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首页> 外文期刊>International journal of mathematics, game theory and algebra >THE ONTOLOGICAL CHARACTER OF MATHEMATICAL OBJECTS: DISPUTES AND DISCUSSIONS
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THE ONTOLOGICAL CHARACTER OF MATHEMATICAL OBJECTS: DISPUTES AND DISCUSSIONS

机译：数学对象的本体论特征：纠纷与讨论

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The history of science and philosophy goes hand in hand with the question of the nature of mathematical objects. By implication, this was already known by the Pythagoreans, even though it was not expressed in the plane of a directly named problem. The philosopher Plato addressed the themes of mathematics especially in the famous dialogues of Politeia (The Republic), Sophist, Parmenides and Epinomis. There is also much to do with mathematics in Aristotle's Metaphysics. Immanuel Kant revived the full question of the nature of mathematical objects. Neo-Kantians are of many minds about this, and their explanations differ in their results. The start of the twentieth century meant a discussion among intuitionism, formalism, logicism and constructivism. This situation made Kurt Goedel famous. Discussions between mathematicians, the Church and others did not clarify the issue. Such discussions ran up again with the philosophers Wittgenstein, Lakatos, Quine and others. Thus, differences between mathematical objects emerged: non-Euclidean geometry, real numbers, complex numbers. My study is an attempt to clarify the situation between the discussants and to offer my own explanation. I try to include important views on the issue and attempt to find arguments in some philosophers of mathematics. I have, for example, a particular discussion with the philosopher Ladislav Kvasz and rely on the findings of anthropologist Claude Levi-Strauss. I partially deal with the arguments of other philosophers, to a large extent with Ludwig Wittgenstein. My conclusion is that strict Platonism in mathematics is not possible, though in many cases, Platonism in mathematics can be considered. I think there are two kinds of mathematical objects. There are mathematical objects that have no support in pure mathematics, that are ontologically problematic. A typical example is complex numbers. In this case, it may be inclined to constructivism. I think that some mathematical entities can be explained as pure mathematical objects using Platonism, while other objects are the construction of man.
机译：科学与哲学的历史与数学对象的性质的问题携手共进。通过暗示，这已经是毕达哥兰人所知，即使它没有在直接命名问题的平面中表达。哲学家柏拉图讨论了数学的主题，特别是在同明亚（共和国），索菲斯特，帕尔梅尼德和胸腺的着名对话中。在亚里士多德的形而上学中也有很多事情。 Immanuel Kant恢复了数学对象性质的全部问题。 Neo-Kantians对此有很多思想，他们的解释在他们的结果中不同。二十世纪的开始意味着直觉，形式主义，帝理主义和建构主义之间的讨论。这种情况使Kurt Goedel有名。数学家，教会和其他人之间的讨论没有澄清这个问题。这种讨论再次与哲学家维特根斯坦，卢卡托斯，奎因等人遇到过。因此，出现了数学对象之间的差异：非欧几里德几何形状，实数，复数。我的研究是澄清讨论者之间的情况并提供自己的解释。我试图在一些问题上包含重要意见，并试图在数学哲学家中找到论据。例如，我拥有与哲学家Ladislav KVASZ的特定讨论，依靠人类学家Claude Levi-Strauss的调查结果。我部分地应对其他哲学家的论点，在很大程度上与Ludwig Wittgenstein在很大程度上。我的结论是，在数学中严格的柏拉米主义是不可能的，但在许多情况下，可以考虑数学中的柏拉米语。我认为有两种数学对象。有数学对象在纯数学中没有支持，即在本体学上存在问题。典型的例子是复数。在这种情况下，它可以倾向于建构主义。我认为一些数学实体可以用柏拉打主义作为纯数学对象来解释，而其他物体是人类的构造。

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