Satisfactory Essays

- 2412 Words
- 10 Pages
- 3 Works Cited

Reflexive Substantion of an One-Way Ascendancy of Mathematics over Ethics

ABSTRACT: Russell and Popper are concordant with Plato with respect to the independence of mathematics upon the sensations. Beth shares the opinion of the complete independence between the world of science and mathematics and that of psychology. Essenin-Vol'pin's opinion is of an ascendance of ethics and jurisprudence over mathematics. For the first time, the position of Plato, Russell, and Popper are substantiated in this paper through Hegel's reflexive natural scientific method. The external activation of numbers into interaction through arithmetical operations, adopted by him, has been taken as a basis of this substantion. This is the reason why mathematical rules of reasoning are exact-they represent a pure product of the 'third world.' The rules of ethics and the related humanities are their reflective approximate reverberations. Ascendancy of the rules of such types of science over mathematics is impossible due to the irreversibility of the reflexion.

The problem of the interaction between the psychical and the thinking worlds as reverberations of the material one has been treated much earlier by ancient philosophy. Plato excludes any dependence of mathematics, it being the most brilliant representative of the mental world, of the sensations. Russell [1] (I. pp. 237-238) is concordant with the above. He considers that the mathematical truth is "applicable solely to the symbols," the symbols being "words," that "do not signify anything in the real world." Thus, the correct opinion, pointed out, remains unsubstantiated, since nowhere is it related to the philosophical categories.

In the substantion, offered by this paper, we proceed from the assumption that the variety of the mathematical symbols, at any rate, is reduced to and ensues from the aim: namely-to study the quantitative characteristics of "the qualities" from "the being." That connects the mathematical symbols with "the real world," i.e.-it reveals the possibility of a substantiating, since those characteristics interact. Following the construction of the foundations of mathematics, we should agree that the interaction among its concepts (i.e. the rules of the mathematical reasoning) is reduced to the interaction among the natural numbers. Hegel defines them reflexively [2], [3] ensuing from "the qualities" of "the beig" which (conversely) indicates that the mathematical truth denotes something "in the real world."

Russell has pointed out that "Hegel's philosophy is very difficult-he is ...the most difficult to grasp of all great philosophers" [1] (III., p. 337), thus associating him with the philosophers "willing to spread confusion in mathematics" [1] (III.

ABSTRACT: Russell and Popper are concordant with Plato with respect to the independence of mathematics upon the sensations. Beth shares the opinion of the complete independence between the world of science and mathematics and that of psychology. Essenin-Vol'pin's opinion is of an ascendance of ethics and jurisprudence over mathematics. For the first time, the position of Plato, Russell, and Popper are substantiated in this paper through Hegel's reflexive natural scientific method. The external activation of numbers into interaction through arithmetical operations, adopted by him, has been taken as a basis of this substantion. This is the reason why mathematical rules of reasoning are exact-they represent a pure product of the 'third world.' The rules of ethics and the related humanities are their reflective approximate reverberations. Ascendancy of the rules of such types of science over mathematics is impossible due to the irreversibility of the reflexion.

The problem of the interaction between the psychical and the thinking worlds as reverberations of the material one has been treated much earlier by ancient philosophy. Plato excludes any dependence of mathematics, it being the most brilliant representative of the mental world, of the sensations. Russell [1] (I. pp. 237-238) is concordant with the above. He considers that the mathematical truth is "applicable solely to the symbols," the symbols being "words," that "do not signify anything in the real world." Thus, the correct opinion, pointed out, remains unsubstantiated, since nowhere is it related to the philosophical categories.

In the substantion, offered by this paper, we proceed from the assumption that the variety of the mathematical symbols, at any rate, is reduced to and ensues from the aim: namely-to study the quantitative characteristics of "the qualities" from "the being." That connects the mathematical symbols with "the real world," i.e.-it reveals the possibility of a substantiating, since those characteristics interact. Following the construction of the foundations of mathematics, we should agree that the interaction among its concepts (i.e. the rules of the mathematical reasoning) is reduced to the interaction among the natural numbers. Hegel defines them reflexively [2], [3] ensuing from "the qualities" of "the beig" which (conversely) indicates that the mathematical truth denotes something "in the real world."

Russell has pointed out that "Hegel's philosophy is very difficult-he is ...the most difficult to grasp of all great philosophers" [1] (III., p. 337), thus associating him with the philosophers "willing to spread confusion in mathematics" [1] (III.

Related

- Powerful Essays
## Ontology of Mathematics

- 1511 Words
- 7 Pages
- 5 Works Cited

Pythagoras is certainly not noting the existence of the formula, but, rather, he is noticing the relation between a hypoteneuse and its sides. This relationship comes to be expressed in his formula. So we already see that while a genuine relationship exists between a hypoteneuse and its sides, a genuine theorem is contingent on language; the language in this case is that of mathematics. We are met, then, with two questions. The rst is whether we should consider the terms of mathematics, such as wo" or four," to abstract or concrete.

- 1511 Words
- 7 Pages
- 5 Works Cited

Powerful Essays - Satisfactory Essays
## Comparing Spinoza’s Ethics and Dostoyevsky’s Notes from the Underground

- 2477 Words
- 10 Pages

Starting with Descartes’ vision of a philosophy with a mathematical certainty, rationalists claimed to have grasped a rather large portion of reality, including the world, God, consciousness, and whatever falls in-between. As empiricists argued, most of this "knowledge" was in effect assumed, a habit, as it had no representation in the real world. The rationalists’ notorious abstractness and their disregard for the seeming discrepancy between their proofs and the real world have been the main reasons for the fearsome opposition and caricature they faced: even Voltaire, though influenced to a great extent by Leibniz’s philosophy, ridicules it in his masterpiece Candide in the form of ludicrously optimistic Pangloss. . Kant, especially, has put a rather impressive dent in the hull of rationalist philosophy, branding it dogmatic metaphysics.

- 2477 Words
- 10 Pages

Satisfactory Essays - Satisfactory Essays
## Hellenistic and Hellenic Interpretation of Popper

- 2385 Words
- 10 Pages

While agreeing with Popper's falsifiability criteria, I question his initial assumptions of the nature of science. He suggests that all scientific thought is purely logical and scientific theories are rigorous, mathematical and precise. While true for most modern theories, this assumption is not true for ancient scientific theories. Modern science is a product of Hellenistic thought, which evolved from Alexandrine culture. Modern theories, as well as those which follow the Hellenistic tradition, are characterized by their narrow focus of logic and mathematics -- they explain how something works (Kuhn 104).

- 2385 Words
- 10 Pages

Satisfactory Essays - Better Essays
The key word there was abstract. The meaning of abstract is “existing in thought or as an idea but not having a physical or concrete existence”, which helps the theory of the non-Platonists. They argue that mathematical statements definitely do not exist physically, hence the word abstract. Following the logic of the non-Platonists, math is therefore: an invented logic exercise with no existence outside of mankind’s conscious thought. The purpose of math, they argue, is to use patterns to discerned by brain, to create useful, but artificial order from

- 1004 Words
- 5 Pages

Better Essays - Better Essays
## Mathematics

- 1081 Words
- 5 Pages

Certainly the effort should be made. Perhaps, through Pythagorean ideas, logicism and Platonism, a firmer understanding can be known of the grasp that mathematics has on the world. Due to the secrecy of the society in which Pythagoras, it is difficult to distinguish between any original works of Pythagoras from those of his followers. However, it is not the author that is important, but rather the notions presented. According to the view of the Pythagoreans that "all is number," the first four numbers have a special significance in that their sum accounts for all possible... ... middle of paper ... ...l proofs for someone who accepts the axioms from which they begin."

- 1081 Words
- 5 Pages

Better Essays - Satisfactory Essays
## Necessary And Infinite Truths Analysis

- 1803 Words
- 8 Pages

In addition to this, Leibniz supports the claim that all necessary truths are demonstrable within a finite series of steps. He does not allow for infinite non-recurring decimal numbers such as pie to be necessary truths because of the infinite step-process involved in the demonstration. The essay will also emphasize the function of Leibniz’s account in the possible world context. It will finally evaluate the extent to which contingent truths can be adequately distinguished from necessity. The analysis of infinite series in mathematical propositions is Leibniz’s source of inspiration for the acc... ... middle of paper ... ...lanation for contingency.

- 1803 Words
- 8 Pages

Satisfactory Essays - Powerful Essays
## Pythagoras and Plato

- 1421 Words
- 6 Pages
- 5 Works Cited

Pythagoras felt that all things could be explained and represented by mathematical formulae. Plato, Socrate’s most important disciple, believed that the world was divided into two realms, the visible and the intelligible. Part of the world, the visible, we could grasp with the five senses, but the intelligible we could only grasp with our minds. In their own way they both sought to explain the nature of reality and how we could know what is real. Pythagoras held that an accurate description of reality could only be expressed in mathematical formulae.

- 1421 Words
- 6 Pages
- 5 Works Cited

Powerful Essays - Good Essays
## Rationalism vs. Empiricism: The Argument for Empricism

- 846 Words
- 4 Pages
- 2 Works Cited

Instead, this school of thought maintains that because the world that we experience through our sense is in a state of constant change it can, therefore, not be relied upon in deriving distinct and reliable truths, also known as absolute truths. Rene Descartes, a seventeenth-century mathematician, was one of the most influential philosophers in rationalism. Descartes, like all rationalists, rely on the absolute truths found only in mathematics and logic, and place ultimate value in analytic statements. "An analytic statement attributes a property to something, and that property is already implicit in the definition of that object or concept". (White & Rauhut, pg.72) Descartes introduced the idea of "radical doubt", as we... ... middle of paper ... ...lank state", provide us with a logical explanatory argument against rationalism.

- 846 Words
- 4 Pages
- 2 Works Cited

Good Essays - Satisfactory Essays
## The Cartesian Doubt Experiment and Mathematics

- 3426 Words
- 14 Pages

The Cartesian Doubt Experiment and Mathematics ABSTRACT: The view that Descartes called mathematical propositions into doubt as he impugned all beliefs concerning common-sense ontology by assuming that all beliefs derive from perception seems to rest on the presupposition that the Cartesian problem of doubt concerning mathematics is an instance of the problem of doubt concerning existence of substances. I argue that the problem is not 'whether I am counting actual objects or empty images,' but 'whether I am counting what I count correctly.' Considering Descartes's early works, it is possible to see that for him, the proposition '2+3=5' and the argument 'I think, therefore I am,' were equally evident. But Descartes does not found his epistemology upon the evidence of mathematical propositions. The doubt experiment does not seem to give positive results for mathematical operations.

- 3426 Words
- 14 Pages

Satisfactory Essays - Satisfactory Essays
## Extending a Kantian Dichotomy to a Poincaréan Trichotomy

- 2976 Words
- 12 Pages
- 5 Works Cited

(1) The product of the two distinctions yields three kinds of knowledge: synthetic à priori, analytic à priori and synthetic à posteriori; analytic à posteriori being impossible. For Kant propositions like; "7+5=12," "all bodies have mass" and "every event has a cause." were synthetic and known à priorily. (2) Post-Kantian philosophy witnessed an attack on the possibility of synthetic à priori knowledge such as the rejections of analysis, geometry and arithmetic as synthetic à priori by Bolzano, Helmholtz and Frege respectively. (3) These were motivated by a fear that Kant's conceptualism, of the mind imposing space and time on the world, may lead to anti-realism, such as that of Husserl's bracketing the existence of the world based on his extensions of Descartes and Kant.

- 2976 Words
- 12 Pages
- 5 Works Cited

Satisfactory Essays