We begin by showing that every theory of the value of uncertain prospects must have one of three unpalatable properties. _Reckless_ theories recommend giving up a sure thing, no matter how good, for an arbitrarily tiny chance of enormous gain; _timid_ theories permit passing up an arbitrarily large potential gain to prevent a tiny increase in risk; _non-transitive_ theories deny the principle that, if A is better than B and B is better than C, then A must be better than (...) C. Having set up this trilemma, we study its horns. Non-transitivity has been much discussed; we focus on drawing out the costs and benefits of recklessness and timidity when it comes to axiology, decision theory, and normative uncertainty. (shrink)

True benevolence is, most fundamentally, a desire that the world be better. It is natural and common, however, to frame thinking about benevolence indirectly, in terms of a desire to make a difference to how good the world is. This would be an innocuous shift if desires to make a difference were extensionally equivalent to desires that the world be better. This paper shows that at least on some common ways of making a “desire to make a difference” precise, this (...) extensional equivalence fails. Where it fails, “difference-making preferences” run counter to the ideals of benevolence. In particular, in the context of decision making under uncertainty, coupling a “difference-making” framing in a natural way with risk aversion leads to preferences that violate stochastic dominance, and that lead to a strong form of collective defeat, from the point of view of betterness. Difference-making framings and true benevolence are not strictly mutually inconsistent, but agents seeking to implement true benevolence must take care to avoid the various pitfalls that we outline. GPI Working Paper No. 16-2022. (shrink)

This thesis consists of several independent papers in population ethics. I begin in Chapter 1 by critiquing some well-known 'impossibility theorems', which purport to show there can be no intuitively satisfactory population axiology. I identify axiological vagueness as a promising way to escape or at least mitigate the effects of these theorems. In particular, in Chapter 2, I argue that certain of the impossibility theorems have little more dialectical force than sorites arguments do. From these negative arguments I move to (...) positive ones. In Chapter 3, I justify the use of a 'veil of ignorance', starting from three more basic normative principles. This leads to positive arguments for various kinds of utilitarianism - the best such arguments I know. But in general the implications of the veil depend on how one answers what I call 'the risky existential question': what is the value to an individual of a chance of non-existence? I chart out the main options, and raise some puzzles for non-comparativism, the view that life is incomparable to non-existence. Finally, in Chapter 4, I consider the consequences for population ethics of the idea that what is normatively relevant is not personal identity, but a degreed relation of psychological connectedness. In particular, I pursue a strategy based in population ethics for understanding the controversial 'time-relative interests' account of the badness of death. (shrink)

Is the overall value of a world just the sum of values contributed by each value-bearing entity in that world? Additively separable axiologies (like total utilitarianism, prioritarianism, and critical level views) say 'yes', but non-additive axiologies (like average utilitarianism, rank-discounted utilitarianism, and variable value views) say 'no'. This distinction is practically important: additive axiologies support 'arguments from astronomical scale' which suggest (among other things) that it is overwhelmingly important for humanity to avoid premature extinction and ensure the existence of a (...) large future population, while non-additive axiologies need not. We show, however, that when there is a large enough 'background population' unaffected by our choices, a wide range of non-additive axiologies converge in their implications with some additive axiology -- for instance, average utilitarianism converges to critical-level utilitarianism and various egalitarian theories converge to prioritiarianism. We further argue that real-world background populations may be large enough to make these limit results practically significant. This means that arguments from astronomical scale, and other arguments in practical ethics that seem to presuppose additive separability, may be truth-preserving in practice whether or not we accept additive separability as a basic axiological principle. (shrink)

We provide conditions under which an incomplete strongly independent preorder on a convex set X can be represented by a set of mixture preserving real-valued functions. We allow X to be infi nite dimensional. The main continuity condition we focus on is mixture continuity. This is sufficient for such a representation provided X has countable dimension or satisfi es a condition that we call Polarization.

I present a new argument that we are much more likely to be living in a computer simulation than in the ground-level of reality. (Similar arguments can be marshalled for the view that we are more likely to be Boltzmann brains than ordinary people, but I focus on the case of simulations.) I explain how this argument overcomes some objections to Bostrom’s classic argument for the same conclusion. I also consider to what extent the argument depends upon an internalist conception (...) of evidence, and I refute the common line of thought that finding many simulations being run—or running them ourselves—must increase the odds that we are in a simulation. GPI Working Paper No. 16-2021. (shrink)

Lewis’s Principal Principle says that one should usually align one’s credences with the known chances. In this paper I develop a version of the Principal Principle that deals well with some exceptional cases related to the distinction between metaphysical and epistemic modal­ity. I explain how this principle gives a unified account of the Sleeping Beauty problem and chance-­based principles of anthropic reasoning. In doing so, I defuse the Doomsday Argument that the end of the world is likely to be nigh. (...) GPI Working Paper No. 8-2021. (shrink)

I explore the possibility of a structuralist interpretation of homotopy type theory (HoTT) as a foundation for mathematics. There are two main aspects to HoTT's structuralist credentials. First, it builds on categorical set theory (CST), of which the best-known variant is Lawvere's ETCS. I argue that CST has merit as a structuralist foundation, in that it ascribes only structural properties to typical mathematical objects. However, I also argue that this success depends on the adoption of a strict typing system which (...) undermines the metaphysical seriousness of this structuralism. Homotopy type theory adds to CST a distinctive theory of identity between sets, which arguably allows its objects to be seen as ante rem structures. I examine the prospects for such a view, and address many other interpretive problems as they arise. (shrink)