Contents

• Stage 1
• Stage 2
• Stage 3
• Stage 4
• In General
• Appendix for Logicians

Schopenhauer said that it helps to have common names for common fallacies. When we do, then we can use them in conversation for quick and clear diagnoses of problems with reasoning. Then we have a better chance to notice them, fix them, and move beyond them.

In that spirit I'd like to name four stages of sophistication in argument, and some associated informal properties of argument. This is not profound. In fact, it's hokey. But I believe that teachers, and others who talk about arguments and evaluate their strengths, will find it helpful to have these names for rapid identification of where we are and where we could be instead.

These stages apply primarily to arguments for ethical and political conclusions. They have very little relevance to arguments for mathematical and scientific conclusions. (For the reason why, see the appendix below.)

Here are some terms to help us understand the stages to follow. Let us say that a positive argument directly supports a conclusion, while a negative argument undermines an opposing conclusion. Let us say that an argument is two-sided if it has both positive and negative components, and one-sided otherwise. Finally, let us say that an argument is responsive if it answers objections to its positive and negative components, and unresponsive otherwise.

Stage 1.  To say nothing in support of your claim. To make an assertion without argument.

This is the absence of argument. If we need another term for it, we can call it dogmatism.

Since there is no argument at all here, we could call it Stage 0. However, I'd like to recognize that it is already an advance on the vagueness which does not assert anything at all.

Stage 2.  To offer a positive or negative argument, but not yet both. To argue one-sidedly.

Stage 2 arguments can be positive or negative. What's distinctive about them is that they are not yet both.

We're not demanding that the positive or negative argument be sufficient, or strong, or even relevant. Hence, these are all Stage 2 arguments:

• Assisted suicide should be legal because liberty is valuable.
• Assisted suicide should be illegal because life is valuable.
• You should vote for Smith because she will balance the budget.
• You should vote against Smith because she once saw a psychiatrist while in college.
• Genocide cannot be all bad. It limits the population.
• The death penalty is justified. It keeps at least one person from hurting anyone ever again.
• Voting is a sham. No nationwide election was ever decided by one vote.
• Cloning human beings is immoral. Every person has a right to be genetically unique.
• Bigotry must be tolerated, because most bigots are sincere.

Stage 2 arguments can be much stronger than these examples. But these weak examples show well what is deficient in any argument limited to Stage 2. Anyone who is paying attention to a controversy can say something positive on one side, or can say something negative against the other. Hence, to hear something on one side of an issue doesn't get us very far. We want to know the best that can be said on one side, and the best that can be said on the other.

We would have the same problem if someone gave 50 distinct and detailed reasons why assisted suicide should be legal. That would be impressive, but there may be 50 entirely adequate rebuttals to these reasons, and then 100 reasons why assisted suicide should be illegal.

In short, a Stage 2 argument for a certain conclusion might be strong, but for all we know the arguments for an alternative conclusion are even stronger. We won't know until we look at the arguments for alternative conclusions. That requires moving beyond the one-sidedness of Stage 2 arguments.

Stage 3.  To offer both a positive and negative argument. To argue two-sidedly.

We're still not demanding sufficiency, strength, or relevance, though we are now demanding two-sidedness.

I'm using the term "two-sidedness" as the alternative to the one-sidedness of Stage 2 arguments. But in fact there may be many more than two alternative positions on an issue. Where there are many alternative positions, a Stage 3 argument criticizes at least one of them. If it criticizes many of them, it could be called "many-sided", but I will continue to call it "two-sided".

Here are some Stage 3 arguments:

• We should regulate handguns because that would reduce the number of accidental and impulsive gun killings every year (positive). The argument that handguns are needed in self-defense is question-begging; if there were fewer guns, there would be less need to use them in self-defense (negative).
• We should not regulate handguns because that would violate the liberty of citizens guaranteed under the Second Amendment (negative). We should make handgun ownership easier rather than more difficult, because an armed society is a safe society (positive).
• Vote for Smith because she will appoint good Supreme Court Justices (positive). Don't vote for the other guy because he accepts money from big corporations (negative).

But if we're still not demanding sufficiency, strength, or relevance, then it's still true that any observant person can say something pro and con on either side of a controversy. Hence to hear something pro one side and something con the other doesn't get us very far.

In short, if we make a two-sided argument and disregard objections to it, and disregard defenses raised against our own objections, then our position might be strong and still be weaker than an alternative position. Only by moving beyond two-sidedness to responsiveness can we tell. We have to examine and answer the objections made against our views, and examine and answer the defenses raised against our objections, not disregard them, if we are to discover whether they have merit.

Another way to put this:  the positive side of a Stage 3 argument might be strong, but for all we know the positive arguments for contrary conclusions are even stronger. Our positive argument might be strong, but for all we know the negative arguments against it show its insufficiency or invalidity. Our negative argument might be strong, but for all we know the position it criticizes can answer it adequately. We won't know whether our strong Stage 3 argument is weaker than its rivals until we see how strong the rival positions are. This requires that we respond to the positive and negative arguments for rival positions.

Stage 4.  To offer positive and negative arguments, to anticipate objections to those, and to respond to those objections. To argue two-sidedly and responsively.

Responsiveness takes two forms. A positive argument is responsive if it seeks out objections and responds to them. A negative argument is responsive if it seeks out rebuttals or defenses and responds to them.

To respond to an objection or rebuttal is to take note of it, to assess its strength, and to articulate the reasons why they do not suffice to overturn one's position or to extract a concession one is not already making.

A two-sided argument is not necessarily responsive. A two-sided argument simply has positive and negative components. But it may disregard objections offered to its positive argument, and disregard defenses offered to its negative argument. If it does disregard these (if it is merely two-sided and not also responsive), then we can't finish the job of assessing the strength of the argument or asertain whether there might be stronger arguments for contrary conclusions. However, when two-sided become responsive, then we can begin to do so.

A negative argument is not "responsive" just because it is in dialogue with an opponent. Responsiveness requires us to confront objections to our own positive and negative arguments. It requires us to go beyond the criticism of others, which occurs with every negative argument at Stage 2 or 3. We must attain a willingness to listen to criticism levelled against us and to answer it. We must realize that even strong arguments can be weaker than some of their counter-arguments. We must commit ourselves to discovering whether this is the case.

Argument becomes serious at Stage 4. At earlier stages there is no requirement that arguments be relevant, strong, or sufficient. Stage 1 assertions may be true, and Stage 2 and 3 arguments may be strong, but they need not be. Even laughable assertions qualify for Stage 1, while even laughable arguments qualify for Stages 2 and 3. Only at Stage 4 does the defining condition of the stage include practices which tend to strengthen arguments.

Stage 4 responsiveness is a practice which tends to improve the relevance, strength, sufficiency, validity, and soundness of our arguments. When we are answering objections to our positive arguments and answering rebuttals to our negative arguments, then we must respond to criticism that our premises are false or irrelevant, reasoning invalid, or language unclear. We must make concessions to strong arguments on the other sides, unless we have strong arguments for not making them. We must identify more and more of the major alternatives to our position and assess their objections to our conclusion and arguments.

To respond to a negative argument against our own position, or a positive argument for a contrary conclusion, calls upon us to uncover its weaknesses, admit its strengths, and then to revise our own argument accordingly. In practice this argument-revision takes many forms. It might mean retracting part of our thesis or one of our arguments for it. It might mean adding an argument specifically against a previously unnoticed alternative, or answering a previously unnoticed objection. It might mean qualifying an unqualified or oversimplified thesis. It might mean acknowledging an exception. It might mean making a concession. It will almost always mean making simple arguments and simple conclusions complex.

How do we find the alternative arguments to which to respond? In general we discover them through study, imagination, and experience. If we have studied a controversy, then we may already know strong arguments on both sides. Even if we have studied, we may open our minds further by trying to imagine arguments against our own positions. Imagination can give us some of the arguments to which we need to respond, but perhaps not the best ones. These tend to come from people who are living in circumstances which we can't imagine. We should expect to strengthen the responsiveness or our arguments with a lifetime of sensitive listening and observation.

While responsiveness tends to strengthen arguments, some Stage 4 arguments will still be stronger than others. However, to improve the weaker Stage 4 arguments, we must stay at Stage 4 and improve our responsiveness. In this sense Stage 4 is the only stage which is dialectically stable, or which does not push responsible inquirers beyond itself. There is no Stage 5.

Responsiveness is a matter of degree. We may be better at responding to objections we actually hear than objections we imagine or anticipate. We may be better at taking relevant evidence into account if it has already been brough to our attention than if we have to seek it out. If many critics are objecting to our positive argument, then we might know or choose to respond to only some. If many opponents we have criticized have offered rebuttals, we might know or choose to respond to only some. But because responsiveness includes a commitment to continue, we are committed to surpass the degree to which we have already been responsive. If one objection is that we are not sufficiently responsive, then we are committed to respond to that objection, as we would to any other objection. If it weren't for the commitment to continue, we could make a lame and pro forma response to criticism, satisfy the Stage 4 definition, and stop. But because at this stage we are committed to respond, we continue to listen, to learn, to revise our conclusion and arguments in light of criticism, and to strengthen them in the process. This is the stage at which argument becomes serious because it is only at this stage that argument has to improve.

Another perspective on this. If you are paying attention to any controversy (assisted suicide, gun control, the death penalty), then you can make Stage 1, 2, and 3 arguments for either side at whim. You could pick your conclusion with the flip of a coin, and instantly support your new conclusion at those levels of sophistication. All you need is to listen to what people are saying. It may be sufficient or insufficient, strong or weak, relevant or irrelevant. In this sense, Stages 1, 2, and 3 are compatible with the random selection of belief. But a stage of argument is finally serious when it is not compatible with the random selection of belief.

Another perspective on this. Since observant people can make Stage 1, 2, and 3 arguments on either side of any major controversy, these arguments do not help us move beyond disagreement to possible truth, correctness, validity, wisdom, or justice. If we want to know what position on gun control we ought to take, and not just what positions can be argued, then we must move to Stage 4 arguments. If we want to use argument as part of an inquiry for an ever-more adequate position, and not as a decoration for a position with which we are already satisfied, then we must move to Stage 4 arguments.

Another perspective on this. The Greek skeptics said that two arguments were equipollent if they were equal in strength or acceptability. Every Stage 1, 2, and 3 argument can be opposed by an equipollent argument by anyone familiar with the subject matter. With Stage 4 for the first time, we reach a level where this is not true. My Stage 4 argument for gun control might, in fact, be equipollent with another one against gun control, but I couldn't produce both arguments on the spot, as an academic exercise, or from mere familiarity with the controversy. Making a Stage 4 argument is my way of showing that I care about what I ought to believe, and the strength of my argument, not merely about the form of argument regardless of strength. A stage of argument is finally serious when we cannot make an equipollent counter-argument at a moment's notice.

In General

I'm not saying that all arguments at the same stage are equally strong. For example, "Vote for Jones because he has a nice smile" and "Vote for Smith because she will protect the envirionment" are both Stage 2 arguments, and not at all equal in strength.

Some cynics complain that all argument is just verbal decoration. This position shows that they are partially right. Stage 2 and 3 arguments are just verbal decoration, even if sincerely and passionately put forward. The reason is that they establish nothing as long as equipollent arguments can be concocted at will.

Assertion (Stage 1) is necessary but not sufficient for argument. Argument (Stage 2) is necessary but not sufficient for two-sided argument. Two-sided argument (Stage 3) is necessary but not sufficient for responsive argument. If it weren't for this last point, we could have switched the order of Stages 3 and 4 (two-sidedness and responsiveness). Inquirers who become responsive at the same time they become two-sided simply skip Stage 3.

Apart from the necessary and sufficient conditions enforcing this sequence in stages, it is my experience that students usually learn the stages in the order presented here. In particular, they learn responsiveness later than they learn two-sidedness. Since the primary purpose of articulating these stages is to use them in teaching, it would matter if students pass through these phases developmentally as well as logically. While we want to students to learn to compose and assess Stage 4 arguments, we might be wrong to expect them to do it too early in their careers.

When students are ready, it may help move them from Stage 3 to Stage 4 to give an assignment somewhat as follows. Take a stand on a moral or political controversy. Imagine a Stage 3 argument against your position. It makes a positive case for a contrary conclusion and a negative case against your conclusion. Now respond to it, amd show that it does not require any concessions from you that you are not already making. If this is too easy, then don't settle for a random Stage 3 argument against your position, but use the strongest arguments you can find against your position. (To students who think this an exercise in "combat", you could reply that it is much more like an exercise in "listening".)

Stage 4 arguments are necessary but not sufficient to make progress. We know they don't suffice because on long-running disputes, like the relative merits of liberty and security, or liberty and equality, or liberty and religious morality, we've had Stage 4 arguments on both sides for centuries and we're no closer to social consensus. This history of sophisticated disputation might well have produced progress in clarifying the issues, and showing which premises tend to favor which conclusions. But it hasn't led us to know which premises we ought to affirm.

With the language of two-sidedness and responsiveness, we can see new logical virtues set in as we advance from stage to stage. From Stage 1 to 2, we move from unargued to argued positions. From Stage 2 to 3, we move from one-sided to two-sided arguments. From Stage 3 to 4, we move from unresponsive to responsive arguments.

Stage Argued? Two-Sided? Responsive? 4 yes yes yes 3 yes yes no 2 yes no no 1 no no no

Appendix for Logicians

1. Note that the four stages are not defined through validity and truth, or validity and soundness. One reason is that validity only applies to deductive arguments, and not all ethical arguments are deductive. The second and more important reason is that I wanted to classify argument strategies which can be carried out validly or invalidly, soundly or unsoundly. These strategies show us that even if a Stage 2 or 3 argument is sound, it can be strengthened, e.g. by becoming two-sided or responsive. If we evaluated arguments only for their validity and soundness, we would miss this.

   Moreover, as teachers we are not comfortable judging a student argument for the truth of its conclusion, but only for the strength of its supporting argument. So we can can comment freely on validity, but tend to steer clear of soundness. Since arguments at all stages can be sound or unsound, we can show students at what stage they are arguing and urge them to advance, still without commenting on soundness. We can assign Stage 4 arguments and nudge students toward this level of sophistication without committing ourselves to comment on the truth of conclusions and without a detour to teach the requirements of validity and soundness.

   In any case, if we do want to comment on validity and soundness, we already have the words "valid", "true", and "sound" (and their negations) to use in conversation and comments on papers. I wanted names for strategies apart from these kinds of strength and weakness. I often want to tell students that their arguments may be valid, even sound, but that they are one-sided or unresponsive.

   Finally, if we are in a dispute with someone, say, about assisted suicide, then we will not be able to apply the label "sound" or "unsound" to either party's arguments non-controversially. The label will be just as contested as the contested conclusions, and for the same reason. I wanted labels which can be applied almost non-controversially, just as we might apply the names of common fallacies. I wanted labels which will draw our attention to features of our arguments which could help us through an impasse. Labels which require us to settle our dispute first would defeat this purpose.

2. Some logicians say that an argument is cogent if it is valid and sound and takes all relevant evidence into account. On this usage, failure to reach Stage 4 does not undermine validity or soundness, but cogency.

   If we consider the failure to reach Stage 4 a fallacy of cogency, then we should be clear what this means. This fallacy does not make an argument invalid or unsound. The fallacy consists in persuading readers, and perhaps ourselves, that we have said enough to tilt the scale of evidence, or that we have said enough to justify a judgment. But until we been responsive to other viewpoints and their supporting arguments, we haven't said enough to justify a judgment. The arguments for other conclusions may be stronger than our own arguments for our own conclusion. We won't know until we examine and respond to them.

3. There are many virtues of strong arguments. Why bother putting them into stages? The answer is to help teachers teach argument, not to illumnate argument as such. This is for pedagogy, not logic. When we identify stages in the sophistication of argument, then we help students identify what is strong, and what is weak, in their method or strategy of argument. If the properties of the stages are already known, then students will know what it takes to advance to higher levels of sophistication.

4. Similarly, there are many virtues of strong arguments, and many ways to put them in stages. Apart from what I've already said about this method of putting them in stages, I can point out that this method does not make the distinction between any two stages a matter of degree. Hence it does not turn on the degree of effort in criticizing alternatives or responding to criticism, or the degree of completeness in acknowleding alternatives or criticism. This is desirable to the extent that it makes the application of the labels non-controversial. (While responsiveness is a matter of degree, the distinction between responsiveness and two-sidedness is not a matter of degree.)

   Nor does the distinction between any two stages depend on being correct. This is desirable to the extent that we want to comment on the sophistication of student arguments without commenting on their correctness.

5. We cannot always distinguish positive and negative arguments. In some disputes, where there are only two options, which are contradictory, an argument for one is also an argument against the other. If my opponent has objected to my positive argument, then my reply has both positive and negative elements —positive for supporting my view, negative for undermining the contradictory view.

6. The reason why these stages of argument apply in ethics, but not mathematics, is that in mathematics a one-sided and unresponsive argument can be perfect. To prove a theorem, you needn't disprove all possible alternatives or answer any objections. At least if we are working in a formal system with stipulated axioms and rules of inference, then we can construct a positive argument without a negative, and without anticipating or answering criticism. In less formalized mathematics, and in natural science, these stages get more traction, though still much less than in ethics and politics. The reason is that in ethics and politics, our premises are as much in dispute as our conclusions. Hence any argument is likely to be criticized for its premises, even if its reasoning from them is impeccable. If ethics and politics had assured premises or stipulated axioms, then the stages would apply to them as little as they do in formal mathematics.

   These stages apply, then, in any discipline where premises are just as much in dispute as the conclusions. Ethics and politics are clearly fields of this kind. Philosophy is preeminently such a field. Hence, it makes more sense to assign a Stage 4 argument in a philosophy paper than in a mathematics paper.