School of Psychological Sciences and Turner Institute for Brain and Mental Health, Monash University, Melbourne, Victoria, Australia; Center for Information and Neural Networks (CiNet), National Institute of Information and Communications Technology (NICT), Suita, Osaka 565-0871, Japan; Advanced Telecommunications Research Computational Neuroscience Laboratories, 2-2-2 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0288, Japan.
National Institute of Advanced Industrial Science and Technology, Tsukuba 305-8566, Japan.
Conscious Cogn. 2022 May;101:103319. doi: 10.1016/j.concog.2022.103319. Epub 2022 Apr 15.
Qualitative relationships between two instances of conscious experiences can be quantified through the perceived similarity. Previously, we proposed that by defining similarity relationships as arrows and conscious experiences as objects, we can define a category of qualia in the context of category theory. However, the example qualia categories we proposed were highly idealized and limited to cases where perceived similarity is binary: either present or absent without any gradation. Here, we introduce enriched category theory to address the graded levels of similarity that arises in many instances of qualia. Enriched categories generalize the concept of a relation between objects as a directed arrow (or morphism) in ordinary category theory to a more flexible notion, such as a measure of distance. As an alternative relation, here we propose a graded measure of perceived dissimilarity between the two objects. We claim that enriched categories accommodate various types of conscious experiences. An important consequence of this claim is the application of the Yoneda lemma in enriched category; we can characterize a quale through a collection of relationships between the quale and the other qualia up to an (enriched) isomorphism.
通过感知相似性，可以对两个意识体验实例之间的定性关系进行量化。之前，我们提出通过将相似性关系定义为箭头，将意识体验定义为对象，可以在范畴论的上下文中定义一类质。然而，我们提出的示例质类别是高度理想化的，仅限于感知相似性为二元的情况：要么存在，要么不存在，没有任何渐变。在这里，我们引入了丰富的范畴论来解决在许多质实例中出现的相似性的分级层次问题。丰富的范畴将对象之间关系的概念从普通范畴论中的有向箭头（或态射）推广到更灵活的概念，例如距离度量。作为替代关系，我们在这里提出了一种对两个对象之间感知差异的分级度量。我们声称丰富的范畴可以容纳各种类型的意识体验。这一主张的一个重要结果是在丰富的范畴中应用 Yoneda 引理；我们可以通过一个质与其他质之间的关系集合来描述一个质，这些关系集合在一个（丰富的）同构下。
