Theoretical construction in physics – The role of Leibniz for Weyl's ‘Philosophie der Mathematik und Naturwissenschaft’

This paper aims at closing a gap in recent Weyl research by investigating the role played by Leibniz for the development and consolidation of Weyl's notion of theoretical (symbolic) construction. For Weyl, just as for Leibniz, mathematics was not simply an accompanying tool when doing physics—for him it meant the ability to engage in well-guided speculations about a general framework of reality and experience. The paper first introduces some of the background of Weyl's notion of theoretical construction and then discusses particular Leibnizian inheritances in Weyl's ‘Philosophie der Mathematik und Naturwissenschaft’, such as the general appreciation of the principles of sufficient reason and of continuity. Afterwards the paper focuses on three themes: first, Leibniz's primary quality phenomenalism, which according to Weyl marked the decisive step in realizing that physical qualities are never apprehended directly; second, the conceptual relation between continuity and freedom; and third, Leibniz's notion of ‘expression’, which allows for a certain type of (surrogative) reasoning by structural analogy and which gave rise to Weyl's optimism regarding the scope of theoretical construction.     

On the origins and foundations of Laplacian determinism

In this paper I examine the foundations of Laplace’s famous statement of determinism in 1814, and argue that rather than derived from his mechanics, this statement is based on general philosophical principles, namely the principle of sufficient reason and the law of continuity. It is usually supposed that Laplace’s statement is based on the fact that each system in classical mechanics has an equation of motion which has a unique solution. But Laplace never proved this result, and in fact he could not have proven it, since it depends on a theorem about uniqueness of solutions to differential equations that was only developed later on. I show that the idea that is at the basis of Laplace’s determinism was in fact widespread in enlightenment France, and is ultimately based on a re-interpretation of Leibnizian metaphysics, specifically the principle of sufficient reason and the law of continuity. Since the law of continuity also lies at the basis of the application of differential calculus in physics, one can say that Laplace’s determinism and the idea that systems in physics can be described by differential equations with unique solutions have a common foundation.     

Leibniz代数的导子扩张

通过给出强双导子的概念,证明强双导子可以给出Leibniz代数的导子扩张,并给出构造Leibniz代数的一种新方法.     

李代数的张量积所确定的Leibniz代数

讨论了李代数(g)以及由这个李代数诱导的Leibniz代数(g)(×)(g)的一些性质,主要从不变双线性型和导子看这两个代数之间的差异,证明了在特定条件下两者的不变双线性型维数是一致的.为进一步确定李代数(g)和(g)(×)(g)的差异,讨论了由(g)(×)(g)诱导的一类重要的李代数(g)(×)(g);最后证明了,如...     

函数的Jackson导数简介

介绍了Jackson导数的相关概念及其性质。     

The concept of transition and its role in Leibniz’s and Whitehead’s metaphysics of motion

Leibniz’s and Whitehead’s analyses of motion are at the heart of their metaphysical schemes. These schemes are to be considered as two blueprints of a similar metaphysical intuition that emerged during two breakthrough eras, that is, the 17th century and the beginning of the 20th century, and retained the Aristotelian idea that existence requires an active principle. The two philosophers’ attempts to elucidate this idea in the context of their analyses of motion still interact with central, longstanding questions in philosophy, in particular that concerning the ontological status of change. For both thinkers, the phenomenon of motion is an example par excellence, of the metaphysically fundamental principle of action that is required for change in the world. I focus on Leibniz’s and Whitehead’s similar understanding of the concept of transition that is inserted as an essential constitutive component of motion and ensures its status as something real.     

莱布尼茨与微积分发明权之争——纪念莱布尼茨诞生360周年

莱布尼茨是卓越的数学家和哲学家，他和牛顿相互独立地创建了微积分。17世纪末，在欧洲爆发了一场激烈的旷日持久的微积分发明权之争。通过争论和调查，人们公认：莱布尼茨和牛顿都是微积分的发明人，他们的微积分各有特色。     

莱布尼茨单子论与建设性后现代主义

莱布尼茨单子有机论和建设性后现代主义的整体有机论,都是在批判机械论的基础上创立的,并试图以之来超越机械论,二者之间有着明显的联系。通过对单子哲学进行深入解读,则会发现诸多建设性后现代主义的思想特征;而对建设性后现代主义进行历史追溯,就会发现单子哲学是后现代整体有机论的重要思想之源。对单子有机论和后现代整体有机论进行比较研究,对于全面理解和阐发它们的深层内涵具有重要现实意义。     

Explaining Leibniz equivalence as difference of non-inertial appearances: Dis-solution of the Hole Argument and physical individuation of point-events

“The last remnant of physical objectivity of space–time” is disclosed in the case of a continuous family of spatially non-compact models of general relativity (GR). The physical individuation of point-events is furnished by the autonomous degrees of freedom of the gravitational field (viz., the Dirac observables) which represent—as it were—the ontic part of the metric field. The physical role of the epistemic part (viz. the gauge variables) is likewise clarified as embodying the unavoidable non-inertial aspects of GR. At the end the philosophical import of the Hole Argument is substantially weakened and in fact the Argument itself dissolved, while a specific four-dimensional holistic and structuralist view of space–time (called point-structuralism) emerges, including elements common to the tradition of both substantivalism and relationism. The observables of our models undergo real temporal change: this gives new evidence to the fact that statements like the frozen-time character of evolution, as other ontological claims about GR, are model dependent.     

Spinoza on the resistance of bodies

Commentators often claim that the bodies of Spinoza’s physics resist the changes they undergo. But it’s not always clear what they mean when they say this, or whether they are entitled to say it. This article clarifies what it might mean to for Spinoza’s bodies to resist change, and examines the evidence for such a view. In the first half, the author argues that there is some limited evidence for such a view, but not nearly as much as people think. In the second half, the author proposes looking for a mental analogue to collision in the realm of ideas and argues that adequacy amounts to a meaningful concept of resistance in Spinoza, albeit one that is incomplete.