# Qualia Space

Qualia spaces are mathematical representations of qualia. Since there are many different conceptualizations of the term qualia, various different notions of qualia space have been introduced, which differ both in meaning and in mathematical form. Much like the case for quality spaces and experience spaces, the empirical driving force behind their definition is that colloquial descriptions of conscious experience might not suffice to precisely define the experience. Spoken language is neither intended nor suitable to describe all details of phenomenal experience.

# Stanley's definition

The term qualia space was introduced by Richard P. Stanley[1] to denote the space of all possible conscious experiences. Here, 'all possible' refers loosely to all conscious experiences which could be experienced by any brain.

Restricting attention to qualia, taken by Stanely to denote perceptual consciousness, as well as static experiences alone, Stanely characterizes the mathematical structure of qualia space by referring to his own intuitions on how qualia would tie into the physical domain. He arrives at the conclusion that qualia space ${\displaystyle Q}$ is a closed pointed cone in an infinite-dimensional separable real topological vector space.

The following gives an example of the type of argument Stanley utilizes: To establish that qualia space is connected, Stanely assumes that there is a continuous mapping between qualia space and physical states spaces as well as a unique 'no experience' quale, and argues that there is a continuous transformation of the physical state underlying every quale to a state with no conscious experience. In in light of the continuity of the mapping from physical states to qualia, this gives rise to a continuous transformation between any quale and the no-experience quale, and hence established that ${\displaystyle Q}$ is connected. The various assumptions which are required for this argument to work are not discussed in noteworthy detail.

Stanley's definition contrasts with experience space as introduced in (Kleiner, Tull 2020)[2] based on their study of the mathematical structure of IIT: One experience space denotes all possible conscious experiences of a single system/organism, while qualia spaces attempt to address all possible experiences right away.

# Clark's quality spaces

In order to avoid use of the loaded term 'qualia', Austen Clark refers to his constructions as 'quality space'. Cf. the entry quality spaces.

# Other definitions

If qualia refer to properties/parts/elements of conscious experience, qualia spaces can be though of as special cases or simplifications of experience spaces.

# References

1. Richard P. Stanley, Qualia Space, Journal of Cognitive Studies, 1999
2. Kleiner and Tull, Mathematical Structure of IIT, 2021