相关论文: Mathematical conceptualism
A physical picture for Quantum Mechanics which permits to conciliate it with the usual common sense is proposed. The picture agrees with the canonical Copenhagen interpretation making more clear its statements.
There is a contemporary trend toward geometrizing all mathematical theories, as proposed by the Langlands program, and, by extension, physical theories as well. Within this paradigm, it becomes possible to represent physical objects as…
Eugene Wigner famously argued for the "unreasonable effectiveness of mathematics" for describing physics and other natural sciences in his 1960 essay. That essay has now led to some 55 years of (sometimes anguished) soul searching ---…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
Traditional cognitive science rests on a foundation of classical logic and probability theory. This foundation has been seriously challenged by several findings in experimental psychology on human decision making. Meanwhile, the formalism…
A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a…
In this paper, we described possible directions for deeper understanding, helping bridge the gap between psychology / cognitive science and computational approaches in sentiment/opinion analysis literature. We focus on the opinion holder's…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
The integration of reasoning and computation services across system and language boundaries is a challenging problem of computer science. In this paper, we use integration for the scenario where we have two systems that we integrate by…
Almost all representations considered in computable analysis are partial. We provide arguments in favor of total representations (by elements of the Baire space). Total representations make the well known analogy between numberings and…
Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…
This paper from 2000 is a presentation of a status qu{\ae}stionis at that tiime, to wit of the problem of the interpretability logic of {\em all}\/ reasonable arithmetical theories. We present both the arithmetical side and the modal side…
We describe a mainstream "universalist" approach to the understanding of mathematics. We then conduct a systematic (but not exhaustive) review of the academic literature on the decolonisation of mathematics and identify how this challenges…
Inferential relations govern our concept use. In order to understand a concept it has to be located in a space of implications. There are different kinds of conditions for statements, i.e. that the conditions represent different kinds of…
Metaphysics is traditionally conceived as aiming at the truth -- indeed, the most fundamental truths about the most general features of reality. Philosophical naturalists, urging that philosophical claims be grounded on science, have often…
Ontologies have been used for the purpose of bringing system and consistency to subject and knowledge areas. We present a criticism of the present mathematical structure of ontologies and indicate that they are not sufficient in their…
We present the foundational theory of condensed sets and basic condensed algebra after having introduced key concepts from category theory and homological algebra. In the later sections, we indicate the relevance of condensed mathematics to…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
Cirquent calculus is a new proof-theoretic and semantic framework, whose main distinguishing feature is being based on circuits, as opposed to the more traditional approaches that deal with tree-like objects such as formulas or sequents.…
We describe and explain the desire, common among mathematicians, both for unity and independence in its major themes. In the dialogue that follows, we express our spontaneous and considered judgment and reservations by contrasting the…