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

Re: Artem Kaznatcheev • Three Types of Mathematical Models

Comment 1

In speaking of models one tends to find denizens of different disciplines talking at cross purposes to one another.  Logicians use the word to describe what may be distinguished as logical models, saying a model is whatever satisfies a theory, anything a theory holds true of, and this is the sense used in the logical subject of model theory.  Almost everyone else uses the word to describe what may be called analogical models, analogues being things holding enough properties in common with other things that learning about Thing 2 (the analogue system) can teach us about Thing 1 (the object system).  It is actually quite easy to integrate these 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.)

• Functional Logic • Inquiry and Analogy
• Propositions As Types Analogy