Software and Math
Ari4 thoughts on software:
Software is best seen as a service, not as a product.
Open source is better, all else being equal.
Reasonable profits are good.
Complexity is an enemy.
A spreadsheet is often a database table lacking a primary key.
It is best to keep data processing close to the data.
Correlation does not imply causation.
Isomorphism does not imply computability.
If the goals above keep conflicting, take a break!
Freyd, Kechris, Scedrov, Vaananen and others on categories, computability, logic, and model theory. Noted 15 March 2019.
https://philpapers.org/rec/LINLII
https://www.sciencedirect.com/science/article/pii/0168007286900461
www.math.caltech.edu/~kechris/papers/Structurable%20FM%20version.pdf
http://www.math.caltech.edu/~kechris/papers/lectures%20on%20CBER01.pdf
www.math.mcgill.ca/bunge/ctatmcgill.html
http://www.math.mcgill.ca/rags/seminar
www.math.mcgill.ca/barr/papers/ctcs.pdf
https://en.wikipedia.org/wiki/Jouko_Väänänen
https://philpapers.org/rec/VNNSOL
https://philpapers.org/rec/MAGOLN
Category Theory.
Constructive category theory summary, noted 8/19.
Reflection principles in the category of sets are equivalent to induction over well-ordered sets. (9/19)
Topos theory, 8/19.
Broad category theoretic study of history and recent results in computability theory. Section 3 includes equivalence classes of proofs; 3.8 introduces topoi, exploring relationships between them and formal languages. Freyd gluing techniques are introduced in 4.4. Classical type theory and non-standard type theory may require consideration in separate categories. (1/20)
Zorn's Lemma helps show connections between model theory, proof theory and programming. Intuitionistic and constructivist contributions are noted.
Other items of current interest.
Benford's Law (2019)
Probability Logic, a recent effort. (2019)
https://arxiv.org/ftp/arxiv/papers/1910/1910.06624.pdf
Algorithms for Beauty?
https://arxiv.org/pdf/1910.06088.pdf
Logic: interesting and useful recent completeness results. IMO K is a pretty strong assumption in a constructivist framework. The proofs themselves rely extensively on non-constructive elementary logic. Some things just never get old! (2019)
https://arxiv.org/pdf/1910.01697.pdf
https://arxiv.org/pdf/1910.00907.pdf
Amazing game-theoretic approach to welfare distribution. It helps illuminate several problems with socialism: the large economy is usually not decomposable into tractable sub-economies. Envy-free solutions in general contradict full decomposability. Adverse selection (IMO in Joseph Stiglitz’ sense) is still an issue. (2019)
https://arxiv.org/pdf/1909.11346.pdf
Envy: I would suggest that we cannot defeat it by using the closed preference sets assumption. In economics this would imply that every situation of resource consumption is zero-sum. Also, as at the end of this paper, the importance of individual leadership is minimized. (1/20)
https://arxiv.org/pdf/2001.03327.pdf
God as Ultrafilter? LOL! I can't help remembering Elizabeth Anscombe echoing Kant about the existence of God: ‘That is not the sort of thing you prove!’ I like to imagine her debating St. Anselm of Canterbury and St. Thomas Aquinas about this. With Karl Barth and Kurt Goedel in the audience taking copious notes? At any rate, this remarkable paper shows interesting and helpful results about reducibility of modal logic and reasoning to first order calculus. (12/19)
https://arxiv.org/pdf/1910.08955.pdf
Structure Theory: recent results in 2019.
https://arxiv.org/pdf/1910.10811.pdf
Recent results on orthostatic intolerance (med x stat). (2019)
https://arxiv.org/ftp/arxiv/papers/1910/1910.10332.pdf
Intuitionistic math: good summary and recent results. Also a constructivist re-presentation of work of Brouwer, Skolem and Lowenheim. (2019)
https://arxiv.org/pdf/1911.09477.pdf
Intuitionistic logic: more history. Although it may have a dubious metaphysical pedigree, it seems to help enforce very conservative procedures for managing computer memory.
https://plato.stanford.edu/entries/intuitionistic-logic-development
https://projecteuclid.org/download/pdf_1/euclid.ndjfl/1093958744
For engineering, interesting categories have morphisms and objects whose costs can be minimized.
Peter P. Chen
https://bit.csc.lsu.edu/~chen/chen.html
https://resources.sei.cmu.edu/library/author.cfm?authorID=4803
Cybersecurity Maturity Model Certification
Data Model as an Architectural View.
References and free eBooks:
Teleology in Logic. You can almost see Prof. Serre's mind work!