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Theoretical Ethics

The Geometry of Ethics

Maurice F. Stanley
University of North Carolina at Wilmington

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ABSTRACT: The language of ethics can be viewed as consisting of de facto analytic claims: ‘Murder is wrong,’ ‘One ought to meet one’s responsibilities,’ etc. I argue that it is narrow-minded to think, as Quine and others do, that we should put scientific and mathematical claims above those of ethics, for the terms of ethics fit together just as geometrical terms do, and it does not matter whether there is any correspondence between such terms and an ‘external world.’ What matters is whether we wish to use ethical language as we do scientific language to understand the world. We posit points in space-time, we posit rights and wrongs. The former are no more real than the latter, and no less. Values, like circles, are no less real for our having imposed them on the Lebenswelt.

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A circle is the set of all points in a plane that are equidistant from a given point. A straight line can intersect a circle in no more than two points. Such statements occur in the language (or language-game, as Wittgenstein would say) of geometry. If you want to understand and use such discourse, you need to be conversant with certain basic concepts such as point and set. You need to know how those words are used. Whether points and sets really exist or not is unimportant for speaking the language of geometry. As Quine has said, there is what we say there is. That is, we are ontologically committed to what we have to say there is in order to get certain jobs done.

What Quine didn’t stress is that our ontological commitments follow our various purposes. If our purpose is to geometrize, measure, survey, then we will find ourselves committed to points, lines, sets, planes and such. If we want to explain the behavior of the chemical elements in a coherent way we will have reason to believe in atoms, electrons, protons, and so forth. It might be that we do not fully know or understand what, or even whether, points and atoms really are; we simply use them to suit our mathematical and scientific purposes.

Quine, with great perspicacity and aptness of expression, pointed out that atoms and electrons are on no sounder epistemological footing than the Greek gods. Professional philosophers are quite familiar with this statement, but have refrained from applying it to the language and concepts of ethics — perhaps because they think the subject of ethics is too loose, not rigorous enough.

The language of geometry of course has a rigorous logic to it — that is, the concepts fit together in certain logical ways. We find that the concepts set and point are such that most other geometrical concepts are understood in terms of them. If someone asks, "Say, what is a point, anyway?" we have a hard time telling him, or her. We say it is something with no size but only a location (which is really very mysterious, isn’t it?) or we might play it smart and say that point and set are undefined in geometry. Anyway the idea is to get started talking geometrically, not worrying about our ontological commitments.

Another interesting feature of geometry is that whatever is said is (what the positivists called) analytic rather than synthetic. Although this distinction has come into disrepute, thanks mostly to the work of Quine, it still is quite serviceable in a rough and imprecise way. Analytic means "true by definition," while synthetic means "true because of the facts." That is, it’s a matter of fact whether, e.g., Madeleine Albright is in Washington now. It’s a matter of definition that all squares have four corners. You can imagine Madeleine Albright being elsewhere than in Washington, but you can’t imagine a square with only three corners.1

In science, especially theoretical science, the same is true. An electron has a negative charge, and if it has a positive charge it can’t be an electron, because "electron" means "a negatively charged particle." Or if I’m going 50 mph and you pass me in the same direction going 65 mph it follows by the logic of physics that you’re going 15 mph faster than I am. Such truths are analytic. They are calculable. That there is a highway patrolman behind a billboard watching you break the speed limit is a matter, however, of observable, empirical fact.

Now I want to argue that the language of ethics, like that of geometry, is likewise analytic. [To my knowledge this position has not been investigated seriously before, but it it not entirely novel — see Locke, Essay vol. II, Bk. IV, Ch. III (p. 208 in Dover Ed.), and also Aquinas, Jefferson, and Kant.] The analyticity of English, terms defined in terms of one another, is one kind of analyticity. But I’m saying that the language-game of ethics contains many analytic truths, and many others that are synthetic.

E.g., "You should pay your debts" (analytic)

"You owe me $2.00" (a factual-ethical statement)

Therefore you should pay me $2.00 (a factual-ethical statement)

In ethics there are certain key concepts in terms of which the others must be understood. The word good: What does it mean? Doesn’t it mean different things for different people and different cultures? Can we really know what it means? Philosophers have offered numerous theories about what it means or about how the word is used or should be used. G.E. Moore suggested that it is an indefinable and that attempts to define it in terms of something else, pleasure, self-fulfillment, or whatever, are bound to fail. But whether we know what good really means or not, we know pretty well how to use it and how it relates to the rest of the language-game of ethics.

For example, what’s bad is not good. What’s right is good. What’s wrong is bad. These are all analytic statements of the type: "all squares have four corners." They are analytic statements in what Carnap called the "material mode."

As another example of an analytic ethical truth, we all know very well that murder is wrong. Anyone who doesn’t know that is, well, crazy and dangerous (or doesn’t know what the words mean). But "Murder is wrong" is not a matter of fact, but a matter of definition. To deny that murder is wrong would be quite as perverse as to suggest that squares have only three corners.

Murder is wrong — this is an analytic truth; and wrong means not right, which means not good — no matter what good means.

I am arguing that "Murder is wrong" is analytic because no examples of okay murders can be found. Is this a proper approach? Wouldn’t it make more sense to declare it analytic and insist that no counterexamples could possibly exist? I am taking the empirical route, accumulating empirical evidence to show that "Murder is wrong" is analytic, and that is what I find in the facts about the relevant English words. The a priori approach is wrong because I learned that murder is wrong by learning English at my Mother’s knee.

My students always protest that, e.g., self-defense is "murder that’s okay," because they don’t know the precise definition of murder.

Which brings up another version of the "mere tautology" argument, found in Jonathan Harrison’s article, "Ethical Objectivism," in the Encyclopedia of Philosophy.


A: Murder is wrong (in fact)

B: Murder is wrong (by defn.)

Harrison says A has substance but B does not. Once such a statement becomes widely accepted, he says, it becomes a truism, whereupon we are reluctant to call anything "murder" if we think it is right. If someone offers a putative counterexample — execution by the state, say, or killing in war — we think such things aren’t wrong, so we infer they can’t be murder. So, he says, "murder is wrong" ceases to guide us. He argues that someone who thinks B may, without inconsistency, also believe that genocide is right, just by maintaining that genocide is not murder!

He thinks we learn murder is wrong by way of an inductive generalization, but we don’t. We learn it when we learn English (or French, etc.).

Furthermore this argument is invalid:

Murder is wrong

Genocide is not murder

Therefore Genocide is not wrong

Harrison says these statements may be all believed together "without inconsistency." But thinking that genocide is not murder is impossible, even nonsensical, because of the actual meanings in English of "murder" and "genocide." Genocide is murder on a monstrous scale.

Anyway, consider

Murder is wrong (by definition) Murder is wrong (in fact)
Joe murdered Tom Joe murdered Tom
Therefore Joe did wrong Therefore Joe did wrong

Notice that both conclusions are "factual-ethical." This means that there is no difference in content between "Murder is wrong (by defn." and "Murder is wrong (in fact)." Notice, too, that "Murder is wrong (in fact)" does not mean "Some murder is wrong" or "Most murder is wrong."

Anyway imagine really doubting that murder is wrong:

"Yes, Joe murdered Tom, but ... (it was self-defense, or in war, etc.)"

None of that makes any sense, because "murder" has an actual meaning in English, as does "genocide," precise as can be.

All you would need to refute the assertion that murder is wrong would be a case of murder that isn’t wrong. But that’s impossible to supply without changing the meanings of murder and wrong. If I "murder someone in self-defense," that would be morally acceptable, wouldn’t it? No, no, that wouldn’t be called murder at all, but self-defense. The expression "murder in self-defense" is what Wittgenstein would have called a breach of the logic of language, what rhetoreticians call an oxymoron, what logicians call self-contradictory; it’s like the expression "square circle"; it’s nonsense.

But what about the killing that goes on in war? Don’t we give medals for that? Yes, but that’s not murder. The infamous case of Lt. Calley and the My Lai Massacre, which occurred in the context of the Vietnam War, shows that even (or especially) a military court distinguishes between the killing that is a natural feature of war, and outright murder. The Army tried Calley for murder, for killing a village full of unarmed civilians. (He was acquitted.)

Or, wouldn’t murdering Hitler have been okay? Wouldn’t that have saved millions of lives? Wouldn’t that be a case in which murder was good? Here we must bite the bullet: Murder is always wrong, and murdering Hitler would have been wrong, too. But perhaps we could get away with claiming that killing Hitler would have been more like self-defense or justifiable homicide than murder. An attempt was indeed made on his life by a group of his officers, and that decision might have been a morally difficult one for the conspirators.

Is abortion murder? This is another hard moral problem. Abortion involves taking "innocent human life," but is a fetus an innocent human life? A person? Murder by definition must involve wrongful and malicious taking of the life of a person (you take the life of a turnip when you pull it up, but that’s not murder). Are abortions done with malice?

Just because you know some geometry doesn’t mean every geometry problem will be a snap. Just knowing a few moral truisms such as Murder is wrong doesn’t mean all ethical problems will be easy. (By the same token great sophistication about ethical thinking hardly guarantees moral perfection, either.) But it is important to observe that the people on either side of the abortion issue seem equally convinced of the moral rectitude and indubitability of their respective moral stands. No facts or observations seem to budge either side. And of course this is the mark of analyticity. We might call such analyticity "de facto analyticity" in recognition of the fact that such analytic truths are only analytically true to those who accept them as principles, and of the fact that they can change."Can’t you see that abortion is murder?"

"Can’t you see that a fetus is not a baby?"

These are not disputes about facts, but about definitions, about basic principles — about which truisms are really true. Each side takes its own beliefs to be self-evident. It is just as if they were saying, "Can’t you see that a square has four corners?"

To the pro-life advocate, saying that a fetus is not a person is like saying that a square doesn’t have four corners. To dispute a fact invites inquiry, observation. But to dispute a de facto analytic truth — a principle — invites outrage. In the same way, you could never prove to me that murder could be morally okay, without getting me to change my definition of "murder," or of "morally okay," because, to me, wrongfulness is built into my concept of murder. That is, to me and to other speakers of English (or, mutatis mutandis, of any natural language) murder means something wrong. Whatever exceptions you might offer, I will try to somehow explain away. This de facto analyticity is not absolute, but it is binding on those who wish to speak the language seriously.

Togoans think genital mutilation is an appropriate way to ensure the fidelity of their women, so you might say it’s "right in Togo." But some Togoan women are leaving Togo (with their daughters), which suggests that not every Togoan accepts the Togoan view on this, and it suggests that the society’s view or the culture’s view can be mistaken. And so the society’s view is not the final arbiter of morality. I believe the arbiter of morality is English (or whatever natural language we learn at our Mother’s knee).

Ethical truths (even though we might dispute them) function like self-evident truths, and these self-evident truths are built into the language. But it must be admitted that geometrical truths do not admit of very much change, while the concepts of ordinary language (of which ethical language is a part) can slip and slide with the times. (2)

Still, the basic terms and axioms of ethical language form a network, a "web of belief" as Quine put it, a structure of meaning. Such words as good, bad, right, wrong, person, theft, murder, ought, should — all are intimately interconnected, just as are the concepts of geometry. All are defined, understood, in terms of one another. For example it is axiomatic in ethics that you can murder only a person — you can’t murder a parrot or a cabbage. You can steal only from another person. You ought not to cheat others — because it’s wrong and you ought not to do anything wrong. You should always pay your debts — because a debt is (or, the word debt means) something you ought to pay, something you are obligated to pay.

Ah, but what if you’ve borrowed Tom’s pistol and now he’s gone mad and wants it back? Well (Kant would say), you ought always to return what you’ve borrowed, to the person you borrowed it from. But in a sense Tom-the-madman is not the same person as the sane Tom. Or you might argue that it does not break our moral rule to defer returning the pistol until Tom’s madness passes. But such gyrations seem silly. You just do not give a pistol to a madman, even if it’s his. That seems quite self-evident, though one could no doubt concoct an exception.

So that’s another difference between ethics and geometry: sometimes one ethical principle will conflict with or override another, and that doesn’t happen in geometry, as far as I know. Ethics is not as pat as geometry. Ethics has a thousand concepts to juggle around, some sharp, some fuzzy, while geometry has only a few, each of which is clear as crystal. (3) On the other hand, even a subject as rigorous as theoretical physics sometimes loosens up and applies Newton’s equations instead of Einstein’s, say, even though Einstein’s are, strictly speaking, more accurate. (The former are true, but the latter are truer, you might say.)

In spite of such dissimilarities as I have noted, ethics still seems to me to be very similar to geometry. And it is worth noting, too, that while geometry applies to a made-up, abstract world of pure mathematical forms, ethics applies to the real world. Indeed, science and mathematics abstract shamelessly from the real, concrete world, the Lebenswelt as Edmund Husserl called it. The "physical universe" is itself a grand abstraction, as clean and tidy as if a muscular custodian had been at work on it with a vacuum cleaner and an industrial-strength cleanser. Geometry structures that ideal world. Quine would say it assists us in the purposes we use it for. Ethics, on the other hand, must operate in the Lebenswelt, a slob’s paradise full of people and values and politics and beauty and crime and God knows what-all.

The bedrock from which any human enterprise must arise, and against which it must be checked, is the world of our common experience. Science posits quarks, forces, ether, etc. to serve its purpose which is to satisfy a kind of adolescent curiosity. Religion has its purpose, too — giving our lives meaning, drama, a story. Law, too, and politics, have their purposes. Each such enterprise has its language-game, with axioms, definitions, theorems, often implicit but still precise.

The language of science represents our human determination to both posit and discover scientific truth. The language of mathematics posits and structures and then discovers what it has set forth. The language of ethics is the application of our human purpose of setting forth an ethical structure for the world. The language of religion sets forth a structure of meaning for the world. The great idealists, commendably, understood this and therefore took ethics and religion very seriously.

The world is structured by our various "languages of" this and that, toward our human purposes. It is narrow-minded (as we learned from the experience of the logical positivists) to insist that scientific language secures ontological commitment but ethical and religious language does not. We need not believe in atoms or points in space-time rather than rights and wrongs. It is a matter of the purposes we have for using the languages of this and that.

Just as the language of geometry structures the spatial aspect of the Lebenswelt, the language of ethics sets forth its value structure. Geometry talks about squares and circles, ethics talks about right and wrong. Physics talks about sub-atomic particles. None of these is more real than any other, as Quine should conclude.

The language of ethics, then, is as trustworthy as that of geometry — maybe more so, for we are human beings, moral agents, first, and geometers (and "lay physicists") after. Most of us would much prefer to deal with a person who was without knowledge of the Pythagorean Theorem than with someone ignorant of right and wrong. Whether right and wrong are out there in an external world is not as crucial as whether we choose to maintain the language of ethics, to impose values upon the Lebenswelt just as the geometer posits space and furnishes it with points and lines.

About Euclidean geometry, we ask: Does it fit the world? About an ethical system we can ask: Does it fit the world? Quine would ask: "Toward what purpose?" Euclidean geometry works for everyday geometrical jobs, and it seems reasonable to think that our ethical intuitions serve us well enough. Whether our human, cultural ethics is "true of the real world" has to be settled by pragmatic considerations.

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(1) As Quine would argue, of course, we have to know the definition of "being in Washington," and square in fact means "four-cornered" in English, which seems to collapse the distinction. Still there are ways to get away with it, I think.

(2) Though not as much as Derrida and the deconstructionists seem to thin, or we couldn’t communicate at all. And we do.

(3) It’s not always easy to find the square in a complex design, but when you do it will have four corners. In the same way it is not easy to tell whether a certain scenario involves murder, but if so it is wrong.

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