Weng Kin San

Roughly, the view I call “Additivism” sums up value across time and people. Given some standard assumptions, I show that Additivism follows from two principles. The first says that how lives align in time cannot, in itself, matter. The second says, roughly, that a world cannot be better unless it is better within some period or another. These principles, while plausible, presuppose a rich underlying structure of value—presuppositions that are implicit in the standard numerical framework of population ethics but that are often overlooked. A careful exploration of Additivism and the case for it reveals intricate connections between substantive questions about what value fundamentally consists in and structural questions about how to aggregate value.

Roughly, the view I call 'Additivism' sums up value across time and people. Given some standard assumptions, I show that Additivism follows from two principles. The first says that how lives align in time can’t, in itself, matter. The second says, roughly, that a world can’t be better unless it’s better within some period or another. These principles, while plausible, presuppose a rich underlying structure of value—presuppositions that are implicit in the standard numerical framework of population ethics but that are often overlooked. A careful exploration of Additivism and the case for it reveals intricate connections between substantive questions about what value fundamentally consists in and structural questions about how to aggregate value.

kk states that knowing entails knowing that one knows, and K¬K states that not knowing entails knowing that one does not know. In light of the arguments against kk and K¬K⁠, one might consider modally qualified variants of those principles. According to weak kk, knowing entails the possibility of knowing that one knows. And according to weakK¬K⁠, not knowing entails the possibility of knowing that one does not know. This paper shows that weak kk and weakK¬K are much stronger than they initially appear. Jointly, they entail kk and K¬K⁠. And they are susceptible to variants of the standard arguments against kk and K¬K⁠. This has interesting implications for the debate on positive introspection and for deeper issues concerning the structure and limits of knowability.

Fitch’s Paradox shows that if every truth is knowable, then every truth is known. Standard diagnoses identify the factivity/negative infallibility of the knowledge operator and Moorean contradictions as the root source of the result. This paper generalises Fitch’s result to show that such diagnoses are mistaken. In place of factivity/negative infallibility, the weaker assumption of any ‘level-bridging principle’ suffices. A consequence is that the result holds for some logics in which the “Moorean contradiction” commonly thought to underlie the result is in fact consistent. This generalised result improves on the current understanding of Fitch’s result and widens the range of modalities of philosophical interest to which the result might be fruitfully applied. Along the way, we also consider a semantic explanation for Fitch’s result which answers a challenge raised by Kvanvig.

Augment the propositional language with two modal operators: □ and ■. Define ⧫ to be the dual of ■, i.e. ⧫=¬■¬. Whenever (X) is of the form φ → ψ, let (X⧫) be φ→⧫ψ . (X⧫) can be thought of as the modally qualified counterpart of (X)—for instance, under the metaphysical interpretation of ⧫, where (X) says φ implies ψ, (X⧫) says φ implies possibly ψ. This paper shows that for various interesting instances of (X), fairly weak assumptions suffice for (X⧫) to imply (X)—so, the modally qualified principle is as strong as its unqualified counterpart. These results have surprising and interesting implications for issues spanning many areas of philosophy.