It's mostly the latter, that the *collection* of lemmas and theorems builds a scaffold (spatial metaphor) or takes the reader on a ride (time metaphor) from components to super-structure, from initial state to final state. Each brick/step in such composition is, *should be*, subject to doubt, as Jon argues. And, in practice, each brick/step is not only subject to doubt, but is also multivalent. A lemma in one argument may be a theorem in another argument. Ideally, mathematical reificationists will assert that the whole collection *must* hang together, for a True ride, or a perfectly solid foundation. And, my own personal view, is that math helps us *be* doubtful by honing disagreeing propositions into contradictions that we *want* (psychologically) to resolve ... It is the very (obsolete) definition of sophistry.
On 1/5/21 12:22 PM, Marcus Daniels wrote: > I'm not sure what you are getting at here. For concreteness, suppose the > books were Sage notebooks, and could export to Maxima or Mathematica. > Couldn’t one be reasonably confident in the correctness of the calculations > by reproducing them with two or more completely independent code bases, as > well as by inspection? Or maybe you mean the books are taking the reader > in some direction, where the reader mostly has to accept the story as one of > many possible stories. And by the time they are to the end of it, they are > committed to a way of thinking? -- ↙↙↙ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/
