This article shows that introducing the positive comparative relation parity only helps one block so‐called “Spectrum Arguments” in order to avoid their unsavoury implications if one specifies parity in a specific way with respect to its persistence. The article illustrates how parity must both admit of persistency and be weakly non‐persistent for parity to block Spectrum Arguments, and identifies some consequences of that discovery for the general debate on Spectrum Arguments, value theory and comparability problems.

Here we introduce a formulation for describing welfare based on a hyperbolic secant function, derived from certain intuitions about the nature of material and experiential conditions, that satisfies a number of normatively critical constraints, making for an elegant and satisfactory welfarist axiology. We first introduce intuitions about experiential conditions, material conditions, and their valences; we second make a mathematical formulation of our hedonic calculus consistent with these intuitions; we third make several manipulations of our formulation in order to make calculations (...) in population ethics; and we fourth show how the calculations are consistent with several critical normative constraints. (shrink)

In his book Reasons and Persons, Derek Parfit proposes the search for a self-consistent theory of population ethics, a theory capable of answering questions about the welfares of populations in a manner that satisfies all of our ethical intuitions, what he calls “Theory X.” But in the same work, Parfit offers what he sees as a major obstacle to that goal, the so-called “Repugnant Conclusion”, worrying whether the most well-off population is an increasingly large population. This problem, along with Roderick (...) Ninian Smart’s “Negative Utilitarianism” and Robert Nozick’s “Utility Monster” belong to a special class of ethical cases dealing with the mathematical limits of zero and infinity: trivial and unreal ethical solutions. These kinds of problems have plagued population ethics since Thomas Malthus first recognized the problem of exponential growth and its deleterious effects on personal wellbeing. In an attempt to answer Parfit, some, such as T. Sider, T. Hurka, and Y. Ng, have suggested formulations of marginal wellbeing without undermining core ethical principles. Other authors, like G. Arrhenius et al., have suggested that Parfit’s problem fundamentally undermines the possibility of a self-consistent population ethics. Here we will suggest that these problems result from an improper inclusion of trivial and unreal numbers into the ethical domain, making what Parfit calls “mistakes in moral mathematics,” and are thus resolved by an exclusion of trivial and unreal numbers from the ethical domain by carefully specifying a welfare function to exclude them. (shrink)

The repugnant conclusion poses a conundrum in population ethics that has evaded satisfactory solution for more than four decades. In this article, I show that the repugnant conclusion can be avoided without sacrificing any moral intuitions. This is achieved using non-Archimedean orders, which admit the possibility of pairs of goods for which no amount of one is better than a single unit of the other. I show with minimal assumptions, not only are such goods sensible, they are compulsory. I show (...) that utilitarianism and expected utility theory in their canonical forms are not in general suitable in this setting, and using these tools naively can lead to ethical errors that are arbitrarily serious. Multi-dimensional lexicographic expected utility representations are required. I use fuzzy sets to show there needn't be a sharp transition between non-Archimedean equivalent goods, and the lexicographic ordering may only manifest asymptotically. This might be unavoidable due to intrinsic physical limits on the ability to discriminate between different goods arising from e.g. quantum mechanics. Limited discriminatory power causes preferences to be non-transitive, which can resolve problems related to so-called `fanaticism' and `recklessness' wherein `rational' decision-makers counterintuitively prefer arbitrary long shot bets to a guaranteed lesser outcome. (shrink)

DRAFT Several philosophers have suggested that it is impossible to formulate a theory of population ethics that simultaneously satisfies all of the necessary conditions set by our ethical intuitions (Arrhenius, 2000; Blackorby et al., 2004). However, we will attempt to demonstrate that, using the Stone-Weierstrass method, starting from scratch with a completely underspecified polynomial approximation function for commensurable cardinal utility (used here as a synonym for welfare) in a domain of commodities and populations, there are possible sets of functions that (...) satisfy many if not all of our ethical intuitions (avoiding the Repugnant and Sadistic Conclusions, and others), thus providing a self-consistent welfarist axiology. DRAFT. (shrink)

DRAFT In what follows, we will attempt to point out two technical loopholes in the proof of the “Impossibility Theorem for Welfarist Axiologies” as proposed by Gustaf Arrhenius (Arrhenius, 2000). The two problems arise from different principles, one from an application of the “Addition Principle” and one from an application of the “Dominance Principle” after a counterintuitive combination of the “No Repugnant/Anti-Egalitarian Conclusion” criteria, the former non-fatal and latter fatal. We will show that these problems arise via two methodologies. 1) (...) We appeal to intuitions with counterexample cases. 2) We replace ordinal priority-ordering with cardinal utility functions (von Neumann & Morgenstern, 1944). If correct, our critique shows that at least one avenue is available to welfarist axiology, which reopens the possibilities of the search for a “Theory X” (Parfit, 1984). DRAFT. (shrink)