Wikipedia:Reference desk/Archives/Mathematics/2023 November 14

= November 14 =

Spinoza's ethics, mathematically analyzed
Is there an attempt to examine Spinoza's ethics mathematically, using the tools of modern mathematics? 2A02:8071:60A0:92E0:785D:C373:7F90:3E99 (talk) 12:34, 14 November 2023 (UTC)


 * There is a six-page paper on the Academia.edu website by Florian Marion, entitled "A Mathematical Interpretation of Spinoza's Ethics: Short preliminary remarks". If you don't have access to Academia, you can ask the author to email you the paper; his email address is on his university webpage. Not necessarily related to ethics, but possibly of interest:
 * J. Friedman, "Some Set-Theoretical Partition Theorems Suggest by the Structure of Spinoza's God", Synthese, 27–1, 1974, p. 199–209.
 * R. Ariew, "The Infinite in Spinoza's Philosophy", in P.-F. Moreau (ed.), Spinoza. Issues and Directions. The Proceedings of the Chicago Spinoza Conference, Brill, 1990, p. 16–31.
 * P. Bussotti, Ch. Tapp, "The influence of Spinoza's concept of infinity on Cantor's set theory", in Studies in History and Philosophy of Science, Part A 40 (1), 2009, p. 25–35.
 * --Lambiam 18:10, 14 November 2023 (UTC)
 * Wow, mathematisized ethics! I wonder if it can calculate how many people need to be on the other track to switch in the trolley problem ;-) NadVolum (talk) 19:47, 15 November 2023 (UTC)

Notation of representations
In the article on the Schur-Weyl duality, why are $$S^2$$ and $$\Lambda^2$$ used for, I think, the sign representation and the trivial representation respectively. I'm not so familiar with the topic and I don't find these symbols used this way in related articles. I suppose $$\Lambda^2$$ just "multiplies away" the sign in this case, but wouldn't something like $$1$$ be the standard notation for the trivial representation? Icek~enwiki (talk) 21:12, 14 November 2023 (UTC)


 * I'm pretty sure they're referring to the symmetric algebra and exterior algebra, with the superscript 2 meaning the second component of these graded algebras. The space of 2-tensors has dimension n2. This breaks up into the symmetric part with dimension (n2+n)/2 and the antisymmetric part with dimension (n2-n)/2. Here, the symmetric part is generated by tensors of the form u⊗v+v⊗u and the antisymmetric part is generated by tensors of the form u⊗v-v⊗u. Note that when k=n the representation given by $$\Lambda^k$$ is simply the determinant. --RDBury (talk) 22:40, 14 November 2023 (UTC)