| What is the origin of numbers? In what way do numbers exist? Have they
always been present as 'Platonic' abstractions, or do they require a mind to bring them
into existence? Can numbers exist in the absence of matter or things to count? Buddhist
philosophy claims that all things arise out of emptiness (Sanskrit sunyata
or shunyata)
According to David Loy, the English word emptiness has a more nihilistic connotation
than the original Sanskrit. The Sanskrit root su conveys the
concept of being swollen with possibility [LOY 1996].
The Kadampa school of Buddhist philosophy claims that all phenomena are ultimately
empty of inherent existence and do not exist as things in themselves. All phenomena exist
solely in dependence on other phenomena, which are themselves empty and dependently
related to other phenomena and so on. No matter how deeply or far back we search, no
phenomenon can ever be found which is fundamental or a 'thing-in-itself'. Neither the
observer nor any observed phenomenon exist independently, but are inextricably
intertwined. This viewpoint is known as dependent relationship.
Geshe Kelsang Gyatso [KELSANG GYATSO 1995] states that there are three levels of dependent
relationship:
(1) Gross dependent relationship - causality - the dependence of phenomena on their
causes.
(2) Subtle dependent relationship - structure - the dependence of phenomena on their
perceived parts (including aspects, divisions and directions).
(3) Very subtle dependent relationship - the dependence of phenomena on imputation by
mind.
These ideas are remarkably similar to the theory of the origins of mathematics first
proposed by the mathematician John von Neumann, who was one of the founders of
computer science. The theory relies on simple maipulations of sets.
A set is a collection of things. An empty set is a collection of nothing at all.
An empty set can be thought of as nothing with the potential to become something
(that is to be become a set with at least one member).
Von Neumann [VON NEUMANN 1923] proposed that all numbers could be bootstrapped out of
the empty set by the operations of the mind.
The mind observes the empty set. The mind's act of observation causes the appearance
another set - the set of empty sets. The set of empty sets is not empty, because it
contains one non-thing - the empty set. The mind has thus generated the number 1 by
producing the set containing the empty set.
Now the mind perceives the empty set and the set containing the empty set, so there are
two non-things. The mind has generated the number 2 out of emptiness. And so it goes on
all the way up.
So, the three levels of dependent relationship postulated by Kadampa Buddhist
philosophy are apparent even at the very deepest level of mathematics.
- Numbers have causes - the algorithms that perform the operations on the sets.
- Numbers have parts and aspects. The number 1 is defined as the set which contains the
empty set and so on.
- And in the final analysis the entire number system has been generated by the play of
mind on emptiness, in the complete absence of the need to refer to any material thing, or
things, which are being counted.
Numbers are non-physical phenomena and need make no reference to physical systems for
their existence. But neither are they inherently-existent entities from the
'Platonic realms'. Numbers are dependently-related manifestations of the working of the
mind.
- Sean Robsville
See also:
The unreasonable effectiveness of mathematics in
science and engineering
'So we are left with something of a mystery. According to the physicalist
worldview, the mind (including mathematicians' minds) is an epiphenomenon of matter which
has evolved solely to ensure the survival of the selfish genes which code for it. Why
should this 'top-level' phenomenon have such intimate access to the 'bottom level'
phenomena such as quantum physics? After all, the two levels are supposedly separated by
less well-understood (in some cases) explanatory layers such as evolutionary psychology,
neurology, cell biology, genetics, molecular biology, and chemistry.'
Emergence
'One interesting aspect of emergent phenomena is the different causal and
organisational relationships which appear at different levels of investigation. For
example, ecology emerges out of biology, which emerges out of chemistry, which emerges out
of physics, which emerges out of mathematics, which emerges out of the mind contemplating
the empty set. Each level of investigation has its own explanatory relationships,
yet if we check carefully there is no 'added extra' coming from the side of the objects.
(Everything is algorithmically compressible without remainder, there are no mysterious
ingredients added as we progress from lower levels to higher levels).'
Meditating on emptiness
'....For a qualified meditator single-pointedly absorbed in emptiness, there is no
difference between production and disintegration, impermanence and permanence, going and
coming, singularity and plurality - everything is equal in emptiness and all problems of
attachment, anger, and self-grasping ignorance are solved...'
Buddhist Teachings
on the mind, personal relationships, meditation and the spiritual path.
Mathematics: The
Bridge to an Integral Science of Experience
The scientific method is generally thought to require that scientific
verification draw only from outer experience, thus excluding all inner experience as a
valid basis for scientific verification. Consequently, the scientific study of
consciousness today is largely limited to the physical sciences and the externally
observable correlates of consciousness. Mathematics, however, provides an example of a
rigorous science based on inner experience that is nonetheless verifiable. Contrary to
widespread belief, it is possible, therefore, for an authentic science to be based upon
inner experience.
Arguments against Buddhism
The best way to understand the strengths of a philosophy is to attempt to
refute it.
References
[KELSANG GYATSO 1995] Gyatso, Geshe Kelsang, Joyful Path of Good Fortune, 2nd Edition -
page 349, (London: Tharpa Publications, 1995, ISBN 0
948006 46 3)
[LOY 1996] Loy, David in the afterword to Swedenborg, Buddha of the North , page 104,
(Swedenborg Foundation, West Chester Pennsylvania, 1996, ISBN 0-87785-184-0)
[VON NEUMANN 1923] cited by Robert Matthews in the Sunday Telegraph 15th October 2000,
page 16.
RATIONAL
BUDDHISM
If we regard Buddhism as a combination of a philosophy, psychology and religion, then how
much mileage can we get from the first two aspects before we have to start invoking
religious faith?
Christian
versus Buddhist worldviews |
