Hard, Harder, and the Hardest Problem: The Society of Cognitive Selves

The hard problem of consciousness is explicating how moving matter becomes thinking matter. Harder yet is the problem of spelling out the mutual determinations of individual experiences and the experiencing self. Determining how the collective social consciousness influences and is influenced by the individual selves constituting the society is the hardest problem. Drawing parallels between individual cognition and the collective knowing of mathematical science, here we present a conceptualization of the cognitive dimension of the self. Our abstraction of the relations between the physical world, biological brain, mind, intuition, consciousness, cognitive self, and the society can facilitate the construction of the conceptual repertoire required for an explicit science of the self within human society

Mathematics for Cognitive Science

That the state-of-affairs of cognitive science is not good is brought into figural salience in "What happened to cognitive science?" (Núñez et al., 2019). We extend their objective description of 'what's wrong' to a prescription of 'how to correct'. Cognitive science, in its quest to elucidate 'how we know', embraces a long list of subjects, while ignoring Mathematics (Fig. 1a, Núñez et al., 2019). Mathematics is known for making the unknown to be known (cf. solving for unknowns). This acknowledgement naturally raises the question: does mathematical knowing inform knowing in general? Here we show that drawing parallels to mathematical knowing can facilitate the advancement of cognitive science (Lawvere, 1994)

Conscious Experience and Designing User Experiences

Neuroscientific discourse on consciousness often resorts to "collection of elements", notwithstanding the Gestalt demonstrations against representing conscious experience as a collection of sensory elements. Here I show that defining conscious experience as an object of the category of conscious experiences, instead of as cohesion-less set of structure-less elements, provides the conceptual repertoire—basic shapes, figures, and incidence relations—needed to reason about the essence of conscious experiences and the essence-preserving transformations of conscious experiences. Viewed in light of the category of conscious experiences, designers of user experience—in designing pre-conceptualized user experiences—are well situated to contribute to the development of the science of consciousness

Isbell Conjugacy for Developing Cognitive Science

What is cognition? Equivalently, what is cognition good for? Or, what is it that would not be but for human cognition? But for human cognition, there would not be science. Based on this kinship between individual cognition and collective science, here we put forward Isbell conjugacy---the adjointness between objective geometry and subjective algebra---as a scientific method for developing cognitive science. We begin with the correspondence between categorical perception and category theory. Next, we show how the Gestalt maxim is subsumed by the mathematical construct of colimit, a generalization of summation. The universal mapping property definitions of mathematical constructs, by virtue of being the best with respect to the universe of discourse, can be learned using reinforcement learning algorithms, which raises the possibility of abstracting the architecture of mathematics by artificial intelligence. Subsequently, we present naturality (to be contrasted with miracles), understood as 'Becoming consistent with Being', which governs the transformations of both things and their theories, as the zeroth law of change. Furthermore, the contrast---physical [mechanism] vs. biological [organism]---is smoothed via natural transformation, wherein transformations are respectful of the cohesion of the objects transformed. In closing, upon recognizing the scientific value of learning difficult-to-master differential calculus by physicists, of learning a strange four-letter language by biologists, and of learning the grammar of our respective mother tongues, we make a case for learning the theory of naturality / category theory for developing cognitive science

Structure and Logic of Conceptual Mind

Mind, according to cognitive neuroscience, is a set of brain functions. But, unlike sets, our minds are cohesive. Moreover, unlike the structureless elements of sets, the contents of our minds are structured. Mutual relations between the mental contents endow the mind its structure. Here we characterize the structural essence and the logical form of the mind by focusing on thinking. Examination of the relations between concepts, propositions, and syllogisms involved in thinking revealed the reflexive graph structure of the conceptual mind. Objective logic of the conceptual mind is calculated from its structure. Noteworthy features of the logic of conceptual mind are: degrees of truth, varieties of negation, admission of contradiction, and the failure of a de Morgan's law. Furthermore, cohesion of the conceptual mind follows from its reflexive graph structure. Our characterization of the structure and logic of mind constitutes a substantial refinement of the contemporary cognitive neuroscientific conceptualization of the mind as a set

Science of Knowing: Mathematics

The 'Science of Knowing: Mathematics' textbook is the first book to put forward and substantiate the thesis that the mathematical understanding of mathematics, as exemplified in F. William Lawvere's Functorial Semantics, constitutes the science of knowing i.e. cognitive science

Objective Logic of Consciousness

We define consciousness as the category of all conscious experiences. This immediately raises the question: What is the essence in which every conscious experience in the category of conscious experiences partakes? We consider various abstract essences of conscious experiences as theories of consciousness. They are: (i) conscious experience is an action of memory on sensation, (ii) conscious experience is experiencing a particular as an exemplar of a general, (iii) conscious experience is an interpretation of sensation, (iv) conscious experience is referring sensation to an object as its cause, and (v) conscious experience is a model of stimulus. Corresponding to each one of these theories we obtain a category of models of conscious experiences: (i) category of actions, (ii) category of idempotents, (iii) category of two sequential maps, (iv) category of brain-generalized figures, and (v) functor categories with intuition as base and conceptual repertoire as exponent, respectively. For each theory of consciousness we also calculate its truth value object and characterize the objective logic intrinsic to the corresponding category of models of consciousness experiences

Gandhi's Satya: Truth entails peace

What is Gandhi’s Satya? How does truth entail peace? Satya or truth, for Gandhi, is experiential. The experiential truth of Gandhi does not exclude epistemological, metaphysical, or moral facets of truth, but is an unequivocal acknowledgement of the subjective basis of the pursuit of objectivity. In admitting my truth, your truth, our truth, their truth, etc., Gandhi brought into clear focus the reality of I and we—the subjects (or viewpoints) of subjective experiences (views). The totality of these subjective viewpoints, along with their mutual relationships, constitutes an objective frame of reference for reconciling or putting together seemingly irreconcilable perceptions into a unitary whole of mutual understanding and an ever more refined comprehension of reality, thereby engendering peace. Considering the generality of the basic tenet—viewpoint dependence of views—of Gandhi’s satyagraha and in view of the kinship between positive conception of peace and unity, I put forward ‘satyagraha for science’ as a method to address numerous foundational problems in various branches of science centered on unity such as the binding problem in neuroscience

Thus spoke Pushpa

There is a lesson from the woods--Bollywood, Kollywood, Mollywood, and Tollywood--of make-believe, which speaks to the core concern of science: the practice of science. Puspha, an Indian movie that brought the movie industry to its senses, with its global popularity has this to say: Be thyself; keep it real. Situated in a remote region aeons apart from the vast concrete and intimate plastic world we are familiar with, the happenings in the distanct and alien universe of discourse--a hamlet adjacent to tribals, forest, and nature--is surprizingly universally relatable. Here I show how the unity of being and the attendant naturality of becoming or, in the words of Tolkien, "the inner consistency of reality" of Pushpa is what made people all over the world relate to each and every character/scene in Pushpa. In doing so, I bring out its (arts and/or humanities) relevance to the practice of science in general and science policy in particular, with emphasis on changing human behaviour, especially in the context of COVID

In Education We Trust

Beginning with an examination of the deep history of making things and thinking about making things made-up in our minds, I argue that the resultant declarative understanding of the procedural knowledge of abstracting theories and building models—the essence(s) of the practice of science—embodied in Conceptual Mathematics is worth learning beginning with high school, along with grammar and calculus. One of the many profound scientific insights introduced—in a manner accessible to total beginners—in Lawvere and Schanuel's Conceptual Mathematics textbook is: the way we ought to think about things varies with the nature of things. In light of the universal yearning for understanding, it may be pedagogically unethical not to teach the eminently learnable Conceptual Mathematics. Summing it all, we need to champion the cause of taking Conceptual Mathematics to classrooms