An impossibility result on methodological individualism

Methodological individualists often claim that any social phenomenon can ultimately be explained in terms of the actions and interactions of individuals. Any Nagelian version of methodological individualism requires that there be bridge laws that translate social statements into individualistic ones. We show that Nagelian individualism can be put to logical scrutiny by making the relevant social and individualistic languages fully explicit and mathematically precise. In particular, we prove that the social statement that a group of (at least two) agents performs a deontically admissible group action cannot be expressed in a well-established deontic logic of agency that models every combination of actions, omissions, abilities, and obligations of finitely many individual agents.

Shadowing for families of endomorphisms of generalized group shifts

<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M1">\begin{document}$ G $\end{document}</tex-math></inline-formula> be a countable monoid and let <inline-formula><tex-math id="M2">\begin{document}$ A $\end{document}</tex-math></inline-formula> be an Artinian group (resp. an Artinian module). Let <inline-formula><tex-math id="M3">\begin{document}$ \Sigma \subset A^G $\end{document}</tex-math></inline-formula> be a closed subshift which is also a subgroup (resp. a submodule) of <inline-formula><tex-math id="M4">\begin{document}$ A^G $\end{document}</tex-math></inline-formula>. Suppose that <inline-formula><tex-math id="M5">\begin{document}$ \Gamma $\end{document}</tex-math></inline-formula> is a finitely generated monoid consisting of pairwise commuting cellular automata <inline-formula><tex-math id="M6">\begin{document}$ \Sigma \to \Sigma $\end{document}</tex-math></inline-formula> that are also homomorphisms of groups (resp. homomorphisms of modules) with monoid binary operation given by composition of maps. We show that the natural action of <inline-formula><tex-math id="M7">\begin{document}$ \Gamma $\end{document}</tex-math></inline-formula> on <inline-formula><tex-math id="M8">\begin{document}$ \Sigma $\end{document}</tex-math></inline-formula> satisfies a natural intrinsic shadowing property. Generalizations are also established for families of endomorphisms of admissible group subshifts.</p>