It’s similar in my perspective to a nuance that exists pervasively today within scientific models. Just because the model allows a prediction doesn’t mean that the model reflects “base reality.”
Our models, our tools, are the results of our observations. If it works to provide a prediction, then it becomes useful. However I feel there’s a disconnect as the nuance of a model vs what is, has been lost among many.
The map is not the territory.
It’s very interesting to see science use mathematical models as objective reality and orthodoxy. I’d say that isn’t science, but words change in meaning with the zeitgeist. Unfortunate in many ways.
I like the way you framed the argument.
Any recent things you’ve read in this realm of subjects that were interesting to you? Any favorite past time papers/books you’d recommend?
I certainly have a lot of recommendations that are topic adjacent, but most of my comment comes from mental revision. I have a horrible habit of reliving previous arguments and trying to find out what I could have said better to win the argument. I had an argument with a law school classmate who had a Masters in Mathematics (now a PhD) while we were on a road trip from Paris to Normandy, during summer abroad, and then ‘invented/discovered’ nature of mathematics was the real crux of the argument. I have spend the last 12 years going over and over and over that argument trying to win it and my comment is a result of that. So my recommendations are not going to be super on point, except to say that the Stanford Encyclopedia of Philosophy entry on the ‘The Philosophy of Mathematics’ [1] and the large list of citations are great, particularly the ones from the sections on Formalism and Fictionalism (but these are not the most interesting reads if you’re not digging for a mic drop quote for your imaginary debate).
For some topic adjacent past time papers, a lot of my comments concerning logic come from the research for my programming language, so I have been immersed in logic and proof theory work for the last six months pretty hard. I think any of the course note PDFs from Frank Pfenning (CS prof at Carnegie Mellon Univ.) are great read in general (and are easily found by googling Pfenning logic course notes and just looking around). If you like video lectures, or just listening to them, any of Pfenning’s lecture sets from the OPLSS session, which are all on YouTube are wonderful, particularly the 5 lectures from 2017 on Substructural Type Systems and Concurrent Programming [2] Also, Noam Zeilberger’s OPLSS lectures on Refinement Types [3] are great and his dissertation was a great read [4]. Finally, Neel Krishnaswami and Dunfield‘s 2 papers on Higher Rank Bidirectional Type Checking [5] was really good (and like all the above the cite lists are a trove of good stuff).
I literally could keep going for hours on great reads in logics and type theory, so if you want more in some area I’ll provide.
It’s similar in my perspective to a nuance that exists pervasively today within scientific models. Just because the model allows a prediction doesn’t mean that the model reflects “base reality.”
Our models, our tools, are the results of our observations. If it works to provide a prediction, then it becomes useful. However I feel there’s a disconnect as the nuance of a model vs what is, has been lost among many.
The map is not the territory.
It’s very interesting to see science use mathematical models as objective reality and orthodoxy. I’d say that isn’t science, but words change in meaning with the zeitgeist. Unfortunate in many ways.
I like the way you framed the argument.
Any recent things you’ve read in this realm of subjects that were interesting to you? Any favorite past time papers/books you’d recommend?