phil/math vs. the textbooks

One point of comparison is that we include dialectical definitions (the term isn't so important right now) in a number of related senses: 

1. We say what things are in part through saying what they are not.
2. We are interested in the genesis (problematical, not strictly historical) of concepts.
3. We present concepts as responses to simpler, failed, attempts to articulate what we’re trying to think of. 
4. We frequently start by stating equivalences of definitions before working with any single definition in detail. 
5. We view overviews and anticipations, i.e., movement back and forth between local and global views, as essential, not an interruption.

Textbook writers (with many honorable exceptions) tend to shun these as introducing too much subjectivity. But we know a priori that a full positive discourse of knowledge does not exist, and that the subjective, the plural, and the negative are deeply linked here. (The concept of dialectic takes the stage again if one wants to pursue this.)

A great practice by someone at St. Andrews: including ‘Obvious method’ and ‘Difficulty’ as headers on a level with ‘Definition’ and ‘Example’!  

_{Last modified: September 24, 2022 .}