We have examined a number of ethical issues. We have seen that many accepted practices are open to serious objections. What ought we to do about it? This, too, is an ethical issue. Here are five cases – all ones that actually happened – to consider.

Oskar Schindler was a minor German industrialist. During the war, he ran a factory near Cracow, Poland. At a time when Polish Jews were being sent to death camps, he assembled a labour force of Jewish inmates from concentration camps and the ghetto, considerably larger than his factory needed, and used several illegal stratagems, including bribing members of the SS and other officials, to protect them. He spent his own money to buy food on the black market to supplement the inadequate official rations he obtained for his workers. By these methods, he was able to save the lives of about 1,200 people.

Dr. Thomas Gennarelli directed a Head Injury Laboratory at the University of Pennsylvania, in Philadelphia. Members of an underground organization called the Animal Liberation Front knew that Gennarelli inflicted head injuries on monkeys there and had been told that the monkeys underwent the experiments without being properly anaesthetised. They also knew that Gennarelli and his collaborators videotaped their experiments to provide a record of what happened during and after the injuries they inflicted. They tried to obtain further information through official channels but were unsuccessful. In May 1984, they broke into the laboratory at night and found thirty-four videotapes.

An oversimplified summary of the first three chapters of this book might read like this: the first chapter sets up a conception of ethics from which, in the second chapter, the principle of equal consideration of interests is derived; this principle is then used to illuminate problems about the sense in which humans are equal and, in the third chapter, applied to nonhuman animals.

Thus, the principle of equal consideration of interests has been behind much of our discussion so far; but as I suggested in the previous chapter, the application of this principle when lives are at stake is less straightforward than when we are concerned with interests like avoiding pain and experiencing pleasure. In this chapter, we shall look at some views about the wrongness of taking life, in order to prepare the ground for the following chapters in which we shall turn to some practical issues about when it is wrong to kill someone and when it is wrong to allow someone to die.

HUMAN LIFE

People often say that life is sacred. They almost never mean what they say. They do not mean, as their words seem to imply, that all life is sacred. If they did, killing a pig or pulling up a cabbage would be as abhorrent to them as the murder of a human being. When people say that life is sacred, it is human life they have in mind. But why should human life have special value?

In the preceding chapter, we examined some general principles about the value of life. In this and the following two chapters, we shall draw from that discussion some conclusions about three cases of killing that have been the subject of heated debate: abortion, euthanasia and killing animals. Of these three, the question of killing animals has aroused the least controversy. Nevertheless, for reasons that will become clear later, it is impossible to defend a position on abortion and euthanasia without taking some view about the killing of nonhuman animals. So we shall look at that question first.

CAN A NONHUMAN ANIMAL BE A PERSON?

We have seen that there are reasons for holding that the killing of a person is more seriously wrong than the killing of a being who is not a person. This is true whether we accept preference utilitarianism, Tooley's argument about the right to life or the principle of respect for autonomy. Even a hedonistic utilitarian would say that there may be indirect reasons why it is worse to kill a person. So in discussing the wrongness of killing nonhuman animals, it is important to ask if any of them are persons.

It sounds odd to call an animal a person, but this may be no more than a symptom of our habit of keeping our own species sharply separated from others. In any case, we can avoid the linguistic oddness by rephrasing the question in accordance with our definition of ‘person’.

Practical ethics covers a wide area. We can find ethical ramifications in most of our choices, if we look hard enough. This book does not attempt to cover the whole area. The problems it deals with have been selected on two grounds: relevance and the extent to which philosophical reasoning can contribute to discussion of them.

The most relevant ethical issues are those that confront us daily: is it right to spend money on entertaining ourselves when we could use it to help people living in extreme poverty? Are we justified in treating animals as nothing more than machines producing flesh for us to eat? Should we drive a car – thus emitting greenhouse gases that warm the planet – if we could walk, cycle or use public transport? Other problems, like abortion and euthanasia, fortunately are not everyday decisions for most of us; but they are still relevant because they can arise at some time in our lives. They are also issues of current concern about which any active participant in a democratic society should have informed and considered opinions.

The extent to which an issue can be usefully discussed philosophically depends on the kind of issue it is. Some issues are controversial largely because there are facts in dispute. Should we build nuclear power stations to replace the coal-fired ones that are a major cause of global warming?

My interest in Statius' Siluae began many years ago when, as an undergraduate at St Andrews University, Scotland, I attended a series of brilliant lectures on these poems taught by Chris Carter. He conveyed to me his excitement about the novelty of the Siluae, their bold experimentation with language and poetic convention. Later, at the start of graduate school at UC Berkeley, the medieval scholar Alain Renoir ordered me to start my studies by reading Statius, who was not at that time of first order of importance for classicists. However, a positive shift in interest in this Flavian poet has taken place, and in this edition I have been able to take advantage of the important textual and literary critical work done on the Siluae in recent decades. In keeping with the aims of the series, I have tried to explain the cultural context of the seven poems of book 2 as well as elucidate Statius' text. It is my hope that this edition will make Statius' Siluae more accessible by contributing to an appreciation of their innovations in style, theme and genre; and by helping elucidate Roman culture in the age of Domitian and Statius' sophisticated engagement with it. Statius, who was born and raised in Naples, wrote the Siluae shortly after the eruption of Vesuvius; his Siluae provide rare, important social testimony to the culture of which the art and artefacts from Pompeii and Herculaneum give us tantalising glimpses.

How to find stationary values of functions of a single variable f(x), of several variables f(x, y, …) and of constrained variables, where x, y, … are subject to the n constraints gi(x, y, …) = 0, i = 1, 2, …, n will be known to the reader and is summarized in Sections A.3 and A.7 of Appendix A. In all those cases the forms of the functions f and gi were known, and the problem was one of finding the appropriate values of the variables x, y, etc.

We now turn to a different kind of problem in which we are interested in bringing about a particular condition for a given expression (usually maximizing or minimizing it) by varying the functions on which the expression depends. For instance, we might want to know in what shape a fixed length of rope should be arranged so as to enclose the largest possible area, or in what shape it will hang when suspended under gravity from two fixed points. In each case we are concerned with a general maximization or minimization criterion by which the function y(x) that satisfies the given problem may be found.

The calculus of variations provides a method for finding the function y(x). The problem must first be expressed in a mathematical form, and the form most commonly applicable to such problems is an integral.

Compared to communication in other species, human speech is a highly differentiated faculty, enabling us to communicate complex information in an efficient way. There are many aspects to the psychological study of language, including its production and understanding (listening, articulation, memorization), and the use of indirect means of communication through writing and reading. In all of these aspects cross-cultural differences can be observed. In this chapter we will deal with the main theme of cross-cultural psycholinguistic research, namely the extent to which underneath different words and rules of grammar there is commonality between languages.

In the first section research on linguistic relativity is presented, addressing the question of to what extent speaking a particular language influences one's thinking. We look at two topics on which much of the discussion about linguistic relativity has been focussed, namely perception and categorization of colors, and orientation in space. We present the case of relativism and counterarguments based on empirical cross-cultural studies. The second section is on universalist approaches, especially the notion of universal grammar. Again, not only the evidence in favor, but also challenges are presented.

On the Internet we present some additional information. There is an entry on language development (Additional Topics, Chapter 8), pointing out some of the complexities a child has to master in order to acquire a language.

The notion of development comes into this book at three levels. First, there is phylogenetic development. It deals with variation across species, and the emergence of new species over long periods of time. This form of development will be discussed in Chapter 11. Second, the term “development” can refer to cultural changes in societies. Development in this sense will be touched upon in Chapter 10 (where we discuss the anthropological tradition of cultural evolution), and in Chapter 18 (where we focus on national development). In the present and the following chapter we are mainly concerned with the course of development of the individual through the life span, or ontogenetic development. In this chapter, we will focus on cultural similarities and differences in developmental patterns in infancy and early childhood; the next chapter will deal with late childhood, adolescence and adulthood.

Culture as context for development

Individual development can be considered as the outcome of interactions between a biological organism and environmental influences. Although we consider the separation of “nature” and “nurture” to be largely an outdated distinction (see Chapter 11, and the last section of Chapter 12), the relative importance of the biological and the cultural (environmental-experiential) components of behavior has formed the major dimension underlying the differences between various schools of thinking on ontogenetic development in the psychological literature.

In Chapter 14, we developed the basic theory of the functions of a complex variable, z = x + iy, studied their analyticity (differentiability) properties and derived a number of results concerned with values of contour integrals in the complex plane. In this current chapter we will show how some of those results and properties can be exploited to tackle problems arising directly from physical situations or from apparently unrelated parts of mathematics.

In the former category will be the use of the differential properties of the real and imaginary parts of a function of a complex variable to solve problems involving Laplace's equation in two dimensions, whilst an example of the latter might be the summation of certain types of infinite series. Other applications, such as the Bromwich inversion formula for Laplace transforms, appear as mathematical problems that have their origins in physical applications; the Bromwich inversion enables us to extract the spatial or temporal response of a system to an initial input from the representation of that response in “frequency space” – or, more correctly, imaginary frequency space.

Some other topics that could have been considered, had space permitted, are the location of the (complex) zeros of a polynomial, the approximate evaluation of certain types of contour integrals using the methods of steepest descent and stationary phase, and the so-called “phase-integral” solutions to some differential equations. However, for these and many more, the brief outlines given in the final section of this chapter will have to suffice.