@article{heller_homunculus_2019,
title = {Homunculus' {Brain} and {Categorical} {Logic}},
volume = {abs/1903.03424},
abstract = {The interaction between syntax (formal language) and its semantics (meanings of language) is well studied in categorical logic. Results of this study are employed to understand how the brain could create meanings. To emphasize the toy character of the proposed model, we prefer to speak on homunculus' brain rather than just on the brain. Homunculus' brain consists of neurons, each of which is modeled by a category, and axons between neurons, which are modeled by functors between the corresponding neuron-categories. Each neuron (category) has its own program enabling its working, i.e. a "theory" of this neuron. In analogy with what is known from categorical logic, we postulate the existence of the pair of adjoint functors, called Lang and Syn, from a category, now called BRAIN, of categories, to a category, now called MIND, of theories. Our homunculus is a kind of "mathematical robot", the neuronal architecture of which is not important. Its only aim is to provide us with the opportunity to study how such a simple brain-like structure could "create meanings" out of its purely syntactic program. The pair of adjoint functors Lang and Syn models mutual dependencies between the syntactical structure of a given theory of MIND and the internal logic of its semantics given by a category of BRAIN. In this way, a formal language (syntax) and its meanings (semantics) are interwoven with each other in a manner corresponding to the adjointness of the functors Lang and Syn. Categories BRAIN and MIND interact with each other with their entire structures and, at the same time, these very structures are shaped by this interaction.},
journal = {ArXiv},
author = {Heller, Michael},
year = {2019},
note = {ZSCC: 0000000
arXiv: 1903.03424},
keywords = {Emergence, Sketchy}
}
@article{tsuchiya_using_2016,
title = {Using category theory to assess the relationship between consciousness and integrated information theory},
volume = {107},
issn = {0168-0102},
url = {http://www.sciencedirect.com/science/article/pii/S0168010215002989},
doi = {10/ggdf95},
abstract = {One of the most mysterious phenomena in science is the nature of conscious experience. Due to its subjective nature, a reductionist approach is having a hard time in addressing some fundamental questions about consciousness. These questions are squarely and quantitatively tackled by a recently developed theoretical framework, called integrated information theory (IIT) of consciousness. In particular, IIT proposes that a maximally irreducible conceptual structure (MICS) is identical to conscious experience. However, there has been no principled way to assess the claimed identity. Here, we propose to apply a mathematical formalism, category theory, to assess the proposed identity and suggest that it is important to consider if there exists a proper translation between the domain of conscious experience and that of the MICS. If such translation exists, we postulate that questions in one domain can be answered in the other domain; very difficult questions in the domain of consciousness can be resolved in the domain of mathematics. We claim that it is possible to empirically test if such a functor exists, by using a combination of neuroscientific and computational approaches. Our general, principled and empirical framework allows us to assess the relationship between the domain of consciousness and the domain of mathematical structures, including those suggested by IIT.},
language = {en},
urldate = {2019-11-22},
journal = {Neuroscience Research},
author = {Tsuchiya, Naotsugu and Taguchi, Shigeru and Saigo, Hayato},
month = jun,
year = {2016},
note = {ZSCC: 0000029},
keywords = {Psychology, Sketchy},
pages = {1--7}
}
@article{ehresmann_conciliating_2015,
series = {Integral {Biomathics}: {Life} {Sciences}, {Mathematics}, and {Phenomenological} {Philosophy}},
title = {Conciliating neuroscience and phenomenology via category theory},
volume = {119},
issn = {0079-6107},
url = {http://www.sciencedirect.com/science/article/pii/S0079610715001005},
doi = {10/f75jzr},
abstract = {The paper discusses how neural and mental processes correlate for developing cognitive abilities like memory or spatial representation and allowing the emergence of higher cognitive processes up to embodied cognition, consciousness and creativity. It is done via the presentation of MENS (for Memory Evolutive Neural System), a mathematical methodology, based on category theory, which encompasses the neural and mental systems and analyzes their dynamics in the process of ‘becoming’. Using the categorical notion of a colimit, it describes the generation of mental objects through the iterative binding of distributed synchronous assemblies of neurons, and presents a new rationale of spatial representation in the hippocampus (Gómez-Ramirez and Sanz, 2011). An important result is that the degeneracy of the neural code (Edelman, 1989) is the property allowing for the formation of mental objects and cognitive processes of increasing complexity order, with multiple neuronal realizabilities; it is essential “to explain certain empirical phenomena like productivity and systematicity of thought and thinking (Aydede 2010)”. Rather than restricting the discourse to linguistics or philosophy of mind, the formal methods used in MENS lead to precise notions of Compositionality, Productivity and Systematicity, which overcome the dichotomic debate of classicism vs. connectionism and their multiple facets. It also allows developing the naturalized phenomenology approach asked for by Varela (1996) which “seeks articulations by mutual constraints between phenomena present in experience and the correlative field of phenomena established by the cognitive sciences”, while avoiding their pitfalls.},
language = {en},
number = {3},
urldate = {2019-11-28},
journal = {Progress in Biophysics and Molecular Biology},
author = {Ehresmann, Andrée C. and Gomez-Ramirez, Jaime},
month = dec,
year = {2015},
note = {ZSCC: 0000018},
keywords = {Biology, Emergence, Neuroscience, Psychology, Sketchy},
pages = {347--359}
}
@article{brown_category_2008,
title = {Category {Theory} and {Higher} {Dimensional} {Algebra}: potential descriptive tools in neuroscience},
shorttitle = {Category {Theory} and {Higher} {Dimensional} {Algebra}},
url = {http://arxiv.org/abs/math/0306223},
abstract = {We explain the notion of colimit in category theory as a potential tool for describing structures and their communication, and the notion of higher dimensional algebra as potential yoga for dealing with processes and processes of processes.},
language = {en},
urldate = {2019-11-22},
journal = {arXiv:math/0306223},
author = {Brown, R. and Porter, T.},
month = feb,
year = {2008},
note = {ZSCC: NoCitationData[s0]
arXiv: math/0306223},
keywords = {Emergence, Neuroscience, Rewriting theory, Sketchy}
}
@article{rosen_representation_1958,
title = {The representation of biological systems from the standpoint of the theory of categories},
volume = {20},
issn = {0007-4985, 1522-9602},
url = {http://link.springer.com/10.1007/BF02477890},
doi = {10/fdgzxz},
language = {en},
number = {4},
urldate = {2019-11-22},
journal = {The Bulletin of Mathematical Biophysics},
author = {Rosen, Robert},
month = dec,
year = {1958},
note = {ZSCC: 0000262},
keywords = {Biology, Sketchy},
pages = {317--341}
}
@article{gromov_structures_nodate,
title = {Structures, {Learning} and {Ergosystems}: {Chapters}},
abstract = {We introduce a concept of an ergosystem which functions by building its ”internal structure“ out of the ”raw structures“ in the incoming ﬂows of signals.},
language = {en},
author = {Gromov, Misha},
note = {ZSCC: 0000010},
keywords = {Biology, Compendium, Emergence, Neuroscience, Sketchy},
pages = {159}
}