Changes of Frame

As noted in section (5.2), Bt is the region actually observed during the motion: The reference body B serves only to label material points. For that reason, to discuss a notion of invariance under observer changes, it is useful to differentiate conceptually between the ambient space for B and the space through which Bt evolves (Figure 20.1). In accord with this:

1. (i) the ambient space through which Bt evolves is termed the observed space;

2. (ii) the ambient space for the reference body B is termed the reference space.

Granted this dichotomy, spatial vectors belong to the observed space, while material vectors belong to the reference space.

Suppose that a frame of reference F for the observed space is prescribed, an assumption tacit in the discussion thus far. Then, roughly speaking, a change of frame is, at each time, a rotation and translation of the observed space.

Introduction

Suppose you have always wanted to travel to Paris but could never afford the trip from New York. And suppose that now a new company, 15-Minute Travel, is offering to send you with their super-high-tech “transporter” machine. Here's how the transporter machine works. You step into a ­fancy-looking booth in New York and, once you are ready to go, you press a green button marked “Paris”. You are then scanned by a device that records the exact position, nature, and velocity of every subatomic particle in your body. This information – your “personal blueprint” – is then recorded on a zirconium microchip. At the same time, your body is disassembled, and the resulting subatomic particles are rearranged, so that they make up a small quantity of “transport dust” – a dense but compact and virtually undamagable ashlike substance. Next, the transport dust and the zirconium chip are safely sealed inside a small cylinder, like the canisters used by drive-through banks, and the cylinder then travels through a special underground tube, powered by electromagnetic technology, at speeds exceeding 10,000 miles per hour. The cylinder arrives at the company's terminal in Paris in less than fifteen minutes and, once it is safely ensconced in a booth just like the one in New York, the transport dust is rearranged, in precise accordance with your personal blueprint. You then emerge from the booth in Paris, feeling as if the whole experience has taken no time at all.

The One-Over-Many Problem

In Plato's dialogue Meno, Socrates says to Meno: “[T]ell me what virtue is in the universal; and do not make a singular into a plural, as the facetious say of those who break a thing, but deliver virtue to me whole and sound, and not broken into a number of pieces.” Socrates wants to know what virtue is, and his plea for it to be presented whole and sound was to make clear that he did not want descriptions of behaviors that make certain kinds of people virtuous (e.g., the virtue of a man is to order the state), and that he was not looking for a list of virtues (e.g., wisdom, humility, piety, temperance, and so on). Socrates wanted to know the common nature of all virtues. He wanted to know about virtuehood, about whatever it is that makes wisdom, humility, and other virtues be virtues. In Meno, Socrates briefly makes similar queries about color and shape. He wanted to know what makes “red” and “green” colors and what makes “round” and “oblong” shapes. In other dialogues, Socrates makes similar requests about the nature of some individual virtues. For example, in Euthyphro, he considers piety. What is it that makes pious things pious? In Charmides, the focus is temperance. What is it that makes temperate things temperate? Questions of this sort are at the heart of The One-Over-Many Problem.

Introduction

Space is not like time. For one thing, there is no intrinsic direction – no metaphysical grain – to any dimension of space. Instead, every spatial dimension is perfectly symmetrical. For another thing, space does not exhibit any movement or flow; unlike time, there is no dynamic aspect to the dimensions of space. And for a third thing, space is ontologically indiscriminate. It doesn't matter whether you're located right here or over there in space, since all spatial locations are equally real. Space just sits there: a gigantic, three-dimensional continuum, static and homogeneous, with nothing but their contents to distinguish one spatial region from another.

Time is different. Time has pizzazz. For starters, there is a distinctive direction to time, sometimes called time's arrow, which points always toward the future. Also, time is dynamic: each moment of time approaches inexorably from the future, enjoys its brief heyday in the spotlight of the present, and then ever after recedes serenely into the shadowy realm of the past. Not only that, but your temporal location does matter, ontologically speaking: for the past is the domain of has-beens, and the future is a land of mere potential. Only the present is truly real.

Or so it might seem. But many have thought otherwise. A large number of philosophers and scientists, especially in the last hundred years, have defended the view that time, despite appearances to the contrary, is one of four more or less similar dimensions of the universe.

The aim of this book is to introduce the philosophically curious to the central topics of contemporary metaphysics.

We expect that our audience will include undergraduate philosophy majors who have maybe already taken an introductory survey course in philosophy or a first course in symbolic logic, and who are now enrolled in a course devoted solely to topics in metaphysics. We also expect that our audience will include graduate students in philosophy who are either getting their first opportunity to tackle contemporary metaphysical issues or are looking for a book to keep on hand as a useful resource as they undertake a rigorous research seminar on some specific metaphysical topic. We hope that many more reflective minds, ranging from the contemplative layperson to sages of the philosophical professoriate, will find our text valuable as a source of sober reasoning and at least the occasional insight.

We have written this book as teachers. Though we realize that there is no way to keep our own philosophical commitments from seeping into our arguments and our choice of topics, we have tried not to make the book a forum for advancing metaphysical doctrines. We have gone out of our way to introduce topics and arguments without pressuring the reader to settle on any definite conclusions. In fact, the reader will find scattered about lots of spots where we cut off the discussion in order to identify the pros and cons of a particular thesis and then move on to another issue.

A familiar, central, and tricky relation

At one time or another, most of us have had the experience of reaching for something too quickly. Let's say you go to grab a biscuit from across the dinner table and bump a glass with your elbow. Water from the glass spills. Not much could be more obvious, it seems, than that you bumped the glass and thereby caused the water to spill. To put this in a grand-sounding way, your bump of the glass stood in the relation of causation to the spill. That is what we are going to try to understand better in this chapter, that relation that holds between the bump and the spill in this mundane example. This is a terrific topic because causation is about as familiar, central, and tricky as metaphysical concepts come.

The spilled-water case should be enough to convince you that causation is a familiar concept. That it is a central concept is also straightforward: it is something we do whenever we affect what is around us. It is something we undergo whenever we are affected by what is around us. Molecular bonding, planetary rotation, human decisions, and life itself are all causal processes. Causation is part of scientific practice: at least typically, a scientific explanation of some event will include some mention of something that caused that event; you can't say why something happened without identifying what caused it to happen. Causation is part of philosophy too.

The Problem of Freedom and Determinism

Suppose that on your way home one day you discover someone else's ­wallet on the sidewalk. It's full of cash, credit cards, and so forth. But it also contains a driver's license, from which you can tell that the wallet belongs to a fellow who lives nearby, in a house that you'll pass on your way home. You deliberate about what to do. You could return the wallet to its owner with all of its contents intact, of course. Or you could return it after taking out some of the cash, or return it after taking out all of the cash, or just leave it where it is, or take out the cash and then leave it where it is. Suppose that while deliberating, you keep thinking about how you would really like to use the money to buy a bunch of new computer games. So in the end, even though you feel a little guilty about doing so, you decide to take all the cash and then leave the wallet where you found it. And that's what you do.

Now let's shift gears for a minute. We all know that the future is to some extent influenced by the past. For example, pink elephants don't just appear out of thin air. In order for a pink elephant to appear in a place, there has to be some sort of history leading up to that elephant being in that place.

The Mind–Body Problem

It is not far from the truth to say that The Mind–Body Problem is the ­problem of understanding the relationship between the mind and the body. But this description is misleading in two different ways. First, we should be aware that philosophers are not that interested in the relationship between the mind and the body, at least not the entire body. For example, there are lots of parts of the body (e.g., the appendix) that don't seem to bear any interesting relationship to our minds. Philosophers tend to focus on the relationship between the mind and the brain, the part of the body that is the (proximate) basis for what goes on in the mind. Second, it's not just mental and neurophysiological objects, entities like the mind and the brain, that are important. For example, there are other mental entities: mental states (e.g., John believing now that it's time for lunch), mental events (e.g., John's present pang of hunger), mental processes (e.g., John's current reflection on how best to avoid further pangs), and so forth. There are also other bodily things: brain states (e.g., the C-fibers of John's brain now firing), brain events (e.g., a signal from another part of John's central nervous system to his brain), brain processes (e.g., those processes in John's brain stem currently regulating his heartbeat), and so forth.

What is metaphysics?

Since this book is called An Introduction to Metaphysics, it makes sense to begin with a short, simple, and clear definition of the word ‘metaphysics’. If only it were that easy.

Part of the problem is that it's practically impossible to get any two philosophers to agree on a single definition of ‘metaphysics’. (And the book is, after all, written by two philosophers.) But there are also issues relating to the strange etymology of the term ‘metaphysics’, and further complications arising from the fact that ‘metaphysics’ has one meaning in ordinary English and another meaning within (academic) philosophy. Nevertheless, we'll do our best in this section to offer the reader what we take to be a reasonable characterization of the field of metaphysics. In fact, we'll offer three different but mutually compatible characterizations.

Let's start with what metaphysics is not. Metaphysics – as we are using the term – is not the study of the occult. Nor is it the study of mysticism, or auras, or the power of pyramids. Although the word ‘metaphysics’ may indeed have all of those connotations in ordinary English, the word is used within academic philosophy in an entirely different way. And this book, as it happens, is meant to be an introduction to the branch of academic philosophy that is known as metaphysics.