In my research outside the classroom, I discovered a famous person – Plato. His view is that there are abstract objects that exist and do not depend on time and space to exist, and therefore are neither physical nor mental, but exist in a third place. I strongly agree with such a view based on rationalism. My next remarks will also be based on this.
We are taught from childhood that natural science disciplines such as physics and chemistry are based on experimentation. And doing experiments is faced with the problem that the experimental environment is difficult to achieve the ideal state. For example, there is a theory in physics that an object is either at rest or in uniform linear motion when the combined force is zero. This theory is based on experimental reasoning because in reality it is not possible to make the friction force disappear completely, so the theory uses reasonable guesses. As a result, the development of natural science disciplines has always faced resistance and limitations because science based on experimental theories can be limited by the time, temperature, and friction of the experimental environment.
For mathematical Platonism, the objects of mathematical study are abstract, but are an objective existence; they do not depend on time, space, or human thought for their eternal existence. Therefore, mathematical truths are discovered rather than invented. As a result, mathematics is not limited in its development by the limitations of its surroundings. In this way, mathematicians were often able to come up with mathematical theories that were ahead of their time. For example, Fermat’s last theorem was formulated as early as the 17th century and was only proved in the late 19th century. Then there is the case of non-Euclidean geometry which was proposed as early as 1813 and was not applied to general relativity by Einstein until the 20th century. And physics, a discipline based on experimental science, will be constantly overturned or revised by later generations. For example, Newtonian mechanics was considered absolutely correct from 1607, but the theory of relativity in 1905 corrected it, and it turns out that Newtonian mechanics hold only at low speeds.
The knowledge brought by mathematics is even greater. In the famous science fiction novel ” Three-Body Problem”, the cutting-edge technology that mankind prides itself on is easily destroyed by alien technology. And what saved humanity was not guns and ammunition, but a theorem – ” Black Forest Theory”. This theory is known in reality as the Fermi paradox. This theory can be simplified as follows: any civilization that exposes its coordinates in the universe will be struck by a higher civilization. Such a law makes fictional alien beings afraid to attack Earth, outweighing countless weaponry. In this way, can we assume that mankind actually possesses very little knowledge and that only the power of mathematics and reason can help humans become more powerful.
Of course, I don’t think that natural science is useless. It can help mankind become more aware of the environment in which they live. But the knowledge that comes from mathematics and logic will be more general and can help humans explore more unknown areas and environments.
Works Cited
Armstrong, A. Hilary. “Platonism | Britannica.” Encyclopædia Britannica, 2020, www.britannica.com/topic/Platonism. Accessed 14 Oct. 2022.
Autor: Athanase Papadopoulos. Strasbourg Master Class on Geometry. Verlag: Zürich, Switzerland, European Mathematical Society, 2012, pp. 1–182.
Linnebo, Øystein. “Platonism in the Philosophy of Mathematics.” Stanford Encyclopedia of Philosophy, Metaphysics Research Lab, Stanford University, 2018, plato.stanford.edu/entries/platonism-mathematics/#WhaMatPla.
The Editors of Encyclopedia Britannica. “Fermat’s Last Theorem | Definition, Example, & Facts.” Encyclopædia Britannica, 9 Mar. 2017, www.britannica.com/science/Fermats-last-theorem.
Yasser, Shehab. “Aliens, the Fermi Paradox, and the Dark Forest Theory: A Game Theoretic View.” Medium, 21 Oct. 2020, towardsdatascience.com/aliens-the-fermi-paradox-and-the-dark-forest-theory-e288718a808. Accessed 14 Oct. 2022.
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