John Machin and Robert Simson on inverse-tangent series for π

Communicated by D. T. Whiteside     

Laws of nature and natural laws

The relationship between conceptions of law and conceptions of nature is a complex one, and proceeds on what appear to be two distinct fronts. On the one hand, we frequently talk of nature as being lawlike or as obeying laws. On the other hand there are schools of philosophy that seek to justify ethics generally, or legal theory specifically, in conceptions of nature. Questions about the historical origins and development of claims that nature is lawlike are generally treated as entirely distinct from the development of ethical natural law theories. By looking at the many intersections of law and nature in antiquity, this paper shows that such a sharp distinction is overly simplistic, and often relies crucially on the imposition of an artificial and anachronistic suppression of the role of gods or divinity in the worlds of ancient natural philosophy. Furthermore, by tightening up the terms of the debate, we see that the common claim that a conception of ‘laws of nature’ only emerges in the Scientific Revolution is built on a superficial reading of the ancient evidence.     

Leibniz on the laws of nature and the best deductive system

Many philosophers who do not analyze laws of nature as the axioms and theorems of the best deductive systems nevertheless believe that membership in those systems is evidence for being a law. This raises the question, “If the best systems analysis fails, what explains the fact that being a member of the best systems is evidence for being a law?” In this essay I answer this question on behalf of Leibniz. I argue that although Leibniz’s philosophy of laws is inconsistent with the best systems analysis, his philosophy of nature’s perfection enables him to explain why membership in the best systems is evidence for being a law of nature.     

John Hunter and his approach to pathology

Given the old conception of the relation greater than, the proposition that the whole is greater than the part is an immediate consequence. But being greater in this sense is not incompatible with being equal in the sense of one-one correspondence. Some who failed to recognize this formulated invalid arguments against the possibility of infinite quantities. Others who did realize that the relations of equal and greater when so defined are compatible, concluded that such relations are not appropriately taken as quantitative relations, at least, not in general. If suitable quantitative relations were to be defined, there was a possibility of retaining either the traditional definition of greater and finding another concept of equality, or of retaining the concept of equality as one-one correspondence and defining greater than so that it is incompatible with equality in this sense. The former alternative was implicitly taken by Bolzano, who never succeeded in defining suitable quantitative relations. The latter alternative was taken by Cantor, and is the basis of his great success in constructing a mathematical theory of the transfinite.     

Kant,causation and laws of nature

In the Second Analogy, Kant argues that every event has a cause. It remains disputed what this conclusion amounts to. Does Kant argue only for the Weak Causal Principle that every event has some cause, or for the Strong Causal Principle that every event is produced according to a universal causal law? Existing interpretations have assumed that, by Kant’s lights, there is a substantive difference between the two. I argue that this is false. Kant holds that the concept of cause contains the notion of lawful connection, so it is analytic that causes operate according to universal laws. He is explicit about this commitment, not least in his derivation of the Categorical Imperative in Groundwork III. Consequently, Kant’s move from causal rules to universal laws is much simpler than previously assumed. Given his commitments, establishing the Strong Causal Principle requires no more argument than establishing the Weak Causal Principle.     

Structuralism and the conformity of mathematics and nature

Structuralists typically appeal to some variant of the widely popular ‘mapping’ account of mathematical representation to suggest that mathematics is applied in modern science to represent the world’s physical structure. However, in this paper, I argue that this realist interpretation of the ‘mapping’ account presupposes that physical systems possess an ‘assumed structure’ that is at odds with modern physical theory. Through two detailed case studies concerning the use of the differential and variational calculus in modern dynamics, I show that the formal structure that we need to assume in order to apply the mapping account is inconsistent with the way in which mathematics is applied in modern physics. The problem is that a realist interpretation of the ‘mapping’ account imposes too severe of a constraint on the conformity that must exist between mathematics and nature in order for mathematics to represent the structure of a physical system.     

Some additional observations on the chemical nature of neutramycin

Zusammenfassung Für das Antibiotikum Neutramycin wird die Summenformel C₃₄H₅₄O₁₄ abgeleitet. Die Methanolyse lieferte die Methylglykoside der Chalcose und Mycinose.     

High angle X-ray diffraction and chemical studies on the nature of fibrous glia

Zusammenfassung Gliafasern wurden chemisch und röntgenographisch untersucht. Aminosäureanalyse und Ultraviolett-Absorption erlauben folgende Feststellungen: Die vonWilke undKircher angenommene Identität von Gliafasern und Fibrin kann nicht bestätigt werden; die Glia widersteht einer 0,1n NaOH Lösung bei 100°C, während Fibrin unter den gleichen Bedingungen rasch gelöst wird; ausserdem sind Glia und Fibrinogen hinsichtlich Aminosäurekomponenten und UV.-Absorption vollständig verschieden. Es bestehen dagegen interessante Ähnlichkeiten zwischen Glia und Keratinen: UV.-Absorption der Glia und des menschlichen Haarkeratins sind fast identisch. Gliafasern enthalten verschiedene Aminosäuren (Glutaminsäure, Asparaginsäure, Valin, Phenylalanin, Glycin) in ähnlichen Mengen wie die Keratine.Ferner finden sich im Gliagewebe Lipoide zu etwa 15% des Trockengewichtes. Die röntgenographische Untersuchung bestätigt die Gegenwart von Lipoiden und weist den Proteinen der Glia die-Konfiguration der k-e-m-f-Gruppe der faserigen Proteine zu. Gliafasern erleiden durch Streckung im Wasserdampf eine typische--Umwandlung.

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From the Institute of normal Anatomy, University of Milan, Italy (Director Prof.A. Bairati), and the Clinic for Occupational Diseases, University of Milan (Director Prof.E. C. Vigliani). The Siemens Kristalloflex III X-ray apparatus, which has been used in this research, is part of the equipment of the Industrial Hygiene Laboratory of the Montecatini Co., attached to the Clinic for Occupational Diseases.