Maoyuan Zhu

Marmodoro (2017. Everything in Everything: Anaxagoras’s Metaphysics. New York: Oup Usa) provides a gunk model for Anaxagoras’s ontology. All elements in the gunk model are some instantiated physical properties — opposites. She suggests regarding these opposites as qualitative gunk. The purpose of this paper is to refute the view that the gunk model for Anaxagoras’s ontology is incompatible with the preponderance principle, which allows certain kinds of opposites to be predominant in certain regions. In my opinion, the incompatibility comes from that Marmodoro confuses the mereological structure and spatial structure of opposites. To clear up this confusion, I elucidate two fundamental concepts pertaining to the gunk model — actual gunk and colocation, and invoke measure-theoretic extension to underpin them. With these resources, I propose a more refined condition for determining preponderance in certain regions, which leads to a gunk model with predominants.

This paper develops a new class of justification logic, the logic of epistemic entitlement. The logic of epistemic entitlement invokes the notion of epistemic entitlement in epistemology, and interprets a justification formula in the form of???? ∶???? as follows: the warrant???? entitles the agent to believe????. In the logic of epistemic entitlement, the formula???? ∶???? is true if and only if???? is true in all possible worlds entitled to be conceived by????. In contrast to the standard epistemic semantics of justification logic, the formula???? ∶???? in Fitting’s model is true if and only if???? is true in all possible worlds that can be conceived of and satisfies the evidential condition: the epistemic state???? ∈ ℰ(????,????) that the epistemic agent is in. Thus, if???? is not a dead point in the model, the point model of???? cannot satisfy both formulas of the form???? ∶???? and????′∶ ¬????. Thus standard justification logic cannot characterize the conflicting beliefs of agents for different warrants. Instead, the logic of epistemic entitlement solves this problem by entitling agents to believe???? and ¬???? on two disjoint sets of possible worlds on????,???? and????′, respectively. ℳ,???? ⊩???? ∶???? if and only if ℳ,???? ⊩???? for every???? ∈????????????(????,????) with????????????. Such an epistemic entitlement in the paper is axiomatized into the logic J_???????????? and the validity of its axioms is verified. And a canonical model of J_???????????? is established to prove its completeness. Finally, extensions of J_???????????? are attempted to explore the logic of entitlement of belief J_EntD4 and logic of entitlement of knowledge J_EntT4.