Defining “Emptiness”
September 30, 2011
Hideto Tomabechi1(http://www.tomabechi.jp)
What is the “emptiness” (“sunya”) that Buddha attained? This
article attempts to formally define “emptiness” using tools of modern
analytic philosophy. As a background overview, let us briefly look over how
Buddha’s enlightenment has been interpreted by Theravada Buddhism and
Mahayana Buddhism.
Emptiness is the Moon, Dependent Origination is the Finger
After the death of Buddha, Buddhism was divided into two major
schools - Theravada Buddhism and Mahayana Buddhism. Theravada
Buddhism describes Buddha’s enlightenment by the concept of “dependent
origination”. In short, dependent origination means “all existence consist ofinterdependence”. “Dependent origination” is based on the idea of “relation
generates existence”, which is opposite of the Western notion of“existenceis what generates relation”. Buddha blew apart the idea that “relation is
generated from existence” which is the hypothesis of Judaism, Christianity
and Brahmanism. Relevance of Buddha’s idea was validated later by modern
mathematics and physics. It’s because modern mathematics, physics andphilosophy validate “no determinacy of existence” after success of
incompleteness theorem in mathematics or after the success of quantum
physics in the world of physics.
There’s no doubt that Buddha attained “dependent origination”
under the Bodhi Tree. However his enlightenment was “emptiness” and not“dependent origination”. “Dependent origination” is the only principle to be

1

Ph.D. Carnegie Mellon University 1993, Department of Philosophy(Computational Linguistics). Currently, Abbot of Markham Lawa Monastery(India). Also, International Director for Tendai Mission Hawaii.

Facebook: http://www.facebook.com/drtomabechi
Japanese version: http://www.tomabechi.jp/EmptinessJapanese.pdf

1used in describing emptiness. Buddha’s teaching was “Do not look at the one
pointing at the moon, but look at the moon”. “Dependent origination” is the“pointing finger” in this sense. Buddha did not talk about emptiness itself.
2600 years ago, it was probably too difficult to address emptiness without
modern tools of philosophy to people without education. Instead, Buddha
preached “dependent origination” which is the philosophy to experience
emptiness. Because of this, there are even some teachings which mixed
emptiness and “dependent origination”, or there are teaching to advocatethat people can attain enlightenment as long as they understand “dependent
origination” therefore meditation training is not necessary. However the ideaof “dependent origination” is not emptiness itself, and understanding of“dependent origination” doesn’t mean that you understand emptiness.
The emptiness discovered by Mahayama Buddhism was “abundant
existence”
Mahayana Buddhism produced many genius leaders. The most
famous of these are Nagarjuna of Indian Buddhism and Tsong Kha Pa of
Esoteric Tibetan Buddhism. These great leaders preached and defined
emptiness and enlightenment based on their achievement of transcendence
and they spread Mahayana Buddhism.	
  Given the number of Buddhists, it’sreasonable to say Buddhism became successful after the development of
Mahayana Buddhism.
Mahayana Buddhism bloomed in China after it was introduced in
the country and Zhi-yi was one of the contributors. The philosophy of
emptiness became rigorously sophisticated in China but surprisingly it’s not
well-recognized today.	
  The development of Mahayana Buddhism should be
acknowledged more in Buddhism history.
Mahayana Buddhism rigorously pursued emptiness that Buddha
preached, and it discovered that the emptiness was not “nonexistence” but“existence”. Mahayama Buddhism discovered that the emptiness means“abundant existence” as it fills the whole universe. The emptiness is to see
the whole universe by focusing one existence, and not to see non-existence byfocusing on one existence.
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Definition of emptiness by formal thinking method from the West
Now how can we formally define Buddha’s “abundant existence” of
emptiness, which is the world of enlightenment that the whole universe canbe seen from looking at one existence? The objective of this article is toattempt to define the emptiness.
It had been difficult for Westerners to accurately understand theconcept of emptiness because mindset in the East is informal while the one
in the West is formal. However now in 21st century, there is awell-systematized formal thinking methodology in the West and that iscalled Modern Analytic Philosophy. Emptiness can be formally defined by
employing Modern Analytic Philosophy so that it assists Westerners with
understanding this concept. Now let’s begin to define “emptiness” of Buddha
with Modern Analytic Philosophy.
Replacing the concept of the universe and existence with Partial Function
Partial Function means “function of division” in short. In Partial Function,
defining one part enables its complementary set, the other parts which is notdefined, to be defined as well.
For example, defining even numbers, which is a partial function,
among the natural numbers also defines all the other natural number which
are odd numbers. Here is another example. Defining “dog” divides theuniverse into dog and non-dog. If you can perfectly define what is a dog, youalso can define the whole non-dog universe.
Furthermore, not only does it define concepts, Partial Function also
defines physical existence. (Here we call “concepts” in physical space as“existence”. ) In the case of defining an existence of a certain individual, firstit divides the universe between the individual and the rest of existence. Then,
if the individual is perfectly defined, this also defines the whole universe
excluding this particular individual. This is the concept and definition ofexistence in Partial Function of Analytic Philosophy.
When comparing concept and existence to Partial Function as
stated above, we see the order of the partial functions according to theamount of information a concept or an existence contains. When there is less3

information it means that a concept or an existence is represented by lessinformation and the less information it represents the higher level ofabstraction becomes. The partial function with less information is Superior
Partial Function and the information with more information is Inferior
Partial Function.
For example in comparing the concepts of dog and animal, “animal”
has less information and “dog” has more information. Therefore, the level ofabstraction is higher in “animal” than “dog” and “animal” is the superior
partial function of “dog”. There is also an order relation. By contrast, there
are times order isn’t generated among partial functions. For example
considering the concept of dog and cat, we cannot tell which concept contains
more information. Therefore order in such cases cannot be determined.
The Universe is Subsumption Partial Ordered Set in Set Theory.
Now we’ll employ a mathematics theory called set theory. When the word of“set” is used, the order of each element in the set doesn’t carry a meaning.
However, when it’s called “ordered set”, each element in the set carries
meaning. Traditionally set is notated as { } and ordered set is noted as < >and it means order has a meaning to it. <1,2,3,4> is a set order.
Let’s define the universe as a set of concept and existence. Then we’ll
employ the amount of information in the concept and existence for orderrelation in order set.
Previously I described as follows: In comparison of concepts of dog

and animal, “animal” has less information and “dog” has more information.
Therefore level of abstraction is higher in “animal” than “dog” and “animal”
is superior partial function of “dog” and there is an order relation.
Such relation of superiority and inferiority is called subsumption order.
Subsume means to arrange elements according to the amount of informationeach element carries. The element with less information subsumes theelement with more information. In this sense “animal” subsumes ”dog”. In
this manner, the set which two arbitrary elements invariably set an order iscalled subsumption orderd set.
On the other hand, as with the concept of dog and cat, a relation
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which can never be put in order by amount of information is calledsubsumption partial order. So, a set always cannot be put in order with thearbitrary two elements is called subsumption partial ordered set
Concepts and existence in the universe include concepts such as“dog” and “cat” that cannot be put in order so that the arbitrary two elements
cannot set up an order. Therefore all the concepts and existence can be
defined as subsumption partial ordered set.
Universe is Subsumption Partial Ordered Set Lattice When Defined by
Lattice Theory
In order to define the universe more accurately we will employ anothermathematics theory named lattice. First I’ll describe what is LUB (least
upper bound) and GLB (greatest lower bound) to help you understandlattice.
Element in common and superior to two arbitrary elements is called
upper bound. Within upper bound, the element most inferior is called least
upper bound (LUB). For example, there is the partial order set of <dog, cat,animal>. Comparing the amount of information each element carries, twoarbitrary elements are “dog” and “cat” and their common superior concept is“animal”. Therefore “animal” is upper bound and LUB (leaset upper bound).
On the other hand, the element in common and inferior of two arbitrary
elements is called lower bound. Within lower bound, the element mostsuperior is called greatest upper bound (GLB). For example given theordered set of <poodle, dog, pet> two arbitrary elements are “pet” and ”dog”
and their common inferior concept is “poodle”. Therefore “poodle” is lower
bound and GLB (greatest lower bound) in this example.
	
 
	
 
	
 
	
 
	
 
	
 

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As stated above, the ordered set which includes either LUB or GLB,
or includes at least one of each within ordered set/partial ordered set iscalled lattice. Previously all the concept and existence of the universe wasdefined as subsumption partial ordered set. Also as stated above there are
LUB and GLB in concept and existence therefore the universe can be definedas subsumption partial ordered lattice.
Emptiness is the Top of the Subsumption Partial Ordered Lattice Universe
Next, let’s look at the two arbitrary concepts or existence of LUB and GLB in
the subsumption partial ordered lattice universe. GLB as two arbitrary
concept or existence in lattice is called “bottom” and LUB as two arbitrary
concept or existence in lattice is called “top”.
When selecting two arbitrary elements in the universe for example
selecting plastic bottle and dog from the universe what are the most inferior
element of the common concept, which is the bottom of the universe of
subsumption partial ordered lattice? Modern Analytic Philosophy it can be
defined as “contradiction” (or “repugnance”) which is just like “plastic bottle
which barks bow-wow ” and contained a little too much information.
Meditation is the Only Way to Experience the EmptinessOn the other hand two arbitrary LUB of the universe and the top of
the universe of subsumption ordered lattice are defined as “plenty existence”
which means specific concept does not exist. In fact Modern Analytic
Philosophy agrees “superior concept of all existence do not exist”. Therefore
universeofwestern

ModernAnalytic

Philosophyisclosedwith“contradiction” at the bottom and opened with “does not exist” on the top.
Now we utilize Buddhism philosophy of Buddha. Buddhist
philosophy considers superior concept of all existence “exists” and this is“emptiness”. “Emptiness” in Buddha’s philosophy is superior concept of all
the existence. Therefore two arbitrary concept of existence of LUB and top of
subsumption partial ordered set lattice of universe becomes “emptiness” byemploying eastern Buddhist philosophy with western Modern Analytic
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Philosophy. Emptiness is the most superior concept in the universe thatcarries the least amount of information. In this sense we can also say thatemptiness potentially includes the whole universe.
As stated above, by integrating western philosophy and eastern
philosophy we can define the universe as subsumption partial ordered latticeof concept and existence which is closed with “contradiction” at the bottom
and also is closed with “emptiness” at the top. Hence we can also define
emptiness as “top of the universe of subsumption partial ordered lattice ofconcept and existence”. Emptiness and dependant arising is two different
concepts as described previously.
As I noted, such perspective toward the universe and emptiness now
coincides with our knowledge in modern mathematics, physics andphilosophy

especiallyafter

successofincompletenesstheoreminmathematics or after the success of quantum physics in the world of physics.
Meditation Practice is the Only Way to Experience Emptiness
It’s vital to remember that the above discussion is only the definition of“emptiness”. Understanding definition of emptiness doesn’t mean that you
understand emptiness. In order to understand emptiness, practicing
meditation is the only way.
Predecessors had created various methods of meditation in order toattain emptiness. For example Zhi-yi, the founder of Tientai school invented
themeditation

methods

named

ConciseSamatha-vipasyanaand	
 disseminated the method in his teaching called “Maha-Samatha-vipasyana”.
“Maha-Samatha-vipasyana” compiled by this pupil still remains this time
provides commentaries about the practice of samatha and cipasyana
meditations. In Theravada Buddhism, samatha and cipasyana meditations
are practiced separately, however Mahayama Buddism does both of them atthe same time. Mahayana Buddhism tries to attain Buddhisthood andexperience emptiness by rigorously looking at ego/atman. Then how does itwork?
As previously stated, modern analytic philosophy defines concepts
and existence by partial function. In the idea of partial function, defining a7part enables to define sub set which is the rest of all part excluding thepreviously defined part. When defining ego/atman of a certain individual, we
divide universe into ego/atman and non-ego/atman. Then the ego/atman of
the individual is perfectly defined, universe of non-ego/atman of theindividual is successfully defined. This means understanding ego/atman
enables us to understand the universe. When you perfectly understandego/atman and see the whole universe, remove ego/atman in the end. By
removing ego/atman from the universe, emptiness will emerge and you canexperience emptiness.
Thus such meditation practice to reach emptiness throughrigorously looking at ego/atman is still remained in teaching of various
Buddhism schools including 12 deeds of Buddha and mid to later stage of
Esoteric Buddhism. Apart from this, some method tries to attain emptinessby gradually reducing information amount and “climbing up the steps(levels) of abstraction”
During the last 2600 years after the enlightment of Buddha,
Buddhism has disseminated around the world. Rigorous practice of
meditation of predecessor enriched system of Buddhism very well.

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