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

Identity in the Mirror of Emptiness

Project Outline


1       Object and Purpose

2       Project Format

3       About Myself

4       Conceptual Outline

4.1     The Creation of Identity

4.2     Identity in pure Mathematics

4.3     Identity in Physics

4.4     Identity and Inherent Existence

1         Object and Purpose

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.

2         Project Format

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.

3         About Myself

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

4         Conceptual Outline

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.

4.1          The Creation of Identity

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 20th 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.

4.2          Identity in pure Mathematics

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 20th 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.

4.3          Identity in Physics

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.

4.4          Identity and Inherent Existence

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.