Hiking about infinity and gnoseology

Dr. Adriana Mascsut

Defining the topic

Gnoseology is the science or word about knowledge (from ancient Greek gnosis-knowledge and logos- word, science).[1] Knowledge as such is, however, difficult to define, representing an extremely complicated topic. There is a definition of knowledge in the Explanatory Dictionary, where this "is the action of knowing and its result: 1. reflection in consciousness of the existing reality, independent of the knowing subject; 2. the fact of possessing knowledge, given information on a subject, on a problem; knowledge"[2].

A more elaborate definition is given in Webster's Dictionary, which defines what the condition of knowing actually means. The state of knowledge involves four aspects related to:

● training;

● experience;

●memorare;

● understanding information.[3]

In turn, the infinite, coming from the Latin word infinitus, refers to a concept that has no boundaries, immeasurable, unlimited[4] , and from a temporal point of view, it refers to an eternal time, meaning an eternity.

Under these conditions, a work on epistemology and the infinite would be an incursion into the knowledge of the infinite, an approximate approach that offers only a limited perspective. The method of study, in this case, would only be narrative and deductive accents[5], but the focus will be on Platonic philosophy because, as the story goes, nothing is new since Plato. [6]

Theme in motion

In general, knowledge can be understood in two ways:

as a progress that takes place inside man (a concept belonging to Plato);

as an increase of man's power over the surrounding world (concept described by Brother Bacon and later, by A. Comte).

The tradition of researching the theory of knowledge begins with the Platonic dialogue Theaitetos, which has as its basic idea the question of what it means to know. Here the character Socrates tries to challenge the sophistic relativism through a discussion with another character, Protagoras. The discussion of the two philosophers lays the foundations for the study of the problems of knowledge, which only in the modern period has become a central research theme.

The concept of knowledge has given rise to a multitude of interpretations over time. Currently, the approach to the theme of knowledge refers to the study of a phenomenon that has a very long history, but which is also a contemporary phenomenon, as it presents special perspectives of future development in a society of knowledge.

In general, knowledge is an aspiration of the human mind. As man accumulates new information, knowledge becomes deeper. Thus, δόξα in the sense of opinion, opinion, doubt, belief or conviction falls into the lower spectrum of knowledge.

Philosophical questions about the nature of knowledge can fall into categories:

the first category of questions focuses on the nature of the object of knowledge;

the second category is centered on the study of the nature of the knowing subject.

Thus, four elements are configured in the knowledge process:

an object;

a subject;

cognitive relationship between object and subject and

knowledge and communication through which objectification and socialization take place.

Therefore, in the theory of knowledge:

the object to be known;

the knowing subject.

In the case of this work, the object to be known would be the infinite, and the knowing subject is the man who wants to know the infinite.

The epistemological relationship between object and subject represents a fundamental problem of philosophy, but there are a number of other aspects that refer to the object of knowledge, as well as to the subject of knowledge or the value of knowledge, included in the epistemological problem of some ancient philosophers such as Socrates, Plato, Aristotle, Democritus.[7]

In the ancient world, there is a form of knowledge highlighted by the existence of a theory of relativization, characterized by issuing different contradictory opinions in the spirit of the sophistic conception. Thus, Protagoras shows that "man is the measure of all things, and Platonic reasoning leads to the idea that to perceive, from a human point of view, means to know"[8].

Following Augustine's reasoning, "knowledge seems to be nothing but a representation in the soul of things, because it cannot be said that it is an assimilation of the known subject with the knowing subject"[9].

There are generally three cognitive levels:

● the level of observational knowledge, which starts from distinct objects, phenomena, processes within which the external and individual features of the studied object will be highlighted through the sense organs;

● the level of empirical knowledge, which refers to the analysis and description of a class of identical objects and the processing of data that are then used in a series of logical operations such as comparison, synthesis, abstraction, generalization;

● the level of theoretical knowledge, which includes the elaboration of concepts and the substantiation of theoretical laws, resulting in an important role of the constructive capacity of the subject of knowledge.[10]

At the base of the conceptualization are four aspects related to the foundations, extent, limits and value of knowledge[11]. Thus, a theory of knowledge is constituted[12], determined by the crisis of metaphysics.

The term Theory of Knowledge was introduced by Eduard Zeller[13] but its roots are in Platonic epistemology. The situation underwent a change in the modern period, when the ancient and medieval metaphysical tradition reached a crisis caused by the need for a scientific explanation of the world. Thus, the theory of knowledge becomes the first philosophy, taking over the position held until then by metaphysics.

Here, some clarifications related to the theme of the work are necessary. Aristotle elaborated a treatise on Metaphysics, first philosophy, in which "it refers to everything that exists, viewed from the strict perspective of its simple existence and not of the relative importance that that body, thing, object, concept, idea, notion would have or not"[14]. The philosopher talks about the conceptual infinity in the treatise on Physics in which he establishes the impossibility of actually knowing the infinite, establishing that there is:

● the extensive infinity;

● the intensive infinite;

● infinite potential;

● present infinitive.[15]

It should be noted that in pre-Soceratic philosophy, the infinite was presented in a confusing way, and in Plato in a transcendent sense, and Aristotle only realized a conceptualization about knowledge and infinity. [16].

Knowledge involves evolution over time and the acquisition of new experiences and determines human reason to acquire new values ​​and, thus, research appears which, starting from human instinctual nature, evolves with the help of will and thought towards the birth of philosophy.[17]

Man from Greek, pre-Socratic and post-Socratic antiquity, in his capacity as a rational being, tries to know the existing reality:

● to determine the quantity, quality and connections between things;

● to establish rules, principles and laws according to which existence is founded.

In the pre-Socratic period, there were philosophers, such as Thales of Miletus, Anaximenes, Anaximander, Heraclitus, Anaxagoras, Empedocles, whose objective of thought was the search for the principle that governs the nature of things and existence, but in their opinion one cannot speak of knowledge, but only known things.

Socrates is the one who focuses on human-centered philosophical study (άνθρωπος), that is, anthropologically, insisting on human perfection from an ethical point of view and making the transition to thinking about thinking. Pre-Socratic and Socratic thinking establishes the study of the problem of the theory of knowledge through which human knowledge becomes a distinct object of philosophical reflection: "The theory of knowledge begins to be seen as a necessary component of any philosophical construction, explaining what it is and how knowledge of the world is achieved by man, the possibility of knowledge, its laws, levels, forms and value."[18]

Only by starting from the human-centered philosophical study can one arrive at an imaginary approach to the infinite.

Man is limited in time and space, and theologically, man is a creature and only God who created him is unlimited in time and space. Philosophically the concept of infinity can be described, but to understand what it looks like does not seem possible: yes.... for example, one can describe and visualize the laptop with which this work was written and one can imagine a philosopher who dreams of reaching infinity who can describe like the horizon where the earth seems to touch the sky.

Conclusions or on the metaphysical dialogue between Paton and Laton

To better understand what an excursus on epistemology and infinity could be, one can imagine a dialogue between:

● Paton, follower of the perennial philosophy and who "believes in a radical gender difference, between the spiritual and the material, between the immortal soul and the perishable body"[19];

● Laton, interested in "science, especially mathematics, and therefore, logic and philosophy of language"[20].

It is a dialogue between Laton, a rigorous scientist who seeks to conceptualize through language an epistemological theory of the infinite who in today's world is a philosopher who works as a trainer for artificial intelligence and various chatbots and Paton, a metaphysician who does transcendental meditations, believes in the immortal soul. Laton would say that man has the epistemological capacity to deepen and conceptualize the infinite, and Paton will say that no matter how many epistemological veils man lifts, he will never reach the supreme level of the divine infinity.

Bibliography

Aristotle, Physics, translation Alexander Baumgarten, Univers Enciclopedic Publishing House, Bucharest, 2018.

Chira, Vasile, Species of the infinite (multidisciplinary course), in https://ebibliothecaseptentrionalis.wordpress.com/2016/10/29/speciile-infinitului-incurs-pluridisciplinar/, 30/01/2025.

Explanatory Dictionary of the Romanian Language, Iorgu Iordan- DEX, Romanian Academy, Institute of Linguistics Second Edition, Univers Enciclopedic Publishing House, Bucharest, 1996.

Dictionary of the English Language Unabridged, MA: Merriam-Webster Inc., Publishers, Springfield, 1993.

Georgescu, Stefan; Mircea Flonta; Ilie Pârvu, Theory of scientific knowledge, Academy Publishing House, Bucharest, 1982.

"Gnoseology", in https://m.dex.ro/gnoseologie, 30/01/2025.

https://carturesti.ro/info/metafizica-1384092766?lang=en-US, 30/01/2025.

"Infinite", in https://m.dex.ro/gnoseologie, 30/01/2025.

Hare R. M, Plato, translated by Matei Pleșu, Humanitas Publishing House, Bucharest, 2006.

Macsut, Adriana, Mihaela, Doxa in Plato's conception, Lumen Publishing House, Iasi, 2019.

Stanciulescu, Dana; Sorin Stanciulescu, Methodology of scientific research, Sitech Publishing House, Craiova, 2018.

Stroe, Constantin, Philosophy. Knowledge. Culture. Communication, Lumina Lex Publishing House, Bucharest, 2000.

Augustin, De Magistro, bilingual edition, translated by Mihai Radulescu and Constantin Noica, introduction and notes by Lucia Wald, Humanitas Publishing House, Bucharest, 1995.

Zeller Eduar, About the meaning and theory of knowledge, Ueber Bedeutung und Aufgabe der Erkenntnistheorie, 1862, cf. German text archive, Google = MDZ Munich, http://www.deutschestextarchiv.de/zeller/erkenntnistheorie/1862/, 07.03.2012.

^[1] "Gnoseology", in https://m.dex.ro/gnoseologie, 30/01/2025.

^[2] Knowledge is defined cf. Explanatory Dictionary of the Romanian Language, Iorgu Iordan- DEX, Romanian Academy, Institute of Linguistics, 2nd Edition, Univers Enciclopedic Publishing House, Bucharest, 1996, p. 250.

^[3] A more detailed presentation about knowledge is made inWebster’s Third New International Dictionary of the English Language Unabridged, MA: Merriam-Webster Inc., Publishers, Springfield, 1993, p.1252.

"Knowledge is the fact or condition of knowing: 1. The fact or condition of knowing something with a considerable degree of familiarity gained through experience or contact or association with the individual or thing in question; 2. Theoretical or practical knowledge, information or understanding about looking at a particular branch of science, art, learning or other area involving study, research or practice and the acquisition of skills; 3. The fact or condition of understanding truth, facts or immediate reality, with the mind or through the senses; perception, knowledge, understanding; 4. The fact or condition of possessing through mental understanding based on training, study, research or experience truths, facts, principles or other objects of perception: the fact or condition of having information or being learned or erudite; 5. The sum total of what is known: the entire body of truths, facts, information, principles or other objects of knowledge acquired by mankind."

^[4] "Infinite", in https://m.dex.ro/gnoseologie, 30/01/2025.

^[5] Consult Dana Stanciulescu, Sorin Stanciulescu, Scientific research methodology, Sitech Publishing House, Craiova, 2018.

^[6] Read Adriana Mihaela Macsut, Doxa in Plato's conception, Lumen Publishing House, Iasi, 2019.

^[7]The epistemological relationship between subject and object in ancient philosophers is presented by Constantin Stroe, Philosophy. Knowledge. Culture. Communication, Lumina Lex Publishing House, Bucharest, 2000, pp. 33, 46, 57.

^[8] Ibidem, p. 65.

^[9]This theory of knowledge is presented by Augustine, From a Magistrate, bilingual edition, translation by Mihai Radulescu and Constantin Noica, introduction and notes by Lucia Wald, Humanitas Publishing House, Bucharest, 1995, p. 41.

^[10] Cf. Constantin Stroe, Philosophy. Knowledge. Culture. Communication, pp. 33, 46,57, on. cit.

^[11] In-depth studies of the theory of knowledge are developed by Ştefan Georgescu, Mircea Flonta, Ilie Pârvu, Theory of scientific knowledge, Academiei Publishing House, Bucharest, 1982, p. 9. It is shown that the theory of knowledge is based on names such as Br. Bacon, Descartes, J. Locke, Leibnitz, D. Hume, Kant.

^[12] The term theory of knowledge is asserted in the 19th century, but it is conceptualized especially in the last decade of the 20th century.

^[13] The term theory of knowledge was introduced by Eduard Zeller in On the meaning and theory of knowledge, Ueber Bedeutung und Aufgabe der Erkenntnistheorie, 1862, cf. German text archive, Google = MDZ Munich, http://www.deutschestextarchiv.de/zeller/erkenntnistheorie/1862/, 07.03.2012.

^[14] https://carturesti.ro/info/metafizica-1384092766?lang=en-US, 30/01/2025.

^[15] Physics III, 5, 204a.

^[16] Vasile Chira, Species of the infinite (multidisciplinary course), in https://ebibliothecaseptentrionalis.wordpress.com/2016/10/29/speciile-infinitului-incurs-pluridisciplinar/, 30/01/2025.

,, If in pre-Socratic philosophers, the idea of ​​infinity is linked to the (confused, often naive) search for the first principle (water, air, apeiron, fire, number, etc.), in Plato the concept of transcendence (and implicitly that of infinity) is thematized not only from a cosmological perspective, but especially from a metaphysical one. Plato speaks of the superintelligible character of Good, that is, of a transcendence with an infinitely more radical status than the transcendence of Ideas over things. The good, as the transcendent source of the intelligible world, coordinates the cognitive activity of the intellect. The contemplative intellect (Nous) is nothing but the faculty through which the spirit takes note of the transcendence and superintelligibility of the idea of ​​Good. In Aristotle, the problem of infinity is treated in a paradoxical way. In addition to the arguments he brings in favor of infinity (the infinity of time, the infinity of number, the inexhaustibility of birth and destruction, the unlimited division of sizes, etc.), the Stagirite also offers evidence that indicates the actual impossibility of infinity."

^[17]Eduard Zeller, on. cit.

^[18] The role of pre-Socratic thought in the history of knowledge is presented by Constantin Stroe, Philosophy. Knowledge. Culture. Communication,Lex Publishing House, Bucharest, 2000, pp. 31-32

^[19] The model Paton and Laton is supported by R.M. Hare, Plato, translated by Matei Pleşu, Humanitas Publishing House, Bucharest, 2006, pp. 48-49. It can be stated that through this symbolism R.M. Hare does a non-formal analysis that is anchored in the mindset of Plato's time. Taking as a starting point the hypothesis that the entire Platonic philosophy is bivalent, being divided into a theory on knowledge and one on virtue, R. M. Hare reiterates the game of the Platonic dialogue and creates two characters - Laton and Paton - who argue the philosopher's points of view in turn. This monograph seeks the sources of the Platonic system. You can consult, in this sense, a fragment from Albiciade dialogue.

„Self-knowledge - Socrates assured Alcibiades - is the condition of any progress in science and virtue. It is, therefore, the condition of any education. It is known that man is made up of body and soul: the soul being the one that commands, and the body the one that obeys; from which it follows that the soul is essential. To know yourself, therefore, you must know your soul. The body, when it wants to know itself, looks at itself in a mirror. Likewise, the soul, in order to know itself, must look at itself in another soul as in a mirror. And in this soul he must consider the faculty proper to the spirit, which is intelligence. It constitutes everything that can be more divine in the soul because in it lies knowledge and virtue, especially the knowledge of good and evil, which make virtue possible. He who looks at himself in the light of this knowledge is most likely to progress in virtue. Knowing what is good and what is bad is the highest wisdom. It is the discovery of the divine element in us, that is, of God in ourselves. This is the only way that can lead us to virtue" (Alcibiades 129b).

^[20] Ibidem.