Research Project, Dr. Dr. Rudolf Matzka, Munich, started June 2006:

Identity in
the Mirror of Emptiness

Project Outline

4.2 Identity in pure
Mathematics

4.4 Identity and Inherent
Existence

This
project will be an investigation into the role of the notion of **identity**
in Western scientific thinking and its relationship to the notion of **inherent
existence** in the Madhyamika teachings. Since these notions are closely
related, and since identity is basic for logics and mathematics, it will be
shown how the Madhyamika teachings have direct relevance for the very core of
scientific thinking. The focus with respect to science is on Mathematics and
Physics.

The result
of this investigation can serve two purposes. For Western scientists it can
help to access the buddhist philosophy, by directing reflection to certain
aspects of their ways of doing science which they may so far have been unaware
of. For Buddhist scholars it can exhibit certain starting points for applying
the Madhyamika dialectics most effectively to refute extreme scientific belief
systems, which are indeed abundant in the modern world. The ongoing dialog
between Buddhist scholars and Western scientists can thereby be raised to a
higher level of precision and intensity.

Work on the
project starts in June 2006.

The output
of the project will be a book describing the whole issue and the research
results in a coherent and commonly accessible way, assuming no specialist
knowledge on the part of the reader.

A suitable
publisher will have to be found.

After
having studied Mathematics, with Physics and Economics as subsidiary subjects,
and after having finished a PhD in Mathematics, I started to work as an
Assistant Professor for mathematical Economics and did another PhD in
Economics. This latter thesis was very much an exercise in the theory of
science, and it implied a deep investigation into basic problems of applying
Mathematics to the real world. After that I left university and became a
software designer.

In the
1980s, I happened to attend Sogyal Rinpoche’s first teaching in Munich, and
followed his teachings for many years. I became part of the Rigpa instructors
team for a couple of years. Later I concentrated on studying Buddhist
philosophy and Western philosophy and science.

Now I feel
the time has come to collect the bits that are missing and to communicate what
I have learned. So I have decided to keep myself free from payed labor for some
time and devote it to this project.

More
details about myself can be found at www.rudolf-matzka.de/person.

The
investigation begins with the observation that there is a strong correspondence
between two concepts, one from the buddhist Madhyamika teachings, the other
from western Logic: **inherent existence** and **identity**. Inherent existence
is what Madhyamika denies of anything we experience, identity is what Logic
assumes of everything it deals with. The main work will be to elucidate the
meaning and function of the identity principle for modern science, and to
clarify its relation to the notion of inherent existence. To the extent that
both concepts overlap in meaning, the Madhyamika teachings are thus
demonstrated to have direct relevance for the very core of scientific thinking.
This is to be explored in detail, focussing on mathematics and physics.

The
identity principle is both very fundamental and very poorly understood. Usually
it is thought of as a principle of Logic: as such it has been formulated by Aristotle.
In modern accounts of Logic, identity has disappeared as a basic principle
because it could not be given a precise and non-trivial expression. While other
logical principles have been subject to lively debate and modification in the
context of non-standard logic, the identity principle has never been debated or
modified in any way, as the 20^{th} century philosopher Gotthard
Günther has observed. There is a reason why the identity principle is so hard
to access in the context of logic: because it is actually not a logical
principle, but a **semiotic** one. That is to say, identity is a principle
that governs our way of using **signs** (characters or phonems or sequences
thereof, like words).

We shall
distinguish two aspects of signs: **syntax**, which is the study of signs or
sign systems in themselves without regard to their meaning, and **semantics**,
the study of the meaning of signs. We shall see that the root of the identity
principle can be found in the realm of syntax. Within this realm identity is
quite straightforward and easy to understand. For signs, taken as objects in
themselves, to have identity is a most natural thing, because that is what they
are constructed for. The syntactic identity of characters, for example, is
constructed by an abstraction process which leads from the concrete appearance
of a black pattern on a white background (the **token**) to an abstract
entity which is a member of the English alphabet (the **type**). The sign
exists as a relation between token and type; the type is the sign’s identity,
the token is its way to manifest. The type is abstract and remote from times
and places, the token is concrete and appears now and here.

Signs are
used to carry meaning, and the relationship between a sign and its meaning is
called the **reference** relation. Usually the reference relation is not
much thought about, we just use signs and take their meanings for granted.
However, somehow each reference relation must have come into being. We shall
call the process of attaching meaning to a sign the **semantic** **loading**
of the sign. Again we distinguish to kinds of loading, primary and secondary. **Secondary**
loading is the process of definition: we load a sign with meaning by combining
the meanings of other signs. Obviously, not all semantic loadings can be of
this kind, there must be another process, which we call **primary** loading.
Primary loading originates from direct experience with that which is going to
be the meaning of the sign.

Primary
semantic loading is the process by which identity is created for things other
than signs. While for signs it is natural to have identity, for other elements
of experience this is not necessarily so. An abstraction process similar to the
creation of a character’s type must have been applied to the other element of
experience before it can become the other end of a reference relation. After
the reference relation has been fixed, the other end of it has become identical
in the same way that the sign is identical, it has inherited the sign’s
identity.

To summarize,
signs play a twofold role in the creation of non-sign identities. Firstly, the
creation of identity for signs serves as a model for the creation of other
identities. Secondly, signs are used to fix those other identities through
reference relations. The process of primary semantic loading, in which all this
happens, will have to be a focus of our investigation.

Whenever we
write, read, speak, listen to people speaking, or think, we use language, and
using language implies using signs. A very special and not so commonly known
language is the **Predicate Language**, the language of modern Mathematics.
This language plays a key role for the current investigation, for two reasons.
Firstly, we will be concerned with exact sciences, and the meaning of the word
“exact science” is that its theoretical core be formulated in the language of
mathematics. Secondly, the language of Mathematics is a **formal** **language**,
which means it is defined by a finite and fixed set of **grammatical**
rules. It is therefore a relatively simple object of investigation, much
simpler than any natural language would be.

In the
early 20^{th} century Russell and Whitehead managed to translate all of
mathematics into a formal language, the Predicate Language, and to translate
all principles of mathematical thinking into a finite and fixed set of **logical**
transformation rules for expressions of the Predicate Language. After this had
been accomplished, the process of mathematical thinking could be entirely
decoupled from the real-world contents being thought about. While in natural
language syntax and semantics are inseparably interwoven, by means of the
Predicate Language syntax became an autonomous realm with a high degree of
independence from semantics.

As we all
know, thinking is impossible without thinking about something. If mathematical
thinking is not thinking about real-world contents, what is it, then, that
mathematicians think about? They think about an abstract universe of things,
properties, functions, and relations. What is such a universe made from? The
answer to this question can be found in Model Theory, which is a branch of **metamathematics**.
Model Theory has the task to prove that specific mathematical theories are free
from contradictions, and this is usually done by constructing a model, that is,
a universe which satisfies the theory in question. Such models are made from
signs and operations on signs.

It is thus
safe to say that the enterprise of pure mathematics is entirely confined to the
realm of signs, both as its medium and as its semantic content. Therefore, the
identity principle is valid in its purest form throughout all of pure
mathematics. That is, all mathematical things, properties, functions, and
relations, are abstract and remote from times and places, entirely unchanging
and unchangeable.

That the
mathematical universe is so clearly limited and so static, produces another
kind of identity behind the scenes, the identity of mathematical thinking. No
other group of people is capable of having this kind of 100% consent about each
and every detail of the domain they are talking about. Any two mathematicians
may differ in their interests or in their capacities, but never in their
judgements of what is mathematically true. In this sense, all mathematicians
are equal, the mathematical thinking of a specific mathematician is but a token
for the one type of mathematical thinking. Or, to phrase it differently, there
is but one mathematical mind, and it manifests itself in the form of individual
mathematicians. The mathematical mind is looking at the mathematical universe
passively and from outside the universe, it is no part of this universe. Thus
in mathematics, the duality of subject and object has transcended the
individual person and has acquired a collective or global character.

This is the
part where most of the research is still to be done. One thing should already
be clear at this point: To the extent that the “real world” is thought of as a
model of a particular mathematical theory, it is necessarily thought as being
devoid of life or mind or subjectivity, even devoid of change. While
mathematical expressions and their meanings are remote from times and places,
physical experiments and measurements are not. This categorical difference
between mathematical and physical objects motivates a kind of mathematical
structure which is supposed to compensate for it, the Euclidian structure of **space
and time**. How this compensation works, and how it fails to work, will be a
central research issue. In general, the role of specific mathematical elements
with respect to creating or stabilising physical identities will be
investigated.

Because
syntax and semantics are so clearly held apart in mathematics, the semantic
interface between mathematics and physics is quite small and easily
comprehensable. This gives us the opportunity to watch how identity is exported
from mathematics to physics through the process of loading mathematical
expressions with physical contents. One important source of information will be
a kind of “thought experiment” concerning selected well-known physical
experiments or measurements. In real physical research, the loading of
mathematical expressions is done by way of definition, using words from natural
language which are already loaded. In our thought experiments, we can
purposefully forget about those words of natural language and thereby
“simulate” a primary semantic loading.

To a
certain extent, physics also inherits from Mathematics the identity or
collective one-ness of the mind doing physical research. In the same way as
with mathematics, it is a mind which looks at the world passively and from
outside the world, not belonging to the world. In quantum physics, for the
first time it appears as if this remote position of physical subjectivity could
not be consistently upheld.

All
conceptual knowledge is identity-based. It is therefore restricted to those
phenomenal realms where the identity principle gives a good approximation.
Identity-based thinking is necessarily focussed on things as the primary
category of thinking, while change and relations are secondary categories.
Change and relations can only be thought of as change of things and as
relations between things. Identity-based thinking therefore excludes all kinds
of phenomena where identity of things is being created or destroyed.

“No things
are produced anywhere at any time, either from themselves, from something else,
from both, or from neither”. This opening statement of Nagarjuna’s
Mulamadhyamaka-Karikas can be understood as saying that the concept of
thingness does not correspond to any of our immediate experience. To be a thing
means to have identity, and identity is the result of an abstraction from more
concrete elements of experience. Strictly speaking, identical things are
abstract and remote from times and places, and that is why they cannot be
produced through any conceivable mode of substantial causation.

The
connection between identity and inherent existence will have to be thoroughly
explored in the course of the project. As a first guess, inherent existence
implies identity, but not vice versa. Abstract things, like numbers or words,
can be identical without inherently existing. For a thing to be thought about,
it is necessary that it be thought as identical, which implies that it can be
thought of independently of anything else. To believe that something inherently
exists means to believe that it exists concretely and substantially, in
addition to being identical.