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Profile: Toby Ord (Oxford University)
  1. Toby Ord, Consequentialism and Decision Procedures.
    Consequentialism is often charged with being self-defeating, for if a person attempts to apply it, she may quite predictably produce worse outcomes than if she applied some other moral theory. Many consequentialists have replied that this criticism rests on a false assumption, confusing consequentialism’s criterion of the rightness of an act with its position on decision procedures. Consequentialism, on this view, does not dictate that we should be always calculating which of the available acts leads to the most good, but (...)
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  2. Toby Ord, Hypercomputation: Computing More Than the Turing Machine.
    In this report I provide an introduction to the burgeoning field of hypercomputation – the study of machines that can compute more than Turing machines. I take an extensive survey of many of the key concepts in the field, tying together the disparate ideas and presenting them in a structure which allows comparisons of the many approaches and results. To this I add several new results and draw out some interesting consequences of hypercomputation for several different disciplines.
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  3. Toby Ord, How to Be a Consequentialist About Everything.
    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 (...)
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  4. Toby Ord, On the Existence of a New Family of Diophantine Equations for Ω.
    We show how to determine the k-th bit of Chaitin’s algorithmically random real number Ω by solving k instances of the halting problem. From this we then reduce the problem of determining the k-th bit of Ω to determining whether a certain Diophantine equation with two parameters, k and N , has solutions for an odd or an even number of values of N . We also demonstrate two further examples of Ω in number theory: an exponential Diophantine equation with (...)
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  5. Toby Ord, Representations of Ω in Number Theory: Finitude Versus Parity.
    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 (...)
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  6. Toby Ord, The Many Forms of Hypercomputation.
    This paper surveys a wide range of proposed hypermachines, examining the resources that they require and the capabilities that they possess. 2005 Elsevier Inc. All rights reserved.
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  7. Toby Ord & Alan Blair, Exploitation and Peacekeeping: Introducing More Sophisticated Interactions to the Iterated Prisoner's Dilemma.
    – We present a new paradigm extending the Iterated Prisoner's Dilemma to multiple players. Our model is unique in granting players information about past interactions between all pairs of players – allowing for much more sophisticated social behaviour. We provide an overview of preliminary results and discuss the implications in terms of the evolutionary dynamics of strategies.
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  8. Toby Ord, Rafaela Hillerbrand & Anders Sandberg, Probing the Improbable: Methodological Challenges for Risks with Low Probabilities and High Stakes.
    Some risks have extremely high stakes. For example, a worldwide pandemic or asteroid impact could potentially kill more than a billion people. Comfortingly, scientific calculations often put very low probabilities on the occurrence of such catastrophes. In this paper, we argue that there are important new methodological problems which arise when assessing global catastrophic risks and we focus on a problem regarding probability estimation. When an expert provides a calculation of the probability of an outcome, they are really providing the (...)
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  9. Toby Ord & Tien D. Kieu, Using Biased Coins as Oracles.
    While it is well known that a Turing machine equipped with the ability to flip a fair coin cannot compute more than a standard Turing machine, we show that this is not true for a biased coin. Indeed, any oracle set X may be coded as a probability pX such that if a Turing machine is given a coin which lands heads with probability pX it can compute any function recursive in X with arbitrarily high probability. We also show how (...)
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  10. Ole Fritjof Norheim, Trygve Ottersen, Alex Voorhoeve, Bonah Chitah, Richard Cookson, Norman Daniels, Nir Eyal, Walter Flores, Axel Gosseries, Daniel Hausman, Samia Hurst, Lydia Kapiriri, Toby Ord, Shlomi Segall & Frehiwot Defaye (2014). Making Fair Choices on the Path to Universal Health Coverage. World Health Organisation.
    This report by the WHO Consultative Group on Equity and Universal Health Coverage addresses how countries can make fair progress towards the goal of universal coverage. It explains the relevant tradeoffs between different desirable ends and offers guidance on how to make these tradeoffs.
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  11. Toby Ord (2009). Plaga. Moralne konsekwencje naturalnej utraty embrionu. Archeus 10:63-79.
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  12. Toby Ord (2008). Response to Open Peer Commentaries on “The Scourge: Moral Implications of Natural Embryo Loss”. American Journal of Bioethics 8 (7):W1 - W3.
    Many of the commentaries have made similar points regarding the nature of full moral status, so I shall begin by addressing these together. They argue that my representation of the Claim is stronger than many proponents of full moral status would accept (Ord 2008). Robert Card (2008) says that I assume that it is equally bad to lose human life at all stages. Russell DiSilvestro (2008) says that I assume a flawed principle that he calls (M). Marianne Burda (2008) says (...)
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  13. Toby Ord (2008). The Scourge: Moral Implications of Natural Embryo Loss. American Journal of Bioethics 8 (7):12 – 19.
    It is often claimed that from the moment of conception embryos have the same moral status as adult humans. This claim plays a central role in many arguments against abortion, in vitro fertilization, and stem cell research. In what follows, I show that this claim leads directly to an unexpected and unwelcome conclusion: that natural embryo loss is one of the greatest problems of our time and that we must do almost everything in our power to prevent it. I examine (...)
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  14. Nick Bostrom & Toby Ord (2006). The Reversal Test: Eliminating Status Quo Bias in Applied Ethics. Ethics 116 (4):656-679.
    Suppose that we develop a medically safe and affordable means of enhancing human intelligence. For concreteness, we shall assume that the technology is genetic engineering (either somatic or germ line), although the argument we will present does not depend on the technological implementation. For simplicity, we shall speak of enhancing “intelligence” or “cognitive capacity,” but we do not presuppose that intelligence is best conceived of as a unitary attribute. Our considerations could be applied to specific cognitive abilities such as verbal (...)
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  15. Jeff McMahan, Nick Bostrom, Toby Ord, Paul E. Hurley, Pekka Väyrynen & Jacob Ross (2006). 10. Joseph Raz, The Practice of Value Joseph Raz, The Practice of Value (Pp. 805-809). Ethics 116 (4).
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  16. Toby Ord & Tien D. Kieu (2005). The Diagonal Method and Hypercomputation. British Journal for the Philosophy of Science 56 (1):147-156.
    The diagonal method is often used to show that Turing machines cannot solve their own halting problem. There have been several recent attempts to show that this method also exposes either contradiction or arbitrariness in other theoretical models of computation which claim to be able to solve the halting problem for Turing machines. We show that such arguments are flawed—a contradiction only occurs if a type of machine can compute its own diagonal function. We then demonstrate why such a situation (...)
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