Analysis 69 (2):401-403 (2009)
Our visual experience seems to suggest that no continuous curve can cover every point of the unit square, yet in the late 19th century Giuseppe Peano proved that such a curve exists. Examples like this, particularly in analysis received much attention in the 19th century. They helped to instigate what Hans Hahn called a ‘crisis of intuition’, wherein visual reasoning in mathematics came to be thought to be epistemically problematic. Hahn described this ‘crisis’ as follows : " Mathematicians had for a long time made use of supposedly geometric evidence as a means of proof in much too naive and much too uncritical a way, till the unclarities and mistakes that arose as a result forced a turnabout. Geometrical intuition was now declared to be inadmissible as a means of proof … "Avoiding geometrical evidence, Hahn continued, mathematicians aware of this crisis pursued what he called ‘logicization’, ‘when the discipline requires nothing but purely logical fundamental concepts and propositions for its development’. On this view, an epistemically ideal mathematics would minimize, or avoid altogether, appeals …
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Hilbert's Philosophy of Mathematics.Marcus Giaquinto - 1983 - British Journal for the Philosophy of Science 34 (2):119-132.
Review of M. Giaquinto's Visual Thinking in Mathematics. [REVIEW]Andrew Arana - 2009 - Analysis 69 (2):401-403.
Visual Thinking in Mathematics: An Epistemological Study.M. Giaquinto - 2007 - Oxford University Press.
Marcus Giaquinto. Visual Thinking in Mathematics: An Epistemological Study. [REVIEW]Jeremy Avigad - 2008 - Philosophia Mathematica 17 (1):95-108.
Epistemology of Visual Thinking in Elementary Real Analysis.Marcus Giaquinto - 1994 - British Journal for the Philosophy of Science 45 (3):789-813.
Review of Marcus Giaquinto, Visual Thinking in Mathematics: An Epistemological Study. [REVIEW]Sun-Joo Shin - 2008 - Notre Dame Philosophical Reviews 2008 (7).
The Search for Certainty: A Philosophical Account of Foundations of Mathematics.M. Giaquinto - 2002 - Oxford University Press.
Review of M. Giaquinto, The Search for Certainty. [REVIEW]Carlo Cellucci - 2003 - European Journal of Philosophy 11:420-423.
Added to index2009-04-11
Total downloads122 ( #38,404 of 2,152,648 )
Recent downloads (6 months)8 ( #90,244 of 2,152,648 )
How can I increase my downloads?