The Logic of
Simple Synthetic Integration
Men all pay homage to what understanding understands, but no one understands enough to
rely upon what understanding does not understand and thereby come to understand. --
Chuang Tzu [C55:5.288]
Reality is not perfection except in the active equilibrium of the fusion of dynamic
opposites. --Purce [P538:19]
3.1 The General Form of Simple Synthesis
If we were to regard logic solely in terms of its mathematical foundation,
then our discussion of its analytic forms in Chapter Two would suffice as a
complete introduction to all the formal relations utilized by logic on its most
abstract level. Bertrand Russell, the modern philosopher primarily responsible
for popularizing the view that logic and mathematics are identical, would affirm
that logic is concerned solely with "'analytic' propositions" [R517:204]--i.e.
with propositions which are both a priori and non-empirical. This approach has
been so widely accepted during the twentieth century because it promises to
ground philosophical speculation once and for all in the solid rock of logical
clarity, and likewise logical thinking in the solid rock of scientific, mathematical
rigor. But in spite of the widespread acceptance of this modern presupposition
concerning the nature of logic, we should not be satisfied with such a one-sided
approach. For the application of the Geometry of Logic to systems in Part Two
depends upon establishing the logical foundation of synthetic reality with equal
rigor.
Both modern and traditional logic do provide us with valuable tools for
the clarification of thought; but each is valid only within the bounds of the
perspective on which it is based. Modern logic, with its firm foundation in
mathematics, is indeed, as Russell insists, entirely analytic. It must be, for it
rules out beforehand the relevance of concrete experience. Traditional logic, too,
is predominantly analytic. However, if we look beyond the narrow scientific
limits of analytic thinking, and open up the field of logic to the realm of
experience and its multifarious art forms, we will find a radically different way
of constructing logical relations: for in addition to the analytic forms of relation
discussed in Chapter Two, experience reveals certain synthetic forms of relation.
In the immediate, non-reflective experience of everyday life, we are often
confronted with situations in which there is no clear-cut distinction between
"positivity" and "negativity". Numerous questions which arise empirically, or
are asked from the synthetic perspective of immediate experience, cannot be
answered with a simple "yes" or "no", but only with "yes and no". This fact
cannot be forced into the neat compartments of a purely analytic system of logic;
yet there is no reason to assume that it is therefore irrelevant to or incompatible
with the structure of logical inquiry. On the contrary, such experiences represent
the "unfolding" of "an essentially logical process" [W533:21]. Since our
expressed interest is in developing an approach to logic which is intuitive as well
as conceptual [see Introduction], the logical basis of such apparently illogical
(i.e. non-analytic) experiences is well within the scope of the Geometry of
Logic. Moreover, some logicians in the West, notably Hegel and the whole
tradition of German Idealism, have expended a great deal of effort in
constructing entire philosophical Systems on the basis of synthetic logic.
Rabel's paraphrase of Kant's definition of the terms "analytic" and
"synthetic" provides a helpful clue as to what is involved in this distinction:
"Analytical judgements explain, synthetical judgements expand" [R422:106; cf.
K105:10-4]. Analysis explains various elements (e.g. concepts) by dividing a
unified whole into its constituent logical parts. Such analytical explanations
sometimes distort the nuances inherent in the original whole, as when a twenty-
four hour period is explained as being composed of "a night and a day"; but this
is only to be expected, for the explanatory power of analysis depends on the
ability to reduce what is complex to what is readily graspable (?!). Synthesis, by
contrast, expands its elements by integrating two or more opposing terms in a
"third term", a "higher unity" which is more than simply the sum of its parts.
The third term transcends the simple opposition posed by the first two terms in a
way which is completely foreign to analysis: it represents both the unity and the
diversity, or indeed, the "unity-in-diversity" of its constituents.
Whereas analysis at its simplest level is a one-step operation yielding two
elements (i.e. a simple division of one into two), synthesis at its simplest level
can be described tentatively as a two-step operation involving three elements.
Using Hegel's well-known terminology, these two steps can be described as (1)
that in which the "thesis" is confronted with an "antithesis", and (2) that in which
the two opposing terms are united and transcended in the form of a "synthesis".
Using arrows to denote the radically dynamic character of synthetic relations, we
can depict these two steps as follows:
Figure 3.1: Hegel's Logic of Synthesis
(a) Step One (b) Step Two
This initial way of mapping synthetic relations will be revised as we take
a closer look at its full logical form, but for now it provides an adequate
description of the general form followed by the simple synthetic operation which
we shall refer to as "synthetic integration".
3.2 A Symbolic Notation for of Synthetic Logic
We have already discussed [in 1.4] the crucial importance for any
modern logical approach of choosing appropriate symbols to represent the key
terms and relations at the outset of any given inquiry. Since the Geometry of
Logic abstracts from all specific types of material terms and relations, we will
once again require only one set of symbols, which can be used to represent the
general character of all synthetic forms of relation. In our elaboration of the
analytic forms of relation the two symbols "+" and "-" were sufficient to define
all the levels of analysis in its most abstract structure. These same symbols are
can also be used to describe the first of the two steps in a synthetic operation
mentioned in 3.1, in which one element (+) is confronted by its opposite (-) [cf.
Figures 3.2a and 3.1a]. But the second step poses a problem, for we clearly
require a new symbol to represent the crucial third term of a synthetic relation
[cf. Figures 3.2b and 3.1b].
Figure 3.2: Symbols of Synthesis
(a) Step One (b) Step Two
Because of the naturally obscure nature of synthetic relations (at least in
comparison to the clear-cut nature of analytic relations), and because no symbol
for "synthesis" (in this non-analytic sense) has been generally accepted in the
past, it will be helpful to discuss several ways of symbolizing this form of
relation. Discussing the pros and cons of several options will help to clarify the
nature of the operation of synthetic integration.
The most obvious way of symbolizing the integration of "+" and "-" in a
single synthetic term is to combine the two to form the symbol " ". This option
has the advantage of explicitly stating the logical roots of the synthesis in such a
way as to reveal why our response to empirical situations evincing synthetic
integration is often "yes and no". But it is also misleading for this very reason.
The mere appending of one symbol (+) to another (-) would seem to imply that
the third term in a synthetic relation is no more than an artificial holding-together
of two entities which remain discrete. (A more adequate response to synthetic
reality might be "yes-no"; yet even this, as we shall see, is expressing a synthetic
situation in analytic terms.) Moreover, the term " " is used in mathematics to
refer to a choice between "+" and "-": "1" means "+1 or -1" (though the force of
"or" is often intended to be inclusive rather than exclusive). The symbol " "
therefore fails to carry with it the implication of transcendence, which is vital to
the process of synthetic integration. Using this symbol would be like mixing a
bucket of black paint with a bucket of white paint and referring to the end
product as "black and white", instead of simply "grey" paint.
The symbol "x" avoids all the drawbacks which plague " ". As the
mathematical sign for multiplication, it has a natural place alongside "+" and "-",
yet it refers (rather appropriately) to a radically different kind of operation. Thus
if these three terms are used to refer to logical forms of relation rather than to
mathematical operations, one would expect them to have parallel, but clearly
distinguishable functions. Such would be the case if we adopted "+", "-" and "x"
as symbols for the three constituents of the synthetic form of relation. For just as
multiplication is related to, yet transcends, the operations of addition and
subtraction, so also synthetic integration is related to, yet transcends, the analytic
division between two opposing terms. The letter "x" is also used as the archetype
of all mathematical variables. Using it in our present context would not imply a
simple choice between one of the two root terms "+" and "-", or both together,
but would open up the possibility of assigning some intermediate value to the
third term. The extent to which a given synthetic relation leans more toward the
"+" or more toward the "-" in its third term could then be determined only on the
basis of a concrete experience involving the particular synthetic operation under
consideration. The suggestiveness of its two mathematical functions, therefore,
makes "x" a strong candidate for a symbolic representation of the third term of a
synthetic operation. Its only drawback is that it could be mistakenly taken to
imply that a given synthetic relation is itself "variable", when in fact, it is every
bit as determinate as are its "+" and "-" roots.
A third option is to attempt to preserve the useful aspects of both " " and
"x" but avoid their drawbacks by using a familiar set of symbols whose ordinary
use is rather more distant from that of "+" and "-". The symbols "0" and "1" fit
nicely into this category. In 1.2 we noted the common use of these symbols to
represent "nothing" and "everything", or "the null class" and "the universe class"
in a given universe of discourse. The distinction between "0" and "1" is itself
based on a first level analytic division; for in relation to "0", "1" is "+", and in
relation to "1", "0" is "-". But if "0" and "1" are regarded as referring not to
numbers or classes, but to synthetic forms of relation, then the function of "+"
and "-" will be to mediate between the extreme functions of "0" and "1". For the
"0" would serve as a hidden term, or presupposition, of all synthetic operations,
and the "1" would represent the "third term" which unites or integrates "+" and
"-" by transcending them both in the form of some sort of conclusion. ("1" is
particularly appropriate to fulfil this integrating, or unifying, role because in its
mathematical meaning it represents the integer which is defined as a numerical
unit.) Thus the full pattern of synthetic integration is a three step process, which
can be mapped as follows:
Figure 3.3: The "0" and "1" of Synthetic Integration
Here, of course, the symbol "1" would not represent "the universe
class", but rather a "unit of synthesis"; likewise "0" would not represent "the null
class", but rather a "pre-synthetic state".3
This symbolism is particularly appropriate when used to represent a chain
of two or more synthetic relations. For the "1" of a given synthetic operation can
act as a "0" for a subsequent synthesis, thus giving rise to the compound symbol
"0". A full treatment of such "complex" synthetic relations will be given in
Chapter Four. At this point, however, we should note that, by combining "0"
and "1" in various ways, we can actually achieve much the same "variable" result
as is suggested by the use of "x", but without implying that the third term of the
synthetic relation is an unknown. The flexibility of these symbols is evident
when one is divided by the other in various combinations: the standard algebraic
symbol for an "indefinite number" is "0/0" and for "infinity" is "1/0"
[B506:6.10-1]; likewise "1/1" represents unity and "0/1" emptiness, or Nothing.
These four ways of dividing the numbers "0" (+) and "1" (-) are related in terms
of a perfect second level analytic division:
Figure 3.4: The Analytic Combination of 0 and 1
Indefinite!(0/0) # # # Unity (1/1) Infinite (1/0) # # # Nothing (0/1)
The arithmetical meanings for these combinations of 0 and 1 can be
transferred directly to the logic of synthesis simply by noting that a synthetic
operation ideally passes through each of these stages as it progresses from an
indefinite "pre-synthetic" state (0), through the extremes of infinite positivity (+)
and empty negativity (-), to a single unified solution (1). Moreover, the reality
that synthetic relations do not always operate according to such a neat plan can be
expressed by representing their outcome in terms of fractions (i.e. real numbers
between 0 and 1). In this way the logic of synthesis can be regarded as the
formal basis of the logic of probability, which is the application of logical laws to
real situations, with a view towards determining the appropriate fraction to
represent the chances of completing a given synthetic operation.
Although the symbols "0" and "1" are obviously superior to " " and "x"
as representations for the third term of a synthetic operation, it will be helpful to
consider one final option by attending to the geometrical shape of the symbol
rather than to its mathematical meaning. That the mathematical symbols "-" and
"+" are appropriate terms for representing analytic relations is confirmed by the
fact that they have the same geometrical shape (a short horizontal line and a
symmetrical cross) as the standard maps for the first two levels of analytic
division [cf. Figures 2.2 and 2.3]. In choosing a symbol for synthetic integration
we should therefore keep in mind the importance of its geometrical value, as well
as the implications, if any, of its ordinary mathematical use. On these grounds
the simple combination of "+" and "-" in " " seems even less appealing, as does
the symbol "x", which is essentially a "+" turned sideways. (Note the "x"
formed by the diagonals of the square, which was established as a standard map
for the inversion of second level analytic division in 2.2.) Neither of these is
sufficiently distinct from "+" and "-" to represent the radical difference between
analytic division and synthetic integration.
At first sight the symbols "0" and "1" fare no better. Since no synthesis
stands alone in actual experience, but is interrelated with other synthetic
operations, the third term not only concludes the given synthesis, but sets the
scene for another; so the symbols "0" and "1" in Figure 3.3 will occur together
in every real synthetic operation. This means that, even though we originally
introduced synthesis as a twofold operation, and even though it appears to
involve four elements when we view it analytically, as in Figures 3.3 and 3.4, it
is properly regarded as a threefold operation. The most appropriate geometrical
figure for mapping the constituents of a synthetic relation, then, is the figure with
three vertices and three sides: the triangle. The simplest and most regular
triangle, the equilateral, is the most likely candidate for an intuitive representation
of these conceptual relations. Mapping synthesis onto the triangle (using "0" and
"1" in the above sense for the time being) enables us to construct the circuit given
in Figure 3.5, in which the primary direction of synthetic influence is indicated
by arrowheads.@ This figure symbolizes the way in which the roots of a
synthesis are opposed to each other, as it were, "horizontally", yet "rise" to a
common, "higher unity" in the third term of the synthetic relation. This same
operation can be mapped onto the well-established analytic figure of a square by
artificially separating the "0" into "0" and "1", and joining two right triangles by
a 11 common hypotenuse [see Figure 3.6].@ Using the right triangle in this
Figure 3.5: The Triangle of Simple Synthetic Relations
Figure 3.6: An Analytic Map of Simple Synthetic
Relations
way is even more appropriate than using an equilateral triangle, since the
difference between the relation of "+" to "-" and the relation of these to "0" and
"1" is symbolized by the difference in length between the hypotenuse and the
shorter sides of each triangle. (Alternatively, if the two triangles in the area of the
square are labelled with "+" and "-", then their common hypotenuse would
represent the synthesis of the two extremes.)
The triangle is clearly more suggestive as a symbol for the threefold
operation of synthesis than is the rather ambiguous "x" or the somewhat
awkward "0". Aside from its rather obscure, technical use in the construction of
formal languages, as a symbol representing sets of "well-formed formula", the
triangle does not have the potentially misleading connotations, resulting from
familiarity of use, which are possessed by all the alternative symbols considered
above. The triangle has been defined in terms of the overall process by which
"+" and "-" produce "+", "x", or "0". However, we have not actually been
searching in this section for a symbol which can represent the entire threefold
operation of synthetic integration, but only the third term of the synthesis.
Whenever the synthetic operation as a whole is concerned, it will therefore be
best to use the symbol " ". The symbol "0" can then 1<1 be reserved for
instances in which the notation requires us to break the synthesis down into its
constituent elements. When the third term alone is referred to without any
intention of distinguishing between its "0" and "1" aspects, the symbol "x" will
sometimes be substituted as its equivalent. Taking advantage of the benefits of
both "01" and "x" will help us avoid wherever possible the rather unfortunate
mixture of metaphors involved in using both mathematical signs and numbers in
the notation of a single expression.
We can test our symbolic notation by applying it to a straightforward
example of synthetic operation, drawn directly from the experience of every
human being. In 1.4 the male (+) and female (-) distinction was mentioned as an
example of a first level analytic division, at least as it applies to the biological
function of the sexes in procreation [see note 1.20]. The whole topic was treated
from an entirely analytic perspective, with a view towards establishing the nature
of such an exclusive (A = -A) relation. Hence the logical status of the child 1/
was not even considered. When this same distinction is treated synthetically, by
contrast, the child takes on an integral role in the overall situation. For it
completes a process which remains partial as long as the "+" and "-" are kept in
opposition: synthesis, whatever it is, certainly involves more than merely two
polar opposites being held together side-by-side.
Procreation is in a sense an imperfect example of synthetic integration,
since it does not result in a third sex, but in a child who is one or the other. As
such, the symbol " " would be appropriate to represent this synthetic role, at least
insofar as it is read as "+ or -". For the offspring will inevitably be fit into one
category or the other. But before it is actually born, the symbol "x" would be
even better, since (barring the intervention of modern medical techniques) the
child's sex is unknown to its parents. If we look beyond the (analytic) sex label,
however, we find that every child is in fact a perfect synthesis of its parents, for
the chromosomes which determine the potential size, shape and character of the
child are drawn from both sources, and are mixed always in quite a unique way.
The " " fails to represent such a mixture, whereas the "x" implies the potential for
a wide spectrum of results. But the "0" is even better, for it implies 1&1 that the
resulting "third term" is a separate individual (1), though defined in terms of its
overall synthetic context ( ), and that some of its characteristics may well have
been present in its parents only covertly (as "0"). Thus we can say that a child
draws "everything" (1) from its parents, yet maintains a transcendence from
them which somehow goes both beyond and before their influence, so that we
can just as accurately say that the child (as the instigator of new syntheses) draws
"nothing" (0) from its parents.
This example serves as a "preview" of the way our new notation--
particularly "x" and "0"--can be used to clarify the various constituents of a
synthetic relation. We must now take a step backwards, and ask what laws form
the basis of this operation of synthetic integration. Only in this way will we then
be adequately prepared to examine in 3.4 other examples of various types of
synthetic integration and fully to appreciate what is involved in the "complex"
forms of relation (discussed in Chapter Four), or in the "compound" forms of
relation (discussed in Part Two), which combine both analytic and synthetic
operations.
3.3 The Logical Laws of Synthetic Integration
We began our investigation of the Geometry of Logic by discussing the
fundamental logical laws of identity (A = A) and non-contradiction (A = -A). We
then witnessed in Chapter Two how these two laws function 1/ as the necessary
presuppositions of analytic division. As such, they should be regarded as "set
apart" from other, secondary laws of formal logic. Yet, because of their
exclusive interest in propositional logic, and their consequent reluctance to
abstract all material elements from their formal logic, most modern logicians now
bunch these laws together with a number of other "fundamental" formal laws,
such as the logical equivalents of the algebraic laws of the commutative,
associative, and distributive relations between elements (i.e. "a+b = b+a",
"(a+b)+c = a+(b+c)", and "a(b+c) = ab+ac", respectively). The irrelevance of
these other formal laws to the operation of analytic division in its most abstract
manifestation (as described in Chapter Two) clearly indicates their secondary
nature: they come into play only when some measure of content is added, even if
it be nothing more than the content implied in the consideration of "propositions
in general".
The question we are now faced with, however, is: What logical laws
form the basis of synthetic integration? Content in some form must be taken into
consideration in order to answer this question; for, whereas analytic division is
the operation which determines the logical structure of thought in general,
synthetic integration is the operation which determines the logical structure of
what we might call (with Kant) sensible intuition in general. These two elements
can be regarded as the formal and material elements in all experience. Hence the
logic of synthesis, which at its simplest and most general is the logic of sensible
intuition, is the polar opposite of the logic of analysis. If the latter is defined in
terms of "analytic a priori" (+-) laws, we can therefore define the former in terms
of "synthetic a priori" (-+). The traditional "laws of thought" must give way in
this context to an equal and opposite set of "laws of intuition". Our task in this
section will be to determine just what these alternative laws are and how they can
best be stated.
This will prepare us to discuss in 3.4 some specific examples of how
synthetic integration is applied in actual situations.
The main problem in dealing with the logic of synthetic integration is
that, by its very nature it cannot be expressed accurately in conceptual terms.
Expression in words (logoi) is naturally suited to describing analytic division,
but must be strained in order to describe synthetic integration (ho logos). In fact,
the only way a logic of synthesis can be developed is to borrow terms and laws
from the logic of analytic division, redefining them in terms of their polar
opposites. The precise meaning of the logical system which results will be
difficult, if not impossible, to conceive in abstraction, since conception is
primarily analytic; but it will nevertheless provide a useful and much needed
explanation of the intuitive form according to which all human experience is
structured.
The law which governs the second step in a synthetic operation is the
opposite of the law of non-contradiction, so we shall refer to it as the "law of
contradiction". This new law states that "A = -A". For in the first step the "+"
empties itself completely of its positive nature and loses itself in the negativity of
its opposite. "A" becomes equal to "-A", yet without losing its discrete nature as
"A". This law of contradiction is the logical basis of the essential tenets of many
world religions, from the Hindu doctrine of the self-emptying of man to become
Brahma, to the Christian doctrine of the self-emptying of God to become man in
Christ. Such doctrines are perverted when they are interpreted in such a way that
the contradiction is resolved or explained away: for the power of religious
discourse is inextricably bound up with its dependence on the laws of synthetic
integration. To interpret them analytically is to render them powerless. As we
shall see, the law of contradiction, "A = -A", "+" becoming "-", is at the heart of
much of our everyday experience, even in the secularized modern world. For in
real experiences we are constantly met with things which are what they are, yet
are their opposites as well--with questions that can be answered not by "yes" or
"no", but by "yes and no".
The law which governs the first and third steps in a synthetic operation is
the opposite of the law of identity, which we shall refer to as the "law of non-
identity". This new law states that "A = A". For 1>/ in the third step the "+"
transcends the entire +/- context, and becomes, as it were, "born again" into a
new form. (A similar process occurs in the hidden first step.) "A" no longer can
be equated with "A", for it is now radically transformed. "A" is the same entity,
yet it is no longer "A": in union with "-A" it is now integrated, it is now "1". We
experience the effects of the law of non-identity whenever we feel something
(either sensibly or emotionally). For to feel is to be confronted with the non-
identity of oneself with oneself, or of an object with itself, to be jarred into an
awareness of the non-conceptual basis of the real world, to realize that A = A.
1+/
Some of the differences between these two laws of synthetic integration
and the two traditional laws of analytic division can be brought to light by
comparing the properties of their respective geometrical representations, the
triangle and the square. The triangle is the only rectilinear figure for which
equality of angles guarantees equality (i.e. proportionality) of shape. This is
exemplified in Figure 3.7:
Figure 3.7: The Relation Between Angles and Shape
(a) In the Triangle (b) In the Quadrilateral
No matter what length is given to the sides of various triangles, if the
three angles are the same in each case, then the shape of each will be equivalent.
If "+" represents the relation "sameness of angles" and "-" represents the relation
"sameness of shape", then the equation "+ = -" (reading "=" as "guarantees")
holds for triangles. For quadrilaterals and all other rectilinear figures, by
contrast, sameness of angles does not guarantee sameness of shape--thus "+ = -
". The consistency of geometrical figures with the laws of synthesis and
analysis, respectively, is due to the fact that geometry is essentially synthetic,
whereas mathematics is essentially analytic: the former deals (albeit with the full
use of analytic tools) with the form of space, the realm of experience, whereas
the latter deals with the realm of thought, in complete abstraction from
experience.
As mentioned above, these two laws of synthetic logic have been
described using the terms of analytic logic. This has two primary consequences,
one beneficial and one detrimental. The beneficial implication is that the four
fundamental laws of logic, two synthetic and two analytic, can be mapped in
terms of a perfect second level analytic relation by contrasting "A = ..." (+) with
"A = ..." (-) on the first level and "...A" (+) with "...-A" (-) on the second:
Figure 3.8: The Four Laws of Formal Logic
(a) Mapped onto the Cross (b) Mapped onto the Square
These maps clarify why the two traditional laws have the appearance of
all-sufficiency: because they occupy the "++" and "--" positions (the first and the
last in Figure 3.8a), it is easy to ignore the polar opposites of each and assume
the relation to be a first level analytic relation between "+" and "-". They do have
a logical priority for this reason, but this should not deceive us into emphasizing
their importance to the complete exclusion of their second level partners. Figure
3.8b is particularly helpful in this regard by positioning the laws of analysis on
one diagonal and those of synthesis on the other, thus implying a more balanced
status.
The detrimental consequence of such an analytic frame of reference stems
from the fact that we in the West have been trained from an early age to assume
(unconsciously) that all of life (thought, intuition, and all the experiences which
they compose) can be adequately interpreted only in terms of the principles of
identity and non-contradiction. As a result we find it difficult, if not impossible,
even to countenance the idea that there may be a different way of thinking
properly about aspects of the world which are not bound by the formal limits of
our analytic thought patterns. The analytic frame of reference merely heightens
the stark contrast between the two methods. Eastern cultures tend to be more
open to the possibility and value of such "non-logical logic". ("To know non-
knowledge is the highest good", says Lao Tzu [L532:71].) Indeed, their
openness to synthetic integration and their interest in its formal basis may help to
explain why, as any reader of ancient Chinese or Indian philosophy will readily
affirm, the philosophers of the East often seem from our analytic perspective to
be inconsistent and unclear in their mode of expression. For just as the intuitive
experience of the Western philosopher too often lacks integrity because of his
inability to force it into the analytic mould, which he has mastered and in which
he excels, so also the Eastern philosopher too often lacks consistency because of
the inherent difficulty in expressing certain thoughts according to the mould
provided by the synthetic integration which characterizes his approach to life.
True integrity and logical consistency are possible only when both of these
extremes join hands and learn from each other, so that synthetic integration and
analytic division are seen as complementary modes of philosophical inquiry,
each with their own legitimate logical foundation. (In Part Two we will
investigate the ways in which these two types of logic work together to produce
compound forms of relation.)
From the logical perspective, analysis precedes synthesis, for the "++"
and "--" relations are themselves a first level analytic relation, which only
includes "+-" and "-+" when it is extended to the second level [see Figure 2.3a].
For this reason a logical treatise should discuss analytic division before
discussing synthetic integration. Without doing so we would have had no means
of describing the latter operation. From the empirical perspective, however,
synthesis precedes analysis: conceptualization depends on the prior existence of a
body of material which is given to it and upon which it can impose its forms.
Prior to analysis, the positive and negative roots of synthetic integration remain
"unknown" (i.e. unspecifiable): all we know is that we experience the
contradictory self-opposition of the synthetic process. Once synthesis is
complete, though, we can turn around and analyze the constituents of the
synthesis. Thus analysis can be mapped onto the standard synthetic map simply
by separating the "0" and "1" in "0" and reversing the arrows [cf. Figure 3.6]:
Figure 3.9: Analysis, Viewed Synthetically
We reverse the flow of synthesis in this way whenever we adopt the laws
of identity and non-contradiction in order to classify the contents of our
experience into similar groups. The step from "1" to "+" and "-" is analytic
division as described in Part One; the step from there to "0" verifies the result by
insuring that the cross between "+' and "-" is always the null class (hence
Boole's equation for the law of non-contradiction: "x(1-x) = 0" [see 1.2]). Such
analytic "exclusion" must not be confused with the synthetic "inclusion"
presented in experience itself, for as we have seen, the latter operates on the
basis of its own quite distinct logical laws.
3.4 Perspectives in Synthetic Applications
The reversal of direction which characterizes the change from analysis to
synthesis and from synthesis to analysis represents a fundamental difference in
the weight which is given to one's perspective in these two operations.
Perspectives arise out of reflection upon one's experience, so the original non-
reflective experience of synthetic integration is in a sense perspectiveless. All the
perspectives we can adopt in reflecting on our experience are present in
experience, but only in a potential state, meshed together in synthetic unity.
Synthetic integration establishes the perspectival basis on which alone analytic
division can be used to discern different perspectives. Synthesis proceeds from
"0" to "1"; analysis begins with the "1" and divides it into the "many". If we
attend to the perspectival shifts involved in synthetic integration, shifts which can
be identified only from the standpoint of analysis, then the laws of synthetic
logic turn out to be less objectionable than they appear to be at first. For the
contradiction can often (though not always) be made more palatable by taking
note of the perspectival difference between the terms on either side of the "=".
Two examples will help to illustrate this point.
First, the whole of modern sub-atomic physics is based on a fundamental
contradiction which has been accepted, but made palatable by means of an
awareness of the perspectival relationship between the two sides of the
contradiction. The contradiction is best known for its application to the physical
theories of light, which can be viewed either as a particle, or as a wave, but not
both. The general principle upon which the theory of light is based is that the
method by which the observer views sub-atomic "objects" (or "observables")
determines, or even changes, its very state. Thus the physicist can measure either
the position or the velocity of an observable, but it is impossible to measure both
at the same time. Once the synthetic experience of a single object manifesting two
contradictory qualities is analyzed in terms of its perspectival basis, it becomes
quite plausible to hold both views simultaneously.
The second example is simply a reminder of what we have already said
about the triangles in Figure 3.7a. If we are asked whether these triangles are
equal, we find ourselves answering "yes and no": yes, they are equal from the
perspective of their angles and their shape; but no, they are not equal from the
perspective of their size. In geometry the "=" sign is often used to relate two
terms which are equal in one sense, though unequal in others. In co-ordinate
geometry, for example, the equation "AB = Y" can be used to describe a line
segment (AB) which is parallel to the Y-axis [W516:165-6], even if it is not
equal in other respects (e.g. does not cross the X-axis at the same point).
It is crucial to understand that such attempts to explain the perspectival
basis of the contradictions of synthetic integration are primarily valuable as aids
to seeing the compatibility of the analytic and the synthetic. "A = -A" and "A =
A" still hold in synthetic integration, even in those cases for which we can
"explain away" their contradictory appearance by analyzing, e.g., the influence
of time in the changes which have taken place. We learn to cope with the rhythm
of "contradiction-resolution" to such an extent that we become unaware of our
constant participation in it--that is, until a contradiction crosses our path which
refuses to submit to the neat categories of perspectival analysis. In such cases we
are left with two alternatives. First, we can refuse to admit its contradictory
nature, and hope we will not suffer any adverse consequences as a result of our
inability to understand it. Or second, we can seek to adopt a new, higher
perspective, from which the contradiction can be taken up into ourselves and
therefore "understood" in a non-discursive sense. Only by adopting the latter
approach is the reciprocal relation between analysis and synthesis fully realized.
The remainder of this section will therefore be devoted to a discussion of several
examples of the many diverse ways synthetic integration manifests itself as a
means of encouraging a heightened perspective.
The simplest and most general description of the content of synthetic
integration is as the process by which "this" becomes united with "that", so that
both together occupy common ground in a new dimension of reality. This union
of "this" and "that" marks the starting-point of philosophers as diverse as the
ancient Chinese Taoist, Chuang Tzu, and modern Western Idealists, such as
Hegel [see e.g. H112:???]. Those who turn around and regard these same terms
analytically end up with a considerably more sterile result: "This remains
identical [i.e. remains a discrete object] and is thereby distinguishable from that"
[S515:404]. But without the synthetic recognition of a common universe in
which "this" and "that" both take part, and in which they may be combined, such
an analytic distinction between them would never be possible. Philosophers who
base their entire Systems on synthetic logic proceed not from the abstract to the
concrete, but from the concrete synthesis between "this" and "that" to more
abstract syntheses such as "self" and "not-self" [e.g. Fichte, F : ], eventually
leading to some ultimately abstract Synthesis--e.g. between "Being" and "Time"
in the form of "Dasein" [Heidegger, H : ], or (for Hegel) between God and the
World in the form of Absolute Spirit (i.e. of Religion and Art in the form of
Philosophy).
Synthetic logic manifests itself in one form or another in virtually every
corner of philosophy. For synthetic operations are involved in the construction
of many arguments. We have already mentioned [in 1.3] that the simple
syllogism is a good example of synthetic reasoning. But even arguments which
are not intentionally syllogistic often manifest the essential characteristics of
synthetic integration by positing a starting-point, connecting it with a condition
with which it would not ordinarily be connected, and drawing a conclusion
which transcends either condition on its own. Kant's "Analogies of Experience"
[K105:218-65] are a typical case in point. He describes three principles as
governing the relations between empirical objects: a permanent substance
persisting through all change (+), the law of cause and effect governing all
change (-), and the integration of these in the postulation of the interrelatedness
of all empirical objects (x). Only by presupposing that substance allows itself to
undergo change (i.e. only when A = -A) are we able to conceive of the objects of
our experience as constituting an unbroken network of integrated relationships.
The contradiction that the permanent changes is easily resolved by viewing the
situation analytically in terms of the distinction between a substance (which is
permanent) and its attributes (which change). But this analytic perspective in no
way nullifies the essential contradiction entailed in adopting a synthetic
perspective on the same subject.
Even the explicitly "analytic philosophy" of the twentieth century is based
on a concept which is primarily synthetic (though their failure to recognize this
fact often results in a distorted appraisal of the role of philosophical inquiry).
Analytic philosophy is based on an analysis of meaning, and the meaning of a
word, if one follows Wittgenstein's lead, is to be found by examining its use.
The analytical tools of modern logic are therefore used to pry the meaning from
the use of philosophical propositions, as well as from those of interest which are
found in ordinary language. What seems to be ignored too often is the synthetic
foundation of all meaning. For, as Stebbing rightly says in S515:499: "Means,
or symbolizes, is a triadic relation; its three terms are: (i) the sound or mark, (ii)
the person using the sound or mark, (iii) that which is referred to." The synthetic
foundation of meaning can be represented by mapping this description directly
onto the triangle of simple synthetic integration:
Figure 3.10: Meaning as a Simple Synthetic Relation
the symbol used 1 to refer
the object the subject
of reference who refers a referent)
Stebbing adds: "When...we say that the word has meaning, then the word must
not be identified with the sound (or mark); it will be the sound (or mark) as used
to refer to something." "Meaning", therefore, refers not just to the third term of
the relation, but to the entire operation of synthetic integration. The meaning of a
word is not to be found in the meaning of the word(hence A = A), but in the use
to which it is put in the real act of reference (where A = -A). This conformity to
synthetic logic does not preclude the possibility of treating the meaning of a
word, once it is given, from a purely analytic perspective. Indeed, analytic
philosophers take this as their starting-point when they analyze the constituents
given in such syntheses. Such analysis may clarify meaning, but on its own it
can never create meaning; nor can it explain how meaning is created. Hence,
although an exclusive concentration on analysis certainly allows the philosopher
to "make sense" (i.e. to produce coherent explanations), it prevents him from
making sense (i.e. from originating new syntheses).
The philosophical question at the heart of the science of cybernetics (viz.:
Can computers think?) can be readily answered once the fundamental difference
between the logic of synthesis and the logic of analysis is understood. A
computer is a logic machine, which can be programmed to do analytic operations
on command. To this extent a computer can think. But real thinking--i.e.
thinking of the sort performed by human beings--is ordinarily more than bare
analysis. For it includes both analysis and synthesis in combination. No machine
will ever be designed which can think synthetically. Programming a computer
with software based on the laws of non-identity and contradiction would be like
switching the machine on while the hardware is immersed in water: the whole
structure of the machine would short-circuit. The most a computer can do is to
ape synthetic operations by mapping them onto analytic models, as exemplified
in Figure 3.6. Just as man's ability to conceptualize depends on intuitive content
upon which its generalizing activity can operate, so also the computer is
powerless until it is programmed and fed specific information and instructions. It
never gives itself its own original intuition; for this it depends on the intervention
of some human agent. Human reasoning is unique precisely because it is able to
combine synthetic and analytic logic in such a way as to produce compound
forms of relation. With these forms, which shall be discussed thoroughly in Part
Two, the Geometry of Logic reaches its climax.
Moral Philosophy, too, is incomplete without a recognition of the
synthetic integration of good and bad in every ethical action. For in moral
experience the good comes out of the bad and the bad out of the good. The
contradiction implicit in the synthetic basis of morality must be taken into account
by any adequate philosophy.
The same is true in the philosophy of religion, or in theology. The
doctrine of the Trinity is an obvious example. According to the traditional
Christian doctrine of the Trinity, either the Father is regarded as the ultimate
source from which both Son and Spirit proceed [see Figure 3.11a] or the Son is
regarded as on a level with the Father, so that the Spirit proceeds from both the
Father and the Son [see Figure 3.11b].
Figure 3.11: The Traditional Conceptions of the Trinity
(a) Priority of the Father (b) Priority of Father and Son Together
In either case the threefold relation has obvious synthetic characteristics,
though in both cases something is missing if the relation is to be a perfect
example of synthetic integration.
Along these lines Jung suggests that the Trinity is in fact a Quaternity in
which one element of the relation has traditionally been ignored [J473: ]. The
fourth "Person", he suggests, is Satan, who can be regarded as the dark side of
God [J524:81]. This puts Satan in a position which seems strange indeed to
most Christian theologians, yet Jung's psychological interpretation of this
doctrine can be defended as being perfectly consistent with the logical structure
of synthetic integration. Any attempt to describe the various forms in which God
manifests himself will be a description of the synthetic integration which begins
with the transcendent God (0) and ends with the Christ (1), the Chief
representative of man before God. The spiritual struggle through which this
incarnation of God must pass is naturally conceived as a struggle between the
"Holy" Spirit (+), the Spirit of Light, and the "Unholy" Spirit (-), the Spirit of
Darkness. This suggests the following analytical map of the synthetic relations
inherent in the Godhead:
Figure 3.12: The Godhead as a Synthetic Relation
The Christ-man
Dark Spirit (-) Holy Spirit (+)
The Father-God (0)
Jung's inclusion of Satan in the Godhead is actually quite consistent with
the traditional conception of Satan as originally occupying an important position
in the Heavenly City. The story of the incarnation of God in the Christ-man then
becomes the account of how God conquers evil by taking its power (the Dark
Spirit) back up into himself, where it belongs, and where it existed before the
Fall. Shortly before realizing this purpose in the act of his death, Christ asserts
his Oneness with the Father (see John 14:9-10 and 17:11). This unity of "1" and
"0", which results when "+" submits to "-" without being totally overcome by it,
perfectly exemplifies the logical form of simple synthetic integration. (Note that
when Christ ascends, when the "1" is withdrawn, the disciples are given the
"Comforter" (+) to help them in the task of taking up the "-" into themselves and
realizing the "1" in themselves, as they await the return of the ultimate "1" which
will mark the end of time.)
Eastern philosophy and religion, as we have already seen [see notes
3.7,11-14], are much more explicit in their dependence on synthetic logic than
Western philosophy and religion. God, or Ultimate Reality, is always regarded
as "a supreme non-duality" which "is inexpressible and non-communicable in
itself, i.e. ... it is totally transcendent [0] (or totally immanent [1], which
amounts to the same [x]...)" [B528:200]. But this ultimate synthetic reality "can
be expressed only in terms of a diametrical polarity", such as "man and woman"
or "god and goddess" (i.e. "+ and -"). The distinction between an emphasis on
the "1" and an emphasis on the "0" in one's religious quest is clearly exemplified
by the distinction between the Hindu, who seeks "the unfoldment of the world"
through the union of opposites in "1", and the Buddhist, who "seeks its [the
world's] regression into the 'unborn, unformed' [the "0"] which is at the basis
of all unfoldment" [214]. Indian Buddhists use the concept of "sahaja" to try to
explain the ineffable starting-point of synthetic integration. The Buddhist,
Bhusukapada, says: "Where there is no self [+], how can there be any non-self
[-]? ...nothing goes or comes, there is neither existence [+] nor non-existence [-]
in sahaja" [29]. This clearly resembles many Chinese descriptions of the "Tao":
"The Way cannot be thought of as being [+], nor can it be thought of as
nonbeing [-]" [C525:25.293], for this duality is bound up in an eternal cycle
between "+" and "-", whose ultimate resolution is apparent only from the higher
(x) perspective of the Tao. From this higher perspective [see W533:74] L532:40
says: "All things under heaven [all "+" and "-" objects] come about in existence
[in "1"]. Existence [1] comes about in non-existence [0]. "The Tao is the overall
" " on which this insight is based.
The logic of synthetic integration is evident in many areas which are quite
removed from the philosophical and theological applications described above.
Not only do we experience time as the synthesis of past (+) and future (-) in the
form of the present (x), but we also experience space and time together in the
synthetic form of space-time, as modern physics now tells us. These intuitive
syntheses are easily ignored by our conscious mind as it goes about the business
of analysis. But when we are asleep, synthetic logic tends to exercise dominance
over analytic logic. Jung and other psychologists have proved that dreams have a
logic of their own which has clear implications for the dreamer's waking
experience. In fact, the logic of dreams is identical to the logic of immediate,
non-reflective conscious experience. Dreams often include elements which seem
quite natural and acceptable as we dream them, but which are obviously
contradictory when we recall them while awake. The obvious interpretation of
this fact is that in dreams the laws of synthetic integration, A = -A and A = A,
operate without being constrained by the laws of analytic division, the laws we
use to reflect upon our dreams once we are awake.
We can conclude this overview of some of the common applications of
synthetic logic by comparing the general difference between the work of the
scientist and the work of the artist. When the scientist observes the world, he
does so in order to gather (synthetic) data for theoretical reflection. But his
theoretical perspective on the empirical world operates primarily in terms of the
laws of analytic logic (especially in the case of the "reductionist"); for the
scientist's task is to discern similarities (A = A) and differences (A = -A) which
regularly occur in the world. The synthetic basis of his observation is irrelevant
to his concern, unless he wishes to adopt a more phenomenological approach--
e.g. by viewing his work as a form of art, or by philosophizing on the overall
nature of the scientific method.
When the artist observes the world, by contrast, he does so in order to
represent what he sees in a new form. So he must first have some (analytic)
understanding of the difference between the forms which are involved. But his
empirical perspective on the world operates primarily in terms of the laws of
synthetic logic; for the artist sees that in experience "A" is not simply "A", but
goes beyond itself into the domain of "-A", and he attempts to depict this process
in his artwork. "A" now represents and is represented by that which it is not. As
a result, the observer of a work of art should be primarily concerned not so much
to determine what it represents through rational analysis, as to perceive the work,
to experience it in such a way that the synthesis it represents becomes a part of
his own experience.
Stebbing classifies logic as essentially a science, although she adds that
the ability to think clearly may be regarded as an art [S515:473]. But the radically
formal logic with which we are concerned is best regarded as neither an art nor a
science, since it serves as the basis of both. For we have seen that, just as
science is rooted in synthetic observation and is fulfilled in an analysis of the
results, so also art is rooted in analytic observation and is fulfilled in the
synthesis of the results. Thus the principles established by the Geometry of
Logic clarify the reciprocal relationship not only between Eastern and Western
philosophical perspectives, but also between the perspectives adopted in the
practice of art and science.
NOTES TO CHAPTER THREE
1. See e.g. R517:194, quoted above in Introduction. The details of Russell's
approach are heavily dependent on the ideas of Frege and Peano. His
achievement was not to initiate the modern approach to logic, but rather to
develop a systematic defence of the unity of logic and mathematics [in R507],
and to use this as a tool for revolutionizing philosophical inquiry, at least in
England [see R517 and his numerous other philosophical publications].
2. The distinction between "static" and "dynamic" interpretations of logical
symbols will be discussed fully in 4.4.
3. The function of "0" in Figure 3.3 provides a logical basis of explanation for
why the concept of "Nothing" is treated almost as a fetish by philosophers such
as Heidegger [see e.g. H144d], who are concerned to expound the metaphysical
foundations of the world as experienced--i.e. on its "existential" structure. Such
endeavors can be rendered rather more easily comprehensible if they are regarded
as attempts to take full account of synthetic forms of relation.
4. This fractional notation would be an appropriate way of representing the type
of synthesis implied in Figure 1.6b. The ideal equivalent to this figure would be
one in which the "B" circle which intersects the "A" circle is replaced by "-A".
Synthetic integration could then be expressed (rather too simplistically) with the
progression of geometrical figures given at the top of the following page.
Another interesting way of representing this fractional notation is by the
use of successively smaller tangent circles, arranged on a coordinate graph as
shown at the bottom of the following page. The large circles represent all the
whole numbers. The smaller circles, as specified between "0" and "1", represent
all real fractions, so that any definite degree of probability in the third term of a
synthetic operation could be represented by one such circle. Irrational numbers
such as n or /2, and imaginary numbers such as /-1, are not represented 1- by
any circle, no matter how minute, since they cannot be represented by a simple
real fraction.
5. See e.g. S515:472-3. Stebbing lists the laws of identity and non-contradiction
first on her list of fundamental logical laws, but adds eight others, implying that
each deserves the same formal status. But with the exception of her third law, the
"law of the excluded middle" [see note 3.8], these other laws are all principles of
deductive or inductive argumentation. Only the first three apply to the relations
between thoughts in general. It is for this reason that they are traditionally
referred to as the "laws of thought" (even by Boole, the founder of the "Algebra
of Logic" [see B506:]).
6. In the context of second level analytic relations, where "+-" is set in
opposition to "++", and "-+" to "--", this law manifests itself as a "law of
polarity", since one term always stays the same. In synthetic relations, however,
there is no such continuity between opposing forces, so the relation remains an
out-and-out contradiction.
7. B528:19 lists "the four great Upanisadic dicta, 'this atma is brahma', 'I and
brahma', 'thou art that', and 'the conscious self is brahma'." Similar
contradictions abound in Chinese philosophy, as when Chuang Tzu describes
the "Tao" in C525:77: "The Way has its reality and its signs but is without action
or form. You can hand it down but you cannot receive it; you can get it but you
cannot see it. It is its own source, its own root.... It exists beyond the highest
point, and yet you cannot call it lofty; it exists beneath the limit of the six
directions, and yet you cannot call it deep. It was born before Heaven and earth,
and yet you cannot say it has been there for long; it is earlier than the earliest
time, and yet you cannot call it old. "The poetry of Lao Tzu is rich with such
contradictions. In L532:41, for instance, he says:
The clear DAO appears to be dark. The DAO of progress appears as
retreat. The smooth DAO appears to be rough. The highest Life appears as a
valley. The highest purity appears as shame. The broad Life appears to be
stealthy. The true essence appears to be changeable. The great quadrant has no
corners. The great instrument is completed late. The great tone has an inaudible
sound. The great image has no form.
8. Consider again the synthetic character of a child: "A child is real and not yet
real, it is in history and not yet historical. Its nature is visible and invisible, it is
here and not yet here" [T523:95]. Such inclusiveness entails, of course, that the
third great traditional law of logic, the "law of the excluded middle", does not
pertain to the logical relations involved in synthetic integration. This law is
subordinate to the laws of identity and non-contradiction because it introduces a
new term, "B", so that "A = B or -B". But the synthetic law of contradiction, "A
= -A", implies that, for some values of "B" at least, "A = B and -B" (i.e. "0 = +
and -").
9. Hume's willingness to compartmentalize his life into the pleasant experiences
of dining, playing backgammon, and making merry with his friends on the one
hand, and the business of constructing a philosophical system on the other
[H58:1.4.7], is a typical example of this lack of integrity--i.e. of the lack of unity
between the life of one's philosophy and the philosophy of one's life. At least
Hume recognized the insufficiency of the analytic as a mould for the synthetic.
10. As with all generalizations, this comparison between East and West should
not be regarded as universally applicable, but only as representing the trends and
patterns which tend to dominate the two approaches to logic and life. In reality,
of course, both analytic and synthetic methods are evident in virtually all
philosophers; their difference lies in the degree to which they suppress one
method and emphasize the other. Moreover, just as the West has had thinkers
such as Hegel and Heidegger for whom synthetic forms of logic were more
attractive than analytic, so also the East has had philosophers, such as the
"Mohists" in ancient China, whose analysis of "disputation" was concerned with
judgments which "follow by strict necessity from the definitions of names"
[G522:37]. But in both cases these examples are exceptions to the general rule.
(As Graham says, "the Mohists were men of a kind very unusual in traditional
China though familiar in Western civilization..." [59].) The fundamental
difference between Eastern and Western tendencies is epitomized by certain
actual differences in how objects are referred to. For example: "whereas in
English a stick has two ends, in Chinese it has two beginnings" [310].
11. Chuang Tzu, whose views on the "perspectiveless" are treated more fully in
note 3.12, believes that the fact "that all things are the same from one point of
view [the synthetic, "A = -A"] and different from another [the analytic, "A = -
A"]" is proof of "the pointlessness 1/ of all disputation" [G522:340]. But as we
shall see in Part Two, such an extreme emphasis on synthesis is not necessary:
analysis and synthesis can be seen as compatible operations.
12. A good example of the way in which synthetic contradiction can be explained
away through adopting an analytic point of view is given by the following
quotation of eight rules of the ancient Chinese Taoists, each followed in brackets
by the translator's "reconstructions" [C525:31.]:
1. Eyes do not see. [The mind does.]
2. An orphan colt has never had a mother. [When it had a mother {it was not an orphan
colt.]
3. If a rod one foot in length is cut short every day by one-{half of its length, it will still
have something left after {ten thousand generations have passed. [By definition. There
{will
always be a half left to cut in half again.]
4. The egg has feathers. [In potentiality.]
5. Things die as they are born. [Through their transformation {from one state to another.
Thus the caterpillar perishes to {become the chrysalis, and the chrysalis to become the
butter{fly.]
6. The shadow of a flying bird has never moved. [Each succeeding {shadow is a different
one, appearing in sequence.]
7. That which has no thickness has no bulk yet covers a thousand {square miles. [The
plane, presumably.]
8. Killing robbers is not killing people. ["Executing" is not {"murdering" and "felons" are
not "people".] While some of these reconstructions are perhaps helpful, they all conceal the
original motivation for putting forward these propositions as logical principles: viz. to
reflect the synthetic laws of contradiction and non-identity which govern our non-reflective
experience of the world, and in so doing to encourage a heightened awareness of one's
perspectival limitations.
13. The presence of so much contradictory language in religious discourse is
surely due to the writer's attempt to challenge his reader into taking up such a
higher level of awareness. B528:18 describes the reaction of Hindu and
Buddhist tantrics to such contradictions: they attempt to reconcile "discursively
contrary notions by raising them to a level of discourse where these
contradictions are thought to have no validity."
14. In C527:34-5 Chuang Tzu says: "'that' comes out of 'this' and 'this'
depends on 'that'--which is to say that 'this' and 'that' give birth to each
other.... [The sage] too recognizes a 'this,' but a 'this' which is also a 'that,' a
'that' which is also 'this.'" Chuang Tzu's works must be read in full in order to
appreciate the extent to which he uses language such as this, which is based on
the logic of synthetic integration. At one point [38], for example, he says: "There
is nothing in the world bigger than the tip of an autumn hair, and Mount T'ai is
little. No one has lived longer than a dead child, and P'eng-tsu [the Chinese
Methuselah] died young. Heaven and earth were born at the same time I was,
and the ten thousand things are one with me." (The Mohist's analytical reply to
Chuang Tzu's merging of "this" and "that" is given in C529:B68,82 [see
R522:36-40,440-1,456-7]. But even the Mohist admits that analytic logic does
not hold true in all cases, for "at the moment of death a thing is both 'horse' and
'non-horse', a man is both alive and dead" [G522:58; cf. C529:A50,88].)
Chuang Tzu is careful to explain, however, that such contradictions are
not intended to be understood at all, but to break through the barrier of the
understanding to reveal a deeper level of reality: "If the Way is made clear, it is
not the Way" [C527:39-40]; "You can talk about it, you can think about it; but
the more you talk about it, the farther away you get from it" [C525:25.293].
Thus, as Graham puts it, "according to Chuang-tzu it is precisely when we
distinguish alternatives, the right and the wrong, the beneficial and the harmful,
self and other, [+ and -,] that we cut ourselves off from the world we objectify,
and lose the capacity of the angler, the carpenter and the swimmer to heed his
total situation with undivided attention and respond with the immediacy of a
shadow to a shape and an echo to a sound" [G522:21]. Unfortunately, Graham's
conclusion, that the Mohist "has progressed a long way ahead of Chuang-tzu"
[40] reveals his failure to grasp the distinction between synthesis and analysis as
two valid ways of approaching the world with logical principles. Indeed, the
word "ahead" here simply means "closer to the Western bias"!
15. Strawson draws an important distinction along these lines "between
questions of meaning and questions of fact" [S535:11]. He also notes that
"character-ascribing expressions have complementaries [i.e. -A's for every A],
and individual-identifying expressions do not" [7]. This is because the latter
refers to a synthetic operation and the former to an analytic operation.
16. According to W533:73, some of the early Church Fathers were rather more
inclined towards such a "high" view of Satan.
17. The same insight can be found in Western mystical traditions in various
ways. In the Cabbalistic cosmology, for example, "The universe...becomes
manifest through the materialization of four progressively denser worlds: Azeluth
(Material), Briah (Creative), Yetzirah (Formative), Assiah (Material)" [P538:22;
s.a. 122]. The exact correspondence between these stages and the "0, +, -, 1"
pattern of synthetic integration is not accidental.