Psittacus I think I genuinely enjoy self-studying. The more I understand a field, the more I appreciate existence itself. I am interested in epistemology and formal languages such as programming languages or the very foundations of mathematics. I just like how cognitive and philosophical foundations relate to math and computer science as a whole.
Let us make a simple comparison between the brain (and in an extended manner the embodied mind) and the computer: First, regarding working speed, the human mind processes information (roughly speaking) around six million eight hundred thousand times slower than an (average) computer and it is around one billion times less accurate (regarding the error's rate per number of operations performed). On the other hand, the human mind is able to do very simple (and at the same time very powerful) conceptual inferences like y = cymbal and Y = tambour, then yYyYyYy = drum set; or if, A = house and B = boat, then A B= houseboat; while this ability is essentially non-existent modern computers. Thus, why not simulate the deductive-pragmatic functioning of the mind with all the strengthens of modern computation ?
In fact, that leads us to a conceptual extension of the church thesis, i.e.,
A mathematical structure (e.g., a concept, a proof, a counterexample, a theory) is effectively calculable (i.e., generated) by a human being's mind iff it can be be computed by a "conceptual" turing machine.
Indeed, there exists a deep computational trinitarianism whose central dogma holds that logic, languages, and categories are but three manifestations of one divine notion of computation. Any concept arising on one aspect should have meaning from the perspective of the other two. If you arrive at an insight that has importance for logic, languages and categories, then you may feel sure that you have elucidated an essential concept of computation. Specifically, mathematics can be formalized in a language called type theory and internalized in structured categories while at the same time, type theory can be interpreted in structured categories.
I think category theory also addresses more general philosophical questions. From the foregoing discussion, it seems natural to think that it should have an impact on virtually every question raised in the philosophy of languages: from the nature of identity criteria to the question of alternative logics. Similar remarks can be made when we turn to ontology, in particular formal ontology: the part/whole relation, system boundaries, notions of spaces, etc. In fact, several philosophers I've spoken to on this subject have suggested a motivation very close to this one. Logic has obvious philosophical relevance in structuralism, as does our knowledge of it.
Finally, both classical and connectionist theories of cognitive architecture seek to explain systematicity (i.e. the property of human cognition that cognitive ability arises in the form of groups of related behaviors) as a consequence of syntactically and functionally compositional representations, respectively. However, both theories depend on ad-hoc assumptions to exclude specific instances of these forms of compositionality (e.g. grammars, networks) that do not account for systematicity. By analogy with the ptolemaic (i.e. geocentric) theory of planetary motion, although either theory can be made to be consistent with actual data, they fail to explain it concretely. In contrast, category theory provides an alternative explanation based on the formal concept of adjunction, which relates a pair of applications preserving a certain structure, called a functor. A functor generalizes the notion of applications between representation states to include an application between state morphisms (or process). From a formal point of view, systematicity is a consequence of a higher-order theory of cognitive architecture, as opposed to first-order theories stemming from classicism or connectionism. I guess category theory offers in that regard a re-conceptualization of the cognitive sciences, analogous to that which Copernicus provided to astronomy, where states of representation are no longer the center of the cognitive universe - replaced by the relations between the applications that transform them.
I think that the relationship between the categories of mathematics and the categories as mental reasoning of philosophy and psychology are ultimately very close. Because it has implications for the structure of the human mind, and therefore for the structure of the reality we perceive and how we think and act on what is perceived, it can provide some support for an Aristotelian-Tomistic philosophy on essences and firm support for reasoning by analogy.
I was passionate about linguistics from an early age, and the Internet facilitated my love for it.
I have become quite interested in linguistics recently, specifically the construction of languages. Do you have any resources to recommend ?
kurisu I don't really like how the academic world is today focused on fields with a clear influence on society and the world. A coherent model in theoretical physics might well provide fertile insights into the structure of the universe and how it works, but from society's point of view it's just a formalism that serves only to feed scientific journals and curious minds. The conditions for obtaining and exercising the role of researcher are difficult precisely in these fields, because these jobs do not correspond to the index that prioritizes the value of a position (this is also one of the reasons why finance or management positions are the best paid) in our contemporary societies. Moreover, contrary to appearances, this is not unique to public research.
To put it plainly, I believe that academic research is pathologically distorted by assumptions about its social influence, and this is asserted first and foremost by the end-of-studies hypothesis, as if this were the end of a simple linear acquisition of skills. In the days of the Aristotelian school (which was also ahead of its time in terms of scientific method and organized research), learning a subject did not lead to the award of a diploma recognized by society; rather, it was a community driven by a fervent desire to understand the world and its mechanics.
Today, knowledge only has value through its social imprint and frankly, that's a shame.
