Philosophia Mathematica 17 (1):95-108 (2008)
Published in 1891, Edmund Husserl's first book, Philosophie der Arithmetik, aimed to ‘prepare the scientific foundations for a future construction of that discipline’. His goals should seem reasonable to contemporary philosophers of mathematics: "…through patient investigation of details, to seek foundations, and to test noteworthy theories through painstaking criticism, separating the correct from the erroneous, in order, thus informed, to set in their place new ones which are, if possible, more adequately secured. 1"But the ensuing strategy for grounding mathematical knowledge sounds strange to the modern ear. For Husserl cast his work as a sequence of ‘psychological and logical investigations’, providing a psychological analysis "…of the concepts multiplicity, unity, and number, insofar as they are given to use authentically and not through indirect symbolizations. "This emphasis on psychology is a reflection of Husserl's training. As a teenager studying in Leipzig, he attended the lectures of Wilhelm Wundt, a seminal figure in the field of experimental psychology. Wundt held that, via introspection, we can study and classify our inner experiences, in much the same way that scientists study the natural world. 2 People working in his laboratory were therefore trained in procedures for observing and reporting on their own thought processes, as a means of gathering scientific data regarding our cognitive faculties. Bridging the gap between psychology and epistemology, Wundt felt that the results of such inquiry could have normative consequences, since the principles of reasoning employed in the sciences not only have their origins in psychological processes, but, moreover, are justified by the fundamental role they play in thought. His two-volume work, Logik , thus combined empirical considerations with a Kantian emphasis on the way that knowledge depends on our cognitive faculties. 3In The Philosophy of …
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
References found in this work BETA
Human Spatial Representation: Insights From Animals.Ranxiao Frances Wang & Elizabeth S. Spelke - 2002 - Trends in Cognitive Sciences 6 (9):376-382.
Nathaniel Miller. Euclid and His Twentieth Century Rivals: Diagrams in the Logic of Euclidean Geometry. Csli Studies in the Theory and Applications of Diagrams.John Mumma - 2007 - Philosophia Mathematica 16 (2):256-264.
Citations of this work BETA
A Formal System for Euclid's Elements.Jeremy Avigad, Edward Dean & John Mumma - 2009 - Review of Symbolic Logic 2 (4):700--768.
Similar books and articles
Review of M. Giaquinto, The Search for Certainty. [REVIEW]Carlo Cellucci - 2003 - European Journal of Philosophy 11:420-423.
Review of M. Giaquinto's Visual Thinking in Mathematics. [REVIEW]Andrew Arana - 2009 - Analysis 69 (2):401-403.
Hilbert's Philosophy of Mathematics.Marcus Giaquinto - 1983 - British Journal for the Philosophy of Science 34 (2):119-132.
The Search for Certainty: A Philosophical Account of Foundations of Mathematics.M. Giaquinto - 2002 - Oxford University Press.
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).
Visual Thinking in Mathematics • by Marcus Giaquinto.Andrew Arana - 2009 - Analysis 69 (2):401-403.
Visual Thinking in Mathematics: An Epistemological Study.M. Giaquinto - 2007 - Oxford University Press.
Added to index2009-02-07
Total downloads45 ( #114,214 of 2,158,795 )
Recent downloads (6 months)3 ( #132,835 of 2,158,795 )
How can I increase my downloads?