Philosophy of Mathematics

Tatiana Ehrenfest-Afanassjewa was an important physicist, mathematician, and educator in 20th century Europe. While some of her work has recently undergone reevaluation, little has been said regarding her groundbreaking work on dimensional analysis. This, in part, reflects an unfortunate dismissal of her interventions in such foundational debates by her contemporaries. In spite of this, her work on the generalized theory of homogeneous equations provides a mathematically sound foundation for dimensional analysis and has found some appreciation and development. It remains to (...) provide a historical account of Ehrenfest-Afanassjewa's use of the theory of homogeneous functions to ground (and limit) dimensional analysis. We take as a central focus Ehrenfest-Afanassjewa's contributions to a debate on the foundations of dimensional analysis started by physicist Richard Tolman in 1914. I go on to suggest an interpretation of the more thoroughgoing intervention Ehrenfest-Afanassjewa makes in 1926 based on this earlier context, especially her limited rehabilitation of a "theory of similitude" in contradistinction to dimensional analysis. It is shown that Ehrenfest-Afanassjewa has made foundational contributions to the mathematical foundations and methodology of dimensional analysis, our conception of the relation between constants and laws, and our understanding of the quantitative nature of physics, which remain of value. (shrink)

Intelligent Design integrates the work of Ilexa Yardley and Stridjom van der Merwe to demonstrate and prove Conservation of the Circle is the Only Dynamic in Nature (The Circular Theory) (Quantum Mechanics) (Metaphysical Naturalism).

Metaphysical Naturalism, Mereological Nihilism, The Circular Theory, and the Unification of Technology, Psychology and Finance.

We investigate the algebraic structures of square grid graphs and obtain isomorphism theorems.

Circular sets are said to provide clear-cut cases of circular orders of ontological dependence. I argue that this claim is unwarranted given the epistemic parity of two principles of set-dependence.

Este volumen, breve pero rico en ideas, en la serie de Cambridge Elements in the Philosophy of Mathematics presenta una visión general del enfoque que su autor ha desarrollado en una serie de trabajos (incluyendo su libro Morality and Mathematics, 2020, del que extrae material que presenta aquí) respecto de una amplia serie de problemas que incluyen, más allá de la filosofía de la matemática, al realismo normativo, modal y lógico. A partir de una discusión acerca de las condiciones que (...) tienen que satisfacerse para que tengamos conocimiento matemático, Clarke-Doane propone que los mismos problemas aparecen en estos otros dominios, y sugiere que adoptemos una misma estrategia (o más bien, el mismo tipo de estrategia) en cada caso. Esta solución consiste en adoptar una forma de pluralismo realista: a pesar de que cada uno de estos dominios es objetivo y de que las verdades que caen bajo cada uno no dependen de lo que nadie piense, cada manera de pensar acerca del dominio es correcta desde cierta perspectiva. La propuesta de Clarke-Doane se alinea con las propuestas de Balaguer (1995), Putnam (1980) y Carnap (1950) y, en efecto, Clarke-Doane sugiere que su forma de pluralismo no es sino la postura de Carnap en clave realista. (shrink)

How the semantic significance of numerical discourse gets determined is a metasemantic issue par excellence. At the sub-sentential level, the issue is riddled with difficulties due to the contested metaphysical status of the subject matter of numerical discourse, i.e. numbers and numerical properties and relations. I propose to set those difficulties aside and focus instead on the sentential level, specifically, on obvious affinities between whole numerical and non-numerical sentences and how their significance is determined. From such a perspective, Frege's 1884 (...) construction of number, while famously mathematically untenable, fares better than other approaches in the philosophy of mathematics. Despite the work's foundational untenability, it is metasemantically superior to extant alternatives. (shrink)

Философский анализ сущности информации и ее отношения к материи. Материалистическая концепция информационного познания мира .

This paper explores the emergence of the mind through the lens of information theory, predictive coding, and radical enactivism. This perspective integrates philosophical and biological insights, offering a naturalistic and contextualist account of the mind’s emergence. The paper highlights the innovative potential of linking predictive and semantic frameworks, reaffirming the relevance of evolutionary and information-based approaches to contemporary debates in cognitive science and philosophy.

Temporal Type Theory (TTT) has been recently introduced as a topos-theoretic approach to understanding the behaviour of systems over time. A truly innovative point of TTT is that it makes truth inherently dependent on time; this is to be contrasted with the classical approach in which past, present and future are related via logical operators. Further on this line of research, the notion of truth is substituted by the ‘time duration’ over which a proposition is true, giving rise to the (...) logic of temporal landscapes. In this paper, we embed the main notions of the Calendar and Time Type System (a framework that was built for reasoning about calendric notions in the context of the Web and is centred around the notion of time granularity) in Temporal Type Theory, attempting to address a common requirement in the practical use of temporal formalisms: the ability to speak about certain time moments and appropriate time windows in (past and future) time, in the form of hours, dates, holidays, etc. With a view to concrete applications, we provide examples on how calendar types can be combined with temporal operators of TTT to augment the expressive power of this framework. In that respect, the addition of calendar types genuinely adds to the range of Temporal Type Theory as a powerful specification language. (shrink)

We determine the strictly positive fragment \(\textsf{QPL}^+(\textsf{HA})\) of the quantified provability logic \(\textsf{QPL}(\textsf{HA})\) of Heyting Arithmetic. We show that \(\textsf{QPL}^+(\textsf{HA})\) is decidable and that it coincides with \(\textsf{QPL}^+(\textsf{PA})\), which is the strictly positive fragment of the quantified provability logic of of Peano Arithmetic. This positively resolves a previous conjecture of the authors described in [ 14 ]. On our way to proving these results, we carve out the strictly positive fragment \(\textsf{PL}^+(\textsf{HA})\) of the provability logic \(\textsf{PL}(\textsf{HA})\) of Heyting Arithmetic, provide (...) a simple axiomatization, and prove it to be sound and complete for two types of arithmetical interpretations. The simple fragments presented in this paper should be contrasted with a recent result by Mojtahedi [ 43 ], where an axiomatization for \(\textsf{PL}(\textsf{HA})\) is provided. This axiomatization, although decidable, is of considerable complexity. (shrink)

A meta-nonfiction, arranged topically, expounding various areas of philosophy and lexical objects. To be used on a theoretical agent as a preimage :: cellular automata of the solvable sort, apriori. Will ruin ab initio qualia runs in some seeds.

How technology turns every human into an epistemologist.

The project is aimed at an arduous task of precise identification of medicinal plant species with the problem being pertinent in those industries that include botany, Ayurveda, pharmacology, and biomedical research. Most of the traditional identification methods are quite serious challenges for users, researchers, and students because they are usually time-consuming, knowledge-intensive, and prone to human errors. Our proposal develops an advanced web-based application for this process by utilizing state-of-the-art methods in image processing and machine learning. We will create a (...) platform where users can upload or take pictures of plant specimens and obtain accurate identifications and comprehensive medical information by using machine learning algorithms with plant species image datasets. This application is done in a way that the interface would be user-friendly and favor research, identification, and learning, especially for Ayurvedic practitioners, biomedical specialists, botanists, and students. Therefore, our project is aimed at developing an exhaustive and reliable solution for medicinal plant identification and study by overcoming the deficiencies of existing systems, such as a small dataset, poor variable quality, and lack of complete medicinal information. (shrink)

The philosophy of superdeterminism is based on a single scientific fact about the universe, namely that cause and effect in physics are not real. In 2020, accomplished Swedish theoretical physicist, Dr. Johan Hansson published a physics proof using Albert Einstein’s Theory of Special Relativity that our universe is superdeterministic meaning a predetermined static block universe without cause and effect in physics. The unity of our universe originates from its creation from the same nothingness under the zero energy universe theory. However, (...) nothingness cannot actually cause a universe to exist on its own under superdeterminism due to the absence of cause and effect in physics. Moreover, nothingness is the absence of anything real and cannot logically be the reality underlying our universe. Consequently, our universe must exist from the reality of the logic or Logos underlying our physical reality resulting from the origination of our universe from the same nothingness or common creation. (shrink)