Cartesian causation: body–body interaction, motion, and eternal truths

There is considerable debate among scholars over whether Descartes allowed for genuine body–body interaction. I begin by considering Michael Della Rocca’s recent claim that Descartes accepted such interaction, and that his doctrine of the creation of the eternal truths indicates how this interaction could be acceptable to him. Though I agree that Descartes was inclined to accept real bodily causes of motion, I differ from Della Rocca in emphasizing that his ontology ultimately does not allow for them. This is not the end of the story however, since two of Descartes’s successors offered incompatible ways of developing his conflicted account of motion. I contrast the occasionalist view of Nicolas Malebranche that changes in motion derive directly from divine volitions with the non-occasionalist claim of Pierre-Sylvain Regis that such changes derive from a nature distinct from God. In light of Della Rocca’s interpretation, it is noteworthy that the issue of eternal truths is relevant to both alternative accounts. Indeed, Regis took the doctrine that such truths are created to provide crucial support for his alternative to an occasionalist account of body–body interaction. What does not help Della Rocca, however, is that Regis’s view of motion requires a fundamental revision of Descartes’s ontology.     

究竟谁是惯性定律的发现者

介绍了笛卡儿以前人们对惯性定律的认识,阐述了笛卡儿及其同时代人对惯性定律的贡献以及牛顿对这一问题的总结。     

Descartes’s changing mind

Descartes is always concerned about knowledge. However, the Galileo affair in 1633, the reactions to his Discourse on method, and later his need to reply to objections to his Meditations provoked crises in Descartes’s intellectual development the import of which has not been sufficiently recognized. These events are the major reasons why Descartes’s philosophical position concerning how we know and what we may know is radically different at the end of his life from what it was when he began. We call this later position Descartes’s epistemic stance and contrast it with his earlier methodological, metaphysical realism. Yet Descartes’s epistemic views cannot be separated from other aspects of his work, for example, his views concerning God, causality, metaphysics, and the nature of science. A further meta-implication is that serious errors await any scholar who cites early Cartesian texts in support of late Cartesian positions, or who uses later texts in conjunction with early ones to support a reading of Descartes’s philosophy.     

笛卡尔唯理论和理性主义美学探微

笛卡尔的唯理论开启了17世纪欧洲大陆理性主义的大门，其文艺主张吹响了新古典主义的号角。他的哲学观对感性经验表示了怀疑和否定，把理性作为认识真理、创作文艺的前提，这就为理性至上的理性主义美学奠定了理论基础。     

从图形“实体”到几何“存在”——对笛卡尔解析几何的哲学反思

笛卡尔的解析几何与欧几里得的《几何原本》在点、线和空间等基本概念上有较大差异。相对于《几何原本》:解析几何中的点可相互区分,且依赖于与其它点的关系而存在;曲线的存在依赖坐标空间整体,同时是点的运动轨迹,与物理运动的可能路径相关;坐标系通过量化空间,提供了对于空间的完整构造。从图形实体到几何存在,是笛卡尔对于数学实在和存在方式所作的区分。     

七、八次方程的笛卡儿做图

利用计算机首次给出了八次方程笛卡儿做图的一个案例，并据此对笛卡儿方程做图方法中代数的作用及其算法实质进行了分析。     

基于广义坐标形式的高斯最小拘束原理的多刚体系统动力学建模

通过采用动能及广义坐标显式的变分形式的高斯原理, 明确了广义坐标形式的高斯拘束中各项的含义, 以此建立以笛卡尔广义坐标表达的一般多刚体系统动力学问题的优化模型, 并研究利用上述模型列写其他坐标体系下的高斯拘束的方法。采用该方法可将多刚体系统的动力学问题变为求拘束极值的问题, 并且只要给出广义笛卡尔坐标与其他广义坐标之间的雅可比关系式, 便可方便地得到该坐标系统下的高斯拘束, 建模过程简单且具有更强的通用性。采用广义笛卡尔坐标及拉格朗日坐标, 对简单刚体的平面运动及定轴转动问题建立动力学优化模型, 并验证了该方法的有效性。     

一个笛卡尔乘积的Hausdorff维数

介绍了康托型集的几个,巨质,讨论一类笛卡尔乘积,在dim.E<1存在一个集合,,其维数满足dim<,H>(E×F)=dim<,H>E+dim<,H>F的情况.进而构造一类Borel集,使得dim<,H>(E×F)=dim<,H>E+dim<,H>F成立.     

试论笛卡尔的直观理论及其影响

笛卡尔是近代第一个比较完整地对“直观”进行定义的哲学家。他承接古希腊哲学传统，对直观理论进行了具有独特意义的阐释，并提出了一个靠直观建立科学认识体系的设想。笛卡尔的直观理论对后世产生了深远的影响，沿着他的这一思路．在西方出现了两条不同的发展路向：倾向于实证主义的直观认识论体系和倾向于人本主义的直观认识论体系。