In any case, explicit evaluation is introduced in the next sentence: “Then, should the coffee market decline, the farmers are still guaranteed a fair price.” The term “fair” is openly evaluative because something is fair only if it meets evaluative standards of fairness. What about the term “should” in this sentence? To say that someone should do something is normally to imply that doing it is good. Here, however, the authors are clearly not saying that the coffee market should decline. That would be bad. In this sentence, “should the coffee market decline . . . ” instead means “if the coffee market declines . . . ”
Another word in this sentence that could be marked is “guaranteed.” To say that a fair price is guaranteed is to say that the farmers are assured of or certain to get a fair price. Who guarantees that fair price? Presumably it is Equal Exchange, since the local law does not require fixed minimum rates. Thus, if we see the leaders of Equal Exchange corporation as the authors of their own advertisement, then “guaranteed” functions as an assuring term, because the authors use it to assure readers that farmers will get a fair price. It is equivalent to saying, “Farmers will surely get a fair price.”
Now that we understand the rest, let’s return to the first word in this sentence. “Then” is an argument marker indicating that the preceding sentence (“We trade directly with small farming cooperatives at mutually agreed-upon prices with a fixed minimum rate”) is a reason for the following sentence (“If the coffee market declines, the farmers are still guaranteed a fair price”). The trade and pricing practices of Equal Exchange give an explanatory reason why prices will remain stable in the face of inevitable market declines. Because of the evaluative terms in this sentence, this argument also presents a justificatory reason to buy Equal Exchange coffee, because its practices promote something good: stability in fairness.
The next sentence explicitly draws this general conclusion: “So have a cup of Equal Exchange coffee and make a small farmer happy.” The word “so” functions as an argument marker that indicates that what follows is a conclusion. What is strange is only that this conclusion is an imperative: “have a cup of Equal Exchange coffee.” Imperatives are not declarative, so they cannot be true or false. That formal feature seems to rule them out as conclusions. However, this conclusion is fine if it is elliptical for “You ought to have a cup of Equal Exchange coffee” or “I recommend that you have a cup of Equal Exchange coffee.” The authors seem to have intended something like these expansions.
The second half of this sentence introduces a new reason: “make a small farmer happy.” The authors do not mention happiness before. The term “happy” is evaluative, assuming that to make people happy is to make them feel good. This positive effect of drinking Equal Exchange coffee thus complements the reasons to avoid maintaining the unfair system. Moreover, the authors drop the guarding terms and suggest that having a cup of Equal Exchange coffee will in fact make a small farmer happy. That stronger claim reaches audiences who are satisfied only if they actually do bring about a good effect and not merely if they have a chance of helping to avoid a bad effect, as the earlier argument claimed. Unfortunately, however, it raises the question of whether having a cup of Equal Exchange coffee really will make a small farmer happy. There are reasons to doubt that, but I will not go into them here.
The next sentence illustrates a common combination of assuring and guarding: “Of course, your decision to buy Equal Exchange need not be completely altruistic.” The phrase “of course” assures readers that what follows is true (without openly specifying any evidence that it is true, although that evidence is coming in the following sentence). What readers are assured of is, however, guarded by the complex phrase “need not be completely.” To say that an act is not completely altruistic is compatible with the act’s being partly altruistic, so it weakens the claim that the act is completely altruistic. Then to say that an act need not be completely altruistic further weakens the claim that it is not completely altruistic. This doubly guarded claim is so weak that it is compatible with the decision’s actually not being altruistic at all, as long as it is possible that the decision is partly altruistic. Nobody could object to that, but how could it be strong enough to support any conclusion? Well, it doesn’t have to, because this sentence is not part of the positive argument for drinking Equal Exchange coffee. Instead, it responds to the possible objection that the authors are asking readers to be altruistic. There is no discounting term, but there does not have to be a discounting term in every case where an objection is discounted. Here the function of discounting an objection is supposed to be clear from the context. The point of doubly guarding the claim about altruism is to discount any objection that the authors are requiring complete altruism. Even selfish bastards will have reason to drink Equal Exchange coffee.
Why? The next sentence tells us: “For we take as much pride in refining the taste of our gourmet coffees as we do in helping the farmers who produce them.” Here the word “for” is an argument marker. We can tell its function because we can replace it with another argument marker—“because”—without changing the basic meaning of the sentence. To say “For we take as much pride . . . ” is equivalent to saying “Because we take as much pride . . . ” Contrast the same word in the next sentence: “For more information about Equal Exchange . . . ” There we cannot substitute another argument marker, since it makes no sense to say “Because more information about Equal Exchange . . . ”
Which argument is marked by the term “for” in the previous sentence? It is simply: “We take as much pride in refining the taste of our gourmet coffees as we do in helping the farmers who produce them. Therefore, your decision to buy Equal Exchange need not be completely altruistic.” The doubly guarded claim is the conclusion, so its weakness makes it easier to support. Of course, refining the taste leaves open the possibility that the taste still needs much more refinement, and taking pride in refining is compatible with that pride being misplaced. Still, the authors are clearly suggesting that their coffees taste very good, and that is a reason to buy them.
Finally, we can combine the two main strands of this argument. One reason to buy Equal Exchange coffee is that doing so can help change a bad system (as well as make a small farmer happy). Another reason to buy Equal Exchange coffee is its refined gourmet taste. The two parts together are supposed to provide a reason for any reader who cares either about helping small farmers or about personally enjoying refined gourmet taste. The people at Equal Exchange take pride in both considerations, but the argument works for readers who care about either consideration alone, even if they care only about the farmers or only about the taste. The argument, thus, becomes stronger by broadening the range of reasons that it shows.
As usual, I am not personally endorsing this argument or its conclusion. Whether or not you are convinced to buy Equal Exchange coffee—indeed, whether or not you even like drinking coffee—the point of this exercise in close analysis is not persuasion. Instead, the goal is understanding. I tried to make this argument look as good as possible so that we can assess and learn from the best reasons for its conclusion.
My other goal was to illustrate how complex even a simple argument can be. Our close analysis revealed how much content and strategy can be uncovered by looking closely at only eight sentences and focusing on argument markers plus guarding, assuring, evaluating, and discounting terms. The process of going through one example in so much detail should, I hope, provide a model to follow in using this technique on other arguments. Close analysis can be applied equally to many other arguments in many other areas. Try it on your own favorite topics. It is fun. It is even more fun to do it with friends so that you can discuss alternative interpretations.
8
HOW TO COMPLETE ARGUMENTS
IN THE PREVIOUS CHAPTER, we saw how to analyze arguments by looking closely at crucial words. This technique of close analysis helps readers locate argument parts—premises and conclusions—that are given explicitly in the
text. Even after such close analysis, we still need to arrange these elements of the argument into an intelligible order and then complete this structure by inserting additional premises that are assumed but not stated openly. This method is called deep analysis. Close and deep analysis can be combined to produce argument reconstruction. The goal of this chapter is to explain deep analysis and illustrate argument reconstruction. First, however, we need to define the standard of validity that will guide these methods.
WHICH ARGUMENTS ARE VALID?
When non-philosophers call an argument valid, they often mean simply that it is good. The word “valid” is then an evaluative term. In contrast, when philosophers (including logicians) call an argument valid, they mean something entirely different that does not imply either that the argument is good or that it is bad.
The notion of validity as it is understood by philosophers concerns the relation between the premises and conclusion in an argument. An argument is valid in this technical, philosophical sense when and only when it is not possible for there to be any situation in which all of its premises are true and its conclusion is false. This definition is also equivalent to defining an argument as valid if and only if at least one of its premises must be false in every possible situation where its conclusion is false. You can think about validity in either of these ways, depending on which formulation makes the most sense to you.
Either way, it is crucial that the definition is about possibility rather than actuality. Whether an argument is valid does not depend on whether its premises or conclusion actually happen to be true. All that matters is whether a certain combination—true premises and a false conclusion—is impossible (in which case the argument is valid) or possible (in which case the argument is invalid).1
As a result, some arguments with true premises and a true conclusion are still not valid. Consider “All citizens of Egypt are less than a kilometer tall, all citizens of Egypt breathe air, so all animals that breathe air are less than a kilometer tall.” These premises and conclusion are all true. Nonetheless, this argument is still not valid because it is possible for the premises to be true when the conclusion is false. Just imagine a possible world where some giraffes grow to more than a kilometer tall. This evolution is possible, and it would make the conclusion false, but both premises could still be true if citizens of Egypt remained just like they are in the actual world. This possibility is enough to show that the argument is not valid in the technical sense of philosophers, despite the three truths it contains.
On the other hand, some valid arguments have false premises and a false conclusion. For example, “All sushi chefs are women, all women play cricket, so all sushi chefs play cricket” is a silly argument, because both premises and its conclusion are false. Despite all of this falsity, it is valid in the technical sense, because it is not possible for its premises to be true when its conclusion is false. If it is false that all sushi chefs play cricket, then there must be some sushi chef who does not play cricket. That sushi chef must be either a woman or not a woman. If that sushi chef is not a woman, then the first premise (“All sushi chefs are women”) is false. And if that sushi chef is a woman, then the second premise (“All women play cricket”) is false, since we are assuming that she does not play cricket. There is no possibility of a combination where both premises are true and the conclusion is false. That makes the argument valid in this technical sense (even though it is a very bad argument in other ways).
To determine whether an argument is valid, one method is to try your best to imagine or describe a situation in which the premises are true and the conclusion is false. If you can describe a situation with this combination of truth values, then the argument is not valid. Of course, you need to be sure that your description really is coherent. You might not notice some incoherence in the description, so you need to look carefully. Still, if you can describe a situation with this combination of truth values that seems coherent after close inspection, that apparent coherence is some reason to believe that the argument is not valid. On the other hand, suppose you fail to find a coherent description with that combination of truth values. Your failure might show only your lack of imagination instead of the validity of the argument. Still, if you tried hard enough, and you could not imagine any situation that makes the premises true when the conclusion is false, that is some reason to believe that the argument is valid. Trying to describe a coherent situation that combines true premises with a false conclusion is, therefore, a useful start in the absence of any more technical method. The best way to master this technique is to discuss cases with friends, who might be able to imagine possibilities that you overlook.
WHEN IS VALIDITY FORMAL?
Some arguments are valid because of their specific words or sentences. The argument “My pet is a tiger, so my pet is a cat” is valid, because it is not possible to be a tiger without being a cat. However, this validity is destroyed if we substitute certain other words, such as in “My pet is a tapir, so my pet is a dog.” Thus, what makes the original argument valid is the (semantic) meanings of its words—“tiger” and “cat.”
In contrast, other arguments are valid by virtue of their form. Consider “My pet is either a tiger or a tapir. My pet is not a tiger. Therefore, my pet is a tapir.” If the conclusion is false (my pet is not a tapir), and the second premise is true (my pet is not a tiger), then the first premise has to be false (my pet is not either a tiger or a tapir). Thus, this argument is valid. Moreover, it remains valid no matter which words are substituted for “tiger” and “tapir” as well as “My pet.” This argument is also valid: “Your pet is either a dog or a pig. Your pet is not a pig. Therefore, your pet is a dog.” So is this one: “My country is either at war or in debt. My country is not at war. Therefore, my country is in debt.” In every case with this form, it is not possible for the conclusion to be false in circumstances where the premises are both true. Thus, this argument is valid by virtue of its form. This argument form is called denying a disjunct (because the “either” and “or” propositions are called disjuncts) or process of elimination (because the second premise eliminates one of the alternatives in the first premise).
It is useful to remember a few other argument forms that are formally valid as well as a few that are not valid by virtue of their form but are often mistakenly thought to be valid. The variables “x” and “y” can be replaced by any sentence as long as the same sentence replaces the same variable wherever that variable occurs. These argument forms are valid:
Modus Ponens: If x, then y; x; so y.
Modus Tollens: If x, then y; not y; so not x.
These argument forms are invalid:
Affirming the Consequent: If x, then y; y; so x.
Denying the Antecedent: If x, then y; not x; so not y.
(These names are derived from calling the “if” clause the antecedent and the “then” clause the consequent in an “if . . . , then . . . ” proposition, which is also called a conditional or hypothetical.) Here are two more valid argument forms:
Hypothetical Syllogism: If x, then y; if y, then z; so, if x, then z.
Disjunctive syllogism: Either x or y; if x, then z; if y, then z; so, z.
If you think about these argument forms and replace their variables with any sentences of your own choice, then you should be able to see which of these forms are valid and why. Formal methods (including truth tables) have been developed for showing validity by virtue of propositional form. Other methods (such as Venn diagrams, truth trees, matrices, and proofs) have also been developed for showing validity by virtue of some non-propositional forms. We will not go into those details here.2 What matters here is only to gain some initial rough feel for which arguments are valid and when their forms make them valid.
WHAT MAKES ARGUMENTS SOUND?
Even formal validity is not enough to make an argument good or valuable. Consider this argument: “If the Amazon is the largest river in the world, then it has the largest fish in the world. The Amazon
does not have the largest fish in the world. Therefore, the Amazon is not the largest river in the world.” This argument has the form modus tollens, so it must be formally valid. However, its conclusion is false, because the Amazon is in fact the largest river in the world. So, how can its conclusion be false when it is valid? The answer is simply that its first premise is false. The largest fish do not live in the largest river.
What makes arguments good is not only validity but soundness. A sound argument is defined as an argument that both is valid and also has all true premises. This definition guarantees that every sound argument has a true conclusion. Its validity ensures that it cannot have true premises and a false conclusion. Thus, the truth of its premises entails that its conclusion cannot be false. That makes soundness valuable.
WHAT ARE YOU ASSUMING?
These notions of validity and soundness are useful for determining when an argument depends on an assumption that it does not state explicitly. This happens often. While you and I are scheduling a business meeting in 2019, you might say,
We should not schedule it for June 4, because that is the last day of Ramadan.
This is all you need to say in order to move our conversation to other possible dates, if you know that we both assume that some people whom we want at the meeting will refuse to meet on the last day of Ramadan. If we add that assumption, then we get a longer argument:
Think Again: How to Reason and Argue Page 11