Marcus Giaquinto. Visual thinking in mathematics: An epistemological study

Philosophia Mathematica 17 (1):95-108 (2009)
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)
DOI 10.1093/philmat/nkn033
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 16,667
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

35 ( #93,308 of 1,726,249 )

Recent downloads (6 months)

1 ( #369,877 of 1,726,249 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.