ABSTRACT: How to characterize the mathematical philosophy of Gaston Bachelard? This question cannot
receive a clear and quick answer. It is practically impossible in any case to study the epistemology of Gaston
Bachelard without being marked by the decisive importance conferred on mathematics. Moreover, it would be
more accurate to speak of an omnipresence of mathematics which leads to a quite singular mathematical
philosophy. Indeed, by closely scrutinizing all the ideas that structure the mathematical thought of Gaston
Bachelard, and by articulating them, we realize that there is in this author a completely new mathematical
philosophy, but sometimes unnoticed. Bachelard claims his philosophy of mathematics, beyond rationalist
qualifications, as being a “constructed realism” and “metaphorism”. This reflection consists of an explanatory
statement of this mathematical philosophy as it comes under the little-known denomination of mathematical
realism of a new kind.
The principle of constructive mathematizability of any theory: A sketch of fo...Vasil Penchev
A principle, according to which any scientific theory can be mathematized, is investigated. That theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather a metamathematical axiom about the relation of mathematics and reality.
Its investigation needs philosophical means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction.
Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom.
An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. Thus the problem which of the two mathematics is more relevant to our being (rather than reality for reality is external only to Gödel mathematics) is discussed. An information interpretation of the Schrödinger equation is involved to illustrate the above problem.
THE THEORY OF EVERYTHING: Esotericism amalgamated to Celestial and Quantum Me...William John Meegan
The spiritual sages of antiquity have already archived in the texts of the sacred scriptures of the world THE THEORY OF EVERYTHING by esoterically amalgamating Celestial and Quantum Mechanic to Esotericism: i.e. The Esoteric Science. The argument that only mathematics can be use to transmit complex conceptual data modules across the epochs of time and space is debunked by the extraordinary complexities that are enshrouded in THE THEORY OF EVERYTHING as envisaged by the ancient esoterists. Mathematics is too limited a branch of science to convey to the human psyche the complexities of the world around it; thus, physics is wrong in believing that THE THEORY OF EVERYTHING can be brought down to a single algebraic equation unless of course physics can convey through it algebraic equation that everything, bar nothing, defines and explains the singularity. Just as modern physics breaks down Einstein equation E=MC², which is a symbolic and alphanumeric algebraic equation denoting that ’Energy equal matter times the square of the speed of light” so too does the sacred scriptures cram pack every indigenous letter of the texts symbolically and alphanumerically for the sole purpose of transmitting to the soul (the lone individual) THE THEORY OF EVERYTHING. In other words the soul: i.e. the MONAD self-defines itself. The singularity can only be defined by everything, for that is its inherent nature. In every sense physicists are unknowingly trying to define God, which cannot be iconically classified by a single algebraic equation; rather, the singularity can only be defined and understood through the mythoi of incalculable esoteric examples for to limit the Theory of Everything to a one or an assortment of examples is to limit conceptually its overall theme.
From the outset of this paper, let me declare that I will be introducing empirical evidence of abstract spiritual laws that literally defy the so-called laws of materialistic physics and it is through these abstract laws that I will prove THE THEORY OF EVERYTHING. It should effectively bring down the house of cards that physics has built for itself under the rubric of Celestial and Quantum Mechanics: i.e. The Theory of the Big and Small. This paper is all about the Theory of the Big and Small; however, this thesis is about the spiritual and the transcendent.
THE THEORY OF EVERYTHING is the main focus of this paper; however, the reader has to be somewhat educated into the sophisticated mathematical and grammatical sciences: i.e. Seven Liberal Arts: Arithmetic, Music/Harmony, Geometry, Astronomy/Astrology, Grammar, Rhetoric and Logic/Dialectics: the Esoteric Science (mystically hidden) symbolically integrated as one unified system of thought into the textual materials of the Judeao Christian Scriptures in order for the reader to have a sense of my theses on this subject matter. I have no intentions of proselytizing anyone into believing in the existence of God and the transcendent; though
Why anything rather than nothing? The answer of quantum mechnaicsVasil Penchev
Many researchers determine the question “Why anything
rather than nothing?” to be the most ancient and fundamental philosophical problem. It is closely related to the idea of Creation shared by religion, science, and philosophy, for example in the shape of the “Big Bang”, the doctrine of first cause or causa sui, the Creation in six days in the Bible, etc. Thus, the solution of quantum mechanics, being scientific in essence, can also be interpreted philosophically, and even religiously. This paper will only discuss the philosophical interpretation. The essence of the answer of quantum mechanics is: 1.) Creation is necessary in a rigorously mathematical sense. Thus, it does not need any hoice, free will, subject, God, etc. to appear. The world exists by virtue of mathematical necessity, e.g. as any mathematical truth such as 2+2=4; and 2.) Being is less than nothing rather than ore than nothing. Thus creation is not an increase of nothing, but the decrease of nothing: it is a deficiency in relation to nothing. Time and its “arrow” form the road from that diminishment or incompleteness to nothing.
.There are different paths to reality, they are determined by the knower, being instrumental methodological study object, epistemological axis, among others. Reality presents several faces, what is observable and what is perceived sensory empirical data obtained correspond to the visible, the main thing is to discover the hidden side, which is behind the perceptible or data. Epistemology is the whole process of obtaining scientific knowledge, ranging from the pre knowledge to get to know the hidden side, one thing is what is seen and what is not, and one that is not seen, is really it is.
The principle of constructive mathematizability of any theory: A sketch of fo...Vasil Penchev
A principle, according to which any scientific theory can be mathematized, is investigated. That theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather a metamathematical axiom about the relation of mathematics and reality.
Its investigation needs philosophical means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction.
Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom.
An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. Thus the problem which of the two mathematics is more relevant to our being (rather than reality for reality is external only to Gödel mathematics) is discussed. An information interpretation of the Schrödinger equation is involved to illustrate the above problem.
THE THEORY OF EVERYTHING: Esotericism amalgamated to Celestial and Quantum Me...William John Meegan
The spiritual sages of antiquity have already archived in the texts of the sacred scriptures of the world THE THEORY OF EVERYTHING by esoterically amalgamating Celestial and Quantum Mechanic to Esotericism: i.e. The Esoteric Science. The argument that only mathematics can be use to transmit complex conceptual data modules across the epochs of time and space is debunked by the extraordinary complexities that are enshrouded in THE THEORY OF EVERYTHING as envisaged by the ancient esoterists. Mathematics is too limited a branch of science to convey to the human psyche the complexities of the world around it; thus, physics is wrong in believing that THE THEORY OF EVERYTHING can be brought down to a single algebraic equation unless of course physics can convey through it algebraic equation that everything, bar nothing, defines and explains the singularity. Just as modern physics breaks down Einstein equation E=MC², which is a symbolic and alphanumeric algebraic equation denoting that ’Energy equal matter times the square of the speed of light” so too does the sacred scriptures cram pack every indigenous letter of the texts symbolically and alphanumerically for the sole purpose of transmitting to the soul (the lone individual) THE THEORY OF EVERYTHING. In other words the soul: i.e. the MONAD self-defines itself. The singularity can only be defined by everything, for that is its inherent nature. In every sense physicists are unknowingly trying to define God, which cannot be iconically classified by a single algebraic equation; rather, the singularity can only be defined and understood through the mythoi of incalculable esoteric examples for to limit the Theory of Everything to a one or an assortment of examples is to limit conceptually its overall theme.
From the outset of this paper, let me declare that I will be introducing empirical evidence of abstract spiritual laws that literally defy the so-called laws of materialistic physics and it is through these abstract laws that I will prove THE THEORY OF EVERYTHING. It should effectively bring down the house of cards that physics has built for itself under the rubric of Celestial and Quantum Mechanics: i.e. The Theory of the Big and Small. This paper is all about the Theory of the Big and Small; however, this thesis is about the spiritual and the transcendent.
THE THEORY OF EVERYTHING is the main focus of this paper; however, the reader has to be somewhat educated into the sophisticated mathematical and grammatical sciences: i.e. Seven Liberal Arts: Arithmetic, Music/Harmony, Geometry, Astronomy/Astrology, Grammar, Rhetoric and Logic/Dialectics: the Esoteric Science (mystically hidden) symbolically integrated as one unified system of thought into the textual materials of the Judeao Christian Scriptures in order for the reader to have a sense of my theses on this subject matter. I have no intentions of proselytizing anyone into believing in the existence of God and the transcendent; though
Why anything rather than nothing? The answer of quantum mechnaicsVasil Penchev
Many researchers determine the question “Why anything
rather than nothing?” to be the most ancient and fundamental philosophical problem. It is closely related to the idea of Creation shared by religion, science, and philosophy, for example in the shape of the “Big Bang”, the doctrine of first cause or causa sui, the Creation in six days in the Bible, etc. Thus, the solution of quantum mechanics, being scientific in essence, can also be interpreted philosophically, and even religiously. This paper will only discuss the philosophical interpretation. The essence of the answer of quantum mechanics is: 1.) Creation is necessary in a rigorously mathematical sense. Thus, it does not need any hoice, free will, subject, God, etc. to appear. The world exists by virtue of mathematical necessity, e.g. as any mathematical truth such as 2+2=4; and 2.) Being is less than nothing rather than ore than nothing. Thus creation is not an increase of nothing, but the decrease of nothing: it is a deficiency in relation to nothing. Time and its “arrow” form the road from that diminishment or incompleteness to nothing.
.There are different paths to reality, they are determined by the knower, being instrumental methodological study object, epistemological axis, among others. Reality presents several faces, what is observable and what is perceived sensory empirical data obtained correspond to the visible, the main thing is to discover the hidden side, which is behind the perceptible or data. Epistemology is the whole process of obtaining scientific knowledge, ranging from the pre knowledge to get to know the hidden side, one thing is what is seen and what is not, and one that is not seen, is really it is.
The problem of effective computation is discussed. Short historical analysis of this problem and basic ways of its development in culture and science, including computer science, are represented. Place the problem of the creation effective calculation in modern science is discussed. Necessity of creation “computation metascience” as system with variable hierarchy (open system) is observed. Polymetric analysis as example of this metascience is represented and discussed.
Intention and attention: Intension, extension, and “attension” of a notion o...Vasil Penchev
One can introduce the concept of “attension” as to any unit enumerated above, e.g. as to a notion.
It means both all individuals of the extension as existing and their wholeness as existing, too
Thus, “attension” is relative to “intension” and “extension”, on the one hand, and to the Platonic “idea” and “eidos”, on the other hand
Furthermore, “attension” can be defined as the application of the “philosophical attention” to any explicit or implicit (e.g. contextual) intension
Attension complements intension to the pair of both biggest and least element of the mathematical structure of lattice extended from the intention of consciousness to the idea therefore giving both logical and ontological structure of the notion or whatever else unit
That structure orders the extension in question in a potential taxonomy (i.e. classification of genera and species), the biggest element of which, i.e. the idea of the thing defined by the extension or even that thing itself or by itself, is generated just by the philosophical attention as the corresponding attension
On the contrary, if the notion or unit is supplied as usual by any logical or ontological structure, thus its attension is implicitly certain, too
https://youtu.be/4V18eP4u8Rw
The critical analysis of the foundation of set theory is proposed. The unity of formal logic and rational dialectics is
the correct methodological basis of the analysis. The analysis leads to the following results: (1) the mathematical
concept of set should be analyzed on the basis of the formal-logical clauses “Definition of concept”, “Logical class”,
“Division of concept”, “Basis of division”, “Rules of division”; (2) the standard mathematical theory of sets is an
erroneous theory because it does not contain definition of the concept “element (object) of set”; (3) the concept of
empty set (class) is a meaningless, erroneous, and inadmissible one because the definition of the concept “empty set
(class)” contradicts to the definition of the logical class. (If the set (class) does not contain a single element (object),
then there is no feature (sign) of the element (object). This implies that the concept of empty set (class) has no
content and volume (scope). Therefore, this concept is inadmissible one); (4) the standard mathematical operations
of union, intersection and difference of sets (classes) are meaningless, erroneous and inadmissible operations
because they do not satisfy the following formal-logical condition: every separate element (object) of the set (class)
must be in only one some set (class) and cannot be in two sets (classes). Thus, the results of formal-logical analysis
prove that the standard mathematical theory of sets is an erroneous theory because it does not satisfy the criterion of
truth
This is a detail esoteric analysis of La Divina Commedia trilogy 'compositional structure'. What this means is that simply by analyzing the amount of books (3), chapters (100) and verses (14,233) In La Divina Commedia I was able, over a fourteen year period, to cull out of it a very sophisticated mathematical system, which Dante Alighieri codified to his work.
The reason that it took fourteen years to publish this work in 1997, from the start of my researches on April 11, 1983, was because I knew through deep analysis that Dante Alighieri could not have accomplished such an amazing mathematical feat unless he had an overall model in which to guide him and for him to work from. It was this model that I was so certain of, which stay my hand at publication though others insisted on the latter. Finally, I did discovery the model that Dante used and I was able with continuous analysis of the mathematical materials I had previously culled from La Divina Commedia to demonstrate that he did indeed used this 10 x 10 mathematical matrix I had envisaged and developed.
In this study there are numerous charts and diagrams to augments this thesis. I originally published this thesis via the Edwin Mellen Press, 1997: THE CONQUEST OF GENESIS: A Study in Universal Creation Mathematics. http://www.williamjohnmeegan.com/
This article shows the evolution from the 17th century speculative Descartes' views to a new, modern, and practical philosophy in the 18th century France. Yet, the core of Descartes philosophy, his critical method, pervives in some 18th century writers such as Rousseau.
The effect of Institutional Ownership, Sales Growth and Profitability on Tax ...AJHSSR Journal
ABSTRACT: This research aims to test, analyze and obtain empirical evidence about the influence of
institutional ownership, sales growth and profitability on tax avoidance. The object of this research is
manufacturing companies in the consumer goods industry sector listed on the Indonesia Stock Exchange (BEI)
in 2018-2022. This research used quantitative research methods and causal research design. The sampling
technique in this research used non-probability sampling with purposive sampling as the basis for determining
the sample so that a sample of 55 samples was obtained. The data used is secondary data obtained from the
official website of the Indonesia Stock Exchange (BEI) during the 2018-2022 period. The data analysis method
used was multiple linear regression analysis with several tests such as descriptive statistical tests, classical
assumption tests, and hypothesis testing using SPSS version 26 statistical software. The results showed that the
institutional ownership variable has no effect on tax avoidance, while the sales growth and profitability has a
negative and significant effect on tax avoidance.
KEYWORDS: Institutional Ownership, Sales Growth, Profitability, Tax Avoidance
MGA ESTRATEHIYA SA PAGTUTURO KAUGNAY SA PASALITANG PARTISIPASYON NG MGA MAG-A...AJHSSR Journal
ABSTRAK: Ang mga estratehiya sa pagtuturo ay mahalagang kasangkapan sa paghahatid ng mabisang
pagtuturo sa loob ng silid. Tinukoy sa pag-aaral na ito ang antas ng kagustuhan ng mga mag-aaral sa pagsasadula,
pangkatang talakayan at paggawa ng mga koneksyon sa tunay na karanasan sa buhay bilang mga estratehiya sa
pagtuturo ng panitikan sa Filipino at pasalitang partisipasyon ng mga mag-aaral sa Baitang 7 ng Misamis
University Junior High School, Ozamiz City. Ang ginamit na disenyo sa pananaliksik na ito ay deskriptivcorrelational. Ang mga datos sa pag-aaral ay nagmula sa kabuuang populasyon na 120 na mag-aaral at tatlong
mga guro na tagamasid sa pasalitang partisipasyon ng mga mag-aaral. Ang Talatanungan sa Kagamitan sa
Pagtuturo ng Panitikan at Checklist batay sa Obserbasyon sa Pasalita na Partisipasyon ay ang instrumentong
ginamit sa pagkalap ng datos. Mean, standard deviation, Analysis of Variance at Pearson Product-Moment
Correlation Coefficient ang mga ginamit na estatistiko na sangkap. Inihayag sa naging resulta na ang tatlong piling
estratehiya sa pagtuturo ng panitikan sa Filipino ay may pinakamataas na antas ng kagustuhan ng mga mag-aaral.
Ang antas ng pakilahok ng mga mag-aaral sa paggamit ng tatlong estratehiya sa pagtuturo ng panitikan ay
pinakamataas na nagpapahiwatig na aktibong nakilahok ang mga mag-aaral sa mga gawain. Inihayag din na
walang makabuluhang kaibahan sa antas ng kagustuhan ng mga mag-aaral sa mga estratehiya sa pagtuturo ng
panitikan sa Filipino. Ito ay nangahulugan na gustong-gusto ng mga mag-aaral ang pagkakaroon ng mga
estratehiya sa pagtuturo. Walang makabuluhang kaugnayan ang kagustuhan sa mga estratehiya at antas ng
pakikilahok ng mga mag-aaral. Hindi nakaapekto sa kanilang pakikilahok ang anumang estratehiyang ginamit ng
guro.
KEYWORDS : estratehiya, karanasan, pagsasadula, pagtuturo, pangkatang talakayan
More Related Content
Similar to About the Mathematical Philosophy of Gaston Bachelard
The problem of effective computation is discussed. Short historical analysis of this problem and basic ways of its development in culture and science, including computer science, are represented. Place the problem of the creation effective calculation in modern science is discussed. Necessity of creation “computation metascience” as system with variable hierarchy (open system) is observed. Polymetric analysis as example of this metascience is represented and discussed.
Intention and attention: Intension, extension, and “attension” of a notion o...Vasil Penchev
One can introduce the concept of “attension” as to any unit enumerated above, e.g. as to a notion.
It means both all individuals of the extension as existing and their wholeness as existing, too
Thus, “attension” is relative to “intension” and “extension”, on the one hand, and to the Platonic “idea” and “eidos”, on the other hand
Furthermore, “attension” can be defined as the application of the “philosophical attention” to any explicit or implicit (e.g. contextual) intension
Attension complements intension to the pair of both biggest and least element of the mathematical structure of lattice extended from the intention of consciousness to the idea therefore giving both logical and ontological structure of the notion or whatever else unit
That structure orders the extension in question in a potential taxonomy (i.e. classification of genera and species), the biggest element of which, i.e. the idea of the thing defined by the extension or even that thing itself or by itself, is generated just by the philosophical attention as the corresponding attension
On the contrary, if the notion or unit is supplied as usual by any logical or ontological structure, thus its attension is implicitly certain, too
https://youtu.be/4V18eP4u8Rw
The critical analysis of the foundation of set theory is proposed. The unity of formal logic and rational dialectics is
the correct methodological basis of the analysis. The analysis leads to the following results: (1) the mathematical
concept of set should be analyzed on the basis of the formal-logical clauses “Definition of concept”, “Logical class”,
“Division of concept”, “Basis of division”, “Rules of division”; (2) the standard mathematical theory of sets is an
erroneous theory because it does not contain definition of the concept “element (object) of set”; (3) the concept of
empty set (class) is a meaningless, erroneous, and inadmissible one because the definition of the concept “empty set
(class)” contradicts to the definition of the logical class. (If the set (class) does not contain a single element (object),
then there is no feature (sign) of the element (object). This implies that the concept of empty set (class) has no
content and volume (scope). Therefore, this concept is inadmissible one); (4) the standard mathematical operations
of union, intersection and difference of sets (classes) are meaningless, erroneous and inadmissible operations
because they do not satisfy the following formal-logical condition: every separate element (object) of the set (class)
must be in only one some set (class) and cannot be in two sets (classes). Thus, the results of formal-logical analysis
prove that the standard mathematical theory of sets is an erroneous theory because it does not satisfy the criterion of
truth
This is a detail esoteric analysis of La Divina Commedia trilogy 'compositional structure'. What this means is that simply by analyzing the amount of books (3), chapters (100) and verses (14,233) In La Divina Commedia I was able, over a fourteen year period, to cull out of it a very sophisticated mathematical system, which Dante Alighieri codified to his work.
The reason that it took fourteen years to publish this work in 1997, from the start of my researches on April 11, 1983, was because I knew through deep analysis that Dante Alighieri could not have accomplished such an amazing mathematical feat unless he had an overall model in which to guide him and for him to work from. It was this model that I was so certain of, which stay my hand at publication though others insisted on the latter. Finally, I did discovery the model that Dante used and I was able with continuous analysis of the mathematical materials I had previously culled from La Divina Commedia to demonstrate that he did indeed used this 10 x 10 mathematical matrix I had envisaged and developed.
In this study there are numerous charts and diagrams to augments this thesis. I originally published this thesis via the Edwin Mellen Press, 1997: THE CONQUEST OF GENESIS: A Study in Universal Creation Mathematics. http://www.williamjohnmeegan.com/
This article shows the evolution from the 17th century speculative Descartes' views to a new, modern, and practical philosophy in the 18th century France. Yet, the core of Descartes philosophy, his critical method, pervives in some 18th century writers such as Rousseau.
The effect of Institutional Ownership, Sales Growth and Profitability on Tax ...AJHSSR Journal
ABSTRACT: This research aims to test, analyze and obtain empirical evidence about the influence of
institutional ownership, sales growth and profitability on tax avoidance. The object of this research is
manufacturing companies in the consumer goods industry sector listed on the Indonesia Stock Exchange (BEI)
in 2018-2022. This research used quantitative research methods and causal research design. The sampling
technique in this research used non-probability sampling with purposive sampling as the basis for determining
the sample so that a sample of 55 samples was obtained. The data used is secondary data obtained from the
official website of the Indonesia Stock Exchange (BEI) during the 2018-2022 period. The data analysis method
used was multiple linear regression analysis with several tests such as descriptive statistical tests, classical
assumption tests, and hypothesis testing using SPSS version 26 statistical software. The results showed that the
institutional ownership variable has no effect on tax avoidance, while the sales growth and profitability has a
negative and significant effect on tax avoidance.
KEYWORDS: Institutional Ownership, Sales Growth, Profitability, Tax Avoidance
MGA ESTRATEHIYA SA PAGTUTURO KAUGNAY SA PASALITANG PARTISIPASYON NG MGA MAG-A...AJHSSR Journal
ABSTRAK: Ang mga estratehiya sa pagtuturo ay mahalagang kasangkapan sa paghahatid ng mabisang
pagtuturo sa loob ng silid. Tinukoy sa pag-aaral na ito ang antas ng kagustuhan ng mga mag-aaral sa pagsasadula,
pangkatang talakayan at paggawa ng mga koneksyon sa tunay na karanasan sa buhay bilang mga estratehiya sa
pagtuturo ng panitikan sa Filipino at pasalitang partisipasyon ng mga mag-aaral sa Baitang 7 ng Misamis
University Junior High School, Ozamiz City. Ang ginamit na disenyo sa pananaliksik na ito ay deskriptivcorrelational. Ang mga datos sa pag-aaral ay nagmula sa kabuuang populasyon na 120 na mag-aaral at tatlong
mga guro na tagamasid sa pasalitang partisipasyon ng mga mag-aaral. Ang Talatanungan sa Kagamitan sa
Pagtuturo ng Panitikan at Checklist batay sa Obserbasyon sa Pasalita na Partisipasyon ay ang instrumentong
ginamit sa pagkalap ng datos. Mean, standard deviation, Analysis of Variance at Pearson Product-Moment
Correlation Coefficient ang mga ginamit na estatistiko na sangkap. Inihayag sa naging resulta na ang tatlong piling
estratehiya sa pagtuturo ng panitikan sa Filipino ay may pinakamataas na antas ng kagustuhan ng mga mag-aaral.
Ang antas ng pakilahok ng mga mag-aaral sa paggamit ng tatlong estratehiya sa pagtuturo ng panitikan ay
pinakamataas na nagpapahiwatig na aktibong nakilahok ang mga mag-aaral sa mga gawain. Inihayag din na
walang makabuluhang kaibahan sa antas ng kagustuhan ng mga mag-aaral sa mga estratehiya sa pagtuturo ng
panitikan sa Filipino. Ito ay nangahulugan na gustong-gusto ng mga mag-aaral ang pagkakaroon ng mga
estratehiya sa pagtuturo. Walang makabuluhang kaugnayan ang kagustuhan sa mga estratehiya at antas ng
pakikilahok ng mga mag-aaral. Hindi nakaapekto sa kanilang pakikilahok ang anumang estratehiyang ginamit ng
guro.
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management is to use regulating the internal interactions within the system, and to decrease the increasing
entropy spontaneously. We propose the principle of social civilization and the developing direction is: freedom
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KEYWORDS: entropy, science, society, management, mind, evolution.
A Model of Disaster Resilience Among Colleges and Universities: A Mixed Metho...AJHSSR Journal
ABSTRACT :This research paper aimed to create a comprehensive framework for measuring disaster
resilience in colleges and universities. The study used a mixed method through Exploratory Factor Analysis
(EFA), which involved analyzing data from a survey questionnaire. The questionnaire was developed based on
in-depth interviews with 12 selected participants from the University of Mindanao, as well as relevant literature
and studies. It was reviewed and validated by 10 experts using a method called Content Validity Ratio (CVR).
This questionnaire was then administered to 400 students from 10 different colleges in University of Mindanao.
After conducting the Exploratory Factor Analysis and performing rotations and iterations, the researchers
identified five main constructs that characterize disaster resilience among colleges (1) disaster preparedness, (2)
disaster awareness, (3) community readiness, and (4) disaster management, (5) disaster resilience. The
researchers aimed to create an organization called “Council of College Disaster Volunteers (CCDV)” which
consist of student volunteers. These factors can be used to develop effective management strategies and
strengthen efforts in preventing and managing disasters and accidents.
KEYWORDS:content validity ratio, criminology, disaster resilience, disaster management, exploratory factor
analysis, and Philippines.
Environmental Struggles and Justice Among Lumad Farmers of Davao CityAJHSSR Journal
ABSTRACT : The study described the various environmental struggles experienced among the participants
and their status in accessing justice. The study followed a qualitative multiple-case study approach; the
participants are the Lumad farmers of Marilog, Davao City selected through a Critical sampling method and
aims to present the environmental violations experienced by the Lumad farmers in Davao City and how it
affected their families and sustenance further, their status in accessing justice is also explored. The study
concluded that the most common struggles the participant experience are Illegal logging and improper waste
disposal, which affect their farms, family, health, and income. Their preferred means to accessing justice is
through barangay settlement; the rigors of accessing courts, such as distance, expenses, fear of ruling, and the
hassle of being called to be present in court, are the most prevalent barriers that hinder the lead farmers from
accessing justice or seeking legal action. Nevertheless, the participants believed that the government would help
them in accessing justice.
KEYWORDS :access to justice, criminology,environmental justice, environmental struggles, lumadfarmers
CYBERBULLYING EXPERIENCES OF UNIVERSITY OF MINDANAO CRIMINOLOGY STUDENTSAJHSSR Journal
ABSTRACT:This paper explores the cyberbullying experiences among Criminology students at the
University of Mindanao. A simple random sampling method was used to distribute the study's online
questionnaire to the respondents and to survey the target population. This study has four hundred (400)
respondents, and the respondents are Criminology students at the University of Mindanao. The findings of this
study revealed that the level of cyberbullying experiences is sometimes manifested. On the other hand, the
cyberbullying experiences of the students indicate a moderate level, which indicates that the cyberbullying
experiences of the respondents are sometimes manifested. Also, the computations showed that among the
indicators presented, the highest mean is obtained in the psychological effect, which implies that there is a
significant effect of cyberbullying experiences of the respondents in terms of the Gender level of the
respondents. Therefore, respondents with a low level of cyberbullying experiences tend to have a moderate level
of cyberbullying experience. However, there is no significant effect in terms of age and year level of the
respondents according to the results regarding the psychological, emotional, and physical impact of
cyberbullying.
KEYWORDS :cyberbullying, emotional, experiences, psychological,physical effect, and simple random
sampling method.
A philosophical ontogenetic standpoint on superego role in human mind formationAJHSSR Journal
ABSTRACT: One of the most significant contributions of psychoanalysis to understand the human being is the
elaboration of a model about the mind from a topical and dynamic perspective. Freud explains the mind by the
constitution of the preconscious, conscious, and subconscious. Later, by three dynamic components: the id, the
ego and the superego. Such an organization of the psychic apparatus supposes not only individual elements, but
social influences along the process of hominization. In this paper, we recover the findings of the renowned
anthropologist Lewis Morgan, trying to link some of them to the psychoanalytic theory. Especially highlighting
the importance of superego in Haidt’s social intuitionism.
Keywords: evolutionism, intuitionism, psychoanalysis, Freud, Haidt, Morgan
Improving Workplace Safety Performance in Malaysian SMEs: The Role of Safety ...AJHSSR Journal
ABSTRACT: In the Malaysian context, small and medium enterprises (SMEs) experience a significant
burden of workplace accidents. A consensus among scholars attributes a substantial portion of these incidents to
human factors, particularly unsafe behaviors. This study, conducted in Malaysia's northern region, specifically
targeted Safety and Health/Human Resource professionals within the manufacturing sector of SMEs. We
gathered a robust dataset comprising 107 responses through a meticulously designed self-administered
questionnaire. Employing advanced partial least squares-structural equation modeling (PLS-SEM) techniques
with SmartPLS 3.2.9, we rigorously analyzed the data to scrutinize the intricate relationship between safety
behavior and safety performance. The research findings unequivocally underscore the palpable and
consequential impact of safety behavior variables, namely safety compliance and safety participation, on
improving safety performance indicators such as accidents, injuries, and property damages. These results
strongly validate research hypotheses. Consequently, this study highlights the pivotal significance of cultivating
safety behavior among employees, particularly in resource-constrained SME settings, as an essential step toward
enhancing workplace safety performance.
KEYWORDS :Safety compliance, safety participation, safety performance, SME
Psychological Empowerment and Empathy as Correlates of ForgivenessAJHSSR Journal
ABSTRACT: The study explores Psychological Empowerment and Empathy as Correlates of Forgiveness.
The two variables are regarded to have influence on the decision one makes to forgive another. The study aimed
at examining the relationships between psychological empowerment and forgiveness, empathy and forgiveness
and to identify which one of the two,Psychological Empowerment or Empathy, is the more powerful predictor of
forgiveness. The study took a survey design with a sample of 350 drawn from a population of university students
using a self-administered questionnaire with four sections: Personal information, Psychological empowerment
scale, Toronto Empathy questionnaire, and the Heartland Forgiveness Scale (HFS). Data analysis employed
Pearson’s product moment correlation and regression analysis to test hypotheses. The results show significant
relationships between psychological empowerment and forgiveness as well as empathy and forgiveness.
Empathy was found to be the more powerful predictor of forgiveness.
KEY WORDS: Psychological empowerment, empathy, forgiveness
Exploring The Dimensions and Dynamics of Felt Obligation: A Bibliometric Anal...AJHSSR Journal
ABSTARCT: This study presents, to our knowledge, the first bibliometric analysis focusing on the concept of
"felt obligation," examining 120 articles published between 1986 and 2024. The aim of the study is to deepen our
understanding of the existing knowledge in the field of "felt obligation" and to provide guidance for further
research. The analysis is centered around the authors, countries, institutions, and keywords of the articles. The
findings highlight prominent researchers in this field, leading universities, and influential journals. Particularly,
it is identified that China plays a leading role in "felt obligation" research. The analysis of keywords emphasizes
the thematic focuses of these studies and provides a roadmap for future research. Finally, various
recommendations are presented to deepen the knowledge in this area and promote applied research. This study
serves as a foundation to expand and advance the understanding of "felt obligation" in the field.
KEYWORDS: Felt Obligation, Bibliometric Analysis, Research Trends
Les autorités traditionnelles et l’administration coloniale au Tchad : 1900-1960AJHSSR Journal
ABSTRACT : In Africa, traditionalauthorities are the guardians of tradition. Recently, however, they have
been caughtbetween tradition and modernity in the exercise of political power in Chad. However, we are
witnessing the revival of chieftaincy and the hybridization of the politicalpowersexercisedwithinit. In this
cohabitation of powers, traditionalauthorityisescapingitsrole as guardian of tradition.
Traditionalauthorityisthereforepresented in itscurrent state, as a proxy for the modern state in traditional
administrative districts. The aim of thisstudyis to analyze the mutations and adaptability of
traditionalauthorityfrom the pre-colonialperiodthrough the colonial period to the post-colonial period. This
workanalyzes the mutations of authorities. The data collected and processedrevealthattraditionalauthorities have
survivedalmosteverywhere, the former chiefdomsdissolvedduringcolonization have been restored by
republicanheads of state, while more and more frequently civil servants, businessmen, academics and
othermembers of the literateelite, whopreviouslyhad no attraction for the position of traditionalchief, are
beingenthroned.
Key words:Authorities, Administration, colonization, Chad, Kanem.
A Conceptual Analysis of Correlates of Domestic Violence and Adolescent Risky...AJHSSR Journal
ABSTRACT: The study explores domestic violence and how it influences adolescent risky behavior.
Domestic violence is a devastating social problem resulting in significant and enduring effects on children,
threatening both their health and emotional well-being. The study aimed at examining the relationships between
domestic Violence and Psychological Empowerment, Domestic Violence and Self-esteem, psychological
Empowerment and Self-Regulation, Self Esteem and Psychological empowerment, Self-Esteem and Selfregulation, Self-Regulation and Adolescent Risky Behavior and identify the stronger predictor of self-regulation
between psychological empowerment and Self-esteem. Adolescent respondents who experienced domestic
violence were purposely selected and guided by teachers and administrators who had provided support to these
children.The questionnaire had six sections namely; personal information, the Child Exposure to Domestic
Violence Scale, the Psychological empowerment scale, the Rosenberg Self-esteem Inventory, and the Brief
Self-Control Scale. Data analysis employed Pearson's product-moment correlation (r) to test hypotheses 1,
2,3,4,5, and 6. Regression analysis was used for hypothesis 7.The results show a significant relationship
between domestic Violence and Psychological Empowerment, Domestic Violence and Self-esteem,
psychological Empowerment and Self-Regulation, Self Esteem and Psychological empowerment, Self-Esteem
and Self-regulation, Self-Regulation, and Adolescent Risky Behavior. The study documents that Psychological
empowerment is a stronger predictor of self-regulation than Self-esteem.
KEYWORDS:Domestic violence, psychological empowerment, self-regulation, and Adolescent risky behavior
Driving Sustainable Competitive Advantage Through an Innovative Aggregator Bu...AJHSSR Journal
ABSTRACT : The aim of the research is to analyze the influence of the aggregation business model on
Sustainable Competitive Advantage (SCA). Through a survey of 216 MSMEs in the creative economy sector
selected randomly using an ex post facto causal research approach, an overview of the aggregator business
model and its impact on financial resources and SCA was obtained. The aggregator business model plays a role
in facilitating increased access to financial resources to meet both available and required working capital for
realizing SCA in Malang's Lokanima area. The strength of ABM lies in understanding the resources needed for
SCA and the effectiveness of mobilizing services while considering the most cost-effective options, including
providing various alternatives in their provision. Financial resources are an important factor supporting the
achievement of SCA. Access to financial resources is key to facilitating business growth and sustainability.
Theoretical implications: The concept of the aggregator business model emphasizes the efficient and effective
collection, aggregation, and distribution of resources in connecting service providers with consumers in an
economical and efficient manner. Practical implications: ABM can enhance the performance of financial
resource provision by optimizing relationships with MSMEs and financial institutions, leading to business
growth and sustainability for MSMEs.
KEYWORDS -Aggregator Business, Creative Economy, Financial Resources, Sustainable Competitive
Advantage
Accuracy of ChatGPT for Basic Values of Trigonometric FunctionsAJHSSR Journal
ABSTRACT : This study analyzes the accuracy of ChatGPT, an artificial intelligence model based on GPT3.5, in determining the values of basic trigonometric functions. To this end, we examine ChatGPT's responses to
sine, cosine, tangent, and cotangent values for a wide range of angles. We compare the results provided by
ChatGPT with the accuracy values determined by basic trigonometry. We also explore differences in accuracy
depending on changes in question complexity and given context. The results show a high level of accuracy of
ChatGPT in determining the values of trigonometric functions, especially for common angles. However, it is
noted that accuracy may be affected in certain cases of extreme angles or complex questions. This analysis
provides an important representation of ChatGPT's capabilities in the field of mathematics, using a new method
for testing the accuracy of artificial intelligence models in determining trigonometric values.
Keywords -Accuracy, AI Model, ChatGPT, Trigonometric Functions, Trigonometry
Postmodern Marketing and Its Impact on Traditional Marketing Approaches: Is K...AJHSSR Journal
ABSTRACT : The essay discusses the concept of postmodern marketing and its impact on marketing theory
and practice. It explores the characteristics of postmodernism, including openness, tolerance, hyper-reality,
fragmentation, and the lack of clear boundaries, and how they challenge traditional marketing approaches. The
paper also looks at the contributions of postmodern marketing to consumer and marketing research and how it
has redefined the way we think about marketing as a science. Ultimately, it raises the question of whether and
how marketing should adapt itself to the new conditions brought about by postmodernism.
KEYWORDS :Postmodernism, Postmodern Marketing, Kotler, Marketing Theory, Postmodern Consumer
Reorientation of Health Service Governance Toward the Fulfillment of Social J...AJHSSR Journal
ABSTRACT: Health insurance is a human right. At the practical level, this health insurance program in
Indonesia is organized by BPJS Kesehatan (Social Security Administering Body for Health). The
implementation of BPJS Kesehatan is still not optimal and effective. Three problems are discussed in this
writing: the dynamics of health insurance governance in Indonesia, the implementation of the fulfillment of the
right to health by BPJS Kesehatan, and the reorientation of BPJS Kesehatan services toward social justice.
These problems are then answered by scientific research methods using a sociological juridical approach.
Complaintsoften occur regarding the regulations, the services provided by the health facility providers, and the
distance between the community and the health facilities. Such complaints affect the public interest in becoming
BPJS Kesehatan participants. The aforementioned conditions must be considered and evaluated for the
government's success in the aspired national health insurance plan.
KEYWORDS -BPJS Kesehatan, Health Insurance, Social Justice
“To be integrated is to feel secure, to feel connected.” The views and experi...AJHSSR Journal
ABSTRACT: Although a significant amount of literature exists on Morocco's migration policies and their
successes and failures since their implementation in 2014, there is limited research on the integration of subSaharan African children into schools. This paperis part of a Ph.D. research project that aims to fill this gap. It
reports the main findings of a study conducted with migrant children enrolled in two public schools in Rabat,
Morocco, exploring how integration is defined by the children themselves and identifying the obstacles that they
have encountered thus far. The following paper uses an inductive approach and primarily focuses on the
relationships of children with their teachers and peers as a key aspect of integration for students with a migration
background. The study has led to several crucial findings. It emphasizes the significance of speaking Colloquial
Moroccan Arabic (Darija) and being part of a community for effective integration. Moreover, it reveals that the
use of Modern Standard Arabic as the language of instruction in schools is a source of frustration for students,
indicating the need for language policy reform. The study underlines the importanceof considering the
children‟s agency when being integrated into mainstream public schools.
.
KEYWORDS: migration, education, integration, sub-Saharan African children, public school
Sport et vieillissement : une analyse de la pratique des activités physiques ...AJHSSR Journal
Abstract : The aim of thispaperis to report on the effects of physicalactivity and sport on the health of older
people. Based on a mixed-methodsapproach, several techniques, namelydocumentaryanalysis and semistructured interviews, wereused in thisresearch in order to obtain a range of data thatwasavailable, accessible
and relevant to the subjectunderstudy. This enabled us to arrive at the resultsaccording to which the
stakeholders' perceptions of theirhealth are based on the practice of physicalactivities and sport as a social
construct in a socio-cultural context. Older people see sport as a way of curingillnesses, but above all as a way
of givingtheir bodies vitality. Othersseeit as a way of reinvigoratingthemselvesafter retirement.
Key words: Ageing, Physical activities, Sports activities, Elderly people.
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About the Mathematical Philosophy of Gaston Bachelard
1. American Journal of Humanities and Social Sciences Research (AJHSSR) 2023
A J H S S R J o u r n a l P a g e | 109
American Journal of Humanities and Social Sciences Research (AJHSSR)
e-ISSN : 2378-703X
Volume-07, Issue-09, pp-109-114
www.ajhssr.com
Research Paper Open Access
About the Mathematical Philosophy of Gaston Bachelard
Jacques CHATUÉ1
, Yves Romeo NOUMBO ZAMBOU2
1
(Department of Philosophy, Psychology, Sociology, Professor- University of Dschang, Cameroon)
2
(Department of Philosophy, Psychology, Sociology, Doctorate Student- University of Dschang, Cameroon)
ABSTRACT: How to characterize the mathematical philosophy of Gaston Bachelard? This question cannot
receive a clear and quick answer. It is practically impossible in any case to study the epistemology of Gaston
Bachelard without being marked by the decisive importance conferred on mathematics. Moreover, it would be
more accurate to speak of an omnipresence of mathematics which leads to a quite singular mathematical
philosophy. Indeed, by closely scrutinizing all the ideas that structure the mathematical thought of Gaston
Bachelard, and by articulating them, we realize that there is in this author a completely new mathematical
philosophy, but sometimes unnoticed. Bachelard claims his philosophy of mathematics, beyond rationalist
qualifications, as being a “constructed realism” and “metaphorism”. This reflection consists of an explanatory
statement of this mathematical philosophy as it comes under the little-known denomination of mathematical
realism of a new kind.
KEYWORDS: Epistemology, realism, mathematics, rationalism.
RÉSUMÉ :Comment caractériser la philosophie mathématique de Gaston Bachelard ? Cette question ne peut
recevoir une réponse claire et rapide. Il est pratiquement impossible en tout cas d’étudier l’épistémologie de
Gaston Bachelard sans être marqué par l’importance décisive conférée aux mathématiques. Il serait d’ailleurs
plus exact de parler d’une omniprésence des mathématiques et qui débouche sur une philosophie mathématique
tout à fait singulière. En effet, en scrutant de près l’ensemble des idées qui structurent la pensée mathématique
de Gaston Bachelard, et en les articulant, on se rend à l’évidence qu’il y a chez cet auteur une philosophie
mathématique tout à fait inédite, mais parfois inaperçue. Sa philosophie des mathématiques, Bachelard la
revendique, au-delà des qualifications d’ordre rationalistes, comme étant un « réalisme construit » et
« métaphorique ». La présente réflexion consiste en un exposé explicatif de cette philosophie mathématique en
tant qu’elle se décline sous la dénomination peu connue de réalisme mathématique d’un genre nouveau.
Mots clés : Épistémologie, réalisme, mathématiques, rationalisme.
I. INTRODUCTION
The epistemological thought of Gaston Bachelard takes shape in contact with the theory of relativity
and quantum mechanics. These two major events in the history of science will induce a new scientific spirit
which obliges, on the one hand, to approach science from a discontinuist angle, and on the other hand, to
analyze how mathematical thought constitutes the axis of research and scientific work. It is the mathematical
structures that preside over scientific heuristics. Mathematics has three main functions for Bachelard: 1) a
heuristic function: mathematics is the engine of scientific research, it constitutes the axis of scientific discovery.
2) a demarcation or even discriminatory function: mathematics makes it possible to distinguish science from all
other forms of non-scientific or pseudo-scientific knowledge. 3) an ontological function: mathematics makes it
possible to penetrate the real, better, to recreate the real. It is relative to this last function that he affirms: "In the
beginning is the Relationship, this is why mathematics reigns over the real"
1
. There is therefore in our author a
mathematical realism whose contours it is necessary to scrutinize and specify. Bachelard obviously evokes
several realisms, which he distinguishes and ranks. It is first of all “naive realism”, which projects onto all
reality the model of immediate realities. Then “philosophical realism”, which posits the fundamental
irrationality of reality. These two realisms have nothing scientific about them. They are different from the
“scientific realism” of modern physics and chemistry, which is first a mathematically "instructed" realism, then
a “scientific technical realism” as the instrumental realization of mathematical idealizations
2
. How, then, can
we grasp the full singularity of this epistemological realism of mathematical essence? In other words, what are
its characteristics?
1
Bachelard, Gaston“Noumenon and microphysics”,in Studies , Paris, Vrin, 1970, p.19.
2
Gaston Bachelard, Applied Rationalism (1949), Paris, PUF, 1975, p.137.
2. American Journal of Humanities and Social Sciences Research (AJHSSR) 2023
A J H S S R J o u r n a l P a g e | 110
II. OF THE EPISTEMOLOGICAL STATUS OF MATHEMATICS
The constructed and metaphorical mathematical realism of Bachelard, who acts as a mathematical
philosopher, is elaborated polemically against the “ontological realism” of the Platonic or Aristotelian type,
against the deductive mathematicism and the reductivist realism of Descartes and Meyerson, against pure
formalism, axiomism and logicism. This mathematical philosophy is distinguished by the epistemological status
conferred on mathematics. For Bachelard, science is a work of application of mathematical thought. Hence the
concept of “applied rationalism”.
Science before Galileo is a meditation on qualities, characterized by a clear cut between mathematics
and the sciences of reality. It is a science based on a split between the rational and the empirical, the abstract and
the concrete, form and content. With the constitution, by the ancient Greeks, of a theoretical and rational
mathematics, clearly detached from the empirical practices of calculation and surveying, knowledge was divided
and divided into two very distinct levels: at the higher level, a purely intellectual, rational which, by giving us
access to a world of eternal essences, of incorruptible realities, truly gives us science. At the lower level, it is
sensible knowledge which, not exceeding the level of opinion, rivets the spirit on matter and phenomena in
perpetual becoming. Thus, in spite of some remarkable exceptions like the work of Archimedes for the
mechanics of the earth, mathematics was kept at a good distance from the studies of nature. This is how Greek
physics, subservient to the diversity of sensory data, will remain a physics of qualities, far from preoccupations
with quantities. It was only in modern times, under the impetus of Galileo, that physics was mathematized.
Mathematics thus opened up to other areas of knowledge, notably physics. It is probably at this moment in
history that we could situate the beginnings of an openness of mathematics to interdisciplinary, with regard to its
strong coupling with physics.
In Essay on approximate knowledge , book which sets up his singularly constructivist mathematical
philosophy, Bachelard starts from nuanced reflections on the Platonism to which mathematical forms invite,
elaborating on what he calls “the progressive character of the metaphorical existence of mathematical being” 3
.
The mathematical realism that he is then willing to admit stems not from Platonic realism where mathematical
beings flourish in the autonomous existence of a stable eternity
4
, but from a “constructive ontology”. "This
constructive ontology, affirms our author, is never at its end since it corresponds rather to an action than to a
discovery" 5
, more precisely: which stems from a process of progressive reification where "the nature of the
given objects gives way to the rules that govern them” and where mathematical beings have no intrinsic reality,
their existence being relative to their domain of definition”. 6
For Bachelard, mathematical beings do not have an
ontological existence in an ideal reality or an “intelligible world" in the manner of Plato, any more than in the
sensible world, such as it is given to our usual experience, as well as conceives it Aristotle.
Plato did not just inaugurate the dualism of soul and body. He also developed a whole radical dualism
between mathematical knowledge and empirical knowledge, his thesis being that mathematical beings, insofar
as they are intelligible essences, basically have no relationship with the universe of materiality or sensible things
of the world. This will be the beginning of a long intellectual tradition making mathematics an intelligible
science which does not have to sully its purity by applying itself to the world of purely corruptible material
phenomena. This explains why the word “Platonism” has become customary today to qualify this realism of
mathematical essences which structures the thought of a good number of contemporary mathematicians for
whom the relationship of mathematics to the other sciences is essentially a relationship of application, and not
of constitution according to an Althusserian terminology. The fact is that Plato understood that any application
of intelligible forms, including mathematics, to the world of materiality is a mark of decay. This opinion will not
be shared by Bachelard, who believes on the contrary that for scientific rationalism, “ application is not
mutilation; scientific action guided by mathematical rationalism is not a transaction on principles […] For
scientific rationalism, application is not a defeat, a compromise” 7
.
Against the deductive mathematicism of Descartes and against the reductivist realism of Meyerson
8
,
Bachelard proposes the inductive approach of mathematical noumena. His criticism of the deductive ideal leads
him to posit that science proceeds from an essentially inductive approach, always opening up to novelty, to the
unpublished. Moreover, noumenal induction suggests the passage from the mathematically thinkable to the
physically possible. One cannot therefore logically reduce mathematics to a descriptive or reductive function.
Mathematics has a creative power and the reality of phenomena is only inferred from the variables of the
equations: "Bachelardian mathematical thought does not follow an identifying approach, reducing the
3
Gaston Bachelard, Essay on approximate knowledge (1928), Paris, Vrin, 1973, p. 186.
4
Cf. Plato, The Republic, Paris , trans. Robert Baccou, Garnier-Flammarion, 1966.
5
Same.
6
Ibid., pp.187-188.
7
Gaston Bachelard, The philosophy of no, (1940), Paris, PUF, Quadrige, 1981,pp.6-7.
8
SeeEmile Meyerson, Identity and Reality, Paris, Alcan, 1908.
3. American Journal of Humanities and Social Sciences Research (AJHSSR) 2023
A J H S S R J o u r n a l P a g e | 111
particularities and diversities of cases to a minimum of similar and common characteristics. For him,
mathematical thought is inventive thought
9
.
Bachelard's mathematical thought also takes shape against mathematical formalism. The fault of
formalism is to remain closed to any attempt at application. Mathematical activity does not flourish in its
constitution as a closed formal system, kept at a distance from reality. For Bachelard, formalism is mathematics
running on empty, seeing in application a form of mutilation:
“If one condemns mathematical realism too soon, it is because one is seduced by the
magnificent extension of formal epistemology, that is to say by a kind of empty
functioning of mathematical notions. But if we do not unduly disregard the psychology
of the mathematician, we soon realize that there is in mathematical activity more than a
formal organization of schemes and that every pure idea is doubled by a psychological
application, of an example that serves as reality. »10
Logicism is not spared from the Bachelardian critique. What characterizes logicism in fact, and which
Bachelard decries, is not only the fact of founding mathematics in logic, but above all, the subjection of
scientific reasoning to the respect of logical constraints which only apply to a stabilized formal structure. There
is here a sort of mechanization of scientific reasoning, a mechanization that prevents us from apprehending
mathematics as a "thought", a thought that fully masters its language:
“We must break with this cliché dear to skeptical philosophers who only want to see
mathematics as a language . On the contrary, mathematics is a thought , a thought sure
of its language. The physicist thinks the experiment with this mathematical thought.11
We cannot therefore reduce mathematics “to the status of simple language which would express, in its
own way, facts of observation”. 12
Mathematics is not intended to summarize experience, it helps to think about
it, to organize it.
III. CHARACTERIZATION OF THE MATHEMATICAL PHILOSOPHY OF GASTON
BACHELARD
It should be noted that the epistemological position of Gaston Bachelard is declined as a “scientific
realism”13
, “a realism made of realized reason” which attributes to mathematics an ontological scope. Indeed, he
posits the “scientific reality”
14
as emerging from a dual work of mathematical construction and technical
production. The “scientific reality” is essentially a mathematical and technical “realization”. The index of the
real is the rationality of the mathematically constructed and technically produced phenomenon. This "scientific
realism", which is developed at a distance from "vulgar realism" and "philosophical realism", animates physics
and chemistry, in that it is "worked on", "rectified", "instructed" by mathematics. But still, physics and
chemistry are of the order of a “realism of scientific technique” 15
, that is to say a technical realization of
mathematical idealizations, in particular algebraic. Bachelard thus grants an ontological existence to
mathematical idealities, not in the sense that mathematics would exist in itself, as essences in a world separated
from the physical universe, but rather in the sense that it is mathematics that allows to penetrate the real, and
participate upstream in the work allowing to invent "from scratch" 16
the phenomena. In 1932, Bachelard
explained that, contrary to what was thought in the 19th century,
namely that science is "real through its objects",
today, “It is now the objects which are represented by metaphors; It is their [mathematical] organization that
appears to be reality”17
. The physical object, “it is the mathematical formula which will give it a shape”18
.
Consequently, reality “has a mathematical meaning before having a phenomenal meaning”19
. In The Philosophy
of No, Bachelard states:
“Reality turns into mathematical realism, then mathematical realism dissolves into a
kind of realism of quantum probabilities.The philosopher who follows the discipline of
9
Jacques Chatué et Al., General introduction to epistemology, Dschang University Press, 2020, p. 40.
10
Gaston Bachelard, The new scientific spirit (1934),Paris, PUF,1984, p.8.
11
Gaston Bachelard, The rationalist activity of contemporary physics, Paris, PUF, 1951, p.42.
12
Dominique Lecourt, The philosophy of science , Paris, PUF, “Que sais-je?”, 2001, p.102.
13
See Applied Rationalism , Paris, Quadrige/PUF, 1949, p. 8.
14
Gaston. Bachelard, The New Scientific Spirit, op. cit., p.9.
15
Ibid., p. 137.
16
See “Noumene and microphysics” in Etudes , Paris, Vrin, 1970, p.19.
17
Ibid., p.13.
18
Ibid., p.15.
19
Ibid., p.17.
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quanta – the schola quantorum – accepts to think all of reality in its mathematical
organization”20
.
The characterization of Bachelard's thought as “scientific realism” is however neither sufficient nor
primary to determine his epistemological position. It is not sufficient, because it is strongly coupled with another
characteristic. “Scientific realism” is linked to what Bachelard calls "discursive idealism" 21
, another name for
“open rationalism” 22
and which corresponds to a break with “immediate idealism”23
, that is to say with the
consideration from an immutable reason to the benefit of a constantly creative mind of its own structures to
adjust to reality; especially mathematical structures. Open rationalism also translates the quality of a scientific
reason that flourishes only in its work of application to the diversity of its fields of study. It is rationalism that
becomes “regional”.
Moreover, this characteristic is not primary, because it results from a conquest. To follow this conquest
is precisely to follow the emergence and promotion of this couple which, according to Bachelard, adequately
describes the scientific spirit in its activity of knowledge and is fixed in the expressions of “applied rationalism”
and “technical materialism or “technical realism”24
.
Bachelard's mathematical philosophy therefore proceeds logically from the characterization of science
as the realization of the rational or the laborious application of the mathematical possible: “the application of
scientific thought seems to us essentially realizing. We will therefore try to show […] what we will call the
realization of the rational or more generally the realization of the mathematical” 25
. Bachelard's mathematical
philosophy, which already takes shape in Essay on Approximate Knowledge , in addition to proceeding from the
actual practice of mathematicians in arithmetic, algebra, analysis or geometry, is a stand against “ontological
realism” in favor of a “constructed realism” and that he “metaphorical realism”. It is “metaphorical” because
“the reality of mathematics resides in their virtuality, that is to say their independence with regard to the
concrete cases in which they are embodied” 26
.
This “metaphorical realism” feeds on the pre-intuitionist theses of French mathematicians from the
beginning of the 20th century
, such as Borel and Baire; theses according to which only entities that can be
calculated or approximated by a calculation are acceptable in mathematics. Bachelard's mathematical realism is
constructed in that he considers mathematics as resulting from a work of rational construction, and which,
beyond their simple heuristic function, also has an ontological significance. Bachelard is however opposed, let
us say it again, to "ontological realism", "realism of mathematical essences" inherited from Plato and which one
finds in famous mathematicians such as Cantor, Gödel, or even Hermite, to whom Bachelard devotes a few
analyzes in Essay on Approximate Knowledge . In his article “Noumene and microphysics” also, Bachelard
makes it known that:
“By its psychologically dynamic and inventive value, mathematical realism, as it
results from its relations with contemporary physics, goes far beyond the completely
Platonic sense in which the realism of Hermit was still placed” 27
.
The fact is that for the Platonist Hermit,
“Mathematical being is, in a way, static […] On the contrary, the reality of
mathematical physics is enriched by a double dynamism: by studying it, we have as
much chance of discovering phenomena as theorems. Moreover, it is always necessary
to come to realize the theorems thus discovered.28
Here, Bachelard opposes the stable mathematical realism of the Platonists with an active and dynamic
mathematical realism which, refusing dualism or the separation between theorems and phenomena, reason and
experience, mathematics and the physical sciences, instead makes mathematics l element that allows phenomena
to be constituted. The relation of mathematics to other disciplines must then be a relation of constitution.
Bachelard is critically part of a movement, that of a mathematical activity which is no longer considered and
considered outside of its relationship to physics and chemistry. This need to no longer cut off mathematics from
other sciences of reality led Bachelard to reject the formalism of pure ideas and the empiricism of the concrete
object.
At this level, we realize that Bachelard's mathematical thought breaks the abstract/concrete,
mathematics/physical sciences dualism and opens up mathematics to the sciences of matter. This is not without
20
Gaston Bachelard, The Philosophy of No , op. cit., p.86.
21
See “Discursive idealism”, in Etudes , p.87.
22
See “ Surrationalism ”, in Etudes , p.12.
23
Ibid., p.91.
24
Gaston Bachelard, The New Scientific Spirit, op. cit., p. 9.
25
Ibid., p.8.
26
Vincent Bontems, Bachelard, Paris, Belles Lettres, 2010, p. 59.
27
Gaston Bachelard, “Noumene and microphysics” in Etudes, op. cit., p.17.
28
Same.
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the detour of an allegiance to Kantianism: “The criticalist philosophy, whose solidity we will underline, must be
modified according to this openness” 29
. Bachelardian mathematics achieves the synthesis of intellectualism and
empiricism. Kant rejected pure intellectualism and radical empiricism, the categorical opposition of which leads
to a split between rational truths and empirical work
30
. Kant, posing the necessary articulation of reason to
experience, refuses to cut off mathematical work from its application to sensible reality. Rational science is no
longer constituted in total independence with regard to experience. In this respect, Bachelard's expression of
“applied rationalism” is very significant, an expression which clearly translates the fact that science for
Bachelard is an applied mathematics. There is therefore no longer a break, in the chain of sciences, between
mathematics and the sciences of reality.
This idea is clearly expressed by one of Bachelard's masters, Léon Brunschvicg, for whom a physics
without mathematics is only a mediation on qualities, while a mathematics which does not apply to study of
reality remains superficial. Commenting on this specific point in Brunschvicg's thought, Robert Blanché asserts:
Just as, he said, a physics lacking the intellectual framework that only mathematics can
provide would not rise above the level of a speculation on qualities, so too in another
sense, an arithmetic which would not already be a physico-arithmetic discipline, that is
to say whose propositions would not remain, directly or indirectly, in connection with
reality, would not deserve the name of science.31
Ferdinand Gonseth, with whom Bachelard has many theoretical affinities, also refuses to admit that the
work of mathematics is carried out at a distance from experience and independently of it. The latter refuses the
break between mathematics and the sciences of reality. There is no pure abstract, nor autonomous concrete. The
abstract is only justified in its act of constituting the concrete. In other words, the abstract can only be conceived
when engaged in a certain realization of the concrete. As such,
“Physics is abstract relative to sensory data, but concrete relative to mathematics, which
itself will become concrete for logic; and logic itself, in its abstract generality, is
ultimately only a “physics of any object.” For the system of logical laws is not fixed ne
varietur and once and for all, it is susceptible to modification and refinement by
opening up to an experience that is never complete. »32
The evocation of these positions or theses helps us to better identify the ideas that contributed to mature
the originality of Bachelard's position. In Applied Rationalism , he defends the necessary collaboration of reason
and experience, the sciences of reality now only having to be constituted by the detour of a rationalization or
mathematization of experience, the only guarantee of access to the apodicticity. However, he proposes, instead
of architectonic rationalism based definitively on stable and immutable principles, an inductive and subversive
mathematical rationalism because it is active and polemical: “Rationalism in action in the physical sciences
cannot be confused with an elementary rationalism, immobilized in the universality of principles. Its role is not
limited to summarizing experiences”.33
It is a rationalism which, elevated above measure and flourishing in calculation, must constantly revisit
its frameworks and principles to adequately interpret experience while also readjusting them so that they retain
their operability.
By this double consideration of an active, creative and creative reason which draws its instruction from
its dialogue with experience, and from an experience itself dynamic, supposed to control the work of reason, the
gap which maintained the gap between mathematics and the sciences of reality. The dialogue is re-established
between reason and experience, mathematics and reality, rational and empirical, abstract and concrete, form and
content. This is the reason why the question of the interdisciplinarity of mathematics is directly consecutive to
the application of rational work.
IV. CONCLUSION
Our fundamental concern was to characterize the mathematical philosophy of Gaston Bachelard. It
seemed to us quite legitimate to characterize it as mathematical realism insofar as it is a “realization of the
rational in physical experience”
34
, “or more generally the realization of the mathematical”
35
And since the sense
of epistemological vector goes from the rational to the real
36
, it is mathematics which makes it possible to infer,
29
Gaston Bachelard, The Philosophy of No, op. quoted,p.11.
30
See Immanuel Kant, Critique of Pure Reason, tr. by A. Tremesaygues and B. Pacaud, 11th
ed., Paris,
Quadrige/PUF, 1986.
31
Robert Blanché, Epistemology, Paris, PUF/ “What do I know? », 1972, p. 84.
32
Ibid., p. 85.
33
Gaston Bachelard, The Rationalist Engagement, op. cit., p.94.
34
Gaston Bachelard, The New Scientific Spirit, op. cit., p. 9.
35
Ibid., p. 8.
36
Same.
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by induction, the existence of physical realities. We have thus been led to observe the particular and privileged
status accorded by our author to mathematics. Mathematics is for Bachelard purveyors of rationality in science.
Science derives its rationality and dynamism from its mathematical roots. Better still, it is mathematics that
constitutes the condition of the possibility of science, in particular of the physical and chemical sciences.
Bachelard thus invites us to consider abstraction as the appropriate and fruitful approach of the scientific spirit.
Mathematical thought forms the basis for the explanation of physical phenomena. Mathematics has an inductive
value in that it makes it possible to infer the existence of physical realities. It is mathematics that gives objects
their reality, aided in this by technical instruments which themselves are “materialized theories”. Scientific
experimentation is a work of technical realization of mathematical noumena. And when Bachelard speaks of
mathematics, he manifests a strong attraction for algebra, which, beyond simple measurement, is a true source
of thought, calculation, invention, inference. Science for Bachelard would therefore only be applied
mathematics.
REFERENCES
[1] D. Lecourt, The Philosophy of Science, Paris, PUF, “Que sais-je?”, 2001.
[2] E. Meyerson, Identity and Reality,Paris, Alcan, 1908.
[3] I. Kant, Critique of Pure Reason, tr. by A. Tremesaygues and B. Pacaud, 11th
ed., Paris, Quadrige/PUF,
1986.
[4] G. Bachelard, Essay on Approximate Knowledge (1928), Paris, Vrin, 1973. Applied Rationalism,Paris,
Quadrige/PUF, 1949. The rationalist activity of contemporary physics, Paris, PUF, 195), The new
scientific spirit (1934), Paris, PUF,1984.
[5] The philosophy of no (1940),Paris, PUF, Quadrige, 1981.
[6] “Noumenon and Microphysics”,in Studies, Paris, Vrin, 1970.
[7] J. Chatué et Al., General Introduction to Epistemology, Dschang University Press, 2020.
[8] Plato, The Republic, Paris, trans. Robert Baccou,Garnier Flammarion, 1966.
[9] R. Blanché, Epistemology, Paris, PUF/ “What do I know? », 1972.
[10] Vincent Bontems, Bachelard, Paris, Belles Lettres, 2010.