Many philosophers have argued that the past must be finite in duration because otherwise reaching the present moment would have involved something impossible, namely, the sequential occurrence of an actual infinity of events. In reply, some philosophers have objected that there can be nothing amiss in such an occurrence, since actually infinite sequences are 'traversed' all the time in nature, for example, whenever an object moves from one location in space to another. This essay focuses on one of the two available replies to this objection, namely, the claim that actual infinities are not traversed in nature because space, time and other continuous wholes divide into parts only in so far as we divide them in thought, and thus divide into only a finite number of parts. I grant that this reply succeeds in blunting the antifinitist objection, but argue that it also subverts the very argument against an eternal past it was intended to save.

I argue that Schopenhauer's ascription of (moral) rights to animals flows naturally from his distinctive analysis of the concept of a right. In contrast to those who regard rights as fundamental and then cast wrongdoing as a matter of violating rights, he takes wrong (Unrecht) to be the more fundamental notion and defines the concept of a right (Recht) in its terms. He then offers an account of wrongdoing which makes it plausible to suppose that at least many animals can be wronged and thus, by extension, have rights. The result, I argue, is a perspective on the nature of moral rights in general, and the idea of animal rights in particular, that constitutes an important and plausible alternative to the more familiar views advanced by philosophers in recent decades.

Timothy Hsiao argues that animals lack moral status because they lack the sort of higher-level rationality required for membership in the moral community. Stijn Bruers and László Erdős have already raised a number of objections to this argument, to which Hsiao has replied with some success. But I think a stronger critique can be made. Here I raise further objections to three aspects of Hsiao's view: his conception of the moral community, his idea of root capacities grounded in one's nature, and his explanation of why cruelty is wrong. I also argue that sentience is a more plausible candidate for the morally salient capacity than rationality.

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Some philosophers contend that the past must be finite in duration, because otherwise reaching the present would have involved the sequential occurrence of an actual infinity of events, which they regard as impossible. I recently developed a new objection to this finitist argument, to which Andrew Ter Ern Loke and Travis Dumsday have replied. Here I respond to the three main points raised in their replies.