Diagrammatic Reasoning from Reflections on Peircean Semiotics

2019 ◽  
pp. 78-83
Author(s):  
Luis Alexander Castro Miguez
Keyword(s):  
Euclidean Geometry ◽  
Deductive Reasoning ◽  
Diagrammatic Reasoning ◽  
Learning And Teaching ◽  
Geometry Problem ◽  
Mathematical Diagrams ◽  
Geometric Diagram ◽  
Peircean Semiotics

The document illustrates some elements of reflection on Peirce's semiotics focused on reasoning through diagrams. The solution of a Euclidean geometry problem is taken as a reference in which mathematical diagrams are recognized as epistemological tools in the learning and teaching of geometry. This is how an interpreter, who systematically observes and experiments with a geometric diagram, generates different interpretants by means of abductive, inductive and deductive reasoning.

Charles Peirce and Bertrand Russell on Euclid

2020 ◽  
Vol 19 (37) ◽  
pp. 79-94
Author(s):  
Irving Anellis
Keyword(s):  
Deductive Reasoning ◽  
Charles Sanders Peirce ◽  
Diagrammatic Reasoning ◽  
Bertrand Russell ◽  
Mathematical Intuition ◽  
Existential Graphs ◽  
Charles Peirce ◽  
The Mind ◽  
Graphical System

Both Charles Sanders Peirce (1839–1914) and Bertrand Russell (1872–1970) held that Euclid’s proofs in geometry were fundamentally flawed, and based largely on mathematical intuition rather than on sound deductive reasoning. They differed, however, as to the role which diagramming played in Euclid’s emonstrations. Specifically, whereas Russell attributed the failures on Euclid’s proofs to his reasoning from diagrams, Peirce held that diagrammatic reasoning could be rendered as logically rigorous and formal. In 1906, in his manuscript “Phaneroscopy” of 1906, he described his existential graphs, his highly iconic, graphical system of logic, as a moving picture of thought, “rendering literally visible before one’s very eyes the operation of thinking in actu”, and as a “generalized diagram of the Mind” (Peirce 1906; 1933, 4.582). More generally, Peirce personally found it more natural for him to reason diagrammatically, rather than algebraically. Rather, his concern with Euclid’s demonstrations was with its absence of explicit explanations, based upon the laws of logic, of how to proceed from one line of the “proof” to the next. This is the aspect of his criticism of Euclid that he shared with Russell; that Euclid’s demonstrations drew from mathematical intuition, rather than from strict formal deduction.

scholarly journals Transitioning from “It Looks Like” to “It Has To Be” in Geometrical Workspaces: affect and near-to-me attention

2016 ◽  
Vol 30 (54) ◽  
pp. 142-164
Author(s):  
Melissa Rodd
Keyword(s):  
Mathematics Education ◽  
Euclidean Geometry ◽  
Teaching Practice ◽  
Deductive Reasoning ◽  
Practitioner Research ◽  
Research Perspective ◽  
Individual Interviews ◽  
Sense Data ◽  
Education Theory ◽  
Learner’S Perspective

Abstract Within a practitioner researcher framework, this paper draws on a particular mathematics education theory and aspects of neuroscience to show that, from a learner’s perspective, moving to a deductive reasoning style appropriate to basic Euclidean geometry, can be facilitated, or impeded, by emotion and/or directed attention. This shows that the issue of a person’s deductive reasoning is not a merely cognitive one, but can involve affective aspects related to perception – particularly perception of nearby sense data – and emotion. The mathematics education theory that has been used is that of the Espace de Travail Mathématique, the English translation of which is known as Mathematical Working Spaces (MWS). The aspects of neuroscience that have been used pertain to the distinct processing streams known as top-down and bottom-up attention. The practitioner research perspective is aligned with Mason’s teaching-practice-based ‘noticing’; qualitative data analysed in this report include individual interviews with school teachers on in-service courses and reflective notes from teaching. Basic Euclidean geometry is used as the medium for investigating transition from ‘it looks like’ to a reasoned ‘it has to be’.

scholarly journals DESARROLLO DEL RAZONAMIENTO DEDUCTIVO A TRAVÉS DE LA GEOMETRÍA EUCLIDIANA

1999 ◽  
Author(s):  
Leonor Camargo Uribe ◽  
Carmen Samper de Caicedo
Keyword(s):  
Euclidean Geometry ◽  
Deductive Reasoning ◽  
Project Development ◽  
Initial Stage

An approximation to the framework of the investigation project «Development of deductivereasoning through Euclidean Geometry» is presented. The project is in an initial stage andthe ultimate goal is to validate a didactical model for the Iearning of Euclidean Geometrywhich emphasizes the development of deductive reasoning.

If Deductive Reasoning Develops, Then …

1991 ◽  
Vol 36 (12) ◽  
pp. 1071-1072
Author(s):  
Kathleen M. Cauley
Keyword(s):  
Deductive Reasoning
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