数学真理

数学真理是相对真理&从第二次数学危机谈起

Mathematical truth is a relative truth & Talking from second mathematics crisis

数学真理困境的自然主义实在论求解

The Naturalistic Realist Solution to the Dilemma of Mathematical Truth

美国当代著名哲学家H·普特南作为科学实在论的主要代表人物之一，其数学真理观对整个数学真理性问题的研究产生了重大的影响，对数学科学的发展具有积极的推动作用。

As one of the exponents of scientific realism Hilary Putnam , a contemporary American famous philosopher , positively influences the research of the problem arising from the whole state of mathematical truth and has put the mathematical science forward with his view of mathematical truth .

形式化与非形式化都是获得数学真理的有效手段。

Both formalization and non-formalization are effective means of acquiring mathematic truth .

数学真理是一个具有不同层次性和等级结构的开放体系；

Mathematic truth is an open system with different levels and frameworks .

论数学真理观的后现代转向

The Postmodern Turn of the View on Mathematic Truth

数学真理的发展及其对自然观演变的启示

The Development of Mathematical Truth and Its Influence on the Evolvement of Worldview of Nature

数学真理的层次理论

The stratified Theory on mathematical Truth

数学真理的再思考

Second Thought on Mathematics Truth

数学真理性的哲学分析

Philosophical Analysis of Mathematical Truth

文中指出根据唯物辩证法中关于一切真理都是相对真理的观点，数学真理当然也是相对真理。

A view was pointed ont in the paper that all truth is relative truth according to materialist dialectic .

数学真理归根结底来自实践，并受实践检验。

In the final analysis , mathematical truth is drawn from practice , as well as examined in practice .

数学真理超越了自然真理的范畴，开始生长出一种新维度&可选择性；

It has transcended the scope of natural truth and has generated a new dimension , i. e. , selectivity .

但最真实的莫过于数学真理，因此当我看到数学盲经理人们无耻地盗用数学真理，渴望为一些无聊的废话披上真理的外衣时，我就会感到心烦意乱。

Truest of all are mathematical truths , and it is therefore upsetting to see them being pilfered shamelessly by innumerate managers eager to lend an aura of fact to what is usually a glob of guff .

表现出特别鲜明的确定性和不确定性.数学理论真理性的检验过程即是数学的应用过程，这一过程通常是间接检验过程，并表现出极度的复杂性。

The process to test the truth of a mathematical theory is a process to apply mathematics to other science .

在逻辑学和数学说，真理是指不容置疑、理所当然的事物。

In logic and math , an axiom is something unquestionable or taken for granted .

片中人们居住的飞船叫做“真理”。在逻辑学和数学说，真理是指不容置疑、理所当然的事物。

The name of the ship that the humans are living on is " Axiom . " In logic and math , an axiom is something unquestionable or taken for granted .

数学并不是绝对真理的单一整体结构。

Mathematics is not a single monolithic structure of absolute truth .

现在我们又陷入规模更大的危机，以至于数学确定性重新受到怀疑，数学真理的真面目究竟是怎样的？

We fall into a crisis again , the certainty of mathematics fall under suspicion again , the author tried to give the truth of mathematics .

特别是20世纪以来诞生的各种数学新理论，正在逐步地改变着数学真理的传统观念。

Especially from the beginning of 20 ~ ( th ) century , the development of various new mathematical theories have been changing traditional notion of mathematical truth step by step .

19世纪以来，数学的发展逐渐形成瓦解神性化形而上学数学真理的知识力量，一场深刻持久的数学真理观念变革拉开了序幕。

Since 19 century , there has been accumulated knowledge that breaks up divine metaphysics gradually in mathematics development . Profound and persistent progress has taken place in the notion about mathematical truth .

回顾数学发展的历史，对数学的本体论、数学的本质及数学理论的真理性等三个基本问题进行了哲学分析。

His paper looks back to the history of mathematics development , and analyses philosophically three basis questions : the ontology of mathematics , the essence of mathematics and the truth character of mathematical theories .

本文结合计算数学这门学科论述了数学实验兴起的由来，数学实验方法的本质及特点，数学实验与真理问题。

At first , this paper expounds in co-ordination with computation mathematics the reasons for the flourish of mathematics experiment , the nature and character of mathematics experiment methods . At last , the relations between mathematics experiment and truth problem are explained .

对于一个数学实在论者来说，一个特别急迫的任务是回答数学证明是如何建立起关于数学对象的真理性问题。

For mathematical realists an especially pressing question is that of how a proof can establish a conclusion about mathematical objects .