In this article I outline the proposal of using category theory to mathematise phenomenology. The rest is for later projects and may simply be mentioned in the conclusion to this article.
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In my PhD I propose that category theory be used in the mathematisation of phenomenology. Mathematising the phenomenality of language comprehension, including the phenomenality of mathematical comprehension, is an initial area for which tools developed in my PhD could be utilised. Mathematising the phenomenality of language comprehension could serve as an initial step towards a mathematisation of the phenomenality of learning. Such research stands to contribute significantly to education and provide a platform for further investigations.
A mathematisation of phenomenology would reveal the kind of manifold within which emotion exists. This âemotion spaceâ may have a complicated topology, potentially involving multiple if not infinite dimensionality. Mathematising the phenomenality of emotion would contribute significantly to disciplines concerned with emotional health. Such an understanding would be a powerful tool in combating illnesses such as depression or schizophrenia.
Given that the architecture of the brain in many animals is similar to that of humans it is likely that the basic structure of the âemotion spaceâ of animals will be similar to that of humans. Research with respect to humans, therefore, could contribute to animal welfare.
The objects (nodes) of phenomenality are constantly in process. Similarly the relations between these objects change across time. Future research into phenomenology needs to develop methodologies and methods that are capable of studying phenomenology as process and relation and evolving within either linear time or time conceived according to a systems internal events. Methodological material in my PhD has contributed towards this goal. Category theory and dynamic systems theory are other approaches that are likely to be efficacious.
The above considerations would be pertinent to any approach to mathematising phenomenality. The project of mathematising phenomenology is likely to provide tools with which to study the processes and relations within phenomenality.