TCS Daily

How to Argue

By Keith Burgess-Jackson - December 11, 2003 12:00 AM

Citizens in a democracy must know two things: how to argue and how to evaluate arguments (so as not to be duped, hoodwinked, railroaded, snookered, or browbeaten). There are two types of argument: inductive and deductive. The difference concerns the relation being asserted between premise(s) and conclusion. When one argues inductively, one claims that the truth of the premises makes the truth of the conclusion probable (or more probable than it would be without the premises). When one argues deductively, one claims that the truth of the premises is incompatible (logically) with the falsity of the conclusion. In other words, the premises entail or necessitate the conclusion. Induction is to probability as deduction is to necessity.


Let us focus on deduction. Suppose I argue as follows, using the letters "p" and "q" to stand for propositions:


1. If p, then q.

2. Not q.


3. Not p.


This is a valid (i.e., truth-preserving) argument form. It is called modus tollens (from the Latin for "denying mode"). The claim is that the premises, 1 and 2, jointly entail the conclusion, 3. If 1 and 2 are true, then so is 3. But this is equivalent to claiming that the following three propositions are incompatible (philosophers use the term "inconsistent"):


1. If p, then q.

2. Not q.

3. p.


To say that these propositions are inconsistent is to say that not all of them can be true. At least one of them, therefore, is false. But which is the false one (or ones)? Here there can be reasonable disagreement. I, the author of the argument, might believe that 3 is false, whereas you might think that 2 is false. Someone else might think that 1 is false. Logic cannot resolve this disagreement. Logic is about structure, not content, about how propositions are related, not about whether they are true. Truth is the province of scientists and ordinary people, not philosophers.


The best argument one can make is a valid deductive argument with necessarily true premises. Let me explain what I mean by "necessarily." Some true propositions are true in virtue of how the world is. The proposition that George W. Bush is president is true, but it need not be. In fact, it wasn't always true and in late January 2009, after eight years of being true, it will no longer be true (a little humor). The proposition that Al Gore is president is false, but it need not be. In fact, it might one day be true (perish the thought - again, a little humor). Propositions of this sort are called contingent propositions (because their truth or falsity is contingent, or dependent, on how things are).


Necessary propositions are different. Necessarily true propositions are true and cannot, logically, be false. Necessarily false propositions are false and cannot, logically, be true. Some necessarily true propositions are true in virtue of their form, such as "Either God exists or God does not exist." Others are true in virtue of their content, such as "All widows are women." (The concept of a widow is such that only a woman can be one.) I said in the previous paragraph that logic is not about whether propositions are true. I can now qualify that. Logic is not about whether contingent propositions are true. Logicians are competent to determine whether propositions are necessarily true or necessarily false.


If I make a valid deductive argument with necessarily true premises, then not only is my conclusion true; it is necessarily true. The necessity is preserved along with the truth. Unfortunately, there are few arguments of this sort. But isn't it almost as good to make a valid deductive argument with contingently true premises? The answer is "Yes," but contingent propositions, especially those of an evaluative nature, are often controversial. I (the arguer) may believe that my premises are true, but unless my interlocutor (audience) agrees, my argument will get no traction. Does that matter? Should I worry that my interlocutor denies (or has doubts about) one of my premises? One thing I might do in this situation is argue for the controverted premise. The conclusion of the new argument is the controverted premise of the old one. But this merely pushes the problem back a step. One of the new premises might be denied or doubted, in which case, if I hope to persuade, I must argue for it.


As this shows, argumentation is difficult and time-consuming. It involves painstaking attention to the logical relations among propositions and to the beliefs of one's interlocutor. Of course, I might give up as soon as my interlocutor denies or doubts one of my premises. But that is a failure of the argument. What was the point of my arguing, anyway? Presumably it was to persuade someone to believe something that was not already believed. But if my interlocutor denies or doubts my starting point, then I have failed to accomplish my goal. I may accuse my interlocutor of being "irrational," "unreasonable," or "pigheaded" (you hear that a lot among philosophers), but this should not bother the interlocutor. He or she may claim to have good reason to deny or doubt the disputed premise. Reasonableness, like beauty, is in the eye of the beholder. One person's reasonable belief is another's absurdity.


All argumentation, to be effective, must be ad hominem in nature. The term "ad hominem" has two very different uses in philosophy. They must not be confused. You have probably heard of the ad hominem fallacy. (A fallacy is an argument that is psychologically attractive but logically infirm; it seems like a good argument, but isn't.) This fallacy consists in dismissing someone's argument on the ground that he or she is a bad person (a Marxist, for example, or a Democrat). This is clearly fallacious, for bad people can make good arguments and good people bad arguments. One cannot transfer goodness or badness from arguers to arguments any more than one can transfer goodness or badness from politicians to policies. Even Hitler was capable of making, and probably did make, a sound argument.


The other use of the term "ad hominem" has nothing to do with fallacies. Indeed, it describes a respectable mode of argumentation. According to the British philosopher John Locke (1632-1704), "A third way [to persuade] is, to press a Man with Consequences drawn from his own Principles, or Concessions. This is already known under the Name of Argumentum ad Hominem" (An Essay Concerning Human Understanding, book IV, chap. XVII, sec. 21).


Let us unpack this. People (most of them, anyway) have principles. Principles have implications. If I can show you that your principle commits you to belief B, then I force you to either embrace B or abandon your principle. Yes, this is coercive. All argumentation is coercive. It is the imposition of a choice by one person on another. In the example given, I tell you that you cannot have both your principle and your belief that non-B (or your nonbelief in B, if you are merely agnostic about it). You can't both have your cake and eat it.


To summarize, the ad hominem fallacy is an attack on a person. It is disreputable and disrespectful. Don't do it. The argumentum ad hominem is an appeal to (i.e., an argument directed to) a person (rather than to the world at large). It is reputable, respectful, and respectable. Do not confuse the two.


Let me illustrate the Lockean ad hominem method. Suppose I believe (as I do) that it is wrong to eat animal flesh. Because I believe it to be wrong, I would like to spread the belief, on the assumption that beliefs are intimately connected with action. (I'm trying to make the world safe for animals.) I could spread the belief in nonrational ways, of course (such as subliminal advertising, deception, and other forms of manipulation), but suppose I wish to persuade rationally. (Philosophers care as much about how they persuade as whether they persuade. This, alas, is not true of lawyers, who are willing to commit fallacies to persuade jurors. It is why many of us who are trained in both fields chose philosophy over law.) I realize that any premise I choose that entails the conclusion will be accepted by some people but not by others. For example, if I begin with a Biblical injunction, I get traction with Christians and perhaps with Jews but not with Muslims or atheists. If I begin with utilitarianism, I get traction with utilitarians but not with Kantians or contractarians. There is no argument for the proposition that it is wrong to eat animal flesh that has premises acceptable to everyone.


Someone might despair at this. Indeed, many philosophers proceed as if they did not grasp this point. But this dooms their arguments to ineffectiveness. What I must do, if I hope to persuade on a large scale, is make several arguments. I must tailor my argument to my audience. Imagine that I am at a conference. Each room has like-minded people in it. One room is filled with utilitarians, one with Kantians, one with feminists, one with Christians, one with conservatives, and so on. I will have to go room to room, making a different argument for each group. I will try to show the Christians, for example, that their beliefs, contrary to what they may have been taught, commit them to according moral status to nonhuman animals. I will try to show Kantians that their teacher, Kant, was mistaken in withholding dignity and respect from nonhuman animals. I will try to show feminists that if they oppose the oppression of women by men, they are committed (on pain of contradiction) to opposing the oppression of animals by humans. And so on for each group. My leverage in each case is the principle of noncontradiction. It is the only leverage a philosopher has, but it is more than enough. Indeed, it is wonderfully effective. It is (forgive the metaphor) the most powerful weapon ever devised.


If effective argumentation is necessarily ad hominem in nature, then evaluation of an argument must attend to its audience. Let me illustrate this with an historical example. The French mathematician/philosopher Blaise Pascal (1623-1662) argued that it is in one's interest to believe in ("wager for") the Christian god. One of his premises implies that there are just two possibilities: Either the Christian god exists or no god exists. Some critics have charged that no self-respecting atheist or agnostic would accept this premise, for obviously there are other logical possibilities: a nonChristian god, for example, or many gods.


Is this a legitimate criticism? No. Pascal's argument was not directed to atheists or agnostics. It was directed to backsliding Christians in general and to his backsliding Christian friends in particular. These individuals, raised in the Christian church, could be presumed to accept the premise, even if an atheist or an agnostic would not. To a backsliding Christian, there really are just two (live) options: the very ones Pascal described. Pascal, who was smarter than any of us (take my word for it), chose his premises wisely; he chose premises that he knew his interlocutors accepted. Any other premises would have frustrated his purpose, which was to save the souls of his benighted, misguided friends.


Is it a criticism of Pascal's wager argument that it won't (or can't) persuade everyone? Consider an analogy. Suppose I build a rocking chair for my five-year old daughter. A friend of mine finds that it's too small for him and concludes that it's a bad chair. "That chair is worthless," he says. "Why would you make a chair that doesn't fit everyone?" My response is that the chair wasn't made for him (or for people his size). It was made for my daughter and for people her size. For them it is just right! Arguments, like chairs and other technologies, are made for particular purposes. It is no criticism that they don't fulfill other, unintended purposes (let alone all purposes).


To repeat my claim, argument, to be effective -- to have any chance of persuading -- must be ad hominem. This is as true of nonevaluative arguments as it is of evaluative (including moral) arguments. The idea is to begin where your interlocutor is, even if you believe it to be false and even if you reject it. Note the implication. As an atheist, I can persuade a theist (a Christian, say) to change his or her beliefs. If the theist resists my conclusion on grounds that I, the critic, don't believe my own premises, I respond that I don't have to. "It's enough that you believe them," I say. "You are committed to changing your beliefs -- if you care about consistency, at any rate." I sometimes hear it said that I am "imposing" my values on others when I argue. This is risible. I'm imposing their values on them. I want my Christian friends to be the best Christians they can be. I want them to have consistent beliefs, to believe what they say, and to practice what they preach. Friendship, as Aristotle explained long ago, is a demanding relationship. This -- promoting personal integrity -- is one of its demands.


I said at the outset that logic cannot tell us which of a set of inconsistent propositions is the false one (or ones). We must decide that on different grounds. Actually, the word "we" is inappropriate here, for different people may decide differently. Think about how your beliefs are (inter)connected. Some beliefs are more entrenched than others in the sense that you would have to abandon more beliefs by abandoning them than by abandoning some other belief. For a theist, the belief that God exists is deeply entrenched, probably more than any other belief. If it turns out to be incompatible with some other, less-entrenched belief, the theist, if rational, will abandon that other belief. Entrenchment, however, is a matter of degree. Even though the logical tension can be resolved by abandoning belief in God, it won't be, it needn't be, and arguably it shouldn't be. We might think of this as epistemic conservatism, for it cautions us to give up as little as possible to maintain overall coherence (i.e., to "conserve" our beliefs). (I leave it to you to describe epistemic liberalism [reform of belief] and radicalism [revolutionary change in belief]. Different people have different epistemic principles.)


This is why it is silly to think that the problem of evil -- the problem of reconciling belief in an all-powerful, all-knowing, perfectly good being with belief that there is evil -- will (or should) turn a theist into an agnostic. Epistemic conservatism dictates that belief in the existence of evil be abandoned before belief in the existence of God, for it is less entrenched. Whatever else you might want to say about it, theism is neither incoherent nor irrational. (See, e.g., Richard Swinburne's book The Coherence of Theism.) But, like any other worldview, theism is costly. To be a consistent theist, you cannot believe just anything (although some people try). It is the job of atheists and agnostics to make theists aware of the epistemic costs of their beliefs. Theists must believe, for example, that for every instance of horrendous and seemingly gratuitous evil, such as a five-year old girl being brutally raped and murdered, or a fawn dying a lingering, agonizing death in a forest fire, there is a greater good realized or a greater evil prevented. For some of us, this is too costly to believe (even if we were inclined to believe it). Others are able and willing to bear the cost. To each his (or her) own.


Arguing is hard, daunting work (although great fun). It requires not just logical skill, which, like any other skill, can be refined and honed, but substantive knowledge of various theories, doctrines, principles, ideologies, and worldviews. In order for me, an atheist, to persuade a Christian to believe this or that, I must know Christianity inside and out. If I were once a Christian, so much the better. In order for me, a deontologist, to persuade a consequentialist to believe that war in Iraq was justified, I must know consequentialism inside and out. All of us have a great deal to learn from one another -- if only we are willing. The flip side is that all of us have a great deal to teach one another -- if only we make the effort.


Alas, teaching and learning require listening and reading skills that are in short supply in our impatient, inattentive, aggressive culture. We value winning more than learning. Argumentation should not be thought of as a contest, much less as warfare. It is more like helping a friend. I want my Christian friends (yes, I have some) to have a coherent body of beliefs. If they care about me, they will want me to have a coherent body of beliefs--even if they also believe, as they probably do, that I will burn in hell forever. They might even try to show me that certain of my beliefs commit me to belief in God. I welcome the attempt. It respects me as a rational being. There is no more shame in being persuaded to change one's beliefs than there is in being helped by a friend to have a more efficiently running automobile. Argue away!


Keith Burgess-Jackson, J.D., Ph.D., writes "The Logic Cop," a regular feature at TCS. He is Associate Professor of Philosophy, Department of Philosophy and Humanities, The University of Texas at Arlington. Burgess-Jackson is coauthor, with the late Irving M. Copi, of Informal Logic, 3d ed. (Upper Saddle River, NJ: Prentice Hall, 1996). He teaches logic on a regular basis. Years ago, someone asked his mother what he does for a living. She said, "I don't know, but it has something to do with arguing." Please visit his blogs at and

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