Chalmers' Axiomatization

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This page summarizes an axiomatization of a theory of conscious experience inspired by the early work of David Chalmers (Chalmers, 1996[1]; Chalmers, 2010[2]). We remark that the following is intended to highlight the relations among various concepts from Chalmers' work as they could figure in a proper grounding of the scientific study of consciousness. It is primarily not intended to be an introduction to the philosophy laid out by David Chalmers.

Physical domain

First, we note that Chalmers' definition of "physical domain" includes what is often called "material" or "physical" configurations, such as neurons or brain tissue, as well as more fundamental physical notions such as "mass, charge, and space-time"[2] or "atoms, electro­-magnetic fields, and so on"[1]. We thus define the term physical domain to refer to all those phenomena which are currently considered to be the subject of natural science (i.e. subjects of physics, chemistry, earth science, biology, etc.).

Causal closure

Chalmers assumes that

"The physical domain is causally closed."[1] "For every physical event, there is a physical sufficient cause."[1]

Function, structure and explanation

Central to Chalmers' grounding are the terms 'function' and 'structure'. "Here 'function' is not used in the narrow teleological sense of something that a system is designed to do but in the broader sense of any causal role in the production of behaviour that a system might perform"[2]. The term 'structure' is used in a spatiotemporal sense. Together, they constitute, according to Chalmers, the notion of explanation which is used throughout contemporary science: "One can argue that by the character of physical explanation, physical accounts explain {\em only} structure and function, where the relevant structures are spatiotemporal structures, and the relevant functions are causal roles in the production of a system's behavior"[2].

We denote this notion of explanation by E1. Assuming some laws or theories relating to the physical domain as given (= accepted by the scientific community by and large) and referring to them as 'accepted theoretical notions', this might be put as follows:

An explanation specifies the function and structure of an explanandum

in terms of the function and structure of accepted theoretical notions.

Phenomenal consciousness

The crucial aspect of Chalmers' grounding is to establish, in a consistent and explicit way, that there are phenomena, related to consciousness, to which no function or structure (as defined above) can be associated. It follows that these phenomena cannot be explained according to E1 and hence, if E1 indeed captures all notions of explanations which are used throughout contemporary science, that they cannot be explained by contemporary science. - There is an [[explanatory gap]. Chalmers refers to these phenomena as "phenomenal consciousness", "phenomenal concepts", "phenomenal qualities" or "qualia"[1] In [2], he prefers to use the term `experience': "Sometimes terms such as 'phenomenal consciousness' and 'qualia' are also used here, but I find it more natural to speak of 'conscious experience' or simply 'experience.'\,". We refer to these phenomena as 'phenomenal aspects of consciousness':

Phenomenal aspects of consciousness are those aspects of conscious experience which do not have a function or structure, where 'function' and 'structure' are as defined above.

The key requirement for this definition of what is to be studied by a science of consciousness to make sense is to establish that there are aspects of experience which satisfy D1, i.e. which neither have a spatio-temporal structure nor a causal role in the production of behaviour. It is the second requirement with respect to which A1 is crucial, for A1 can be utilized to argue that nothing non-physical can have a causal influence on the physical domain. Therefore, all aspects of experience which do not have a spatio-temporal structure (e.g. in the Cartesian sense of being non-extended in space and space-time) automatically satisfy D1. We will not review the various arguments which aim to prove the existence of phenomenal aspects of consciousness at this point.

The goal of the scientific study of consciousness

It may be conjectured that what is to be studied in the scientific study of consciousness are, according to this grounding, phenomenal aspects of consciousness and their relation to the physical domain. Since these are, by definition, not accessible to the usual scientific methodology, Chalmers proposes that the task of a science of consciousness is to find what he calls "psychophysical laws"[1] which relate the physical domain to phenomenal aspects of consciousness. Due to Assumption A1 and an underlying stance on the nature of causality "[t]hese laws will not interfere with physical laws; physical laws already form a closed system. Instead, they will be "supervenience laws, telling us how experience [= phenomenal aspects of consciousness] arises from physical processes"[1]. In combination with E1, this implicitly points at the major parts of the methodology to be used according to this proposal.


Chalmers' grounding raises several questions related to the definition and ontological status of causality, to the validity of Assumption A1, to the nature of experiments in his grounding, and to the validity of the subsumed notion of explanation. There may be conceptual problems that make it questionable whether a scientific research program based on this grounding can be carried out at all (cf. e.g. Appendix B in [3]).

Furthermore, any scientific approach based on this grounding faces the question of which mathematical structure one is to use in order to describe phenomenal aspects of consciousness when formulating "psychophysical laws". Whereas the physical domain comes with a clear-cut mathematical structure, Chalmers' grounding merely asserts that the phenomenal aspects form a set and offers no systematic way of tying additional mathematical structure to the phenomenology of experience.


  1. 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Chalmers, David J. The conscious mind: In search of a fundamental theory. Oxford university press, 1996.
  2. 2.0 2.1 2.2 2.3 2.4 Chalmers, David J. The character of consciousness. Oxford University Press, 2010.
  3. Kleiner, Johannes. "Mathematical Models of Consciousness." Entropy 22.6 (2020): 609.