Switch to: References

Citations of:

Philosophy of mathematics and deductive structure in Euclid's Elements

Mineola, N.Y.: Dover Publications (1981)

Add citations

You must login to add citations.

Completion, reduction and analysis: three proof-theoretic processes in aristotle’s prior analytics.George Boger - 1998 - History and Philosophy of Logic 19 (4):187-226.details Three distinctly different interpretations of Aristotle’s notion of a sullogismos in Prior Analytics can be traced: (1) a valid or invalid premise-conclusion argument (2) a single, logically true conditional proposition and (3) a cogent argumentation or deduction. Remarkably the three interpretations hold similar notions about the logical relationships among the sullogismoi. This is most apparent in their conflating three processes that Aristotle especially distinguishes: completion (A4-6)reduction(A7) and analysis (A45). Interpretive problems result from not sufficiently recognizing Aristotle’s remarkable degree of metalogical (...) Download Export citation Bookmark 7 citations
Why Euclid’s geometry brooked no doubt: J. H. Lambert on certainty and the existence of models.Katherine Dunlop - 2009 - Synthese 167 (1):33-65.details J. H. Lambert proved important results of what we now think of as non-Euclidean geometries, and gave examples of surfaces satisfying their theorems. I use his philosophical views to explain why he did not think the certainty of Euclidean geometry was threatened by the development of what we regard as alternatives to it. Lambert holds that theories other than Euclid's fall prey to skeptical doubt. So despite their satisfiability, for him these theories are not equal to Euclid's in justification. Contrary (...) Download Export citation Bookmark 7 citations
The mathematical form of measurement and the argument for Proposition I in Newton’s Principia.Katherine Dunlop - 2012 - Synthese 186 (1):191-229.details Newton characterizes the reasoning of Principia Mathematica as geometrical. He emulates classical geometry by displaying, in diagrams, the objects of his reasoning and comparisons between them. Examination of Newton’s unpublished texts shows that Newton conceives geometry as the science of measurement. On this view, all measurement ultimately involves the literal juxtaposition—the putting-together in space—of the item to be measured with a measure, whose dimensions serve as the standard of reference, so that all quantity is ultimately related to spatial extension. I (...) Download Export citation Bookmark 5 citations
Cognitive processing of spatial relations in Euclidean diagrams.Yacin Hamami, Milan N. A. van der Kuil, Ineke J. M. van der Ham & John Mumma - 2020 - Acta Psychologica 205:1--10.details The cognitive processing of spatial relations in Euclidean diagrams is central to the diagram-based geometric practice of Euclid's Elements. In this study, we investigate this processing through two dichotomies among spatial relations—metric vs topological and exact vs co-exact—introduced by Manders in his seminal epistemological analysis of Euclid's geometric practice. To this end, we carried out a two-part experiment where participants were asked to judge spatial relations in Euclidean diagrams in a visual half field task design. In the first part, we (...) Download Export citation Bookmark
From practical to pure geometry and back.Mario Bacelar Valente - 2020 - Revista Brasileira de História da Matemática 20 (39):13-33.details The purpose of this work is to address the relation existing between ancient Greek practical geometry and ancient Greek pure geometry. In the first part of the work, we will consider practical and pure geometry and how pure geometry can be seen, in some respects, as arising from an idealization of practical geometry. From an analysis of relevant extant texts, we will make explicit the idealizations at play in pure geometry in relation to practical geometry, some of which are basically (...) Download Export citation Bookmark

1
2