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Josh Hoffman: on 3/25/22 at 0:32am UTC, wrote Chair: Ariel Zeleznikow-Johnston Speakers: Johannes Kleiner, LMU ...


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December 6, 2022

CATEGORY: Blog [back]
TOPIC: Consciousness Talks 10: Mathematical Phenomenology 1 - Kleiner & Saigo by Hayato Saigo [refresh]
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FQXi Administrator Josh Hoffman wrote on Mar. 25, 2022 @ 00:32 GMT
Chair: Ariel Zeleznikow-Johnston


Johannes Kleiner, LMU

Title: “Qualitative Structure, Automorphism Groups and Private Language”

Abstract: It is generally agreed upon that qualities of conscious experience instantiate structural properties, usually called relations. They furnish a representation of qualities (or qualia, in fact) in terms of a mathematical space Q (rather than a set), which is crucial to both modelling and measuring of conscious experience.

What is usually disregarded is that “only such structural properties generalize across individuals” (Austen Clark), but that qualities themselves as differentiated by stimulus specifications, behavior or reports do not. We show that this implies that only the part of Q which is invariant with respect to the automorphism group has a well-defined referent, while individual elements do not. This poses a prima facie limitation of any theory or experiment that aims to address individual qualities. We show how mathematical theories of consciousness can overcome this limitation via symmetry groups and group actions, making accessible to science what is properly called private language.

Hayato Saigo, NIBST

Title: “3 Reasons Why You Should Care About Category Theory”

Abstract: Category theory is a branch of mathematics which have been used to organize various regions of mathematics and related sciences from a radical “relation-first” point of view. Why consciousness researchers should care about category theory?

There are (at least) 3 reasons:

1 Everything is relational

2 Everything is relation

3 Relation is everything

In this talk we explain the reasons above more concretely and introduce the ideas to utilize basic concepts in category theory for consciousness studies.

Keywords: #Consciousness #Saigo #Catagory_Theory #Relational_Dynamics

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