Colin allen, wendell wallach, and iva smit maintain in “why Machine Ethics?” that it is time to begin adding ethical decision making to computers and robots. They point out that “[d]riverless [train] systems put machines in the position of making split-second decisions that could have life or death implications” if people are on one or more tracks that the systems could steer toward or avoid. The ethical dilemmas raised are much like the classic “trolley” cases often discussed in ethics courses. “The computer revolution is continuing to promote reliance on automation, and autonomous systems are coming whether we like it or not,” they say. Shouldn't we try to ensure that they act in an ethical fashion?

Allen et al. don't believe that “increasing reliance on autonomous systems will undermine our basic humanity” or that robots will eventually “enslave or exterminate us.” However, in order to ensure that the benefits of the new technologies outweigh the costs, “we'll need to integrate artificial moral agents into these new technologies … to uphold shared ethical standards.” It won't be easy, in their view, “but it is necessary and inevitable.”

It is not necessary, according to Allen et al., that the autonomous machines we create be moral agents in the sense that human beings are. They don't have to have free will, for instance. We only need to design them “to act as if they were moral agents … we must be confident that their behavior satisfies appropriate norms.”

Introduction

In this paper i will discuss some of the broad philosophical issues that apply to the field of machine ethics. ME is often seen primarily as a practical research area involving the modeling and implementation of artificial moral agents. However this shades into a broader, more theoretical inquiry into the nature of ethical agency and moral value as seen from an AI or information-theoretical point of view, as well as the extent to which autonomous AI agents can have moral status of different kinds. We can refer to these as practical and philosophical ME respectively.

Practical ME has various kinds of objectives. Some are technically well defined and relatively close to market, such as the development of ethically responsive robot care assistants or automated advisers for clinicians on medical ethics issues. Other practical ME aims are more long term, such as the design of a general purpose ethical reasoner/advisor – or perhaps even a “genuine” moral agent with a status equal (or as equal as possible) to human moral agents.

In our early work on attempting to develop ethics for a machine, we first established that it is possible to create a program that can compute the ethically correct action when faced with a moral dilemma using a well-known ethical theory (Anderson et al. 2006). The theory we chose, Hedonistic Act Utilitarianism, was ideally suited to the task because its founder, Jeremy Bentham (1781), described it as a theory that involves performing “moral arithmetic.” Unfortunately, few contemporary ethicists are satisfied with this teleological ethical theory that bases the rightness and wrongness of actions entirely on the likely future consequences of those actions. It does not take into account justice considerations, such as rights and what people deserve in light of their past behavior; such considerations are the focus of deontological theories like Kant's Categorical Imperative, which have been accused of ignoring consequences. The ideal ethical theory, we believe, is one that combines elements of both approaches.

The prima facie duty approach to ethical theory, advocated by W.D. Ross (1930), maintains that there isn't a single absolute duty to which we must adhere, as is the case with the two aforementioned theories, but rather a number of duties that we should try to follow (some teleological and others deontological), each of which could be overridden on occasion by one of the other duties.

It is a remarkable aspect of the “unreasonable effectiveness of mathematics in the natural sciences” (Wigner 1960) that a handful of equations are sufficient to describe mathematically a vast number of physically disparate phenomena, at least at some level of approximation. Key reasons are the isotropy and uniformity of space-time (at least locally), the attendant conservation laws, and the useful range of applicability of linear approximations to constitutive relations.

After a very much abbreviated survey of the principal properties of vector fields, we present a summary of these fundamental equations and associated boundary conditions, and then describe several physical contexts in which they arise. The initial chapters of a book on any specific discipline give a far better derivation of the governing equations for that discipline than space constraints permit here. Our purpose is, firstly, to remind the reader of the meaning accorded to the various symbols in any specific application and of the physics that they describe and, secondly, to show the similarity among different phenomena.

The final section of this chapter is a very simple-minded description of the method of eigenfunction expansion systematically used in many of the applications treated in this book. The starting point is an analogy with vectors and matrices in finite-dimensional spaces and the approach is purposely very elementary; a “real” theory is to be found in Part III of the book.

Green's functions permit us to express the solution of a non-homogeneous linear problem in terms of an integral operator of which they are the kernel. We have already presented in simple terms this idea in §2.4. We now give a more detailed theory with applications mainly to ordinary differential equations. The next chapter deals with Green's functions for partial differential equations.

The determination of a Green's function requires the solution of a problem similar to (although somewhat simpler than) the original one, but the effort required is balanced by several advantages. In the first place, and at the most superficial level, once the Green's function G is known, it is unnecessary to solve the problem ex novo for every new set of data: it is sufficient to allow G to act on the new data to have the solution directly. Secondly, and most importantly for our purposes, Green's function theory provides a foundation for the various eigenfunction expansion and integral transform methods used in Part I of this book. Thirdly, even if the Green's function cannot be determined explicitly, one can base on it the powerful boundary integral numerical method outlined in §16.1.3 of the next chapter. Furthermore, once an expression for the solution of a problem – even if not fully explicit – is available, it becomes possible to deduce several important features of it, including bounds existence, uniqueness and others.

In many ways the sphere is the prototypical three-dimensional body and the consideration of fields in the presence of spherical boundaries sheds light on several features of more general three-dimensional cases.

In all the examples of this chapter extensive use is made of expansions in series of Legendre polynomials, for axi-symmetric problems, or spherical harmonics, for the general three-dimensional case. After a review of the polar coordinate system, we begin with a summary of the properies of these functions which are dealt with in greater detail in Chapters 13 and 14, respectively. While the axi-symmetric situation is somewhat simpler, it is also contained as a special case in the general three-dimensional one and it is therefore expedient to treat it as a special case of the latter.

We start with the general solution of the Laplace and Poisson equations (§7.3) and apply it to several axisymmetric (§§7.4 and 7.5) and non-axisymmetric situations. In all these cases the radial part of the solution consists of powers of r. The examples in the second part of the chapter (§7.13 and §7.14) deal with the scalar Helmholtz equation, for which the radial dependence is expressed in terms of spherical Bessel functions, the fundamental properties of which are summarized in §7.12. The last four sections deal with problems involving vector fields and vector harmonics.

This chapter collects in a simplified form some ideas and techniques extensively used in Part I of the book. This material will be revisited in greater detail in later chapters, but the brief summary given here may be helpful to readers who do not have the time or the inclination to tackle the more extensive treatments.

§2.1 continues the considerations of the final section of the previous chapter and further explains the fundamental idea underlying the method of eigenfunction expansions. While this method may be seen as an extension of the elementary “separation of variables” procedure (cf. §3.10), the geometric view advocated here provides a powerful aid to intuition and should greatly facilitate an understanding of “what is really going on” in most of the applications of Part I; the basis of the method is given in some detail in Chapters 19 and 21 of Part III.

§2.2 is a reminder of a useful method to solve linear non-homogeneous ordinary differential equations. Here the solution to some equations that frequently arise in the applications of Part I is derived. A more general way in which this technique may be understood is through its connection with Green's functions. This powerful idea is explained in very simple terms in §2.4 and, in greater detail, in Chapters 15 and 16.

Green's functions make use of the notion of the so-called “δ-function,” the principal properties of which are summarized in §2.3. A proper theory for this and other generalized functions is presented in Chapter 20.