Notes on measurement in biology is methodized by theory

I opened this article [@montevil:2019:measurement] by Montévil immediately after I received an e-mail notificaiton from ResearchGate, as from it’s title its a very important article in my categorical metrology project, and Montevil’s work with Longo on theoretical biology is important, even if I haven’t figured out how it fits yet.

He quotes Einstein:

whether you can observe a thing or not depends upon the theory which you use. It is the theory which decides what can be observed.

This is an ‘ideoscopic’ claim, to use Peirce’s terminology, in the sense that special observation requires some form of construction.

Aside: how are introduction and elimination rules in logic related to preparation and measurement rules in science? A Baez paper discussed the braket notation as preparation and observation. I believe that prepration proceeded from the unit and observation ‘collapsed’ to the unit. Paul Taylor had a nice dicussion in an online forum about how logical introduction and elimination rules could be interpreted as the natural transformations defining the unit and counit of an adjunction. (how would I re-find this discussion - it was on substitution)

In looking for Taylor’s article I looked at his paper “Towards a unitied treatment of induction” [@taylor:1996:towards]. He refers to category theory as ‘the diagrammatic tradition’ in contrast to the ‘symbolic tradition’. Taylor also states that Lawvere’s ambition was ‘to do set theory without elements’.