To understand the purpose of Peirce’s lecture hall illustrations I think we need to consider how these sorts of expository examples come into being. Having crafted a few myself the technique is much like the Art of the Story Problem I remember from my days teaching math. We have a universe of discourse circumscribed by a particular subject matter, say linear algebra, plane geometry, the quadratic formula, or the like, and we have a set of methods that work well enough in that context to recommend their use to others. The methods themselves have been abstracted and formalized over the years, if not millennia, to the point of being detached from everyday life and potential practice, so we flesh them out with names and local habitations and narrative figures designed to tutor nature — or at least the students thereof.
The main thing we want from our stock examples and story problems is to show how it’s possible to bring a body of abstract ideas to bear on ordinary practical affairs. We are thus reversing to a degree the process by which a formalized subject matter is abstracted from a host of concrete situations, but only to a degree, as dredging up the mass of adventitious and conflicting details would be too distracting. Instead we stipulate a hypothetical state of affairs whose concrete structure falls under the class of ideal structures studied in our formal subject matter.
- Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
- This Blog • Survey of Pragmatic Semiotic Information
- My Notes • Information = Comprehension × Extension
- C.S. Peirce • Upon Logical Comprehension and Extension