1. Valid​ity and soundness

As Boonin and Oddie (the authors of our first reading) stress, philosophy is concerned to a great extent with giving and assessing arguments. Much of ethics is in particular concerned with giving and assessing ethical arguments.

An argument involves making a claim (the “conclusion” of the argument) for certain reasons (the “premises” of the argument). To put the point metaphorically, the conclusion is built on the premises.

A good argument is one that succeeds in proving its conclusion – that is, it succeeds in demonstrating that the claim that is at issue is true for the reasons that are given. For an argument to be successful (or “sound,” as it is technically put) it must satisfy two conditions. First, it must be valid (another technical term, whose meaning will be explained in just a moment), and, secondly, all of its premises must be true. The argument will not be sound unless it satisfies both conditions. If it satisfies neither of the conditions, or if it satisfies one but not the other, it will be unsound; that is, it will not succeed in proving its conclusion true.

First co​ndition:

An argument is valid when its conclusion follows from its premises. Or, to put this same point in another way: an argument is valid if, and only if, it is impossible for all of its premises to be true without its conclusion also being true. This may be hard to grasp in the abstract, so let’s consider some examples.

Socrates

Suppose I say that Socrates is mortal, and suppose that for some reason you doubt that this is true and so you ask me why I make this claim. (Why would you doubt this? Heaven knows. But bear with me. This is just an illustration.) In other words, you ask me what my reason or reasons are for saying that Socrates is mortal. What you’re doing is asking me for an argument. And suppose I reply: “Socrates is mortal because, first, all men are mortal and, second, Socrates is a man.” Is this a good argument – is it sound? Let’s take a look.

The argument I’ve given you (I’ll call it Argument A) consists in three statements – two premises and a conclusion. It can be represented as follows:

Statement (1) is the first premise, statement (2) is the second premise, and statement (3) is the conclusion of the argument. (The symbol ∴ is to be read as saying “therefore.”) As I’ve noted, for the argument to be sound it has to satisfy two conditions – it has to pass two tests. The first test is that of validity. Is Argument A valid? Does its conclusion follow from its premises? The answer is Yes. Why? Because it’s not possible for its premises to be true without its conclusion also being true. If all men are mortal and Socrates is a man, then Socrates has to be mortal. Accepting the premises of the argument commits you to accepting its conclusion. It would be inconsistent for anyone to say, “Oh, I grant that all men are mortal and that Socrates is a man. Nonetheless, Socrates is not mortal.” The inconsistency of such a position can be confirmed by drawing a diagram.

Imagine that there are two circles, one containing all the men that exist and the other containing all the mortals that exist. Now consider the first premise of Argument A: (1) All men are mortal. This premise claims, in effect, that there is a certain relation between the two circles. It says that the circle of men is wholly contained within the circle of mortals: all men are mortal(s). And so we have this picture for premise (1):

Now consider the second premise: (2) Socrates is a man. This says, in effect, that Socrates is inside the circle of men. That is:

Now, what happens when you put both of the premises together? This:

And notice what has happened. In putting the premises together, you’ve automatically pictured the conclusion as well. Since Socrates is inside the small circle, and the small circle is inside the larger circle, Socrates is and has to be inside the larger circle as well. That is: (3) Socrates is mortal. Given the premises, the conclusion is inescapable. That’s why Argument A is valid.

Aristotle

For contrast, let’s consider an obviously invalid argument.

Imagine that I now say to you that ​Aristotle is mortal and that you doubt this and ask me why I think it’s true. And suppose I reply: “Aristotle is mortal because, first, all men are mortal and, second, Socrates is a man.” That is:

You’d be puzzled. What does Socrates’s being a man have to do with Aristotle’s being mortal? Nothing, of course, and that’s why the argument is no good – it’s invalid. To put the point graphically: the premises of Argument B result in the same diagram as before, namely,

But Aristotle is nowhere to be found in this diagram! For all the premises tell us, he could be floating way out in “space” somewhere:

Of course, we know that Aristotle’s not out there, that he’s somewhere inside the small circle along with Socrates. But that’s not the point. The point is whether it’s possible for the premises of Argument B to be true without its conclusion being true as well, and the diagram just given shows that this is possible. Accepting the premises does not commit you to accepting the conclusion. That’s why Argument B is invalid.

I think it’s pretty clear that there’s something obviously right about Argument A and obviously wrong about Argument B. They wear their validity and invalidity, respectively, on their sleeves. The conclusion of Argument A clearly follows from (or fits with) its premises, whereas that’s not true of the conclusion of Argument B and its premises. But sometimes things aren’t so obvious. Suppose I say to you that some men are intelligent and that you doubt this. (If you do, I suspect you’re a woman.) So you ask me for an argument, and I say in reply:

Is this argument valid? It might seem that it is. Consider the following diagram:

Notice how in this diagram the circle of intelligent beings intersects not only the circle of humans (as stated in the first premise of the argument) but also the circle of men (as stated in the conclusion). But we should not be misled by this diagram. When it comes to testing whether an argument is valid, the pertinent question is not whether it’s possible for the premises to be true along with the conclusion, but rather whether it’s possible for the premises to be true without the conclusion. For if this is possible – if it’s possible for the premises to be true without the conclusion – then the conclusion does not follow from the premises, and so the argument is invalid. And the fact is that the conclusion of Argument C does not follow from its premises, as the following diagram confirms:

Notice that this diagram manages to depict the premises without the conclusion. (How come? Well, when you think of it, it’s possible that all the intelligent humans are women. Of course, in defense of men around the world, I must immediately hasten to add that, although this is possible, it is in fact not true!)

There are some more points that we should note about validity. First, validity is a matter of form rather than content. That is, whether an argument is valid depends on how it is structured rather than on what it says. Consider, for example, the following “counterpart” to the situation involved with Argument A above. Suppose I say that Socrates is immortal, and suppose that, reasonably enough, you doubt that this is true and so you ask me why I make this claim. And suppose I reply: “Socrates is immortal because, first, all men are immortal and, second, Socrates is a man.” This argument can be represented as follows:

Question: Is this argument valid? Answer: Yes. Why? Because of its form. The relevant picture is this:

Brad Pitt

Suppose I say that Brad Pitt is very hot, and you ask me why I say this, and I reply excitedly, “Because he’s a star!”.

Here’s my argument, put formally:

You might wonder just what’s going on. What do I mean by “star”? What do I mean by “hot”? Suppose that, when I say that all stars are very hot, I mean “star” in the astronomical sense and “hot” in the temperature sense, but, when I say that Brad Pitt is a star, I mean “star” in the Hollywood sense and, when I say that he’s hot, I mean that he’s sexy. Well, then, it’s clear that the argument is not valid after all, because I’m equivocating when using the terms “star” and “hot”; that is, I’m using them in different senses. If, however, I’m not equivocating in the use of these terms, then the argument is valid. Perhaps what I mean is this:

Like Argument A*, Argument D* clearly has serious problems, but one problem it doesn’t have is that of being invalid, as the following diagram confirms:

Second co​n​dition:

If Arguments A* and D* are valid, where is it that they go wrong? The answer is that they fail to satisfy the second condition needed for an argument to succeed – not all of their premises are true. In the case of Argument A*, the guilty premise is the first one, which states that all men are immortal. In the case of Argument D*, the guilty premise is the second one, which states that Brad Pitt is an astronomical star. (Even here there could be ambiguity, of course. Given the context, what the second premise means is that Brad Pitt is a star in the astronomical sense of “star,” that is, that he’s one of those things we see up in the sky on a clear night. So understood, the premise is obviously false. If what was meant instead by “astronomical star” was that Brad Pitt is an especially big star in the Hollywood sense, then I suppose the premise would be true.)

Why is it so important that an argument satisfy both the conditions mentioned? Because the whole point of giving an argument is to prove that what you’re claiming to be true is true, and you’ve done this if your claim (a) follows from (b) true premises, but you haven’t done this if your argument fails either the first condition or the second (or both).

***Here is a good place to stop and consider Questions 4, 5, and 6 on the Practice Questions for Module 1.***

Let’s take stock of the arguments considered so far.

Argument A is valid, so it passes the first test. Whether it is sound, then, depends on whether it also passes the second test. Are all of its premises true? Yes. So Argument A is sound.

Like Argument A, Argument A* is valid, but, since it has a false premise, it is unsound.

Argument B is invalid, so it fails the first test. Since an argument has to pass both tests to be sound, it’s clear that Argument B is therefore unsound. (This is true despite the fact that the argument actually passes the second test – all of its premises are indeed true.)

Argument C is invalid, and therefore unsound, regardless of whether all of its premises are true (which presumably they are).

Whether Argument D is valid depends on whether the terms “star” and “hot” are being used equivocally. (Again, it is valid only if there is no equivocation.) Whether its premises are true depends on just how these terms are to be interpreted.

Final re​marks:

Here are some very important final points to bear in mind.

First, a sharp distinction is to be drawn between the terms “true” and “false,” on the one hand, and the terms “valid,” “invalid,” “sound,” and “unsound,” on the other. Only individual statements (like those that constitute the premises and conclusions of arguments) are true or false; arguments taken as a whole cannot be either true or false. For example, the first premise of Argument A* is false, its second premise is true, and its conclusion is false. Argument A* itself, though, is neither true nor false. By the same token, only arguments taken as a whole are valid, invalid, sound, or unsound; individual statements cannot be valid or invalid, sound or unsound. For example, Argument A* is valid but unsound; the individual statements that constitute the premises and conclusion of this argument are neither (in)valid nor (un)sound.

Second, don’t confuse the two tests for soundness. Whether an argument is valid is one thing; whether its premises are true is an entirely separate matter. Consider Argument A*, for example. It passes the first test but fails the second. Or consider Argument B. It passes the second test but fails the first. Both of these arguments are therefore unsound. (Of course, some arguments – like Argument A, for example – pass both tests and are therefore sound. And still other arguments fail both tests and are of course therefore unsound.)

Third, if an argument is unsound, this does not mean that its conclusion is false. (Consider Argument B which is invalid, and therefore unsound, even though its conclusion is true.) An unsound argument is simply one that has not succeeded in proving its conclusion true. (We know that the conclusion of Argument B is true, but not for the reasons given by the premises of that argument.) This is a very important point. What it means is that correctly rejecting another person’s argument as unsound (because it fails one or other or both of the tests mentioned above) does not justify rejecting the conclusion of that argument. This person may have failed to prove his point, but his point might still be true. Perhaps some other argument would succeed where the present one has failed. If you want to reject this person’s position, you must come up with a sound argument of your own against it.

***Here is a good place to stop and consider Questions 7, 8, and 9 on the Practice Questions for Module 1.***

2. Common type​s of argume​nts

In our first reading, Boonin and Oddie identify five common types of argument that occur in some of our other readings. Below I will re-present them in such a way that it is clear that any argument of one of these types is valid. (That is, it is clear that anyone who accepts the premises of such an argument is committed to accepting its conclusion as well.) Thus, whether some particular argument of one of these types is sound will depend on whether it passes the second test for soundness, that is, on whether it satisfies the condition of having premises that are all true.

Type I – Arguments f​rom analogy:

Arguments of this type have the following form:

Note that premise (2) says that acting in one way is morally just like acting in another. A possible instance of this premise would be: abortion is morally just like infanticide. (Infanticide is the killing of infants.) Notice that the premise doesn’t say that acting in the one way is exactly like acting in the other in all respects. Abortion, for example, is not exactly the same thing as infanticide. For one thing, abortion involves terminating the life of a pre-natal individual, whereas infanticide involves terminating the life of a post-natal individual. For another, abortion involves extracting the fetus from the mother’s womb, whereas infanticide doesn’t involve any such activity. What someone who makes the claim that abortion is morally just like infanticide is saying is simply that there is no morally relevant difference between the two and hence that they are to be given the same moral evaluation.

We will come across arguments of Type I when we discuss Ericsson’s article on prostitution and Fullinwider’s article on war. Again, any argument of this type is valid, but whether it is sound is another matter. (Is it the case, for example, that abortion is morally just like infanticide? That’s something we’ll be discussing later.)

​Type II – Bare-difference arguments:

Arguments of this type have the following form:

Once again, the relation between abortion and infanticide could be used to give an illustration of an argument of this type. Someone might try to present a pair of cases that are exactly alike, except that one involves abortion and the other infanticide, then claim that, despite this difference, the two cases are morally equivalent, and then go on to conclude that abortion is therefore morally just like infanticide. (On the basis of this conclusion, he might then go further and try using it as the second premise in an argument of Type 1 in order to reach the final conclusion that abortion is morally wrong.)

We will come across an argument of Type II when we discuss Rachels’s article on euthanasia. Once again, any argument of this type is valid, but whether it is sound is another matter.

Type III – Arguments from inference to the best explanation:

Arguments of this type have the following form:

We will come across arguments of this type when we discuss Marquis’s article on abortion, Singer’s article on famine relief, and Regan’s article on the treatment of animals.

Type IV – Arguments by process of elimination:

Arguments of this type have the following form:

We will come across an argument of this type when we discuss Ericsson’s article on prostitution.

Type V – Arguments by reduction to absurdity:

Arguments of this type have the following form:

We will come across arguments of this type when we discuss the relation between God and morality, Boonin’s article on same-sex marriage, Norcross’s article on abortion, and Arthur’s article on famine relief.

Arguments of Types I and II are intimately concerned with the moral justifiability of discrimination, regarding which there is the following important principle:

The Principle of Comp​ara​tive Justice:
It is morally wrong to engage in discrimination based on irrelevant differences.

The fundamental idea here, one with which we are all familiar, is that cases that are equal in relevant respects ought to be treated equally (while cases that are unequal in relevant respects ought to be treated according to their relevant differences). In one way or another, the issue of discrimination will crop up repeatedly in our discussions. Notice that, although the word “discriminate” usually has a bad connotation, the Principle of Comparative Justice does not condemn all discrimination. It only condemns unjust discrimination – discrimination that is based on irrelevant differences. (Of course, a very important question then arises: when is a difference relevant, and when is it irrelevant? This is not always an easy question to answer.)

Arguments of Type III and, especially, V are very common. They involve rendering explicit the implications of a view. Arguments of Type III have to do with recognizing how a moral principle can result in verdicts that may be surprising and even unwelcome when it is applied in a new context. Arguments of Type V give expression to the fact that, if a claim or view has unacceptable implications, then it too is unacceptable. (Suppose, for example, that, according to a certain “worldview,” the world will come to an end on December 1, 2016. Well, if the world doesn’t end then, that view must be rejected.) A great deal of philosophy involves tracing the implications of views as a way of testing whether they (the views) are acceptable. This is something else that will crop up repeatedly in our discussions.

Arguments of Type IV are delicate. Remember when I said earlier that it can happen that an argument is unsound but its conclusion is nonetheless true? It might seem that arguments of Type IV ignore or even deny this fact, but actually they don’t. What they aim to establish is something more subtle, namely, that, given the persistent failure to prove a certain claim true, it is reasonable, at least for the time being (that is, unless and until some new argument succeeds where previous arguments have failed), to assume that the claim is not true.

One final point. The material covered in this section is difficult and abstract. You should not expect to grasp it all immediately. You should therefore not be freaking out because there are parts of it (perhaps large parts) that you don’t yet understand. What you should do is go back over it again (and again). You should also be patient. You will soon see this material being applied in the discussions that follow and, when you do, that should be of considerable help to you in coming to terms with it. Use this section as a guide to these future discussions, and then come back to this section, using the discussions themselves in turn as a guide to the material in this section.

***Here is a good place to stop and consider Questions 10 and 11 on the Practice Questions for Module 1.***