The Tinctures and Implicit Quantification Over Worlds

Abstract
Jay Zeman one must keep a bright lookout for unintended and unexpected changes thereby brought about in the relations of different significant parts of the diagram to one another. Such operations upon diagrams, whether external or imaginary, take the place of the experiments upon real things that one performs in chemical and physical research. Chemists have ere now, I need not say, described experimentation as the putting of questions to Nature. Just so, experiments upon diagrams are questions put to the Nature of the relations concerned (4.530). 1 The diagrammatic nature of mathematical reasoning suggests that as my power to create diagrams increases, so too will my capacity for fruitful mathematical reasoning. Peirce's own work involved an unending series of experiments with different diagrammatic notations, all interesting, some difficult, some extremely fruitful. And the diagrammatic notations available are not only a function of some kind of “internal mental activity.” As Dewey has noted, “Breathing is an affair of the air as truly as of the lungs; digesting an affair of food as truly as of tissues of stomach” (Dewey, 15); so analogously is mathematical reasoning an affair of the diagrams available as truly as of the “mind” (which is then not limited to something inside the head, but includes the relevant diagrams, “external” as well as “internal”); so does mathematical reasoning have its “alembics and cucurbits” just as surely as does chemistry. In doing mathematical reasoning, we make of the diagrams “instruments of thought,” and advances in the technology of diagrams can directly affect our patterns of reasoning. I can imagine Peirce spending hours (and dollars) in a modern artists' supply store.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
Options
 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 Translate to english
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 10,747
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

No references found.

Citations of this work BETA

No citations found.

Similar books and articles
Jessica Carter (2010). Diagrams and Proofs in Analysis. International Studies in the Philosophy of Science 24 (1):1 – 14.
Analytics

Monthly downloads

Added to index

2010-12-22

Total downloads

4 ( #252,470 of 1,098,870 )

Recent downloads (6 months)

1 ( #286,682 of 1,098,870 )

How can I increase my downloads?

My notes
Sign in to use this feature


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