Results 1 
4 of
4
VISUALIZATION OF ORDINALS
, 2007
"... We describe the pictorial representations of infinite ordinals used in teaching set theory, and discuss a possible use in naturalistic foundations of mathematics. ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
We describe the pictorial representations of infinite ordinals used in teaching set theory, and discuss a possible use in naturalistic foundations of mathematics.
Loss of vision: How mathematics turned blind while it learned to see more clearly
 In B. Löwe and T. Müller (Eds.), Philosophy of Mathematics: Sociological Aspects and Mathematical Practice
, 2010
"... The aim of this paper is to provide a framework for the discussion of mathematical ontology that is rooted in actual mathematical practice, i.e., the way in which mathematicians have introduced and dealt with mathematical ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
The aim of this paper is to provide a framework for the discussion of mathematical ontology that is rooted in actual mathematical practice, i.e., the way in which mathematicians have introduced and dealt with mathematical
ORIGINAL ARTICLE Visualisation and proof: a brief survey of philosophical
, 2006
"... Abstract The contribution of visualisation to mathematics and to mathematics education raises a number of questions of an epistemological nature. This paper is a brief survey of the ways in which visualisation is discussed in the literature on the philosophy of mathematics. The survey is not exhau ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract The contribution of visualisation to mathematics and to mathematics education raises a number of questions of an epistemological nature. This paper is a brief survey of the ways in which visualisation is discussed in the literature on the philosophy of mathematics. The survey is not exhaustive, but pays special attention to the ways in which visualisation is thought to be useful to some aspects of mathematical proof, in particular the ones connected with explanation and justification. 1 Foreword It is a great honour to be asked to contribute to this special issue in memory of Hans Georg Steiner. He was a friend and mentor who had an enormous impact on the field of mathematics education, as acknowledged in the volume dedicated to him, Didactics of mathematics as a scientific discipline, which appeared in 1994 to mark both his 65th birthday and 20 years of work at the Institut für Didaktik der Mathematik (IDM) in Bielefeld. I had the great pleasure and privilege of meeting
Proofs, Pictures, and Euclid
, 2007
"... The prevailing conception of mathematical proof, or at least the conception which has been developed most thoroughly, is logical. A proof, accordingly, is a sequence of sentences. Each sentence is either an assumption of the proof, or is derived via sound inference rules from sentences preceding it. ..."
Abstract
 Add to MetaCart
(Show Context)
The prevailing conception of mathematical proof, or at least the conception which has been developed most thoroughly, is logical. A proof, accordingly, is a sequence of sentences. Each sentence is either an assumption of the proof, or is derived via sound inference rules from sentences preceding it. The sentence appearing at the end of the sequence is what has been proved. This conception has been enormously fruitful and illuminating. Yet its great success in giving a precise account of mathematical reasoning does not imply that all mathematical proofs are, in essence, a sequence of sentences. My aim in this paper is to consider data which do not sit comfortably with the standard logical conception: proofs in which pictures seem to be instrumental in establishing a result. I focus, in particular, on a famous collection of picture proofs—Euclid’s diagrammatic arguments in the early books of the Elements. The familiar sentential model of proof portrays inferences as transitions between sentences. And so, by the familiar model, Euclid’s diagrams would at best serve as a