他写的逻辑，数学哲学著作和语言。
He wrote philosophical works about logic, mathematics, and language.
在数学哲学中，认为数学是从逻辑推导出来的一种论点。
In the philosophy of mathematics, the thesis that all mathematical propositions are expressible as or derivable from the propositions of pure logic.
数学哲学观解决“什么是数学”的问题，是数学教学理论的基础。
The views of mathematics philosophy are the base of the mathematics teaching theories.
“数学观”是指人们对数学的总的根本的看法，属于数学哲学的范畴。
The conception of mathematics is defined as how to think about mathematics in all. It belongs to philosophy of mathematics.
数学哲学、数学史与数学教学有机结合，已成为当今世界数学教育的热点问题。
The organic synthesis of mathematical philosophy, mathematical history and mathematical teaching has become a hot topic of mathematical education.
数学哲学、数学史与数学教学有机结合，已成为当今世界数学教学的热点问题。
The combination of mathematics philosophy and mathematics history with mathematics teaching has become a hot topic of mathematics teaching in the world.
大多数学科有自己的哲学，举例来说，科学哲学、数学哲学、逻辑哲学、法律哲学和历史哲学。
Most academic subjects have a philosophy, for example the philosophy of science, the philosophy of mathematics, the philosophy of logic, the philosophy of law, and the philosophy of history.
从数学哲学、数学教育学、心理学等多重视角深入探讨、分析、研究数学教学模式的理论基础。
Discuss, analysis and research the theoretic basis of the mathematics teaching models from the viewpoints of mathematics philosophy, mathematics education and psychology.
这一个问题，若是换做康德来问，则可能会变成：「（由哲学家主导的）数学哲学是如何可能的?。
An important problem arises from the subjects itself: How can I —— of anyone who is not a mathematician —— talk about this? What right has a philosopher to talk about mathematics?
每一门教育科目都由学校系统地开设，例如语文、数学、科学和哲学。
Every subject of education in school is systematic, such as Chinese, mathematics, science and philosophy.
其次，学校的每一门教育科目都是系统的，如语文、数学、科学和哲学。
Secondly, every subject of education in school is systematic, such as Chinese, mathematics, science and philosophy.
视觉化对象并归纳数学规律的能力这样的问题连一些最优秀的诗人和哲学家都无法解答，又如何能让一个人找到那些问题的答案呢？这一点并不明朗。
It's not obvious how the capacity to visualize objects and to figure out numerical patterns suits one to answer questions that have eluded some of the best poets and philosophers.
人类的自由意志似乎是最难以处理的哲学课题，远非数学证明所能表达。
Human free will might seem like the squishiest of philosophical subjects, way beyond the realm of mathematical demonstration.
世界也不是最后的定论，你们记住，哲学问题不像数学问题，因此没有答案。
The world is not the last word. You remember, it's not like a mathematical problem so there's no solution.
乔查尼先生穿着像个流浪汉，然而却是个深解人类多种领域学问的大师，包括科学，数学，哲学，特别是犹太法典《塔木德》他都擅长。
Chouchani dressed like a vagabond but was a master of vast areas of human knowledge, including science, mathematics, philosophy and especially the Talmud.
这些哲学和数学问题成了我们的困惑。
These problems of philosophy and mathematics are personal riddles also; was it always just like this, and did we fail to notice?
当其他方法——数学证明、档案研究、哲学推理——更切合时，科学精神就推崇那一方法。
Where other methods - mathematical proof, archival research, philosophical reasoning - are more relevant it calls for them instead.
1713年牛顿在进一步阐发其经典代表作“自然哲学的数学原理”的证据与推理过程的注释里写道。
In the General Scholium (from the 1713 edition) of his masterpiece Mathematical Principles of Natural Philosophy (1686), Newton writes.
高德的不完备定理更像是一组非常有趣的关于逻辑和哲学的数学定理，而不是严格意义上的科学。但是整体上，这些逻辑和哲学与科学密切相关。
It is not strictly science, but rather a very interesting set of mathematical theorems about logic and the philosophy that is definitely relevant to science as a whole.
这一领域的先驱中最早的是希腊数学家和哲学家克劳迪•托勒密(约公元90年～168年)，历史上多称他托勒密。
At the forefront of the pioneers in the field was the Greek mathematician and philosopher Claudius Ptolemaeus (c. AD 90 ?168), more popularly known to history as Ptolemy.
牛顿的研究成果在1687年首次出版的《自然哲学的数学原理》一书中发表。 在这本书里牛顿对以前科学家所关心的大部分力学难题做出了解答。
The outcome was the famous "Principia Mathematica", first published in 1687, in which Newton presented solutions to most of the problems of motion that had concerned earlier scientists.
另一个哲学家，笛卡尔在思考上帝万能的时候觉得，如果万能的上帝无法改变数学，那么便不能称为万能。
And another philosopher, Descartes, in thinking about God's omnipotence, thought that it wouldn't be good enough if God as omnipotent couldn't change the facts of mathematics.
他建议，比如将孩子们集合到一个团队中就某一问题展开辩论，可以让他们更轻松地掌握数学或哲学中的抽象问题。
He suggests, for example, that children may have an easier time learning abstract topics in mathematics or physics if they are put into a group and allowed to reason through a problem together.
当时狄拉克的同行们正在为他们的公式的哲学内涵争论不休，而他认为语言是靠不住的，在理论物理上数学有着绝对的优势。
But while his colleagues struggled with the philosophical implications of their equations, Dirac thought words were treacherous and saw merit only in mathematics.
笛卡尔除了是哲学家之外也是一位杰出的数学家，对于还记得这点的人来说以上这种偏见应该并不让人惊讶。
This bias shouldn't surprise those who remember that Descartes was a brilliant mathematician in addition to being a philosopher.
艾萨克·牛顿爵士是英国物理学家，数学家，天文学家，自然哲学家，炼金术师以及神学家。
Sir Isaac Newton was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian.
这些专业包括数学、物理、哲学和语言学。
These majors include mathematics, physics, philosophy and linguistics.
这些专业包括数学、物理、哲学和语言学。
These majors include mathematics, physics, philosophy and linguistics.
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