ability of the faculty
of sensibility to discern the presence or not of clarity to a proposition, what Leibniz calls
monadic mode. Kant ends the discourse by stipulating that all empirical findings lead to a
posteriori predicates, which imposes a notion of purity on the a priori propositions: some a
priori propositions might become impure when broken down by the empiric notion of the
subject-predicate operators. When such operator is not found, Kant determines that the a
priori proposition is of a pure nature, what lead to the name of the book to begin with.
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On Kant’s belief System
For Kant, God was instrumental in defining all a priori aesthetics, viz. freedom, the
immortality of the soul, and moral law. At The Critique of Practical Reason a table containing
interesting determinations is found, and below reproduced:
Figure 2: subjective v. objective determinations (Kant, 1781)
It is only through the subjective empirical and objective determinations that one can
furnish the principles of moral law necessary for men to absorb the practical reasons. Thus,
subjective empirical determinations are incapable of adding value to the code of moral law, but
objective determinations are based on reason. Once accepted the subjective empirical nature
of the moral law, it is now left to be determined the necessary completeness of the principle of
summom bonum, viz. morality and happiness per se. Kant stipulates that morality could only be
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proven through the postulate of immortality, being it the affirmation that only via immortality
that one could achieve plain morality. Similarly it is only via morality that one could achieve
plain happiness; these however point to the necessary condition of the existence of an
adequate cause capable of providing such apices, viz. God only could emanate true happiness
and morality. It must therefore be postulated that the existence of God is the condition Cine
Qua Non for the possibility of the summum bonum: only though this condition an object of the
will is necessarily connected with the moral legislation of pure reason (pp. 119).
On the notion of Prophesy
It follows that Kant closed the door on any kind of acceptance of God’s intervention on
the physical world for it would entitles God with an attribute of modifier of space and time.
Further in Kant’s rational system, God as actor was ruled out for there was no reason for such
things as creation in time and space, miracles, prophecies or the interference by God in any way
into the usual world. From Kant on it became acceptable to proclaim a religion without a creed
or worship. Consequently, religion for the vast majority has being reduced to aesthetics. Kant’s
philosophy was later to be accepted prima facie by various well known philosophers who
further pushed it into a system of their own. Particularly in Germany Kant found some bold
disciples, confident of augmenting his reasons further than before, being the most visible Hegel
and Fichte. The former made reality simply a product of the mind with the idea of Kant himself
being the ultimate reality, though many philosophers claimed that Hegel is only as Kantian as
his interest lie. These are the disciples of Kantian philosophy – anyone whose believes in
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Idealistic pantheism. Kant's conclusion on metaphysics is to equate it to an agnostic form – men
would never attain scientific knowledge of substances beyond the scientific experimentation
allows men, and God would not provide beyond the transcendental aesthetics.
Summary
This section of the essay analyzed the foundation of philosophical and theological
aspects of human knowledge as defined by these four thinkers. Inasmuch as their theories are
concerned, there is a clear split between viewpoints: Rambam and Leibniz share the notion that
God as defined by Scripture created and manages the world allowing humans to acquire
knowledge from its Scripture. Spinoza and Kant rejected the same notion, however for different
reasons. The next section of this essay narrows the focus on their legacy from an epistemic and
metaphysic broad sense to a predictability sense dissecting the thinker’s acceptance of
prophesies.
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Literature Review Essay
The analysis phase as presented above indicates a clear division of theologico-logical
affiliation that lies on the boundaries of 1700. From one angle there is a true affiliation of
Judeo-Christian pairing on the acceptance prima facie of creationism and its divine
predetermination of the world events as if God has provided a non-deterministic finite state
automata where all possible transitions were mapped as e-transitions which would then entail
a predisposition a priori of events, even if these were only to be proven a posteriori. Consider
Rambam’s choices of total acceptance of divine authority, authorship, and deterministic
metaphysics; in his 13 principles of Faith (The Guide for the Perplexed, 1173) he mapped all
possible human actions, being past, present or future, on the shoulders of God, so much so that
acceptance of prophetic statements fall rightly so in the hands of the omnipotent God.
Therefore it is rightly observed that this Godly acceptance of all possible things that befalls
humans correctly aligns with the theologico-logical thought process of the times. Curiously at
the same period (plus or minus 150 years) almost all body of cabbalistic work was produced,
reorganized and accepted as divine just as the Torah itself was9. Inasmuch as Rambam’s work
could be detached from the Zohar it is also plausible that the 12 century rabbinical schools got
permeated with cabbalist works and therefore there is a chance that Rambam’s mind got
acquainted with mystical thoughts of the cabbalists of yesteryears. Consequently The Guide
addresses issues of acceptance of premonitions and prophesies with candid eyes, more so than
an expected body of world would had it not been permeated with mystical values from the
9 Please consult Rabbeinu Bahya’s work or Ibn Gabirob for complete details of the Zorah’s thought process.
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Zohar. With the same lenses an examination of Spinoza is performed: during the mid 1600 the
status of the Zohar grew in both acceptance and creed. It is therefore not surprising that the
rationalism of Spinoza rejected all body of work from a Judaic perspective. It is however very
prudent to inspect the fact that Spinoza was a reject of the Judaic society of Amsterdam so
there is a debate whether or not he rejected the body of work he grew up with and learnt well
because he clearly did not accept it or because he felt betrayed. Regardless of the reasons
associated with the rejection, Spinoza spearheaded the movement against Jewish mysticism
and almost all Jewish theologico-logical values, and infused his own rationale, mostly adapted
from Rambam in true aspects, but devoid of God as understood by Judaism. Regarding his
impact on philosophy is it clear Spinoza impacted the world in a huge way, being considered the
father of pantheism by some and the father of pan-atheism by others. Accepting the fact
Spinoza was rejected for over 150 and later hailed as true messiah thereafter shows the
tendency for Spinozism to be taken as a religion rather than a philosophy; however this is also
not totally correct as Spinoza accepted Christianity as his favorite faith. It is debatable whether
or not Spinoza would accept the title of messiah but nonetheless whenever one proclaims it
accepts Spinoza’s God, one equates him with a messenger with messianic value systems. Not
surprising the modern scholars pinpoints Spinoza against its contemporaneous Christian
philosopher Leibniz since the latter criticized of the former almost as soon as being made aware
of him. However Leibniz himself was suffering from ridicule and plagiarism about the invention
of infinitesimal calculus, which was claimed by Newton almost at the same time. Since Leibniz
was less flamboyant than Newton, and the British Empire liked the idea of superiority at all
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costs whenever an invention was in risk of being taken by an enemy country, Leibniz spent a
great deal of energy proving that he did not copy Newton’s calculus, thus allowing Spinoza to
slide free of criticism for some time. After being acquitted of plagiarism charges in the court of
opinions Leibniz was then being challenged yet again, this time by the renaissance latter
players, Kant to be exact. Being that Kant rejected the Cartesian model adopted by both
Spinoza and Leibniz, it is no surprise that Kant’s views are in orthogonal axis with the latter two.
Now while Rambam and Leibniz accepted divine premonitions, Spinoza and Kant rejected
these. Notice that no attempts to find a correlation of the motives for acceptance and rejection
is drawn since suffice to say none could be clearly stated. Additionally this essay seeks no
objective in debating this fact, which would be an essay on itself if such task was to be taken.
Literacy Conclusion
Rather, this essay objective is to demonstrate that from 1100 onwards there were
illustrious minds accepting a priori hypothesis of prophesy and pre-determinism of Scriptures,
and just as many rejecting the hypothesis. Consequently in lights of true rationalism, history
proved that the hypothesis is to be rejected, and in lights of metaphysics and epistemology, the
hypothesis is to be accepted. It is therefore no surprise to find the same debate playing in the
arena of popular debate in today’s date. The final portion of this essay focuses on the latest
trend of analysis of the same debate, this time in a digital world. The Application section of this
essay provides the reader with an analysis of the mathematics of Null-Hypothesis applied to the
Torah Codes, or the presence of hidden prophesies at Scriptures that were determined a priori
45
but only capable of being discovered a posteriori, giving a true meaning of prophesy to this
codes.
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Practical Application – WRR Algorithm in the nutshell
Up until now this essay concerned itself with the theories that sustain a possible
acceptance a priori of what is the focus of the application: The Torah Codes. In the next
paragraphs a thorough explanation of the Codes would be provided, following by a
mathematical treatise in statistical inference and a test of the null hypothesis. Since the topic is
still an open ended question, this essay would not attempt to prove or disprove the claims;
rather it concerns itself only with the mathematical acceptance of the hypothesis taking into
consideration its historical value.
Preliminary Concepts
Following the footsteps of previous section of this essay, a series of preliminary
concepts are now presented in order to provide a substantial framework in which further
concepts are weaved in. The order in which the concepts appear are important as one adds
sustenance to the following, both in terms of historical understanding as well as mathematical
background. The Equidistant Letter System is analyzed in details, and its cousin, the Gematria
Letter System, is found at Appendix A of this essay.
Equidistant Letter System
The system introduced here is the Equidistant Letter System, hereinafter ELS, which
concerts itself in dissecting a text into groups such that the starting point of each one is a skip
of a certain number of letters from the preceding group, and a skip of a certain number of letter
from the succeeding group. As an example, Rambam’s Mishneh Torah discussed the section of
Exodus and the observance of the Passover, and noticed a few times that the for name of his
47
book Mishneh Torah, from the first letter M of Mishneh to the letter preceding T of Torah is
exactly 613 letters. The Rambam discovered this without the use of computers and was amazed
to find out the numeric distances equate to the number of divine obligations bestow upon the
Jewish people by God. A few centuries after, another famous rabbi, Rabbi Bahya ben Asher(?-
1340) , noticed the ELS distribution on Genesis focusing on the attributes of God as defined by
The Rambam. A little over six hundred passed since anyone else investigated this phenomenon.
In mid-1980 this phenomenon attracted the attention of some scholars that begun to speculate
about this fact and whether or not it was a simple curiosity of there was more into it. Two
mathematicians and one psychologist published a paper in 1994, hereinafter the WRR, where
this curiosity was further examined using Kant’s pure logic methods. They created a two-
dimensional array and used quantitative measures to see whether or not equidistant letters
sequences appeared in close proximity to one another. Their conclusion shocked the world as
they found what was first proposed by Rabbi Bahya 600 years before: the existence of hidden
messages on Scriptures. Since new concepts are now present, viz. proximity, skip, and
quantitative measures, there is now a need for this essay to correctly establish these concepts
for the sake of consistency, alongside with the ELS mathematical background.
ELS Definition and Nomenclature
Let be a language, and let T(L,S) be a text using L. Define a grammar G =
(N, ,P,S) to be a formal grammar such that all rules in P are in accordance with either one of
the four algebras defined before. Further assume that there exists transitions such that
where A in is N, and are members of , and y is any symbol belonging to the
Kleene union closure between N and . That is, L is a formal grammar by definition over the set
48
of . For T, define a transition by which the space is removed and replaced by the empty
string. Randomly select a starting Ordinal and call it . Define by skip the difference between
the letter at Ordinal and Ordinal and fix it.
Theorem 1:
An ELS Ḝ is a sequence of letters in T such that their ordinal positions form an arithmetic
progression
Proof: By applying the definition of ELS and noticing that any formal language over a grammar
yields via a transition either another non-terminated member of the grammar or a termination
member, and knowing that T is finite, one is capable of constructing a non-deterministic finite
state machine where the transitions are mapped. Since there would be either a direct transition
of an ε-transition, either the last letter is either a member of the original set or the empty set
assuring that the skip produces another transition, this time with a closed loop back to the
termination node of the empty string.
QED.
49
Figure 3: Rambam's title in a cluster with skip 50 (Haralick, 2000)
Definition 1: Using Theorem 1, start a sequence of letters in such format:
An ELS is a tuple Ḝ such that m is the starting ordinal point, d the skip, and n
the length of the ELS according to [eq.10].
Definition 2: A cylinder is a matrix in such that and is formed
by theorem 1 with d=1. For the sake of simplicity the pictorial representation of such
cylinder would be done in such way as to mimic the writing of the matrix above at the
surface of a soda can as shown below:
50
Figure 4: a typical cylinder (WRR, 1994)
Definition 2: On a given cylinder and an ELS Ḝ
a) Let the number of vertical columns be known as the row length of the cylinder and
be called h.
b) The distance between any two letter and on a given cylinder is MIN(i-j,j-i)
c) Let the beginning position be called Ḝ
d) Let the end position called Ḝ
e) Let the number of letters called Ḝ
f) Let the skip be called Ḝ
g) The compactness Constant Κ is defined as restrictive measure for the skip
h) Let the character string formed by all letters of the ELS be called Ḝ
Lemma 2.1: For any given ELS Ḝ ,
Corollary 2.1: The norm of the gematria Ḡ of an ELS Ḝ is
∑
Lemma 2.2: An ELS Ḝ is said to be an ELS of keyword ẇ when Ḝ
Lemma 2.3: An ELS Ḝ is said to be an ELS of keyword ẇ for text T iff Ḝ satisfies Lemma 2
and Ḝ
51
Ḝ Ḝ Ḝ
Ḝ Ḝ Ḝ Ḝ
Lemma 2.4: The set of all ELS ℮ associated with a word ẇ and text T is given by
{
Compactness of an Array
There is one idea left to solidify and is that of the meaning of close, i.e., how closed are
the ELS to one another. Recall WRR’s (1994) definition of row length for the next series of
definitions.
Definition 3: Let be two ELSs. Let be the distance between
consecutive letters of , respectively. Let be the minimum distance between
two given letters of . The distance between these ELSs in an array with row
length is therefore defined as:
( )
Definition 4: The compactness of is defined as:
( ) 1/ ( )
52
Definition 5: Let and be two ELS. From a set
pick here is the largest integer closest to . Repeat the same process of . A
compact array of Κ = 1010 is called the maximum compactness and is formed as:
( ) ∑ ( )
∑ ( )
Conversely there is a minimum compactness which is formed as:
( ) ( )
Domain of minimalism
Definition 6: Given a word and a text , and chose
that spells at text for which is minimal over (possible all of) . The domain of
minimalism of is defined as maximal segment that satisfies:
Definition 7: Given two words w and w’ and a text T such that is an ELS for w and is
an ELS for w’, then is called the domain of simultaneous minimalism.
Definition 8: The length of the domain established by definition 7 relative
to the text T is weight assigned to the pair .
Corollary 8.1: Define ( )
. For any two words w and w’, define the sum
over all ELSs spelling out w and w’, respectively, as:
∑ ( )
10 Further down there would be an explanation of why Κ is set to 10.
53
The meaning on Ω is the measure of maximum closeness of the more noteworthy
appearances of w and w’ in text T, that is, the closer these words are, the larger Ω is (WRR,
pp.7).
Explanatory narrative of the Process
The process of extracting ELS from a given text was formalized and the axioms for which
it describes the process were either delineated or appointed as an Annex found at Appendix A.
Inasmuch as the process itself seems straightforward, it clearly leaves a gap in formalization
whereupon the size of the word w plays a role. WRR found that words whole length are less
than 5 and higher than 15 diverges the process by either making the predicted number of ELS
tend to zero or divergent. To see this phenomena suffice to notice that the compactness
constant Κ (WRR set it to 10) is the upper limit of the equation
where D is the restrictive skip factor such , L is the length of
the text T, and k is the length of word w such that . It is not immediately clear why
this restriction was imposed by WRR, however when tests were run for increased values of the
compactness constant the time to halt of the algorithm grew asymptotically for the same test
words.
Perturbations over the Arithmetic Progression
The notion of two word’s proximity as a measure of the arithmetic progression of each
characters takes is further analyzed when a shift left and right in allowed to the progression
common difference d. Corollary 8.1 defined the proximity of two words as an inverse measure
of the distances between these. There is however a need to determine if the proximity is larger
54
or smaller than an expected value. In order to find the expected value, WRR introduced the
perturbations over the arithmetic progression in order to determine a relative distance which is
smaller when the words are unusually closer to each other or close to 1 when they are
unusually far. Define by mode a triple of integers in the range and
define as an ELS obtained by taking
. That is, the perturbation
impacts the all but the first two characters of the word and allows for the relative
positioning of the character when shifted right or left by mode. When the relative position is
zero, the perturbation factor disappears and the perturbed ELS is the same as the ELS .
Although WRR chose to only perturbed the last three characters of any given word for technical
reasons the actual reasons were not made clear; many attempts were made to perturb all but
the first two characters of any word and absent a longer running time there seems to be no
statistical errors between the calculations done by perturbing the last three when compared to
the ones where all but the first two were perturbed.
-Perturbed Distances
From corollary 8.1 and applying the perturbations as defined above a new corollary is
achieved, this time as an explanation for -proximities.
Corollary 8.2: For any two words w and w’, define the sum over all ELSs
spelling out w and w’, respectively, as:
∑ ( )
55
The meaning on is the measure of relative closeness of the more noteworthy
appearances of w and w’ in text T, that is, the relatively closer these words are, the larger
is (WRR, pp.7).
Definition 9: Denote by the set of all where there the sum is
not zero. Denote by the number of elements of . Denote by
the number of triples such that .
If , then define
Corollary 9.1: the lower , the unusually closest w is to w’.
Statistical Analysis of
Previously, Corollary 9.1 introduced the most important finding of WRR, the relative
closeness of w to w’ as a measure of unusually closeness of these words with respect to the
compactness constant . Let then N be the total number of pairs for which there exist
such . Let k be the number lower than N such that
. Define now such
that
∑( )
Equation 17 informs that should be uniformly distributed over (0,1] then re
presents the probability that at least k out of N is less than or equal to 0.2 (or
). However
ignores all distances higher than 0.2 and also does not weight in different
56
that are lower or equal to 0.2. In order to find a measure that is sensitive to the closeness of the
distances within the range established, define:
∏
where N is define as above, and function F is defined as
(
)
ELS Hypothesis – encoded Text versus Monkey Text
In order to qualify a text where ELS are found in close proximity, two definitions are
necessary, one defining the probability to find ELS in a code that was written with that intention,
and another where such findings are nothing else but statistically probable.
Definition 9: Consider a text T where ELS are found such that the values of [eq.18] and
[eq.19] satisfy [eq.16]. Such text is Encoded if and only if there is a probability less than or equal
to 0.02 of finding two worlds w and w’ whose ELS are in close proximity as defined by *eq.16+.
Otherwise the text is called a Monkey Text.
Nomenclature 1: For the remainder of this essay, denote by D a text that is
probabilistically encoded, by M a text that is not, by G the text from the Book of Genesis11, B
the text from Moby Dick, and by E a set of evidences.
Definition 10: The conditional probability that given the evidence E a table containing
pairs of words is put by design, or P(E|D) is given by:
11
There are several transliterations of the Bible’s first book (Genesis) and there is no real difference from one to
another; so long as the same transliteration is used across different books there is no implication on the transliteration model itself.
57
Problem 1: Assume a text T is Encoded, i.e. it satisfies definition 9 above. Without
knowing a priori if said T is of type D or M, assume as boundary conditions the following:
P(M) = P(D) = 0.5
That is, there is an unbiased opinion about T from the start. Now assume there is
evidence E showing that there is a probability of 0.001 that M contains a pair of words that
satisfies Definition 9 above, and denominate said probability using [eq. 20], P(E|M) = 0.001.
Using the boundary conditions and P(E|M) above at [eq.20] yields:
Since there is no predictable model to determine P(E|D), assume that each value of
P(E|D) is found using the assumption of “equal probability of ignorance” so the expected value
of P(E|D) is found via:
(
)
The graph below shows the values of P(E|D) by increments of P(E|M). The graph shows
that for a text T to deemed of type D the experiments must show a p-value no greater then
0.0277, and to be 95% sure that T is of type D the experiments must show a p-value no greater
than 0.001. WRR set the standards for the experimentation at 2% (or 0.02) which is slightly
lower than the minimum value as set forth above, and yields a probability of 92.14% that the
closeness of the words are not coincidental.
58
Using the previous findings and definitions yields the hypothesis for this essay’s
application:
Sample an M text at for a series of word pairs, hereinafter called a table. Let the area of
the best closest distances of this table be called A. Let P(A|G) be the probability in which
we observe the same best table A in G for a randomly selected pair of words. Further let
be some relatively small compactness value.
Hypothesis - : The text G is such that , which
indicates a higher probability than expected by chance that correlated words w and w’
have their respective ELSs in an unusually compact arrangement.
Null-Hypothesis - : The Text G is such that regardless of evidence.
Findings
The next series of paragraphs detail the findings of running WRR in a C# code. The
algorithm is in essence the same as explained by WRR but without the need to spill
intermediate files between the steps.
y = -107.55x3 + 27.879x2 - 4.0559x + 0.9936 R² = 0.9998
0.00000
0.10000
0.20000
0.30000
0.40000
0.50000
0.60000
0.70000
0.80000
0.90000
1.00000
0 0.02 0.04 0.06 0.08 0.1 0.12
P(D|E)
P(D|E)
Linear (P(D|E))
Poly. (P(D|E))
59
Algorithm 1: WRR
Given two words and
For each word
remove from the text any incidence of characters not matching
Seek each character of the word in the encrypted code with mode
Calculate the extensions
Set the domain
Calculate the distances from each domain and find the minimum distance
Appendix C contains the C# code implementation for this algorithm. The program is a
Windows program that accepts a list of words or operates on a pair of words.
The code was written following WRR algorithms in a quest to allow the testing of
different values and words. A test was run using the same two words as defined by WRR to
make sure the algorithm was implemented the right way. Once the process was calibrated the
whole list was ran using both G and M as input.
Calibration
The only calibration done was to ascertain that the response for the two values as
presented by WRR (pp. 4) yielded the same response as the algorithm predicted. Consequently
word one is set to MTNYH and word two is set to CDQYHW, using the Hebrew equivalent table
as defined by Appendix B. The experiment when ran with these two words returns 0.016 (2/125)
which represents that these two words are unusually closed together in G:
60
Figure 5: C(w,w') for calibration pair
Once the algorithm was calibrated, a series of runs were produced, either via pairing
unique sequences as found by lists one and two of WRR (1987) and WRR (1994). Compare the
same run with the calibration pair with text M; this experiment when ran with these two words
returned a p-value of 0.616, showing the indeed M is highly randomized and finding the pair
used for calibration was a tad worse than tossing a coin. A graphical comparison shows the
distribution of values for the calibration pair over both G and M, and the fact that these two
words in M are found in intervals of great distances as well as closeness in a fashion that fair
even worse than P(M) = P(D) = 0.5.
Once the code is calibrated correctly, the de facto proof of the null hypothesis would
come if a pair of historically associated events link w and w’ and they are found in close
proximity to one another as stated by the Torah Code hypothesis.
0.00E+00
2.00E+05
4.00E+05
6.00E+05
8.00E+05
1.00E+06
1.20E+06
1.40E+06
1.60E+06
-62-54-46-38-30-22-14 -6 2 10 18 26 34 42 50 58
C(w
,w')
C(w,w') for text G
C(w,w') for text G
61
Figure 6: C(w,w') for calibration pair on G and M
Both statistical values as represented by [eq. 17] and [eq.19] were collected and plotted
as and respectively:
Results of List one
List one as shown by Appendix D was collected by WRR and shown a historically
dependent link between the each word of the list and hope to find these in a fashion proving
the Torah Code hypothesis over text G and finding these in a fashion that proves the null
hypothesis over text M. List one in its original form contains the appellations of famous rabbis
and their birth and/or death dates. In order to show the null hypothesis suffices to run the test
with the last name of the appellation and one of the dates, whichever date is found. The
simplified list one is found at Appendix E. The list was further scrubbed to remove two dates
-62
-56
-50
-44
-38
-32
-26
-20
-14 -8 -2 4
10
16
22
28
34
40
46
52
58
C(w
,w')
[-mode,+mode] distribution
C(w,w') comparison
C(w,w') for text M
C(w,w') for text G
62
where the length of the combined word was less than 5 characters. The abridged list was then
pumped on the software and the process was set to run to check the pairs of the abridge list:
Figure 7: snapshot of the ELS program running with the items of the abridged list
Conclusion
When comparing the modern way to seeking comfort when tragedy strikes with the
prophetic words of the people of the bible striking similarities are uncovered: in today’s date
society seeks affirmation of events in different ways, being biorhythm, astrological maps, or
hidden codes on Scriptures. In earlier days people sought affirmations through the words of the
prophets. The analysis of fours thinkers with a span of 600 years proven that acceptance of
prophetic views oscillated from peeks to troughs during the course of history. The Torah Codes
as explained herein sought to uncover through mathematics and computing power the hidden
messages and affirmation of events just as yesteryear prophets sought to predict doom and
destruction. A clear difference between these lies of Kant’s definitions of pure reason: the
63
Torah Codes does it a posteriori whereas the prophets did it a priori. A candid analysis clearly
shows that in fact both approaches are a posteriori even though the perception of prophetic
doom was given prior to doom and the Torah Code shows after. As Leibniz concluded in MD,
the prophetic word is parallel to God’s work when done by His agents. In this case, Leibniz
would have concluded that, absent the fact that a pure Kantian vision precludes a priori status
to prophesy since the mere act of foretelling the future implies in an experimentation to prove
whether or not the foretold message in fact happened, the monadic agent is the same one that
can change the outcome, hence regardless of the message being foretold by the prophet, it is
God the agent of change, thus a priori by definition. On the same lines, Spinoza ought to reject
the idea of a Torah Code (Lin, 2007, pp. 7) per definition, as it would inject a self-causation
status to Torah itself, and being that the latter is not Natura Naturans, quod erat
demonstrandum. At least The Rambam would see absolutely no problem in accepting prima
facie the Torah Codes since his thirteen principles include a commandment to accept Torah as
true.
Author’s opinion about the Torah Codes
Up until now, this essay spoke in a narrative voice, absent of personal opinions from the
standpoint of a first voice. It is however important to note some comments from the author as
far as the process of programming the code finder algorithm and understanding of the
intricacies were concerned. The author voiced two sets of opinions, one on the physical
inconsistencies, and another on the logical inconsistencies.
64
Physical Inconsistencies when compared with an epistemological viewport
It is rather strange that after I programmed the software I noticed that most of WRR’s
arguments lie on a very thin border between acceptance and rejection of bona-fide pairs of
words. So if one is to side with Rambam that Torah is true and knows past, present, and future,
any ELS would satisfy [eq. 17], which is clearly not true. If we side with Kant there would be no
possible ELS found from choices a priori, which in essence of purism is true, but in a relaxed
understanding of a priori (meaning without knowing whether or not a pair would satisfy [eq.
17]) is found to be also not true since the calibration pair given above yields a number for [eq.
17] which satisfies the hypothesis. It is truly incomprehensible for a Spinozist to even fathom
such experiment as the Torah is nothing else but a mere book with no different attributes than
any other text T. Lastly anyone following Leibniz would be hard pressed to comprehend why a
pair of words satisfies the hypothesis but a similar pair satisfies the null hypothesis. In fact, the
whole conception of Torah Codes shows a distinct favoritism to some pairs in contrast to
others, which in my opinion support the critics of WRR and concludes that the Torah Codes
cannot be seen as a modern prophecy vehicle where Torah itself prophesizes. It is noteworthy
to acknowledge that indeed, an unnatural cluster of seemingly related words is found at G but
not at M, which may drive the momentum from a belief system standpoint. It is also
noteworthy that WRR (although perhaps innocently) used a list of rabbis that show the cluster
more clearly than perhaps another list. Conjectures aside, I ran the code on spelling variations
of the rabbis and indeed found larger clusters instead, which as I indicated, seem to create
favoritism in lights of prophesy. My exposé on the four thinkers demonstrates that prophesy is
either to be accepted or to be reject regardless of the prophet, so when the expectation is that
65
Torah itself is acting as prophet these variations do impose a larger degree of resistance
towards scientific acceptance, since Scripture itself comments that prophets spoke in the
language understood by the audience.
Logical inconsistencies when compared with an epistemological viewport
Stephen Hacking emphatically states that the world obeys the second law of
thermodynamics (Hacking, 2000). It would therefore be logically inconsistent that the Torah
would yield results of prophesy under a higher degree of entropy than the one I started with. It
would be the same as expect that logically a system would begin in chaos and somehow orders
itself. In fact the opposite happens. So it seems inconsistent with all laws of physics that seeking
ELS, which is clearly more entropic than the original Torah text, would produce hidden truths. I
would expect the opposite to be the case. Another fact that strikes as inconsistent is that, as
the text got scrambled, the codes mysteriously disappear as WRR’s experiments demonstrated
(WRR, 1997, pp 9). But I would expect the original positioning of the characters to be
immaterial with respect to the results since nothing is being added or removed from the
original text, only shuffled; the experiment ought to only proof that the algorithm is
inappropriate. The entropy of the system did change as I scramble the code, so perhaps the
failure to observe ELS on a scrambled text is due only to my lack of capabilities to find a new
algorithm suitable to find ELSs on a scrambled text.
As more and more scientific scrutiny was imposed on the WRR experiment and new
results demonstrated that small changes on the order of the pairs and word spelling produced
huge discrepancies on the results, the topic of ELS was left more as a belief system than a
scientific experiment. Perhaps the future would provide us with an algorithm that finds the
66
same ELS on scrambled version of the Torah, which would at least give credence to the fact that
the second law of thermodynamics is indeed being violated on both cases, a fact that can be
attributed only to God.
67
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APPENDIX A
Gematria
Historically the Jewish people throughout centuries consulted rabbis before the birth of
a child in order to find out if the numerical value of the chosen name was good or bad. It is
therefore important do differentiate the meaning of good or bad in terms of the numerical
value of a name: good means it equates to a value module another such that the result is a
factor of another value considered by Jewish values to be good, otherwise it is considered not
so good, or simply bad. The system by which these mathematical operations are carried is
called Gematria. Mathematically speaking, the system is rather simple, consisting in one of the
four different algebras over the system, being these: 1) The Absolute value, 2) The Ordinal
Value, 3) The Reduced Value, and 4) The Integral Reduced value. The system based itself in the
axiom that the numerical equivalence of Hebrew letters is not coincidental, following a defined
path which is mapped by these four different algebraic operations.
The Absolute Value Algebra (Normative Value)
In this algebra each letter of the Hebrew alphabet, hereinafter called א-ב, is given a
value equal to a predefine map. Since the א-ב is finite, the value loops through in a cycle giving
the first letter the numerical value equivalent to the following:
[eq.1]
As such, consider l = א, then v (א) with cycle c = 0, i.e., the very first time equals 1 since
the Normative Value for א is 1. For the next cycle, c is 1, and then v (א) = 1000 * 1, or 1000, and
so on. The same applies for ב, which has a normative value of 2. For cycle 1, v (ב) = 1000 * 2
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yielding 2000. The same process is repeated for each letter, and for each cycle. The map value
each letter consists of 10 to the power of 0 times the indexed value of each letter until the 9th
letter. Then for the next 9 letters the power is upped and the process continues until the 19th
letter. The next 9 letters follow suit, this time for power of 2, yielding a system which starts at 1
and ends at 900, juxtaposing each number to achieve a full system from 1 to 999.
Thus for the Normative Value it is produced the following table for v (l):
Letter V(letter) Letter V(letter) Letter V(letter)
100 ק 10 י 1 א
200 ר 20 כ 2 ב
300 ש 30 ל 3 ג
400 ת 40 מ 4 ד
500 ך 50 נ 5 ה
600 ם 60 ס 6 ו
700 ן 70 ע 7 ז
800 ף 80 פ 8 ח
900 ץ 90 צ 9 ט
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Table 1: Hebrew Normative Values for cycle 1
The Ordinal Value Algebra
In this algebra each letter of the א-ב is given a value equal to its predecessor plus one.
Since the א-ב is composed of 27 letters the system simply assigns each letter a number.
The Reduced Value Algebra
In this algebra each letter of the א-ב is given a value equal to its predecessor plus one up
to the 9th letter. From then on the cycle is repeated, this time however c is always zero at [eq.1]
and therefore the system is reduced to three sets of 9 values, each one cycling with the
previous one.
The Integral Value Algebra
In this algebra a total numerical value of a word is reduced to one digit. If the sum is
higher than 9 the integer values of the total are repeatedly added to each other yielding a
single digit value. The Integral value does not operate on a given letter and could be leveraged
with the three other algebras independently.
Ginsburg’s (2002) summarizes the algebras with the help of the following tables:
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Table 2: Gematria Tables (Ginsburgh, 2002)
Letter Filling Algebra
Another system is sometimes used when not only the value of the letter is calculated
from the tables above but also the spelling of the letters is factored using the same tables, and
the result is the value of the Gematria for that specific word. Therefore Letter Filling could
potentially result in more than one value, given that the spelling of Hebrew letters sometimes
varies without loss of generality. However the end value one gets from different spelling, they
are all considered good if at least one of these yields a value from the set of good values.
The meaning of Good (and its corollary)
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In Jewish theology, Good numbers are the ones that have the same Gematria as a set of
commonly accepted Godly emanations such as Life (Chai in Transliterated Hebrew, and חי in
Hebrew). חי is composed on two letters, Chet (ח) and Yod (י), together yields, again using [eq.1],
v(ח) + v(י) = 18 = 10 + 8. Therefore it is considered that any word whose Integral value yields 18
is symmetrical to Life. A corollary is that any word, whose Integral value yields the same
Gematria as death, sorrow, etc, is considered not good. Here the terms bad is loosely used to
address the corollary.
Operations over the various algebras
As expected, the algebras above provide some operations to be performed over the set
and its members.
Ordinal Pairing
The first basic pattern transformation over the א-ב is named the Albam method, where
the 22 first letters are blocked into two groups and , and then paired up together as a
new set composed of the pair formed by the ordinal pairing according to the formula below:
( | )
From [eq.2] it is seen that since the א-ב is extended to 27 letters, the whole א-ב does not
consist of a closed set. Therefore a corollary of [eq.2] states:
( | )
Therefore equation [eq.3] yields a set which contains the remainder letters of the א-ב, and
consequently:
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⨄
The א-ב does not appear to have some elements as found in numeric sets such as the
Identity element, and the Zero element, however there is a clever way to achieve such
equivalent elements; for the Identity element suffice to say that Integral Algebra produces the
following: and if it is allowed the reduction algebra to be inclusive within a
group, the Zero element is found using [eq.6]. As such, the Identity element is any
letter yields a reflection on itself. In order to facilitate the Gematria work ahead this
essay will assume א as the general Identity element. The table below shows the tuple pairing of
the two groups:
Albam Method
ל א
מ ב
נ ג
ס ד
ע ה
פ ו
צ ז
ל ח
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מ ט
י ק
כ ר
Table 3: Tuple pairing for Ordinal Pairing Operation
Reflexivity Properties
The second basic pattern transformation over the א-ב is named the Atbash method,
where the each letter is substituted with the equivalent ordinal in reverse order. It is therefore
a reflexive operator applied to a Set such that:
That is, the first letter is reflected with the last one, the second one with the second last one,
and so forth.
Reflexive Pairing Properties
The third basic pattern transformation over the א-ב is named the Achbi method, and is
combination of the Pair Ordinal with the Reflexive Property. In this transformation each letter
is substituted with the equivalent Paired Ordinal in reverse order as defined by the following
equation:
( | )
That is, the first letter at Group 1 is reflected with the last one at Group 2, the second one with
the second last one, and so forth.
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Ordinal Triple Properties
The fourth basic pattern transformation over the א-ב is named the Ayik-Becker method,
and is the Tuple Ordinal over the Set . In this transformation the S is split in three
groups and tuples are formed according to the following equation:
This transformation yields a table as shown below:
ק י א
ר כ ב
ש ל ג
ת מ ד
ך נ ה
ם ס ו
ן ע ז
ף פ ח
ץ צ ט
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Table 4: Tuple Ordinal Transformation
Reduced Reflexive Property
The fifth basic pattern transformation over the א-ב is named the Achas-Beta. In the
Achas-Beta system, the Set is reduced by only considering the first 21 letters of the
and then splitting the Set in three groups of 7 letters each. Then the tuples is
formed as defined by [eq.8].
Reflexive Tuple Properties
The sixth basic pattern transformation over the Set א-ב is named the Atbach. In the
Atbach, an extension of the fourth system is presented; in this transformation each letter is
substituted with the equivalent Tuple Ordinal in reverse order as defined by the following
equation:
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APPENDIX B
Hebrew Equivalence Table
Letter Equivalent Letter Equivalent Letter Equivalent
Q ק Y י ( א
R ר K כ B ב
$ ש L ל G ג
T ת M מ D ד
N נ H ה
S ס W ו
) ע Z ז
P פ X ח
C צ + ט
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APPENDIX C
C# Code for the ELS algorithm as defined by WRR
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APPENDIX D
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APPENDIX E
