走向自然哲学数学原理的必要变革
Towards a necessary change in the mathematical principles of natural philosophy
摘要：
数学是人类和物理学的自然语言，它必须不断适应我们的需要和我们的自然感知。因此，数学概念并不是绝对的。虽然数学理论是我们心灵的构造，并且在这样的理论中对象的存在是理论的一致性或连贯性的问题（这使我们能够独立于其他理论来研究它们），但在物理学中，数学结构是连贯的或一致的是不够的，这些结构必须与现实有更切实的联系。因此，任何数学模型在物理学中不一定是合适的。那么，物理学中的点的概念，这个用来代表现实对象的基本概念，有什么意义呢？如果我们考虑到，在一个好的现实模型中，一个具有物理参照物的数学对象的存在，必须等同于它的构造、感知和物理存在的验证的可能性，而对一个对象的不存在的反驳并不一定意味着有可能找到一个对其存在的检验。然后，人们会发现数学语言的结构变得更加丰富，点的概念被更直观和可感知的概念所取代。一方面，这可能使我们走向一个没有无穷大、没有悖论的物理学，另一方面，这也限制了数学和心理实验在物理学中的应用。
英文摘要：
Being mathematics a natural language to Mankind and to physics, it must be constantly adapted to our necessities and our natural perception. Then, mathematical concepts are not absolute to reality. Although mathematical theories are constructions of our mind, and the existence of objects in such theories is a matter of consistency or coherence of the theory (this allows us to study them independently of other theories), in physics its not enough that mathematical structures are coherent or consistent, these must have a much more tangible reference to reality. Therefore any mathematical model not necessarily is appropriate in physics. So, what sense has the concept of a point in physics, that elementary notion used to represent the objects of the reality. If we consider that in a good model of reality, the existence of a mathematical object with a physical reference must be equivalent to the possibility of its construction, perception and verification of physical existence, where the refutaction of the non-existence of an object does not necessarily mean that it is possible to find a test of its existence. Then, one obtains that the mathematical language becomes richer in structures, where the point concept is replaced by more intuitive and perceivable concepts. On the one hand, this possibly can lead us to a physics without infinites, and without paradoxes, on the other hand, one restricts the use of mathematics and the use of mental experiments in physics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
