PMMC is a seminar that started in 2023 which encompasses mathematical and computational models of cognition and consciousness. Its aim is to stay updated on novel findings and emerging computational frameworks related to cognition and consciousness. The particularity of this seminar is to go into the technical details (mathematical and formal) of these models and the associated results. The sessions are longer than usual seminars (2h).
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If you are interested in speaking at the seminar, please send me a message to gregoireserper 'at' gmail 'dot' comAbstract: Consider the possibility that all experiences in consciousness are generated, via acts of perception, decision and action, in a stochastic dynamical process on a network of mutually interacting agents. “Conscious agents” need not be human; and there may be levels, such that a process that is conscious at one level may not be so at another level. Under this hypothesis, we propose a precise definition of a network of conscious agents and define the stochastic process undergone by the phenomenology of a single agent. Within the phenomenal dynamics, we propose a precise definition of “observer,” such that acts of observation are acts of participation, prescribed by limited observational capacity. In this view, an observer is an agent whose perceptual space is contained in the perceptual space of the observed - and the same holds for their action spaces. Thus both observer and observed participate as dynamical parts of an underlying conscious dynamics. Along with these notions is developed a logic of observation, one that comports well with previously studied logics of belief. This observational, or “trace,” logic is more general than those describing classical or quantum logics. We further suggest how to view our current theories of fundamental physics as projections of special instances of conscious dynamics. The projection involves identifying some communicating classes of conscious dynamics as “particles” and specifying which properties of the asymptotic dynamics correspond to physical properties. One goal is to establish these correspondences by recognizing the projection as one from conscious dynamics to the “surfaceology” currently being actively studied in positive geometries as applied to high-energy physics.
Abstract: In this talk I aim to show how the act of naming, in our activity as interpretants/observers is formally and fundamentally related to both our being, and to the Gödelian structure of understanding of our relationships with formal systems. I show that the way that self-reference arises for beings/observers/interpretants is formally identical with the way self-reference is essential to the incompleteness of formal systems. This places the problem of the relationship of meaning and formalism in a new light. I give a new solution to that relationship, but the full question of how meaning and formalism relate remains open and this must be so.
The formalism behind this talk is as follows: An arrow of reference is given, from A (a name) to B (a being so named) as in A—> B. The “indicative shift” of A—> B is a new arrow of reference from #A (a meta name for A that is associated with the context or being in which A is held) to BA (the concatenation of B with its name A). Thus A—> B shifts to #A—> BA. This shift is meant to model our personal linguistic action in acquiring the name of B. When I know you, then your name is shifted, and you and your name appear together in my cognition. When I know you, recognize you, but cannot find your name, then there is a gap that needs to be filled! The operator # connotes the way my holding of the name A becomes related to the appearance of the name A with the person B and this is denoted by #A —> BA. When # itself (my naming process) has a name, then self-reference occurs. M —> # shifts to #M —> #M. #M is a combination of my being and the name of my naming process. In that combination #M becomes my own name. This formalism of reference and self-reference can be seen in the linguistics of everyday naming, and it is intrinsically linked to the Goedelian forms of self reference and to the diagonal process of Georg Cantor, the founder of the Theory of Sets. These connections will be discussed in the talk.
Abstract: Influential theories of consciousness rely on the notion of self-representational mental state and non-wellfounded explanation – let us call them NWF-TOCs (see Kriegel and Williford (2006) and especially Williford 2006). However, many philosophers and logicians have pointed out that self-referential representations and non-wellfounded explanations may be in some sense “pathological”. Think of a representation which represents its own falsehood (the liar paradox), or of the explanation of the birth of an individual who time-travelled and accidentally killed their grandfather before he had any children (the grandfather paradox). One may wonder whether the pathological character of self-referential representations and non-wellfounded explanations prevents them from playing the role that NWF-tOCs are supposed to play. Over the past ten years, I have been trying to develop a conceptual framework for assessing the pathological character of self-referential representations and non-wellfounded explanations (see especially Billon 2019, 2021, forthcoming). In this talk, I will present this conceptual framework and try to apply it to NWF-TOCs.
Abstract: Neurons in the brain are often considered the elementary units of biological computation. Various codes, either spike-based or rate-based, have been proposed to support computations distributed in the brain. These theories leave open the question of how computations may be implemented in organisms lacking a nervous system, such as unicellular organisms. These organisms, however, may engage in simple purposeful behaviors like phototaxis or chemotaxis and can be seen as performing computation during such behaviors. We show that biochemical cascades can be seen as implementing Bayesian computations related to such behaviors.
Abstract: Any theory of consciousness must answer to the phenomenologically invariant or essential structures of consciousness. What are these structures? And how do the various attempts to model them mathematically relate to one another? After considering some possible answers to these questions, I focus on one essential phenomenological structure of consciousness, pre-reflective self-consciousness, discuss one way of articulating it mathematically (using the theory of nonwellfounded sets), and conclude with some open questions about how this model may relate to other mathematical and quasi-mathematical efforts in the "ballpark" (e.g., D. Hofstadter's "Strange Loops", F. Varela's and H. Maturana's notion of Autopoiesis, IIT, and the PCM).