Reasoning
Copyright © 2004 by Joel Marks
Please note: Some of the arguments used as examples in this text, intended originally as a handout for my students, may have come from other sources, which are long since lost to my memory. Apologies to the authors. The analyses, however, are my own. Also, apologies to the reader for the omission of some marks of punctuation, which seem to have been lost in transferring the text to this website.
Rational Argument, Part I: Recognizing an Argument
There is a special structure in a great deal of what you read and hear and think and write and speak which the study of reasoning can make you aware of. I do not mean simple grammatical structure, such as sentences and nouns and verbs. I am talking about logical structure. If you become aware of the logical structure of language, you will gain power of understanding, power of criticism, power of expression. In this short essay I will introduce you to the basics of logical structure.
Just as the sentence is the basic unit of grammar, so the argument is the basic unit of logic. The business of a sentence is to express a thought. The business of an argument is to defend a claim. An example of an argument is
Reagan was a good President because he reduced inflation.
The claim being defended is
Reagan was a good President.
Just as a sentence has (grammatical) parts, so an argument has (logical) parts. A sentence consists of a subject and a predicate. An argument consists of premisses and a conclusion. In the argument from above, the premise is
Reagan reduced inflation
and the conclusion is
Reagan was a good President.
The premisses of an argument, therefore, constitute the defense of the conclusion of the argument. We can also say that the premisses of an argument are intended to provide a reason for believing the conclusion. This is why disciplines such as philosophy, science, and mathematics are said to be rational: These disciplines employ arguments, an argument incorporates a reason for believing something, and the Latin word for reason is "ratio."
It makes sense that "rational" has this meaning. It seems eminently rational to provide reasons for what one believes or claims, or at least to be prepared to do so or be able to do so. For example, consider the bald statement
Reagan was a good President.
If a person made this statement but had nothing more to say about the matter, no reason to back up his claim, we might wonder how rational he was being. Maybe he believes that Reagan was a good President solely because all of his friends believe it and he has never thought about the matter at all. Compare this situation to the one where, if pressed, a person could explain that
Reagan was a good President BECAUSE he reduced inflation.
This person would seem to be more rational, at least in this one instance, simply because she is able to give a reason for what she believes.
Logical Language
Someone once remarked that human beings live in a sea of arguments. Someone else has observed that fish may be unaware of water since, for them, it is everywhere. Just so, human beings often have trouble recognizing the arguments that bombard their ears, fill up their minds, and cross their lips. In this chapter I will discuss some ways of detecting arguments.
The best clue to the presence of an argument is a certain kind of language. This remark must immediately be qualified, however, because language is a notoriously slippy phenomenon. Certain words often serve as inference (i.e., argument) indicators; but many of these very same words commonly serve other linguistic functions as well, and so they are not to be relied upon absolutely as guides to the presence of an argument. Nevertheless, they do often help you to pick out an argument.
As you have probably observed from the various examples of arguments I have already given, the word "because" is a very common inference indicator. This word introduces the premise(s) of an argument, and, hence, indicates that an argument is present. (But already you should be alerted to an important exception, for the word "because" is also frequently to be found in explanations as opposed to arguments. More on this in a later chapter.)
In the last paragraph I myself presented an argument, namely: "This word ['because'] introduces the premise(s) of an argument, and, hence, indicates that an argument is present." In this argument, "hence" functions as an inference indicator. Unlike "because," "hence" introduces the conclusion of an argument; nonetheless, since a conclusion is also part of an argument, the presence of "hence" reveals the presence of an argument.
This brief review reveals that there are two basic kinds of inference words: those which introduce a premise and those which introduce a conclusion. The most common word of the former sort is "because." Synonyms of "because," such as "since" and "for," also frequently serve as premise introducers. The most common conclusion introducer is the word "therefore." Some typical synonyms of "therefore" are "hence," "thus," "so." and "then" (but not "if/then").
Finally, it is important to realize that an argument can be present without any inference indicator word. For example,
The sky is cloudy. It's going to rain.
Clearly the word "therefore" is implied; hence, this is an argument.
Symbolism
Because certain logical relations and logical words occur repeatedly in argumentation, it is convenient to use symbols to abbreviate them. Since, however, this is not a primer in symbolic logic, I shall keep the symbolism to a minimum. For our purposes as reasoners we can get along quite nicely with just the following few conventions.
1. The line. Although "therefore" and "because" introduce different components of an argument, they express the identical logical relation. Hence it is possible to adopt a single symbol which stands for this relation and so can substitute for both words. Let us, then, adopt the convention of using a horizontal line to stand for the logical relation; and this line shall be read as "therefore" when reading from top to bottom and as "because" when reading from bottom to top. So, for example, the following three expressions are equivalent:
(1) Reagan is a good President because he reduced inflation
(2) Reagan reduced inflation; therefore Reagan is a good President
(3) Reagan reduced inflation
-----------------------------------
Reagan is a good President
2. Capital letters. As we have seen, an argument consists of statements (in a certain relation). These statements may be simple or else may themselves consist of other statements. An example of a statement which consists of other statements is
If Jane is your sister, then Jane is female.
The component statements here are
Jane is your sister
and
Jane is female.
A capital letter may be used to abbreviate any simple statement in an argument. Thus, for example, "Jane is your sister" could be abbreviated as "S" (where the "S" serves mnemonically to pick out "sister"), "Jane is female" could be abbreviated as "F," and "If Jane is your sister, then Jane is female" could be abbreviated as "If S then F."
3. The dash. For the purposes of reasoning it is often useful to distinguish a positive assertion from a denial. An example of a positive assertion is
The earth is flat.
An example of a denial is
The earth is not flat.
Let us use a dash to indicate a denial (analogously to the use of the negation sign and the minus sign in arithmetic). So for example "F" could stand for "The earth is flat," and " F" could stand for "The earth is not flat." Note that a denial is equivalent to asserting that something is false; "The earth is not flat" means the same thing as "It is false that the earth is flat." Yet another way to think about the relation between positive assertion and denial is to note that "The earth is flat" is equivalent to saying "It is true that the earth is flat," while "The earth is not flat" is equivalent to saying "It is not true that the earth is flat."
4. The tilde. A defining characteristic of every statement is that it is either true or false. For example, the statement "The earth is flat" is false, and the statement "The earth is round" is true. Sometimes, though, we do not know the "truth value" of a particular statement. For example, "There are exactly three hundred and five craters on the planet Pluto" is either true or false, but we do not know which. A statement of this sort may be called "moot," and the tilde can abbreviate it, as in "˜P."
Argument vs. Non Argument
One way to come to understand the concept of argument is to consider what sorts of things are not arguments. When I speak of "argument" in this essay, I am usually referring to rational argument. So the first thing to distinguish rational argument from is non rational argument. Non rational argument is probably what is most often meant by the word "argument" in everyday speech. Non rational argument occurs whenever two (or more) people are involved in an emotional verbal disagreement. "You're a liar!" "I am not!" And so forth.
Rational argument is nothing like this. Rational argument is not any kind of disagreement or even behavior. A rational argument is simply a set of statements, one or more of which constitute a reason for believing another of them.
While it is important to recognize that an argument consists of statements, it is equally crucial to recognize that an argument always contains more than one statement. The key to distinguishing all of the following sorts of non arguments from arguments is that an argument is not a statement but is instead a set of at least two statements (which bear a certain relation to each other). All of the following examples of non arguments are statements of various sorts which are easily confused with arguments.
1. A HYPOTHETICAL STATEMENT IS NOT AN ARGUMENT. Example:
If Sally is your sister, then Sally is female.
Here is one way to convince yourself that this is not an argument. Suppose that it were an argument; then the conclusion would be "Sally is female" and the premise would be "Sally is your sister." However, the given sentence does not make either of these claims; an "if...then" sentence is purely hypothetical, which is to say that it is only talking about what would be the case were something else the case (Sally would be female were Sally your sister). But an argument is claiming that something (the conclusion) is the case because something else (the premise[s]) is the case (Sally is female because Sally is your sister). In other words, the "if...then" sentence can be true even if one or both of its component clauses are false, but the corresponding argument cannot be a good one unless both components are true.
2. AN EXPLANATION IS NOT AN ARGUMENT. Example:
The sky is blue because of the refraction of the sun's rays.
Here again you can convince yourself that this is not an argument by imagining what it would be like if it were an argument. The conclusion would be "The sky is blue," and the premise would be something like "The sun's rays are refracted as they pass through the atmosphere." The giveaway here is that the "conclusion" is something which is not controversial. No one would ever be trying to argue that the sky is blue; everybody already knows this. (A qualification here is that context can make a difference; if we happened to be discussing, say, the planet Mars, the blue sky example could be an argument.) Therefore, what is being provided is most likely an explanation of why the sky is blue, rather than a reason for believing that the sky is blue. (Note: Explanations, like any other statements, can be false.)
3. A COMPOUND STATEMENT IS NOT AN ARGUMENT. Example:
First I will drive to New York, and then I will drive to Baltimore.
Again try the "suppose test." If this were an argument, the conclusion would be "I will drive to Baltimore," and the premise would be "I will drive to New York." Now, the sentence in question does establish a relation between these two component clauses or statements; however, it is not the right kind of relation for an argument. In an argument, a reason is being given to believe a claim. But in this sentence it is surely not the case that my driving to New York is being given as a reason for you to believe that I will drive to Baltimore. The relation between the components of the given sentence is simply one of conjunction or perhaps of sequence. An argument requires that the intended relation be one of rational support.
Rational Argument, Part II: Evaluating an Argument
There is more to being rational than simply providing a reason for a claim. The reason should be a good one. There are two main tests for quality of an argument: (1) Does the conclusion follow from the premisses? (2) Are the premisses true? An argument which passes both of these tests is a sound one. A sound argument shall be our standard of good reasoning.
Validity
An argument is valid if its conclusion follows from its premise(s); it is invalid otherwise.
What does the phrase "follows from" mean? It turns out that the entire field of LOGIC is devoted to the study of this concept. Hundreds of books have been written over thousands of years in the attempt to clarify it. The investigation of validity is one of the most fascinating adventures of the intellect, and I would encourage any of you who are so inclined to pursue it in a course on logic. However, for the purposes of reasoning, you need only gain some familiarity with the use of validity for the evaluation of arguments. (It is like the difference between learning how to drive a car and learning how a car works.)
To begin with it is possible to appreciate validity in a strictly intuitive way. Examples have already been given of valid and invalid arguments in earlier chapters. I am sure you had no difficulty in sensing what was good or bad in those arguments.
Unfortunately, many arguments are not so simple nor so simply evaluated. Therefore let me suggest another way to think about validity and invalidity in general which may help you to deal with the more difficult cases: Ask yourself whether the conclusion of the argument would be true (or, at least, would probably be true) were the premise(s) of the argument true.
Consider the following argument:
(1) All whales have wings
(2) All winged animals can fly
-----------------------------------
All whales can fly
This argument is valid. Why? Well, imagine a world in which all whales have wings and all winged animals can fly. Wouldn't it also be true in such a world that all whales can fly?
Now consider this argument:
(1) If Mary is my sister, then Mary is female
(2) Mary is female
-----------------------------------
Mary is my sister
This argument is not valid; i.e., it is invalid. You can discover this simply by employing the test I have suggested. For suppose that both premisses are true; thus, Mary is female and furthermore, if Mary is my sister, then Mary is female (which is just a way of saying that in order to be someone's sister, you must be female). Must it also be true that Mary is my sister? Not necessarily. In fact, not even probably. For there are probably millions of Marys who are female but not my sister, and the argument does not give you any reason for believing that the Mary in question is one who is my sister (or even that I have a sister!).
Truth of the premisses
While validity is an intuitive notion, it may strike you as exceedingly odd that an argument such as the one above about flying whales can turn out to be valid. Whales can't fly, so how can an argument having "All whales can fly" as its conclusion be a valid one?
The way out of this quandary is to realize that "validity" is being used in a technical sense; it means exactly what I said it means in the previous section, and nothing more. So, for example, to say that an argument is "valid" is not to say that the argument is a good one. The technical term "sound" has been reserved for that meaning, and in order to be a sound argument an argument must not only be valid but also contain all and only true premisses.
Why study validity (hence, logic) in the first place, then? Precisely because there are two essential conditions of a good argument. TRUE PREMISSES ALONE DO NOT A GOOD (i.e., SOUND) ARGUMENT MAKE. An argument must also be valid in order to be sound.
So, for example, we have already seen a case of an argument passing the validity test without passing the truth of the premisses test (from now on I shall refer to the second test simply as the "truth test"), namely,
(1) All whales have wings
(2) All winged animals can fly
-----------------------------------
All whales can fly.
We can also have an argument containing true premisses which is nonetheless invalid, for example,
(1) All dogs have lungs
(2) All birds have lungs
-----------------------------------
Dogs are birds.
To be a sound argument an argument must have BOTH a conclusion that follows from the premisses AND premisses that are true. Here is an example of such an argument:
(1) The Moon orbits the Earth
(2) The Earth orbits the Sun
-----------------------------------
The Moon orbits the Sun.
Truth of the conclusion
Note that the conclusion of a sound argument is true. And this after all is our goal: truth. This is ultimately why we care about reasoning and logic and validity and soundness: They help to lead us to truth.
Another way to put this is to say that arguments can take us from things already known to new knowledge. In the immediately preceding example, I dare say it comes as a revelation to many people to realize that the Moon orbits the Sun; and yet this conclusion follows quite naturally from the juxtaposition of the premisses, whose truth is already recognized by everyone.
In a way, reasoning can be like pulling a rabbit out of a hat. It is a wonderful thing really a way to expand our knowledge indefinitely, without having to lift a finger, as it were. Indeed it has been remarked that the majority of our knowledge of the world comes not from observation but from inference.
It is essential to understand, however, the proper place of the truth of the conclusion in the evaluation of an argument. Strictly speaking, the truth of the conclusion does not enter into the evaluation. Recall again the two tests for the quality of an argument: (1) validity of the inference and (2) truth of the premisses. When we consider an argument, we are typically in some doubt about the truth of the conclusion. This is precisely why we are considering an argument at all. If we were certain of the truth of a given claim, we would have no need to consider a reason to believe it. Thus it would be question begging to allow our opinion of the conclusion to enter into our evaluation of the argument.
(I should introduce a caveat at this point. While it is indeed question begging to evaluate an argument on the basis of its conclusion, it does not follow that it is never legitimate to do so. For example, were someone to propose an argument for the claim that all blue eyed people should be exterminated, I think we should rightly decline to hear it out. On the other hand, it can be just as important to insist on the logical point I have been making. Consider how absurd it must have seemed to most people a few hundred years ago when Copernicus asked them to listen to his arguments for the claim that the Earth moves around the Sun. And more recently we know how difficult, even to the point of seeming morally objectionable, it has been for some people to entertain the hypothesis that people have descended from nonhuman animals. Perhaps then we should err on the side of nonsense and be prepared to hear out an argument for just about any claim whatsoever, for from time to time the "nonsense" may turn out to be true.)
Falsity of the conclusion
Yet another important "fine point" is that the conclusion of an argument has not been shown to be false just because the argument has been shown to be unsound. Soundness of an argument does imply the truth of the conclusion, but unsoundness does not imply the falsity of the conclusion. This point can be simply illustrated; the following argument is unsound and yet it has a true conclusion:
(1) Whales live in the sea
(2) Only mammals live in the sea
-----------------------------------
Whales are mammals.
The significance of demonstrating that an argument is unsound (or "bad" or "flawed" or "faulty") is that the reason given is not adequate to establish the truth of the conclusion. Thus, the falsity of the conclusion does not follow from the unsoundness of the argument, for, for all one knows, there may exist some other, better reason (i.e., argument) for believing the conclusion. For example, in the case of the whales:
(1) Only mammals suckle their young
(2) Whales suckle their young
-----------------------------------
Whales are mammals.
There is only one way to demonstrate that a certain claim is false and that is to argue directly for the falsity of the claim. (And of course the argument must be sound.) For example,
(1) No mammal is a fish
(2) Whales are mammals
-----------------------------------
It is false that whales are fish (or "Whales are not fish").
Please understand that the conclusion of this argument is, "It is false that whales are fish" (the conclusion, as always, is whatever comes beneath the line), and, as always, it is the truth of the conclusion that the argument is concerned to establish. It so happens that to establish the truth of the conclusion of this argument is to establish the falsity of the claim, "Whales are fish."
Procedure
As a general policy I would recommend examining the validity of an argument first. Thus, the algorithm for the evaluation of an argument goes like this:
1. Is the argument valid? If NO, stop (the argument is invalid, hence unsound). If YES, proceed to the next step.
2. Is the topmost unexamined premise of the argument true? If NO (the premise is false or moot), stop (the argument is unsound). If YES, proceed to the next step.
3. Is there another premise? If NO, stop (the argument is sound; hence the conclusion is true). If YES, return to the preceding step.
In order to do this job properly, however, there may need to be some preliminary steps. The basic idea is to put an argument into a standard form, which will most readily lend itself to the application of the algorithm and, thereby, most clearly reveal the quality of the argument. We may label this preliminary procedure the "reconstruction of the argument." The rest of this chapter discusses various aspects of reconstruction.
Enthymemes
Very often a part of an argument is left unstated, either because it is considered obvious or because it is being assumed (perhaps unconsciously). For example, someone might argue, "Sal is female because Sal is John's sister." At first glance it looks like the argument has a single premise, thus:
Sal is John's sister
-----------------------------------
Sal is female.
But what makes the inference so plausible? On what basis can the conclusion be seen to follow from the premise? Is it not that sisters are female? In other words, does not the argument contain a second, implied premise? The complete argument, then, would look something like this:
(1) Sal is John's sister
(2) If a person is a sister, then that person is female
-----------------------------------
Sal is female.
An argument which is only partially stated is called an enthymeme.
It is a very good idea to try to state all of the premisses and the conclusion of an argument when you are in the process of evaluating the argument. Why? For one thing, an arguer is sometimes unaware of the unstated part of her own argument, and were she made aware of it, she might disavow it, or at least entertain some doubt regarding it, thereby losing some degree of confidence in her position, if not outright abandoning it.
Here is a thought provoking example. After narrowly escaping some disaster to which others have fallen victim, it is not uncommon for a person to exclaim, "Thank God! (There but for the grace of God go I.)" Sometimes such an experience will actually lead to a renewal of religious faith. As a matter of "psycho-logic," this cannot be disputed. But what is the logic of the matter? There seems to be (among others perhaps) this implicit argument:
God has spared me from a disaster which befell others
-----------------------------------
God is good.
But for this argument to be valid, it must also contain some such premise as, "If God has spared me, while letting others perish, God is good." But this premise is rather curious, to say the least, and I think many people would instantly be struck by its curiousness were they but made explicitly aware of it. Hence also their confidence in their newfound faith might be shaken. (From a religious standpoint this might be considered unfortunate, but from a rational standpoint this would be considered proper.)
How can you tell what the missing part of an enthymematic argument is? The key here is validity. Normally one should employ a "Principle of Charity" (with respect to validity, anyway) and assume that one's interlocutor is rational. Hence, the argument may be presumed to be valid. It is then up to you to use your sense of validity to "fill in the blank(s)" of the argument.
How, specifically, can you go about this? Taking a course in formal logic would be of tremendous assistance. In the meantime, there is an "informal" method you can employ. Recall the test of validity from the preceding chapter: An argument is valid if the truth of the premisses guarantees or at least makes likely the truth of the conclusion. In other words, to determine whether an argument is valid, you can ask yourself, "If the premisses were all true, would the conclusion then be true also?"
Applying this test to the present situation, one way to fill in the missing or implicit premise of a valid argument would be to ask yourself, "What else (besides the already explicitly stated premise[s]) would need to be true in order to guarantee that the conclusion is true also?" For example, presented with the argument, "There is no cheese on the Moon, so there are no mice on the Moon," you could reason as follows: "Suppose it is true that there is no cheese on the Moon. Then what else would have to be true in order for it to be true that there are no mice on the Moon?" The answer, presumably, is that mice need cheese in order to live; hence, that is the missing premise.
Paraphrase
An argument is composed of statements. In the preceding section we considered the necessity of providing the statements that are omitted from enthymemes. But sometimes it is necessary to do some work even when a statement is given. This is because a statement may appear in abbreviated form, or in ambiguous form, or in some other form which obscures its meaning.
As a rule it should be possible for each component statement of an argument to stand alone both grammatically and semantically. That is to say, it should be expressible as a complete sentence, and the meaning of its component words should be understandable without recourse to other sentences. For example, the argument, "Jim should emigrate because he thinks life in the U.S. is too frenetic," could be rendered as,
Jim thinks life in the U.S. is too frenetic
-----------------------------------
Jim should emigrate from the U.S.
Notice that the pronoun "he" in the premise was replaced by the proper noun "Jim" to make clear who "he" is, and the phrase "from the U.S." was added to the conclusion to clarify from where Jim should emigrate.
Another example is, "You might be hijacked if you vacation in Europe, so don't do it." A paraphrase of (the conclusion of) this argument calls for more extensive rewording than occurred in the preceding example; for "don't do it" we might substitute, "You should not vacation in Europe."
Condensation
The arguments we have been analyzing in this text have been in "skeletal" form; that is to say, nothing but the "bare bones" brief statements of the premisses and conclusion has been exhibited in order to put each argument into its most logically perspicuous form. In "real life," of course, arguments are rarely to be found in this form. Usually they are expressed more verbosely ... although "verbose" is not really the correct word since I do not mean to suggest that it is always inappropriate to "flesh out" an argument. Indeed, expanding arguments into texts is one of the essential rational activities. A whole book can be devoted to the working out of a single argument. Nonetheless, for logical purposes it is often of great value to try to extract the essence of a passage of text by distilling it into explicit argument form. It is not inconceivable that by this means three hundred pages of text could be condensed into three short sentences ... each (the text and the synopsis) serving to illuminate the other.
This work is very demanding. One must strive to be absolutely faithful to the arguer's intentions. Inevitably this involves interpretation; thus the work can be creative as well as analytical. Cultivation of these skills could take a lifetime.
Concatenation
The components of an argument are statements the premisses as well as the conclusion. A statement is in essence an assertion. Thus, even though a statement may be functioning, within the context of one argument, as a premise in support of another assertion (the conclusion of that argument), it may itself require support from some logically prior statement (in another argument). Again: Within any given argument a statement functions in a particular way; however, one and the same statement can function differently in different arguments. Specifically, a premise of one argument can be the conclusion of another. ("One man's ceiling is another man's floor.")
For example, someone might argue, "Reagan is a good President because he has brought prosperity to this land." The premise of this argument is, "Reagan has brought prosperity to the U.S." But it would certainly be reasonable for an interlocutor to question the truth of this premise. Thus, the arguer would be obliged to back it up with further argument, in effect transforming the premise of the first argument into the conclusion of a second argument. The second argument might go like this: "Since Reagan was elected to office, the gross national product has increased by such and such percent; therefore Reagan has brought prosperity to this land." (Of course it would still be possible to dispute the truth of the premise of this argument, not to mention the validity of the argument, and so the dialogue goes on....)
In effect what we end up with is a "piggyback" argument, which could be diagramed thus:
The GNP of the U.S. has increased by n% since Reagan took office
-----------------------------------
Reagan has brought prosperity to the U.S.
-----------------------------------
Reagan is a good President.
We may refer to the statement held in common by the two arguments "Reagan has brought prosperity to the U.S." as a "subconclusion" since it is the conclusion of a component of the piggyback argument but not the final conclusion. Such concatenation of arguments into a piggyback or "line of argument" can go on indefinitely. In analyzing passages of text you will want to be on the lookout for this kind of logical ordering of statements as well as the more straightforward single argument variety.
Summary analysis
Consider this argumentative passage:
Gun control wouldn't make the world completely safe. Neither would nuclear disarmament. For people are always going to have hostile and aggressive tendencies that get out of control. So there's no need to limit weapons. Small or big, they aren't the problem.
The first thing to do is to clarify the structure of the argument. Keep rereading the passage, trying out various analyses, and checking them against the passage. When I did this, this is what I came up with:
People are always going to have aggressive tendencies
-----------------------------------
Control of weapons would never make the world completely safe
-----------------------------------
There is no point to controlling weapons.
Notice that I had to rearrange the order of the statements in the passage in order to come up with the appropriate logical ordering. I also condensed and paraphrased in order to express what I see to be the essence of the argument.
The argument is still not quite in proper form to be evaluated, for it is still enthymematic. Some assumptions are being made to support the inferences, so these should be exhibited too. The complete argument, then, looks like this:
(1) People are always going to have aggressive tendencies
(2) So long as people have aggressive tendencies, controlling weapons will not make the world completely safe
--------------------------------------------------------------
(3) Control of weapons will never make the world completely safe
(4) If a certain course of action will not meet with total success, there is no point in embarking upon it at all
--------------------------------------------------------------
There is no point to controlling weapons
Now I am ready to evaluate the argument. Recalling the algorithm, I should consider the validity first. But since I already made use of my sense of validity in order to fill in the blanks of the enthymematic inferences, I know that the argument is in valid form. Therefore I should check the truth of the premisses, one at a time. (1) and (2) strike me as plausible. Since (3) follows, I accept (3) as well. (4), however, strikes me as utterly implausible in a word, false. And I should think its implausibility would be readily apparent to anyone, including the person who wrote the original passage, were she but aware that it is a part of her argument. Therefore I conclude that the argument does not work, and so the conclusion of the argument that there is no point to controlling weapons has not been shown to be true. (Of course it hasn't been shown to be false either; an argument for that conclusion namely, that there is some point to controlling weapons would have to be constructed independently and then itself evaluated for soundness.)
Dialogue and Dialectic
The notion of dialogue is implicit in what we have already discussed in this primer. The word itself reveals its meaning: "di" means two (as in "dissect" an angle) and "logue" derives from the Greek word "logos," which means, well, word, and also speech and reason (as in "logic"!). Hence, a dialogue is two people reasoning with each other.
It could be maintained that dialogue is an even more essential form of reasoning than argument. Certainly one is most likely to come upon arguments in the context of a dialogue. I cannot provide a definitive explanation of why this is so, but it just seems to be the case that rational thinking itself goes on best when there is a give-and-take process of verbal exchange.
However, a dialogue does consist of arguments. That is the first connection to what we have already discussed. Each of the two parties to a dialogue is giving a reason or reasons to believe his or her claim. The simplest form of dialogue, then, is for two people, who happen to disagree with each other about something, to give their respective reasons for believing their respective claims.
For example, Person A may believe that the Earth is spherical, while Person B may believe that the Earth is flat. So far that is just a difference of opinions. A dialogue would come into being when both A and B back up their beliefs with arguments. Person A might point out that the Earth's shadow during an eclipse of the Moon is curved, while Person B could adduce the generally level lay of the land on which we walk.
But as we saw in Part II of this booklet, it is not enough to give a reason for something: What is wanted is a good reason, a sound argument. Otherwise, a dialogue would always leave us with a stalemate, since by definition both parties or interlocutors ("inter" = between and "locutor" = speaker, as in "locution") have given arguments for their opposing positions. In other words, if what we seek from a dialogue is more than simply a discussion or airing of views but, as with an individual argument, an effort to arrive at a true conclusion, then the dialogue's component arguments must also be evaluated.
This brings us to a more focused sort of dialogue, which is sometimes called dialectic (again, "two speaking," as in "lecture"). Here one employs the critical tools we discussed in Part II in order to assess the quality of each argument, that is, its validity and the truth-values of its premisses.
However, there is one major "wrinkle" about a critical dialogue or dialectic, that distinguishes it from the simpler form of dialogue with which we began. The latter begins with arguments for opposing positions. But a critical argument begins with a single argument for a single position. The other interlocutor then offers a second argument that is critical of the first argument.
Thus, if Person A were to argue as follows:
The shadow of the Earth during an eclipse of the Moon is curved
---------------------------------------------------------------
The Earth is spherical
Person B might argue in turn:
(1) A's argument presumes that only the Earth's being spherical could account for a curved shadow on the Moon
(2) But the Earth's shadow projected onto the Moon might also be curved if the Earth were flat but round like a discus
---------------------------------------------------------------
A's argument is invalid (hence unsound).
In other words, Person B has highlighted a flaw in Person A's argument: The reason Person A gave for believing that the Earth is curved does not establish definitively that the Earth is spherical because an alternative explanation is also available. Hence the conclusion of A's argument does not follow logically from its premise; hence A has not made her case.
So you see that there is nothing essentially new here; this type of argument evaluation was thoroughly discussed in Part II. The only novelty is that we are explicitly recognizing the evaluation of an argument as constituting another argument in its own right. For convenience we are also assigning the two arguments to different people (A and B); and in reality two people are often involved in such a dialogue, but one person is capable of conducting such a dialogue in his or her own mind.
The rest of our discussion of dialogue in this booklet will continue to concentrate on this critical sort of dialogue.
Objections
The second argument in a critical dialogue is known as an objection. (We can call the first argument the "main argument.") What is special about an objection is that it is an argument about another argument. Hence its conclusion will always have one of two forms:
(1) "The main argument is invalid," or
(2) "The main argument contains a (or at least one) false or moot premise."
This, again, follows from what we know from Part II about the evaluation of an argument. Since an objection is really nothing more than the reasoned (negative) evaluation of an(other) argument, it will be defending the claim that one or the other of the two possible defects any argument can have is in fact a feature of the main argument under consideration.
Our example in the previous chapter was an objection of Type 1, i.e., an invalidity objection. Here is an example of a dialogue containing a false (or moot) premise objection:
Main Argument:
Just as the Sun is in the sky during the daytime, the Moon is in the sky at night
----------------------------------------------------------------
The Moon is rightly called the nighttime Sun
Objection:
The Moon is not always in the sky at night; it is up in the daytime just as much
-----------------------------------------------------------
The main argument has a false premise (hence it is unsound).
Notice that a successful objection does not necessarily "destroy" the main argument. In fact, often a good objection can be viewed as an opportunity to strengthen the main argument. Thus, in this last example, the main argument could be reformulated thus:
Just as the Sun is the brightest light in the daytime sky, so the Moon is the brightest light that ever appears at night
-----------------------------------------------------------------
The Moon is rightly called the nighttime Sun.
The premise is now more precise and yet at the same time more flexible in allowing for a favorable interpretation; the argument thereby offsets the objection that was given and perhaps precludes any others besides.
Similarly, in the case of the invalidity example in the previous chapter, Person A could respond to B's objection by trying to modify or clarify the original argument. I suggest the strategy of Exercise 3, which is, in effect, to incorporate the objection into the main argument (seize the bull by the horns, as it were, or bite the bullet, so to speak!), thus:
(1) Earth's shadow during an eclipse of the Moon is curved
(2) Only Earth's being spherical could cause this curved shadow
---------------------------------------------------------------
The Earth is spherical.
Now the argument is valid. Of course it remains for A to try to defend the new premise.
Replies
An essential fact about an objection, as we have seen, is that it is an argument. Hence it consists of a premise or premisses and a conclusion. But this implies, in turn, that an objection can itself be objected to!
An objection to an objection is known as a reply. The most typical sort of dialogue contains a main argument, an objection, and a reply. The upshot of such a dialogue is that Person A (the label I've given to the person who makes the original argument) has successfully defended against a dialectical attack.
Here is an example:
Main Argument:
Cheating is harmful
-------------------
Cheating is wrong
Objection:
Cheating helps the cheater get a better grade with less work
------------------------------------------------------------
The main argument has a false premise (hence it is unsound)
Reply:
Getting a better grade with less work is only a short-term gain; the long-term result could well be quite detrimental to the cheater; furthermore, there are others besides the cheater who can be hurt by cheating, such as classmates, the teacher, future employers, etc.
-------------------------------------------------
The objection is invalid (hence unsound; hence the main argument has not been refuted).
Finally it should be noted that a reply, being an objection, is itself also an argument, and hence can also be objected to! An objection to a reply is called a counterreply (for you see, being an objection to an objection, it is a kind of reply). Obviously this process can be iterated indefinitely: After a counterreply there can be a countercounterreply, etc. But in practical affairs, dialogues are typically short ... ending with the first reply, as I have said, or often even with a resounding objection to the main argument.
However, that does not mean than an issue has been put to rest, or even an argument. For, in the case of a dialogue ending with a successful reply, it is forever open to somebody to think of a new objection to the main argument. On the other hand, even in the case of a successful objection, there is still the possibility, as illustrated in the previous chapter, that someone will someday reformulate the original argument so that it can withstand the objection (call this a response to the objection, as opposed to a reply). And in any case, even a definitive objection does not establish the falsity of the main argument's conclusion, but only the inadequacy of the reason that has been given to believe it; who can rule out that somebody will not come up with a better argument for it in the future?
Having now presented the logical skeleton of dialectic, I would also like to emphasize that the skeleton needs to be fleshed out in any actual instance of rational debate. One must be especially on one's guard against generating a dialogue artificially, by withholding essential explanation from the exposition of the original argument. This would be called setting up a straw man, which is of course easily knocked down. Thus, in the example from above --
Cheating is harmful
-------------------
Cheating is wrong
this main argument might have worked by itself, without need of a reply to an objection, had it simply been spelled out to begin with. What does the premise mean? Presumably it is referring to all of the sorts of things that were mentioned in the reply above (long-term detriment to the cheater, harm to classmates, the teacher, future employers, etc.). In, say, an essay about the ethics of cheating, such items should be mentioned right at the start, and fully explained and defended with examples. Only then should you consider if there is a possible objection to the argument.
By the (other side of) the same token, you cannot "win" in dialectic simply by ignoring possible objections to your argument. And let me assure you (from my decades of experience with dialectic) that you don't ever have to "worry" that there won't be a strong or an interesting objection to your best argument. If you put on your thinking cap, or try out your argument on somebody else, you are likely to find that your argument can be plausibly criticized. At that point you may in turn be able to come up with a good reply (or a response, as in the previous chapter); but don't attempt to shortchange dialectic by underestimating the universe's creative capacity to engender objections!
Please note: Some of the arguments used as examples in this text, intended originally as a handout for my students, may have come from other sources, which are long since lost to my memory. Apologies to the authors. The analyses, however, are my own. Also, apologies to the reader for the omission of some marks of punctuation, which seem to have been lost in transferring the text to this website.
Rational Argument, Part I: Recognizing an Argument
There is a special structure in a great deal of what you read and hear and think and write and speak which the study of reasoning can make you aware of. I do not mean simple grammatical structure, such as sentences and nouns and verbs. I am talking about logical structure. If you become aware of the logical structure of language, you will gain power of understanding, power of criticism, power of expression. In this short essay I will introduce you to the basics of logical structure.
Just as the sentence is the basic unit of grammar, so the argument is the basic unit of logic. The business of a sentence is to express a thought. The business of an argument is to defend a claim. An example of an argument is
Reagan was a good President because he reduced inflation.
The claim being defended is
Reagan was a good President.
Just as a sentence has (grammatical) parts, so an argument has (logical) parts. A sentence consists of a subject and a predicate. An argument consists of premisses and a conclusion. In the argument from above, the premise is
Reagan reduced inflation
and the conclusion is
Reagan was a good President.
The premisses of an argument, therefore, constitute the defense of the conclusion of the argument. We can also say that the premisses of an argument are intended to provide a reason for believing the conclusion. This is why disciplines such as philosophy, science, and mathematics are said to be rational: These disciplines employ arguments, an argument incorporates a reason for believing something, and the Latin word for reason is "ratio."
It makes sense that "rational" has this meaning. It seems eminently rational to provide reasons for what one believes or claims, or at least to be prepared to do so or be able to do so. For example, consider the bald statement
Reagan was a good President.
If a person made this statement but had nothing more to say about the matter, no reason to back up his claim, we might wonder how rational he was being. Maybe he believes that Reagan was a good President solely because all of his friends believe it and he has never thought about the matter at all. Compare this situation to the one where, if pressed, a person could explain that
Reagan was a good President BECAUSE he reduced inflation.
This person would seem to be more rational, at least in this one instance, simply because she is able to give a reason for what she believes.
Logical Language
Someone once remarked that human beings live in a sea of arguments. Someone else has observed that fish may be unaware of water since, for them, it is everywhere. Just so, human beings often have trouble recognizing the arguments that bombard their ears, fill up their minds, and cross their lips. In this chapter I will discuss some ways of detecting arguments.
The best clue to the presence of an argument is a certain kind of language. This remark must immediately be qualified, however, because language is a notoriously slippy phenomenon. Certain words often serve as inference (i.e., argument) indicators; but many of these very same words commonly serve other linguistic functions as well, and so they are not to be relied upon absolutely as guides to the presence of an argument. Nevertheless, they do often help you to pick out an argument.
As you have probably observed from the various examples of arguments I have already given, the word "because" is a very common inference indicator. This word introduces the premise(s) of an argument, and, hence, indicates that an argument is present. (But already you should be alerted to an important exception, for the word "because" is also frequently to be found in explanations as opposed to arguments. More on this in a later chapter.)
In the last paragraph I myself presented an argument, namely: "This word ['because'] introduces the premise(s) of an argument, and, hence, indicates that an argument is present." In this argument, "hence" functions as an inference indicator. Unlike "because," "hence" introduces the conclusion of an argument; nonetheless, since a conclusion is also part of an argument, the presence of "hence" reveals the presence of an argument.
This brief review reveals that there are two basic kinds of inference words: those which introduce a premise and those which introduce a conclusion. The most common word of the former sort is "because." Synonyms of "because," such as "since" and "for," also frequently serve as premise introducers. The most common conclusion introducer is the word "therefore." Some typical synonyms of "therefore" are "hence," "thus," "so." and "then" (but not "if/then").
Finally, it is important to realize that an argument can be present without any inference indicator word. For example,
The sky is cloudy. It's going to rain.
Clearly the word "therefore" is implied; hence, this is an argument.
Symbolism
Because certain logical relations and logical words occur repeatedly in argumentation, it is convenient to use symbols to abbreviate them. Since, however, this is not a primer in symbolic logic, I shall keep the symbolism to a minimum. For our purposes as reasoners we can get along quite nicely with just the following few conventions.
1. The line. Although "therefore" and "because" introduce different components of an argument, they express the identical logical relation. Hence it is possible to adopt a single symbol which stands for this relation and so can substitute for both words. Let us, then, adopt the convention of using a horizontal line to stand for the logical relation; and this line shall be read as "therefore" when reading from top to bottom and as "because" when reading from bottom to top. So, for example, the following three expressions are equivalent:
(1) Reagan is a good President because he reduced inflation
(2) Reagan reduced inflation; therefore Reagan is a good President
(3) Reagan reduced inflation
-----------------------------------
Reagan is a good President
2. Capital letters. As we have seen, an argument consists of statements (in a certain relation). These statements may be simple or else may themselves consist of other statements. An example of a statement which consists of other statements is
If Jane is your sister, then Jane is female.
The component statements here are
Jane is your sister
and
Jane is female.
A capital letter may be used to abbreviate any simple statement in an argument. Thus, for example, "Jane is your sister" could be abbreviated as "S" (where the "S" serves mnemonically to pick out "sister"), "Jane is female" could be abbreviated as "F," and "If Jane is your sister, then Jane is female" could be abbreviated as "If S then F."
3. The dash. For the purposes of reasoning it is often useful to distinguish a positive assertion from a denial. An example of a positive assertion is
The earth is flat.
An example of a denial is
The earth is not flat.
Let us use a dash to indicate a denial (analogously to the use of the negation sign and the minus sign in arithmetic). So for example "F" could stand for "The earth is flat," and " F" could stand for "The earth is not flat." Note that a denial is equivalent to asserting that something is false; "The earth is not flat" means the same thing as "It is false that the earth is flat." Yet another way to think about the relation between positive assertion and denial is to note that "The earth is flat" is equivalent to saying "It is true that the earth is flat," while "The earth is not flat" is equivalent to saying "It is not true that the earth is flat."
4. The tilde. A defining characteristic of every statement is that it is either true or false. For example, the statement "The earth is flat" is false, and the statement "The earth is round" is true. Sometimes, though, we do not know the "truth value" of a particular statement. For example, "There are exactly three hundred and five craters on the planet Pluto" is either true or false, but we do not know which. A statement of this sort may be called "moot," and the tilde can abbreviate it, as in "˜P."
Argument vs. Non Argument
One way to come to understand the concept of argument is to consider what sorts of things are not arguments. When I speak of "argument" in this essay, I am usually referring to rational argument. So the first thing to distinguish rational argument from is non rational argument. Non rational argument is probably what is most often meant by the word "argument" in everyday speech. Non rational argument occurs whenever two (or more) people are involved in an emotional verbal disagreement. "You're a liar!" "I am not!" And so forth.
Rational argument is nothing like this. Rational argument is not any kind of disagreement or even behavior. A rational argument is simply a set of statements, one or more of which constitute a reason for believing another of them.
While it is important to recognize that an argument consists of statements, it is equally crucial to recognize that an argument always contains more than one statement. The key to distinguishing all of the following sorts of non arguments from arguments is that an argument is not a statement but is instead a set of at least two statements (which bear a certain relation to each other). All of the following examples of non arguments are statements of various sorts which are easily confused with arguments.
1. A HYPOTHETICAL STATEMENT IS NOT AN ARGUMENT. Example:
If Sally is your sister, then Sally is female.
Here is one way to convince yourself that this is not an argument. Suppose that it were an argument; then the conclusion would be "Sally is female" and the premise would be "Sally is your sister." However, the given sentence does not make either of these claims; an "if...then" sentence is purely hypothetical, which is to say that it is only talking about what would be the case were something else the case (Sally would be female were Sally your sister). But an argument is claiming that something (the conclusion) is the case because something else (the premise[s]) is the case (Sally is female because Sally is your sister). In other words, the "if...then" sentence can be true even if one or both of its component clauses are false, but the corresponding argument cannot be a good one unless both components are true.
2. AN EXPLANATION IS NOT AN ARGUMENT. Example:
The sky is blue because of the refraction of the sun's rays.
Here again you can convince yourself that this is not an argument by imagining what it would be like if it were an argument. The conclusion would be "The sky is blue," and the premise would be something like "The sun's rays are refracted as they pass through the atmosphere." The giveaway here is that the "conclusion" is something which is not controversial. No one would ever be trying to argue that the sky is blue; everybody already knows this. (A qualification here is that context can make a difference; if we happened to be discussing, say, the planet Mars, the blue sky example could be an argument.) Therefore, what is being provided is most likely an explanation of why the sky is blue, rather than a reason for believing that the sky is blue. (Note: Explanations, like any other statements, can be false.)
3. A COMPOUND STATEMENT IS NOT AN ARGUMENT. Example:
First I will drive to New York, and then I will drive to Baltimore.
Again try the "suppose test." If this were an argument, the conclusion would be "I will drive to Baltimore," and the premise would be "I will drive to New York." Now, the sentence in question does establish a relation between these two component clauses or statements; however, it is not the right kind of relation for an argument. In an argument, a reason is being given to believe a claim. But in this sentence it is surely not the case that my driving to New York is being given as a reason for you to believe that I will drive to Baltimore. The relation between the components of the given sentence is simply one of conjunction or perhaps of sequence. An argument requires that the intended relation be one of rational support.
Rational Argument, Part II: Evaluating an Argument
There is more to being rational than simply providing a reason for a claim. The reason should be a good one. There are two main tests for quality of an argument: (1) Does the conclusion follow from the premisses? (2) Are the premisses true? An argument which passes both of these tests is a sound one. A sound argument shall be our standard of good reasoning.
Validity
An argument is valid if its conclusion follows from its premise(s); it is invalid otherwise.
What does the phrase "follows from" mean? It turns out that the entire field of LOGIC is devoted to the study of this concept. Hundreds of books have been written over thousands of years in the attempt to clarify it. The investigation of validity is one of the most fascinating adventures of the intellect, and I would encourage any of you who are so inclined to pursue it in a course on logic. However, for the purposes of reasoning, you need only gain some familiarity with the use of validity for the evaluation of arguments. (It is like the difference between learning how to drive a car and learning how a car works.)
To begin with it is possible to appreciate validity in a strictly intuitive way. Examples have already been given of valid and invalid arguments in earlier chapters. I am sure you had no difficulty in sensing what was good or bad in those arguments.
Unfortunately, many arguments are not so simple nor so simply evaluated. Therefore let me suggest another way to think about validity and invalidity in general which may help you to deal with the more difficult cases: Ask yourself whether the conclusion of the argument would be true (or, at least, would probably be true) were the premise(s) of the argument true.
Consider the following argument:
(1) All whales have wings
(2) All winged animals can fly
-----------------------------------
All whales can fly
This argument is valid. Why? Well, imagine a world in which all whales have wings and all winged animals can fly. Wouldn't it also be true in such a world that all whales can fly?
Now consider this argument:
(1) If Mary is my sister, then Mary is female
(2) Mary is female
-----------------------------------
Mary is my sister
This argument is not valid; i.e., it is invalid. You can discover this simply by employing the test I have suggested. For suppose that both premisses are true; thus, Mary is female and furthermore, if Mary is my sister, then Mary is female (which is just a way of saying that in order to be someone's sister, you must be female). Must it also be true that Mary is my sister? Not necessarily. In fact, not even probably. For there are probably millions of Marys who are female but not my sister, and the argument does not give you any reason for believing that the Mary in question is one who is my sister (or even that I have a sister!).
Truth of the premisses
While validity is an intuitive notion, it may strike you as exceedingly odd that an argument such as the one above about flying whales can turn out to be valid. Whales can't fly, so how can an argument having "All whales can fly" as its conclusion be a valid one?
The way out of this quandary is to realize that "validity" is being used in a technical sense; it means exactly what I said it means in the previous section, and nothing more. So, for example, to say that an argument is "valid" is not to say that the argument is a good one. The technical term "sound" has been reserved for that meaning, and in order to be a sound argument an argument must not only be valid but also contain all and only true premisses.
Why study validity (hence, logic) in the first place, then? Precisely because there are two essential conditions of a good argument. TRUE PREMISSES ALONE DO NOT A GOOD (i.e., SOUND) ARGUMENT MAKE. An argument must also be valid in order to be sound.
So, for example, we have already seen a case of an argument passing the validity test without passing the truth of the premisses test (from now on I shall refer to the second test simply as the "truth test"), namely,
(1) All whales have wings
(2) All winged animals can fly
-----------------------------------
All whales can fly.
We can also have an argument containing true premisses which is nonetheless invalid, for example,
(1) All dogs have lungs
(2) All birds have lungs
-----------------------------------
Dogs are birds.
To be a sound argument an argument must have BOTH a conclusion that follows from the premisses AND premisses that are true. Here is an example of such an argument:
(1) The Moon orbits the Earth
(2) The Earth orbits the Sun
-----------------------------------
The Moon orbits the Sun.
Truth of the conclusion
Note that the conclusion of a sound argument is true. And this after all is our goal: truth. This is ultimately why we care about reasoning and logic and validity and soundness: They help to lead us to truth.
Another way to put this is to say that arguments can take us from things already known to new knowledge. In the immediately preceding example, I dare say it comes as a revelation to many people to realize that the Moon orbits the Sun; and yet this conclusion follows quite naturally from the juxtaposition of the premisses, whose truth is already recognized by everyone.
In a way, reasoning can be like pulling a rabbit out of a hat. It is a wonderful thing really a way to expand our knowledge indefinitely, without having to lift a finger, as it were. Indeed it has been remarked that the majority of our knowledge of the world comes not from observation but from inference.
It is essential to understand, however, the proper place of the truth of the conclusion in the evaluation of an argument. Strictly speaking, the truth of the conclusion does not enter into the evaluation. Recall again the two tests for the quality of an argument: (1) validity of the inference and (2) truth of the premisses. When we consider an argument, we are typically in some doubt about the truth of the conclusion. This is precisely why we are considering an argument at all. If we were certain of the truth of a given claim, we would have no need to consider a reason to believe it. Thus it would be question begging to allow our opinion of the conclusion to enter into our evaluation of the argument.
(I should introduce a caveat at this point. While it is indeed question begging to evaluate an argument on the basis of its conclusion, it does not follow that it is never legitimate to do so. For example, were someone to propose an argument for the claim that all blue eyed people should be exterminated, I think we should rightly decline to hear it out. On the other hand, it can be just as important to insist on the logical point I have been making. Consider how absurd it must have seemed to most people a few hundred years ago when Copernicus asked them to listen to his arguments for the claim that the Earth moves around the Sun. And more recently we know how difficult, even to the point of seeming morally objectionable, it has been for some people to entertain the hypothesis that people have descended from nonhuman animals. Perhaps then we should err on the side of nonsense and be prepared to hear out an argument for just about any claim whatsoever, for from time to time the "nonsense" may turn out to be true.)
Falsity of the conclusion
Yet another important "fine point" is that the conclusion of an argument has not been shown to be false just because the argument has been shown to be unsound. Soundness of an argument does imply the truth of the conclusion, but unsoundness does not imply the falsity of the conclusion. This point can be simply illustrated; the following argument is unsound and yet it has a true conclusion:
(1) Whales live in the sea
(2) Only mammals live in the sea
-----------------------------------
Whales are mammals.
The significance of demonstrating that an argument is unsound (or "bad" or "flawed" or "faulty") is that the reason given is not adequate to establish the truth of the conclusion. Thus, the falsity of the conclusion does not follow from the unsoundness of the argument, for, for all one knows, there may exist some other, better reason (i.e., argument) for believing the conclusion. For example, in the case of the whales:
(1) Only mammals suckle their young
(2) Whales suckle their young
-----------------------------------
Whales are mammals.
There is only one way to demonstrate that a certain claim is false and that is to argue directly for the falsity of the claim. (And of course the argument must be sound.) For example,
(1) No mammal is a fish
(2) Whales are mammals
-----------------------------------
It is false that whales are fish (or "Whales are not fish").
Please understand that the conclusion of this argument is, "It is false that whales are fish" (the conclusion, as always, is whatever comes beneath the line), and, as always, it is the truth of the conclusion that the argument is concerned to establish. It so happens that to establish the truth of the conclusion of this argument is to establish the falsity of the claim, "Whales are fish."
Procedure
As a general policy I would recommend examining the validity of an argument first. Thus, the algorithm for the evaluation of an argument goes like this:
1. Is the argument valid? If NO, stop (the argument is invalid, hence unsound). If YES, proceed to the next step.
2. Is the topmost unexamined premise of the argument true? If NO (the premise is false or moot), stop (the argument is unsound). If YES, proceed to the next step.
3. Is there another premise? If NO, stop (the argument is sound; hence the conclusion is true). If YES, return to the preceding step.
In order to do this job properly, however, there may need to be some preliminary steps. The basic idea is to put an argument into a standard form, which will most readily lend itself to the application of the algorithm and, thereby, most clearly reveal the quality of the argument. We may label this preliminary procedure the "reconstruction of the argument." The rest of this chapter discusses various aspects of reconstruction.
Enthymemes
Very often a part of an argument is left unstated, either because it is considered obvious or because it is being assumed (perhaps unconsciously). For example, someone might argue, "Sal is female because Sal is John's sister." At first glance it looks like the argument has a single premise, thus:
Sal is John's sister
-----------------------------------
Sal is female.
But what makes the inference so plausible? On what basis can the conclusion be seen to follow from the premise? Is it not that sisters are female? In other words, does not the argument contain a second, implied premise? The complete argument, then, would look something like this:
(1) Sal is John's sister
(2) If a person is a sister, then that person is female
-----------------------------------
Sal is female.
An argument which is only partially stated is called an enthymeme.
It is a very good idea to try to state all of the premisses and the conclusion of an argument when you are in the process of evaluating the argument. Why? For one thing, an arguer is sometimes unaware of the unstated part of her own argument, and were she made aware of it, she might disavow it, or at least entertain some doubt regarding it, thereby losing some degree of confidence in her position, if not outright abandoning it.
Here is a thought provoking example. After narrowly escaping some disaster to which others have fallen victim, it is not uncommon for a person to exclaim, "Thank God! (There but for the grace of God go I.)" Sometimes such an experience will actually lead to a renewal of religious faith. As a matter of "psycho-logic," this cannot be disputed. But what is the logic of the matter? There seems to be (among others perhaps) this implicit argument:
God has spared me from a disaster which befell others
-----------------------------------
God is good.
But for this argument to be valid, it must also contain some such premise as, "If God has spared me, while letting others perish, God is good." But this premise is rather curious, to say the least, and I think many people would instantly be struck by its curiousness were they but made explicitly aware of it. Hence also their confidence in their newfound faith might be shaken. (From a religious standpoint this might be considered unfortunate, but from a rational standpoint this would be considered proper.)
How can you tell what the missing part of an enthymematic argument is? The key here is validity. Normally one should employ a "Principle of Charity" (with respect to validity, anyway) and assume that one's interlocutor is rational. Hence, the argument may be presumed to be valid. It is then up to you to use your sense of validity to "fill in the blank(s)" of the argument.
How, specifically, can you go about this? Taking a course in formal logic would be of tremendous assistance. In the meantime, there is an "informal" method you can employ. Recall the test of validity from the preceding chapter: An argument is valid if the truth of the premisses guarantees or at least makes likely the truth of the conclusion. In other words, to determine whether an argument is valid, you can ask yourself, "If the premisses were all true, would the conclusion then be true also?"
Applying this test to the present situation, one way to fill in the missing or implicit premise of a valid argument would be to ask yourself, "What else (besides the already explicitly stated premise[s]) would need to be true in order to guarantee that the conclusion is true also?" For example, presented with the argument, "There is no cheese on the Moon, so there are no mice on the Moon," you could reason as follows: "Suppose it is true that there is no cheese on the Moon. Then what else would have to be true in order for it to be true that there are no mice on the Moon?" The answer, presumably, is that mice need cheese in order to live; hence, that is the missing premise.
Paraphrase
An argument is composed of statements. In the preceding section we considered the necessity of providing the statements that are omitted from enthymemes. But sometimes it is necessary to do some work even when a statement is given. This is because a statement may appear in abbreviated form, or in ambiguous form, or in some other form which obscures its meaning.
As a rule it should be possible for each component statement of an argument to stand alone both grammatically and semantically. That is to say, it should be expressible as a complete sentence, and the meaning of its component words should be understandable without recourse to other sentences. For example, the argument, "Jim should emigrate because he thinks life in the U.S. is too frenetic," could be rendered as,
Jim thinks life in the U.S. is too frenetic
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Jim should emigrate from the U.S.
Notice that the pronoun "he" in the premise was replaced by the proper noun "Jim" to make clear who "he" is, and the phrase "from the U.S." was added to the conclusion to clarify from where Jim should emigrate.
Another example is, "You might be hijacked if you vacation in Europe, so don't do it." A paraphrase of (the conclusion of) this argument calls for more extensive rewording than occurred in the preceding example; for "don't do it" we might substitute, "You should not vacation in Europe."
Condensation
The arguments we have been analyzing in this text have been in "skeletal" form; that is to say, nothing but the "bare bones" brief statements of the premisses and conclusion has been exhibited in order to put each argument into its most logically perspicuous form. In "real life," of course, arguments are rarely to be found in this form. Usually they are expressed more verbosely ... although "verbose" is not really the correct word since I do not mean to suggest that it is always inappropriate to "flesh out" an argument. Indeed, expanding arguments into texts is one of the essential rational activities. A whole book can be devoted to the working out of a single argument. Nonetheless, for logical purposes it is often of great value to try to extract the essence of a passage of text by distilling it into explicit argument form. It is not inconceivable that by this means three hundred pages of text could be condensed into three short sentences ... each (the text and the synopsis) serving to illuminate the other.
This work is very demanding. One must strive to be absolutely faithful to the arguer's intentions. Inevitably this involves interpretation; thus the work can be creative as well as analytical. Cultivation of these skills could take a lifetime.
Concatenation
The components of an argument are statements the premisses as well as the conclusion. A statement is in essence an assertion. Thus, even though a statement may be functioning, within the context of one argument, as a premise in support of another assertion (the conclusion of that argument), it may itself require support from some logically prior statement (in another argument). Again: Within any given argument a statement functions in a particular way; however, one and the same statement can function differently in different arguments. Specifically, a premise of one argument can be the conclusion of another. ("One man's ceiling is another man's floor.")
For example, someone might argue, "Reagan is a good President because he has brought prosperity to this land." The premise of this argument is, "Reagan has brought prosperity to the U.S." But it would certainly be reasonable for an interlocutor to question the truth of this premise. Thus, the arguer would be obliged to back it up with further argument, in effect transforming the premise of the first argument into the conclusion of a second argument. The second argument might go like this: "Since Reagan was elected to office, the gross national product has increased by such and such percent; therefore Reagan has brought prosperity to this land." (Of course it would still be possible to dispute the truth of the premise of this argument, not to mention the validity of the argument, and so the dialogue goes on....)
In effect what we end up with is a "piggyback" argument, which could be diagramed thus:
The GNP of the U.S. has increased by n% since Reagan took office
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Reagan has brought prosperity to the U.S.
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Reagan is a good President.
We may refer to the statement held in common by the two arguments "Reagan has brought prosperity to the U.S." as a "subconclusion" since it is the conclusion of a component of the piggyback argument but not the final conclusion. Such concatenation of arguments into a piggyback or "line of argument" can go on indefinitely. In analyzing passages of text you will want to be on the lookout for this kind of logical ordering of statements as well as the more straightforward single argument variety.
Summary analysis
Consider this argumentative passage:
Gun control wouldn't make the world completely safe. Neither would nuclear disarmament. For people are always going to have hostile and aggressive tendencies that get out of control. So there's no need to limit weapons. Small or big, they aren't the problem.
The first thing to do is to clarify the structure of the argument. Keep rereading the passage, trying out various analyses, and checking them against the passage. When I did this, this is what I came up with:
People are always going to have aggressive tendencies
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Control of weapons would never make the world completely safe
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There is no point to controlling weapons.
Notice that I had to rearrange the order of the statements in the passage in order to come up with the appropriate logical ordering. I also condensed and paraphrased in order to express what I see to be the essence of the argument.
The argument is still not quite in proper form to be evaluated, for it is still enthymematic. Some assumptions are being made to support the inferences, so these should be exhibited too. The complete argument, then, looks like this:
(1) People are always going to have aggressive tendencies
(2) So long as people have aggressive tendencies, controlling weapons will not make the world completely safe
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(3) Control of weapons will never make the world completely safe
(4) If a certain course of action will not meet with total success, there is no point in embarking upon it at all
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There is no point to controlling weapons
Now I am ready to evaluate the argument. Recalling the algorithm, I should consider the validity first. But since I already made use of my sense of validity in order to fill in the blanks of the enthymematic inferences, I know that the argument is in valid form. Therefore I should check the truth of the premisses, one at a time. (1) and (2) strike me as plausible. Since (3) follows, I accept (3) as well. (4), however, strikes me as utterly implausible in a word, false. And I should think its implausibility would be readily apparent to anyone, including the person who wrote the original passage, were she but aware that it is a part of her argument. Therefore I conclude that the argument does not work, and so the conclusion of the argument that there is no point to controlling weapons has not been shown to be true. (Of course it hasn't been shown to be false either; an argument for that conclusion namely, that there is some point to controlling weapons would have to be constructed independently and then itself evaluated for soundness.)
Dialogue and Dialectic
The notion of dialogue is implicit in what we have already discussed in this primer. The word itself reveals its meaning: "di" means two (as in "dissect" an angle) and "logue" derives from the Greek word "logos," which means, well, word, and also speech and reason (as in "logic"!). Hence, a dialogue is two people reasoning with each other.
It could be maintained that dialogue is an even more essential form of reasoning than argument. Certainly one is most likely to come upon arguments in the context of a dialogue. I cannot provide a definitive explanation of why this is so, but it just seems to be the case that rational thinking itself goes on best when there is a give-and-take process of verbal exchange.
However, a dialogue does consist of arguments. That is the first connection to what we have already discussed. Each of the two parties to a dialogue is giving a reason or reasons to believe his or her claim. The simplest form of dialogue, then, is for two people, who happen to disagree with each other about something, to give their respective reasons for believing their respective claims.
For example, Person A may believe that the Earth is spherical, while Person B may believe that the Earth is flat. So far that is just a difference of opinions. A dialogue would come into being when both A and B back up their beliefs with arguments. Person A might point out that the Earth's shadow during an eclipse of the Moon is curved, while Person B could adduce the generally level lay of the land on which we walk.
But as we saw in Part II of this booklet, it is not enough to give a reason for something: What is wanted is a good reason, a sound argument. Otherwise, a dialogue would always leave us with a stalemate, since by definition both parties or interlocutors ("inter" = between and "locutor" = speaker, as in "locution") have given arguments for their opposing positions. In other words, if what we seek from a dialogue is more than simply a discussion or airing of views but, as with an individual argument, an effort to arrive at a true conclusion, then the dialogue's component arguments must also be evaluated.
This brings us to a more focused sort of dialogue, which is sometimes called dialectic (again, "two speaking," as in "lecture"). Here one employs the critical tools we discussed in Part II in order to assess the quality of each argument, that is, its validity and the truth-values of its premisses.
However, there is one major "wrinkle" about a critical dialogue or dialectic, that distinguishes it from the simpler form of dialogue with which we began. The latter begins with arguments for opposing positions. But a critical argument begins with a single argument for a single position. The other interlocutor then offers a second argument that is critical of the first argument.
Thus, if Person A were to argue as follows:
The shadow of the Earth during an eclipse of the Moon is curved
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The Earth is spherical
Person B might argue in turn:
(1) A's argument presumes that only the Earth's being spherical could account for a curved shadow on the Moon
(2) But the Earth's shadow projected onto the Moon might also be curved if the Earth were flat but round like a discus
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A's argument is invalid (hence unsound).
In other words, Person B has highlighted a flaw in Person A's argument: The reason Person A gave for believing that the Earth is curved does not establish definitively that the Earth is spherical because an alternative explanation is also available. Hence the conclusion of A's argument does not follow logically from its premise; hence A has not made her case.
So you see that there is nothing essentially new here; this type of argument evaluation was thoroughly discussed in Part II. The only novelty is that we are explicitly recognizing the evaluation of an argument as constituting another argument in its own right. For convenience we are also assigning the two arguments to different people (A and B); and in reality two people are often involved in such a dialogue, but one person is capable of conducting such a dialogue in his or her own mind.
The rest of our discussion of dialogue in this booklet will continue to concentrate on this critical sort of dialogue.
Objections
The second argument in a critical dialogue is known as an objection. (We can call the first argument the "main argument.") What is special about an objection is that it is an argument about another argument. Hence its conclusion will always have one of two forms:
(1) "The main argument is invalid," or
(2) "The main argument contains a (or at least one) false or moot premise."
This, again, follows from what we know from Part II about the evaluation of an argument. Since an objection is really nothing more than the reasoned (negative) evaluation of an(other) argument, it will be defending the claim that one or the other of the two possible defects any argument can have is in fact a feature of the main argument under consideration.
Our example in the previous chapter was an objection of Type 1, i.e., an invalidity objection. Here is an example of a dialogue containing a false (or moot) premise objection:
Main Argument:
Just as the Sun is in the sky during the daytime, the Moon is in the sky at night
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The Moon is rightly called the nighttime Sun
Objection:
The Moon is not always in the sky at night; it is up in the daytime just as much
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The main argument has a false premise (hence it is unsound).
Notice that a successful objection does not necessarily "destroy" the main argument. In fact, often a good objection can be viewed as an opportunity to strengthen the main argument. Thus, in this last example, the main argument could be reformulated thus:
Just as the Sun is the brightest light in the daytime sky, so the Moon is the brightest light that ever appears at night
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The Moon is rightly called the nighttime Sun.
The premise is now more precise and yet at the same time more flexible in allowing for a favorable interpretation; the argument thereby offsets the objection that was given and perhaps precludes any others besides.
Similarly, in the case of the invalidity example in the previous chapter, Person A could respond to B's objection by trying to modify or clarify the original argument. I suggest the strategy of Exercise 3, which is, in effect, to incorporate the objection into the main argument (seize the bull by the horns, as it were, or bite the bullet, so to speak!), thus:
(1) Earth's shadow during an eclipse of the Moon is curved
(2) Only Earth's being spherical could cause this curved shadow
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The Earth is spherical.
Now the argument is valid. Of course it remains for A to try to defend the new premise.
Replies
An essential fact about an objection, as we have seen, is that it is an argument. Hence it consists of a premise or premisses and a conclusion. But this implies, in turn, that an objection can itself be objected to!
An objection to an objection is known as a reply. The most typical sort of dialogue contains a main argument, an objection, and a reply. The upshot of such a dialogue is that Person A (the label I've given to the person who makes the original argument) has successfully defended against a dialectical attack.
Here is an example:
Main Argument:
Cheating is harmful
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Cheating is wrong
Objection:
Cheating helps the cheater get a better grade with less work
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The main argument has a false premise (hence it is unsound)
Reply:
Getting a better grade with less work is only a short-term gain; the long-term result could well be quite detrimental to the cheater; furthermore, there are others besides the cheater who can be hurt by cheating, such as classmates, the teacher, future employers, etc.
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The objection is invalid (hence unsound; hence the main argument has not been refuted).
Finally it should be noted that a reply, being an objection, is itself also an argument, and hence can also be objected to! An objection to a reply is called a counterreply (for you see, being an objection to an objection, it is a kind of reply). Obviously this process can be iterated indefinitely: After a counterreply there can be a countercounterreply, etc. But in practical affairs, dialogues are typically short ... ending with the first reply, as I have said, or often even with a resounding objection to the main argument.
However, that does not mean than an issue has been put to rest, or even an argument. For, in the case of a dialogue ending with a successful reply, it is forever open to somebody to think of a new objection to the main argument. On the other hand, even in the case of a successful objection, there is still the possibility, as illustrated in the previous chapter, that someone will someday reformulate the original argument so that it can withstand the objection (call this a response to the objection, as opposed to a reply). And in any case, even a definitive objection does not establish the falsity of the main argument's conclusion, but only the inadequacy of the reason that has been given to believe it; who can rule out that somebody will not come up with a better argument for it in the future?
Having now presented the logical skeleton of dialectic, I would also like to emphasize that the skeleton needs to be fleshed out in any actual instance of rational debate. One must be especially on one's guard against generating a dialogue artificially, by withholding essential explanation from the exposition of the original argument. This would be called setting up a straw man, which is of course easily knocked down. Thus, in the example from above --
Cheating is harmful
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Cheating is wrong
this main argument might have worked by itself, without need of a reply to an objection, had it simply been spelled out to begin with. What does the premise mean? Presumably it is referring to all of the sorts of things that were mentioned in the reply above (long-term detriment to the cheater, harm to classmates, the teacher, future employers, etc.). In, say, an essay about the ethics of cheating, such items should be mentioned right at the start, and fully explained and defended with examples. Only then should you consider if there is a possible objection to the argument.
By the (other side of) the same token, you cannot "win" in dialectic simply by ignoring possible objections to your argument. And let me assure you (from my decades of experience with dialectic) that you don't ever have to "worry" that there won't be a strong or an interesting objection to your best argument. If you put on your thinking cap, or try out your argument on somebody else, you are likely to find that your argument can be plausibly criticized. At that point you may in turn be able to come up with a good reply (or a response, as in the previous chapter); but don't attempt to shortchange dialectic by underestimating the universe's creative capacity to engender objections!
posted by jmarks at 11:58 AM
