This paper examines several aspects of Alexander Wendt's Quantum Mind and Social Science. The paper questions the nature of the task, as ontologies are debated in a scientific field once there is a widely accepted substantive theory that stands in need of interpretation, as with Newtonian physics or quantum mechanics; doing this job for international relations (IR) is highly questionable give that there is no widely accepted substantive theory of IR that needs an interpretation. Second, the paper questions Wendt's view of the consequences for ontology of quantum theory being replaced in the future; Wendt the interpretation of the history of science maintains that in the physical sciences a new theory subsumes the older theory, including its ontology. But, this seems to misread history, while the empirical content of classical physics is subsumed by relativity theory, it is far from true that the former's ontology was subsumed. The ontologies are in sharp contrast. The paper raises questions also about the notion of ‘truth’ and of the meaningfulness of evaluative concepts like ‘justice’.

This paper considers a generalisation of selection functions over an arbitrary strong monad T, as functionals of type $J_R^T X = (X \to R) \to TX$. It is assumed throughout that R is a T-algebra. We show that $J_R^T$ is also a strong monad, and that it embeds into the continuation monad $K_R X = (X \to R) \to R$. We use this to derive that the explicitly controlled product of T-selection functions is definable from the explicitly controlled product of quantifiers, and hence from Spector’s bar recursion. We then prove several properties of this product in the special case when T is the finite powerset monad ${\cal P}_{\rm{f}} \left( \cdot \right)$. These are used to show that when $TX = {\cal P}_{\rm{f}} \left( X \right)$ the explicitly controlled product of T-selection functions calculates a witness to the Herbrand functional interpretation of the double negation shift.

We use supernatural bundles to build $\mathbf{GL}$ -equivariant resolutions supported on the diagonal of $\mathbb{P}^{n}\times \mathbb{P}^{n}$ , in a way that extends Beilinson’s resolution of the diagonal. We thus obtain results about supernatural bundles that largely parallel known results about exceptional collections. We apply this construction to Boij–Söderberg decompositions of cohomology tables of vector bundles, yielding a proof of concept for the idea that those positive rational decompositions should admit meaningful categorifications.

It is well known that, given an endofunctor H on a category C , the initial (A+H-)-algebras (if existing), i.e. , the algebras of (wellfounded) H-terms over different variable supplies A, give rise to a monad with substitution as the extension operation (the free monad induced by the functor H). Moss [17] and Aczel, Adámek, Milius and Velebil [12] have shown that a similar monad, which even enjoys the additional special property of having iterations for all guarded substitution rules (complete iterativeness), arises from the inverses of the final (A+H-)-coalgebras (if existing), i.e. , the algebras of non-wellfounded H-terms. We show that, upon an appropriate generalization of the notion of substitution, the same can more generally be said about the initial T'(A,-)-algebras resp. the inverses of the final T'(A,-)-coalgebras for any endobifunctor T' on any category Csuch that the functors T'(-,X) uniformly carry a monad structure.