Toby Ord

Over the last few decades, there has been an increasing interest in global consequentialism. Where act-consequentialism assesses acts in terms of their consequences, global consequentialism goes much further, assessing acts, rules, motives — and everything else — in terms of the relevant consequences. Compared to act-consequentialism it offers a number of advantages: it is more expressive, it is a simpler theory, and it captures some of the benefits of ruleconsequentialism without the corresponding drawbacks. In this paper, I explore the four different approaches to global consequentialism made by Parfit, Pettit and Smith, Kagan, and Feldman. I break these up into their constituent components, demonstrating the space of possible global consequentialist theories, and I present two new theories within this space.

We present a new method for expressing Chaitin’s random real, Ω, through Diophantine equations. Where Chaitin’s method causes a particular quantity to express the bits of Ω by fluctuating between finite and infinite values, in our method this quantity is always finite and the bits of Ω are expressed in its fluctuations between odd and even values, allowing for some interesting developments. We then use exponential Diophantine equations to simplify this result and finally show how both methods can also be used to create polynomials which express the bits of Ω in the number of positive values they assume.