This paper challenges the soundness of the two-dimensional conceivability argument against the derivation of phenomenal truths from physical truths (cf. Chalmers in The conscious mind, Oxford University Press, Oxford, 1996; The character of consciousness, Oxford University Press, Oxford, 2010) in light of a hyperintensional regimentation of the ontology of consciousness. The regimentation demonstrates how ontological dependencies between truths about consciousness and about physics cannot be witnessed by epistemic constraints, when the latter are recorded by the conceivability-i.e., the epistemic possibility-thereof. Generalizations and other aspects of the philosophical significance of the hyperintensional regimentation are further examined.

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This essay examines the philosophical significance of Ω-logic in Zermelo-Fraenkel set theory with choice (ZFC). The dual isomorphism between algebra and coalgebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of Ω-logical validity can then be countenanced within a coalgebraic logic, and Ω-logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of Ω-logical validity correspond to those of second-order logical consequence, Ω-logical validity is genuinely logical, and thus vindicates a neo-logicist conception of mathematical truth in the set-theoretic multiverse. Second, the foregoing provides a modal-computational account of the interpretation of mathematical vocabulary, adducing in favor of a realist conception of the cumulative hierarchy of sets. * Forthcoming in d'Alfonso and Berkich (eds),'On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence -Themes from IACAP 2016' (Springer: 2018). further be defined via automata. In Section 3, I examine how models of epistemic modal algebras to which modal coalgebraic automata are dually isomorphic are availed of in the computational theory of mind. Finally, in Section 4, the philosophical significance of the characterization of the modal profile of Ωlogical validity for the philosophy of mathematics is examined. I argue (i) that it vindicates a type of neo-logicism with regard to mathematical truth in the set-theoretic multiverse, and (ii) that it provides a modal and computational account of formal grasp of the concept of 'set', adducing in favor of a realist conception of the cumulative hierarchy of sets. Section 5 provides concluding remarks.