Happy Birthday, Charles Sanders Peirce❢ — September 10, 1839

Re: Artem Kaznatcheev • Three Types of Mathematical Models

Comment 1

In talking of models we often find denizens of different disciplines talking at cross purposes to one another.  Logicians use the word to describe what we might call logical models, saying that a model is whatever satisfies a theory, anything that a theory holds true of, and this is the sense they use in the logical subject of model theory.  Almost everyone else uses the word to describe what we might call analogical models, analogues being things that share enough properties with other things that learning about Thing 2 (the analogue system) can teach us about Thing 1 (the object system).  It is actually not difficult to integrate the dual senses of the word model into a coherent picture of the whole situation, namely, the triadic relationship among objects, analogues, and theories.

Comment 2

I’m presently in the middle of some very tedious work and will have to keep my nose to the grindstone for fear of never working up the fortitude to face it again, so for now I’ll just link to some very rough notes and hope for a chance to give them a proper set-up later.  (Full disclosure — I view almost everything from a Peircean perspective.)

• Inquiry and Analogy
• Propositions As Types