Download PDF by Karine Chemla, Renaud Chorlay, David Rabouin: The Oxford handbook of generality in mathematics and the

By Karine Chemla, Renaud Chorlay, David Rabouin

Generality is a key price in clinical discourses and practices. all through background, it has obtained numerous meanings and of makes use of. This number of unique essays goals to inquire into this variety. via case reviews taken from the heritage of arithmetic, physics and the existence sciences, the ebook offers proof of alternative methods of knowing the final in a variety of contexts. It goals at displaying how collectives have valued generality and the way they've got labored with particular sorts of "general" entities, strategies, and arguments.

The books connects heritage and philosophy of arithmetic and the sciences on the intersection of 2 of the main fruitful modern strains of study: old epistemology, during which values (e.g. "objectivity", "accuracy") are studied from a ancient point of view; and the philosophy of medical perform, within which conceptual advancements are obvious as embedded in networks of social, instrumental, and textual practices. every one bankruptcy offers a self-contained case-study, with a transparent exposition of the clinical content material at stake. the gathering covers quite a lot of medical domain names - with an emphasis on arithmetic - and ancient sessions. It therefore permits a comparative viewpoint which implies a non-linear development for a heritage of generality. The introductory bankruptcy spells out the foremost concerns and issues to the connections among the chapters.

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The third “epistemic configuration” Chorlay analyzes presents several features of wider relevance for our inquiry. In this context, the approach to the notion of function has been entirely renewed. However, in line with the systematic exploration of the conditions of validity of statements, a new feature in the practice of generality has appeared: the classification of functions into classes. Accordingly, the statement of a theorem makes clear for which class it can be asserted. ” Chorlay emphasizes how various types of mathematical means are put into play, and even shaped, to carry out this new task in a precise way.

The discovery of these genres and species becomes the purpose of the naturalist’s classificatory activities, now practiced in an upward way. The effort bears on identifying key features that enable the naturalist to recognize genres. Moreover, the system of names Linnaeus suggests is tightly related to this practice of grouping, since it aims to help practitioners situate genres and species as groups that present natural divisions with one another, as reflected in the terminology. Seen from a higher perspective, these names can be considered as symbolic tools shaped to facilitate the circulation within the system of general entities.

Moreover, these general objects are connected with each other in a scale of decreasing generality. ” However, the article gives a prominent role to linear operations. These are also general objects Banach considers in his PhD thesis. Further, even though most theorems about them are clearly motivated by the intention of solving functional equations, some theorems seem to indicate that Banach also considers them for their own sake. Perhaps, Jaëck suggests, in the 1922 article, one can detect some reflexivity vis-​à-​vis operations and thus the constitution of a general object of the second type.

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