Mathematics is either inconsistent or incomplete.
What is your philosophical interpretation of Gödel’s incompleteness theorems?
#math #mathematics #maths #logic #MathematicalLogic #gödel #kurtgödel #godel #KurtGodel #Philosophy #PhilosophyOfMathematics #PhilosophicalLogic #philosophyoflogic #logic
Franci Mangraviti and Viviane Fairbank have produced a really helpful annotated reading list of papers on the relationship between feminist philosophy and logic. There’s a lot there that I was familiar with, but plenty more that is new to me, and I’m looking forward to reading more.
If you’re interested in the relationship between philosophy and logic, and have any sympathy at all with feminist critiques of social practices, I think you’ll find this helpful. https://diversityreadinglist.org/blueprint/feminist-logic/
After a short summer break exploring Scotland, it’s time to slowly get back into the saddle, giving a few talks, and preparing for the new academic year’s teaching.
First up, a short visit to Bochum for a PhD exam, and an impromptu talk on non-classical models for the identity predicate.
https://consequently.org/presentation/2023/exploring-three-valued-models-for-identity/
And (even though it may come last when you are learning a theory) the feeling is what comes *first* to for person who creates the theory - they have a *feeling* about a given phenomenon, and then they articulate some of it in a theory.
Hi,
I'm a researcher interested in theoretical computer science, software engineering, mathematical logic, also related philosophical topics.
My recent papers:
Mathematics:
"On proving consistency of equational theories in Bounded Arithmetic". Arnold Beckmann and Yoriyuki Yamagata, preprint: https://arxiv.org/abs/2203.04832
"Consistency proof of a fragment of PV with substitution in bounded arithmetic." Yoriyuki Yamagata, The Journal of Symbolic Logic 2018: https://arxiv.org/abs/1411.7087
Software Engineering:
(2020). "Falsification of cyber-physical systems using deep reinforcement learning", Yamagata, Y., Liu, S., Akazaki, T., Duan, Y., & Hao, J, IEEE Transactions on Software Engineering, 47(12), 2823-2840 (2021), https://staff.aist.go.jp/yoriyuki.yamagata/paper/falsify.pdf
Philosophy:
, "On the notion of validity for the bilateral classical logic", Suzuki, Ukyo & Yamagata, Yoriyuki, preprint: https://philpapers.org/rec/SUZOTN
Extra: COVID19
"Individual-based epidemiological model of COVID19 using location data". In 2022 IEEE International Conference on Big Data (Big Data) (pp. 4434-4442). IEEE., https://staff.aist.go.jp/yoriyuki.yamagata/paper/covid19.pdf
#Logic #MathematicalLogic #BoundedArithmetic #SoftwareEngineering
#Philosophy
#PhilosophicalLogic
#PhilosophyOfLanguage
#COVID19 #Introduction
We consider pure equational theories that allow substitution but disallow induction, which we denote as PETS, based on recursive definition of their function symbols. We show that the Bounded Arithmetic theory $S^1_2$ proves the consistency of PETS. Our approach employs models for PETS based on approximate values resembling notions from domain theory in Bounded Arithmetic, which may be of independent interest.
J Lou
Greg Restall
Jencel Panic
Yoriyuki Yamagata