As opposed to overdemanding principles which ask individuals to sacrifice too much, there are overpermissive principles which ask individuals to sacrifice too little. Determining the extent to which one should sacrifice often comes with the need of understanding what is of moral significance. By analysing different readings of moral significance, and singling out one specific interpretation of moral significance which links moral significance to gaining or losing a considerable amount of welfare, I demonstrate that one of the well-known principles of (...) Peter Singer, the Weaker Principle of Sacrifice, is overpermissive as it exempts deliberately cultivated morally significant lavish pursuits from the domain of sacrifice. Overpermissiveness not only renders moral principles unreasonably broad but also causes burdens to be distributed unjustifiably in a comparative sense, where some parties are assigned a moral obligation whereas others are not. (shrink)

Effective altruism is a movement which aims to maximise good. Effective altruists are concerned with extreme poverty and many of them think that individuals have an obligation to donate to effective charities to alleviate extreme poverty. Their reasoning, which I will scrutinise, is as follows: -/- Premise 1. Extreme poverty is very bad. -/- Premise 2. If it is in our power to prevent something very bad from happening, without thereby sacrificing anything else morally significant, we ought, morally, to do (...) it. -/- Premise 3. Individuals ought to choose the effective option in preventing very bad things. -/- Premise 4. Donating to effective charities is one of the best ways to alleviate extreme poverty. -/- Conclusion. Individuals ought to donate to effective charities working towards extreme poverty alleviation where doing so does not require them to give up anything of moral significance. -/- I will scrutinise each of these premises in turn. -/- For Premise 1, I focus on hedonistic utilitarianism and criticise its outlook on extreme poverty. I claim that hedonistic utilitarianism might be problematic for effective altruism. -/- Premise 2 is Peter Singer's Weaker Principle of Sacrifice. I introduce several possible interpretations of it, and press several objections to it by stressing overpermissiveness, luck, and rights. I defend strengthening the Weaker Principle of Sacrifice without making it overdemanding. -/- I claim that Premise 3 can be attractive to both consequentialists and non-consequentialists. Nevertheless, by showing that effectiveness sometimes violates fairness, I propose a method which avoids always helping the greater number and always giving everyone equal chances of being helped, which is compatible with effective altruism. -/- Against Premise 4, I assess the systemic change objection, which states that effective altruism unjustifiably distracts individuals from systemic change. By considering risk and the moral standing of the future extremely poor, I claim that the systemic change objection is partially successful, but cannot undermine effective altruism. -/- After analysing all of these, I argue that individuals have an obligation to donate to effective charities to alleviate extreme poverty where doing so does not require them to give up anything of moral significance. (shrink)

We develop a dimension theory for D-semianalytic sets over an arbitrary non-Archimedean complete field. Our main results are the equivalence of several notions of dimension and a theorem on additivity of dimensions of projections and fibers in characteristic 0. We also prove a parameterized version of normalization for D-semianalytic sets.

The theory of algebraically closed non-Archimedean valued fields is proved to eliminate quantifiers in an analytic language similar to the one used by Cluckers, Lipshitz, and Robinson. The proof makes use of a uniform parameterized normalization theorem which is also proved in this paper. This theorem also has other consequences in the geometry of definable sets. The method of proving quantifier elimination in this paper for an analytic language does not require the algebraic quantifier elimination theorem of Weispfenning, unlike the (...) customary method of proof used in similar earlier analytic quantifier elimination theorems. (shrink)