*Qualia Space and Category Theory* https://www.researchgate.net/publication/281238031_QUALIA_SPACE_AND_CATEGORY_THEORY
Conscious experiences are characteristically qualitative. The difference between, for example, the black color and the bitter taste of coffee is not one of quantity but that of quality. The qualitative universals (black, bitter) given in particular experiences, i.e. qualia, combine into the seamless unity of our conscious experience. We need, as a first step towards consciousness science, a scientific account of the qualitative nature of qualia and of a process to put together qualities into the cohesion of consciousness. The problematics of quality and cohesion are not unique to consciousness studies. In mathematics, the study of qualities (e.g. shape) resulting from quantitative variations in cohesive spaces led to the axiomatization of cohesion and quality. Using the mathematical definition of quality, herein we model qualia space as a categorical product of qualities. Thus modeled qualia space is a codomain space wherein composite qualities (cf. black AND bitter) of conscious experiences can be valued. As part of characterizing the qualia space, we provide a detailed exemplification of the mathematics of quality and cohesion in terms of the categories of idempotents and reflexive graphs. More specifically, with qualities as commutative triangles formed of cohesion-preserving functors, first we calculate the product of commutative triangles. Next, we explicitly show that the category of idempotents is a quality type. Lastly, as part of showing that the category of reflexive graphs is cohesive, we characterize the adjointness between functors relating cohesive graphs to discrete sets. In conclusion, our category theoretic construction of qualia space is a formalization of the binding of intensive colors and extensive shapes into the cohesive colored-shapes of our conscious experiences. Compared to the feature-vector accounts of conscious experiences, our product-of-qualities account of consciousness is a substantial theoretical advance. ... A brain can be thought of as a universal measurement device (Grossberg, 1983), measuring the physical world, and with conscious experiences as values of the neural measurements. Though there is much within a given conscious experience that lends itself to be quantified (e.g. intensity of pain), there is also much that remains beyond the reach of quantities (i.e. the quality of pain). These qualitative universals given in particular conscious experiences are called qualia (Lewis, 1929, p. 121). Within this framework, we need a space: qualia space (Balduzzi & Tononi, 2009; Stanley, 1999), to serve as codomain in which the neural measures can be valued. In the case ofquantitative measurements, for example, the real number line serves as a codomain of values. In the case of brains measuring things in the world, we need a space which can serve as a space of values for qualities such as taste and smell. Analogous to the case of quantitative measurements, wherein additional dimensions are introduced (e.g. plane) to deal with more than one quantity (Lawvere & Rosebrugh, 2003, p. 59), we need a product space of qualities that can serve as a codomain space of values for composite qualities (Lawvere, 2008). Once we have a qualia space of composite qualities, we can characterize its geometry (figures and their incidences) and algebra (functions and their determinations). This qualia space can then be related to the physical stimulus spaces and the corresponding spaces of neural processing. ... @philipthrift -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/7163a34f-178c-445a-8bdd-ed0614f6063f%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
