scholarly journals A Logically Formalized Axiomatic Epistemology System Σ + C and Philosophical Grounding Mathematics as a Self-Sufficing System

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1859
Author(s):  
Vladimir Olegovich Lobovikov
Keyword(s):  
Mathematical Knowledge ◽  
A Priori ◽  
Knowledge System ◽  
Axiomatic System ◽  
Formal Epistemology ◽  
Empirical Knowledge ◽  
The Subject ◽  
Arithmetic System ◽  
First Time ◽  
Gödel’S Theorem

The subject matter of this research is Kant’s apriorism underlying Hilbert’s formalism in the philosophical grounding of mathematics as a self-sufficing system. The research aim is the invention of such a logically formalized axiomatic epistemology system, in which it is possible to construct formal deductive inferences of formulae—modeling the formalism ideal of Hilbert—from the assumption of Kant’s apriorism in relation to mathematical knowledge. The research method is hypothetical–deductive (axiomatic). The research results and their scientific novelty are based on a logically formalized axiomatic system of epistemology called Σ + C, constructed here for the first time. In comparison with the already published formal epistemology systems X and Σ, some of the axiom schemes here are generalized in Σ + C, and a new symbol is included in the object-language alphabet of Σ + C, namely, the symbol representing the perfection modality, C: “it is consistent that…”. The meaning of this modality is defined by the system of axiom schemes of Σ + C. A deductive proof of the consistency of Σ + C is submitted. For the first time, by means of Σ + C, it is deductively demonstrated that, from the conjunction of Σ + C and either the first or second version of Gödel’s theorem of incompleteness of a formal arithmetic system, the formal arithmetic investigated by Gödel is a representation of an empirical knowledge system. Thus, Kant’s view of mathematics as a self-sufficient, pure, a priori knowledge system is falsified.

Mathematical Knowledge and the Interplay of Practices

2015 ◽  
Author(s):  
José Ferreirós
Keyword(s):  
Mathematical Knowledge ◽  
A Priori ◽  
Philosophy Of Mathematics ◽  
Advanced Mathematics ◽  
New Approach ◽  
Agent Based ◽  
Epistemology Of Mathematics ◽  
Actual Experience ◽  
Elementary Math ◽  
Mathematical Tradition

This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, the book uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, the book shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. It argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. It demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, the book challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.

Educación y valores

2014 ◽  
pp. 83
Author(s):  
Sabino de Juan López
Keyword(s):  
Key Words ◽  
A Priori ◽  
Palabras Clave ◽  
The Subject ◽  
The Relationship ◽  
Problem Of The Criterion

RESUMEN En el artículo se ofrece una reflexión en torno a la educación y valores. Tras una referencia a los diferentes sentidos en que se puede plantear el problema en función de la forma como se puede entender la relación entre los dos sustantivos “educación” y “valores”, la reflexión se centra en algunos problemas relacionados con los valores en cuanto contenidos de la educación. Primeramente se refiere al problema del criterio en función del cual determinar los valores de la educación, concluyendo en que el criterio no podía ser ni de carácter a priori, ni empírico, sino “sintético”. A continuación, se afronta el problema del principio, de la fuente de los valores, o la concreción del criterio de los valores de la educación, entendiendo que éstos deberían ser determinados a partir del sujeto de la educación. Se concluye con la referencia a una exigencia de los valores de la educación, la configuración de una totalidad unitaria e interactiva. Palabras clave: educación, valores, fuente de valores, integración, cultura EDUCATION AND VALUES ABSTRACT The article offers a reflection on education and values. After a reference to the different senses in which one can pose the problem in terms of how you can understand the relationship between the two nouns “education” and “values”, reflection focuses on some problems related to the values in the contents of education. First, it concerns the problem of the criterion against which to determine the values of education, concluding that the criterion could be neither a priori in nature, not empirical, but “synthetic”. Herein, the problem of principle is faced, the source of values, or the realization of the criterion of the values of education, understanding that these should be determined from the subject of education. It concludes with the reference of a requirement of the values in education, setting up a unitary and interactive whole. Key Words: education, values , power values , integration, culture

СОЦИАЛЬНАЯ КОНФЛИКТОЛОГИЯ: ТЕОРЕТИКО-ИСТОРИЧЕСКИЙ АСПЕКТ

2020 ◽  
Vol 15 (2) ◽  
pp. 68
Author(s):  
А. Н. Сухов
Keyword(s):  
Theory And Practice ◽  
Important Task ◽  
Social Conflicts ◽  
Psychological Approach ◽  
Structure Dynamics ◽  
History Of ◽  
The Subject ◽  
First Time

This given article reveals the topicality not only of destructive, but also of constructive, as well as hybrid conflicts. Practically it has been done for the first time. It also describes the history of the formation of both foreign and domestic social conflictology. At the same time, the chronology of the development of the latter is restored and presented objectively, in full, taking into account the contribution of those researchers who actually stood at its origins. The article deals with the essence of the socio-psychological approach to understanding conflicts. The subject of social conflictology includes the regularities of their occurrence and manifestation at various levels, spheres and conditions, including normal, complicated and extreme ones. Social conflictology includes the theory and practice of diagnosing, resolving, and resolving social conflicts. It analyzes the difficulties that occur in defining the concept, structure, dynamics, and classification of social conflicts. Therefore, it is no accident that the most important task is to create a full-fledged theory of social conflicts. Without this, it is impossible to talk about effective settlement and resolution of social conflicts. Social conflictology is an integral part of conflictology. There is still a lot of work to be done, both in theory and in application, for its complete design. At present, there is an urgent need to develop conflict-related competence not only of professionals, but also for various groups of the population.

Thermodynamics in Geochemistry

1993 ◽  
Author(s):  
Greg M. Anderson ◽  
David A. Crerar
Keyword(s):  
Teaching Experience ◽  
Graduate Level ◽  
Years Of Teaching Experience ◽  
The Subject ◽  
First Time

This textbook and reference outlines the fundamental principles of thermodynamics, emphasizing applications in geochemistry. The work is distinguished by its comprehensive, balanced coverage and its rigorous presentation. The authors bring years of teaching experience to the work, and have attempted to particularly address those areas where other texts on the subject have provided inadequate coverage. A thorough review of the necessary mathematics is presented early on, both as a refresher for those with a background in university calculus, and for the benefit of those coming to the subject for the first time. The text is written for students in advanced undergraduate or graduate-level geochemistry as well as for all researchers in this field.

Anisotropic Elasticity

1996 ◽  
Author(s):  
T. T. C. Ting
Keyword(s):  
Composite Materials ◽  
Elastic Constants ◽  
Piezoelectric Materials ◽  
Anisotropic Materials ◽  
Anisotropic Elasticity ◽  
Stress Singularities ◽  
Comprehensive Survey ◽  
The Subject ◽  
Key Topics ◽  
First Time

Anisotropic Elasticity offers for the first time a comprehensive survey of the analysis of anisotropic materials that can have up to twenty-one elastic constants. Focusing on the mathematically elegant and technically powerful Stroh formalism as a means to understanding the subject, the author tackles a broad range of key topics, including antiplane deformations, Green's functions, stress singularities in composite materials, elliptic inclusions, cracks, thermo-elasticity, and piezoelectric materials, among many others. Well written, theoretically rigorous, and practically oriented, the book will be welcomed by students and researchers alike.

Self and Selves

2017 ◽  
Author(s):  
Ralph C.S. Walker
Keyword(s):  
Personal Identity ◽  
Moral Philosophy ◽  
A Priori ◽  
The Status ◽  
The Subject ◽  
Synthetic A Priori

Kant is committed to the reality of a subject self, outside time but active in forming experience. Timeless activity is problematic, but that can be dealt with. But he holds that the subject of experience is not an object of experience, so nothing can be known about it; this raises a problem about the status of his own theory. But he ought to allow that we can know of its existence and activity, as preconditions of experience: the Critique allows that synthetic a priori truths can be known in this way. However, its identity conditions remain unknowable. Kant’s unity of apperception shares much with Locke’s continuity of consciousness, but does not determine the identity of a thing. Personal identity is bodily identity. Only Kant’s moral philosophy justifies recognizing other selves; it could warrant ascribing a similar status to animals.

Oxford Studies in Epistemology Volume 6

2019 ◽  
Keyword(s):  
Decision Theory ◽  
A Priori ◽  
Formal Epistemology ◽  
Ethics Of Belief ◽  
Naturalized Epistemology ◽  
New Developments ◽  
The Status ◽  
Important Field ◽  
Belief Justification

Oxford Studies in Epistemology is a biennial publication offering a regular snapshot of state-of-the-art work in this important field. Under the guidance of a distinguished editorial board composed of leading epistemologists in North America, Europe and Australasia, it publishes exemplary papers in epistemology, broadly construed. Topics within its purview include: (a) traditional epistemological questions concerning the nature of belief, justification, and knowledge, the status of skepticism, the nature of the a priori, etc.; (b) new developments in epistemology, including movements such as naturalized epistemology, feminist epistemology, social epistemology, and virtue epistemology, and approaches such as contextualism; (c) foundational questions in decision-theory; (d) confirmation theory and other branches of philosophy of science that bear on traditional issues in epistemology; (e) topics in the philosophy of perception relevant to epistemology; (f) topics in cognitive science, computer science, developmental, cognitive, and social psychology that bear directly on traditional epistemological questions; and (g) work that examines connections between epistemology and other branches of philosophy, including work on testimony, the ethics of belief, etc. Topics addressed in volume 6 include the nature of perceptual justification, intentionality, modal knowledge, credences, epistemic supererogation, epistemic and rational norms, expressivism, skepticism, and pragmatic encroachment. The various writers make use of a variety of different tools and insights, including those of formal epistemology and decision theory, as well as traditional philosophical analysis and argumentation.

scholarly journals Per Ravenna trecentesca: nuove proposte per l’assetto architettonico di Santa Maria in Porto Fuori

2019 ◽  
Vol 82 (1) ◽  
pp. 3-31
Author(s):  
Fabio Massaccesi
Keyword(s):  
Fourteenth Century ◽  
Second World War ◽  
World War ◽  
The Subject ◽  
First Time ◽  
Santa Maria ◽  
Second World ◽  
The Church

Abstract This contribution intends to draw attention to one of the most significant monuments of medieval Ravenna: the church of Santa Maria in Porto Fuori, which was destroyed during the Second World War. Until now, scholars have focused on the pictorial cycle known through photographs and attributed to the painter Pietro da Rimini. However, the architecture of the building has not been the subject of systematic studies. For the first time, this essay reconstructs the fourteenth-century architectural structure of the church, the apse of which was rebuilt by 1314. The data that led to the virtual restitution of the choir and the related rood screen are the basis for new reflections on the accesses to the apse area, on the pilgrimage flows, and on the view of the frescoes.

Offshore Claims and Problems in the North Sea

1965 ◽  
Vol 59 (3) ◽  
pp. 505-522 ◽  
Author(s):  
Richard Young
Keyword(s):  
North Sea ◽  
Large Scale ◽  
Geneva Convention ◽  
Legal Principles ◽  
The North ◽  
Legal Problems ◽  
The North Sea ◽  
The Subject ◽  
First Time ◽  
Economic Considerations

The possible presence of very large petroleum and natural gas reserves in the area beneath the North Sea is currently the subject of intense investigation. If confirmed, as seems likely in at least some localities, this occurrence will raise legal problems of considerable interest and complexity. For the North Sea is not merely an oilfield covered by water: for centuries it has been one of the world's major fishery regions and the avenue to and from the world's busiest seaports. Thus all three of the present principal uses of the sea—fishing, navigation, and the exploitation of submarine resources—promise to meet for the first time on a large scale in an area where all are of major importance. The process of reconciling the various interests at stake will provide the first thoroughgoing test of the adequacy and acceptability of the general principles laid down in the 1958 Geneva Convention on the Continental Shelf and should add greatly to the practice and precedents available in this developing branch of the law. In the present article an attempt is made to review some of the geographical and economic considerations involved in the North Sea situation, to note some of the technical and legal developments that have already taken place, and to consider these elements in the light of the various interests and legal principles concerned.

Necessity, Certainty, and the A Priori

1988 ◽  
Vol 18 (1) ◽  
pp. 43-66 ◽  
Author(s):  
Albert Casullo
Keyword(s):  
Cognitive Processes ◽  
Mathematical Knowledge ◽  
A Priori ◽  
Theory Of Knowledge ◽  
A Posteriori ◽  
Unitary Theory ◽  
Knowledge Based

Empiricist theories of knowledge are attractive for they offer the prospect of a unitary theory of knowledge based on relatively well understood physiological and cognitive processes. Mathematical knowledge, however, has been a traditional stumbling block for such theories. There are three primary features of mathematical knowledge which have led epistemologists to the conclusion that it cannot be accommodated within an empiricist framework: 1) mathematical propositions appear to be immune from empirical disconfirmation; 2) mathematical propositions appear to be known with certainty; and 3) mathematical propositions are necessary. Epistemologists who believe that some nonmathematical propositions, such as logical or ethical propositions, cannot be known a posteriori also typically appeal to the three factors cited above in defending their position. The primary purpose of this paper is to examine whether any of these alleged features of mathematical propositions establishes that knowledge of such propositions cannot be a posteriori.

Sign in / Sign up

Export Citation Format

Share Document