Critical Thinking, Reasoning, and Argument Critical thinking is used in many contexts and has different connotations. Often it is applied to contexts such as interpreting texts, evaluating artistic expression, and so on. For our purposes, however, we will characterize critical thinking as openly and explicitly deliberating whether to accept or reject claims or beliefs. Critical thinking often involves reasoning. Reasoning or rationality implies that we accept or reject beliefs objectively. In other words, the reasons that persuaded us to accept or reject some belief would be equally persuasive to other individuals. In this respect, rationality implies intersubjectivity. Reasoning, therefore, is a process that should transcend prejudices, narrow self- interest, and sheer emotional motivations. Often, our reasoning is directed at matters of fact these are beliefs about what obtains in the world. For example, whether unicorns exist or not is a factual matter. But, critical thinking and reasoning can also consider matters of value. These are typically questions of what is good, evil, right or wrong. For instance, whether deceiving someone is ever morally right or justified is a question that at least in part depends on values. In either case, though, decisions about these beliefs can be critically examined and reasoned about. Specimens or expressions of reasoning are called arguments. Arguments are comprised by evidence and claims. Both claims and evidence are represented by statements. A statement is a sentence that expresses what is either true or false. In grammar, statements are called declarative sentences. The claim or conclusion is the point of the argument; it expresses what we are asked to accept as true. The evidence is what is offered to persuade us to accept the truth of the claim. Rational arguments are those whose evidence supports the claim by means of some generally accepted form of reasoning. These are sometimes called logical arguments. Arguments are normally spoken or written. In normal discourse, arguments may be expressed in spoken or written passages that contain a variety of other sentences whose function is to advance the narrative. Interrogatory sentences ( Are you a real American?), exclamatory sentences ( You must believe me! ), and others do not actually express statements. Consequently, strictly speaking, they are not considered parts of an argument. In addition to what is stated, sometimes elements of an argument may be implied by what is said but not strictly expressed. Consequently, it is permitted and often useful to rephrase or reconstruct arguments in order to identify the evidence and claim more precisely. For example, someone might utter the following. When I woke up this morning, I thought that it must have rained last night because the streets were wet. Here we have a simple argument that might be analyzed in the following manner. (E) the streets are wet this morning (E) when it rains, the streets get wet (C) it rained last night The second piece of evidence, of course, is implicit but normally understood in a commonsense context. It is needed in order to express the connection between rain and wetness. Although we should, we don t always express every detail in our arguments. - 1-
Arguments or inferences that have missing or implied pieces are sometimes called enthymenes. Notice, though, that the evidence is not conclusive. It is possible that it did not rain; instead a street cleaner might have doused the streets early in the morning. Even so, it is a plausible claim. As we shall see, evaluating how well the evidence supports the claim depends more on the kind of reasoning employed than the subject matter of the argument. For convenience, we will reconstruct arguments by simply listing the evidence sometimes called premisses 1 and indicating the conclusion afterwards and below a line. The triple dot signifies the conclusion and is usually read as therefore. So, the previous example would be rewritten the streets are wet this morning when it rains, the streets get wet it rained last night Some specimens of argument are not rational arguments at all. These usually express what is called informal fallacies. (You can find out more about them in a special section.) Logical Reasoning We learn about things in the world either by direct experience or by inference. Direct experience is the immediate observation provided by the senses (seeing, hearing, touching, etc.). For example, if someone says that his/her automobile is red, we can inspect it to see what color it is. This is knowledge (or learning) by direct experience. On the other hand, inference involves deriving some statement from the evidence at hand. Inferences are so common that we are unaware of how often we depend upon them in normal circumstances. For instance, if we walk up to the front door of a friend s home and hear voices within, it would be normal to believe that someone is home. Of course, the sound of voices could be from the television left on when the occupants departed. Thus, we have inferred that the sound of voices implies that people are inside. Logical reasoning is a formalized way of making and analyzing inferences. Specifically, a logic is a system that explains how claims can be correctly derived from evidence or sets of premisses. In short, there are potentially many different logics that is, different systems that formalize inferential reasoning. Intuitively, we evaluate any logic using a principle called the Criterion of Adequacy (CoA). Basically, it states in any argument, as the evidence increases, the extent to which the collected (true) evidence supports or warrants the conclusion as measured by the logic should also increase. Moreover, it should better discriminate related false claims as false and true claims as true. 2 In other words, a logic that satisfies its CoA will provide us with a method by which we can determine whether an argument is good or bad, i.e., whether the evidence supports the claim. Furthermore, it should help us decide the truth- value of related claims. Imagine an argument of the form, p q - 2-
A logic that satisfies its CoA would tell us how well the evidence p supports the claim q. If that support is sufficient, then we should expect that q is true and that not- q (or it is not the case that q ) is false at least to the extent to which that CoA warrants. As we shall see, not all logical inferences carry the weight of absolute certitude, though some do. Perhaps surprisingly, not all forms of reasoning have been formalized logically. Logicians have identified at least major three types of reasoning: deductive, inductive, and abductive reasoning. Each of these classifications intends to specify a particular style of reasoning or inference. We will adapt an example conceived by American philosopher and logician, Charles Sanders Pierce (pronounced purse ) to illustrate. 3 Imagine that you enter a room where you find a table. On the table, there is a bag that contains solid- colored marbles. You examine all of the marbles in the bag. In this context, a deductive inference on the facts would be all the marbles in this bag are white this is a marble from this bag this marble is white Suppose instead of inspecting them in advance, you draw one marble at a time from the bag. An inductive inference might take this form, I have examined at least two- thirds of the marbles in this bag each of the observed marbles was white I expect that the next marble that I pick out of the bag will be white Finally, an abductive inference would be fashioned along these lines. Suppose that there were several other bags of marbles on the table. You examined each and found that they contained marbles that were not colored white. If we saw some white marbles on the table, we would then infer there is only one bag on the table containing only white marbles there are several white marbles on the table these white marbles must have come from that bag As you can see, these instances represent very different styles of inference. Deductive inferences are conclusive. We can decide up or down without any recourse to additional information. You don t have to step foot inside the room to know whether this inference is good or bad. On the other hand, inductive and abductive inferences are not conclusive in the same manner. We do have to consider other factors in assessing their merit. This is not to say that deductive inferences are better than the other two varieties: only that they are different. Let s examine these styles of reasoning more closely. Deductive Reasoning and Arguments Deductive arguments are those that are conclusively provable. Deductive reasoning has been thoroughly studied and formalized. Deductive arguments are classified as valid or invalid. Informally, a valid deductive argument exhibits the strongest logical connection between the evidence and conclusion. Specifically, a (deductively) valid argument is one for which it is logically impossible for the premisses (evidence) to be true and the conclusion false. Note that the reference here is logically impossible. This means that affirming the evidence and denying the truth of the conclusion leads to an inconsistency or logical contradiction. Very strong indeed. - 3-
Consider this syllogistic chestnut as an example of a deductively valid argument. All men are mortal Socrates is a man Socrates is mortal The point is that if the premisses are true, then the conclusion must also be true. For instance, if we denied that Socrates was mortal after all, then the general statement that All men are mortal would now be false. But, it can t be both true and false at the same time. This would be a logical contradiction. So, if the premisses are indeed true, then the conclusion must also be true. There is an important distinction to be made however. The argument s validity doesn t guarantee the truth of the conclusion per se. In other words, it is possible for the conclusion to be false but only when the evidence fails likewise. For example, if the historical figure Socrates never existed, then Socrates is a man would be false. As a result, the conclusion would likewise be false. In spite of this, the argument would still be valid. In short, deductive validity expresses a technical or formal property of the argument. In fact, we could standardize the structure of this argument in the following manner. All M are P (All) S are M (All) S are P S, M, and P are properties that designate class membership (for example, being human, being mortal, and being Socrates ). But, these variables may also signify other properties as well. Thus, there is an indefinite number of potential arguments that could be derived from this form. All of them would be deductively valid. Arguments that lack the formal property of deductive validity are, of course, deductively invalid: it is logically possible for the premisses to be true and the conclusion false. Our initial example works here. the streets are wet this morning. when it rains, the streets get wet. it rained last night. We can accept that both premisses are true, but still maintain that the conclusion is false. (Remember the street cleaner explanation.) The connection between the evidence and the conclusion is simply not strong enough to satisfy the deductive CoA. Invalid arguments oddly enough could have true conclusions after all. The bottom line, though, is that the evidence has little or nothing to do with warranting our belief in the conclusion. Deductively invalid arguments with true conclusions are no more than lucky guesses. We would hope that our deductively valid arguments have warranted (true) evidence. These are called sound arguments. On the other hand, arguments that have evidence containing false statements are unsound. Deductive reasoning plays a significant but only a small role in most of the inferences that we make in normal circumstances. In practical contexts, our inferences usually lack the certainty or completeness required for deductive validity. Even so, other forms of reasoning can be rationally compelling. Inferences of this sort are usually categorized as defeasible reasoning. 4-4-
Technically, deductively valid inferences or arguments are classified as monotonic reasoning. Specifically, if the conclusion can be inferred from a given set of premisses, then adding additional evidence has no effect on its validity. For example, consider this new version of the previous syllogistic example. All men are mortal Socrates is a man Socrates is married to Xanthippe Socrates is mortal Even though the new premiss is true, it has no real impact on the validity of the argument. An argument doesn t become more valid or less valid; it is valid or invalid pure and simply. In short, deductively valid inferences satisfy logical entailment. To put it another way, the knowledge expressed by the conclusion is contained within the premisses. There is no need to consult any other information. But there are many other contexts in which adding new information can change our opinion about the truth of some claim. For example, it is usually reasonable to seek a second opinion on medical diagnoses especially when the consequences are significant. In these instances, corroborating evidence adds weight to the original diagnosis. On the other hand, contradictory evidence would likely diminish its warrant. Thus, defeasible reasoning signifies rational inferences that have warrant but fail the standards of deductive validity. Formal systems that seek to capture this style of reasoning are usually called non- monotonic logics. There are a variety of types of inferences that fit this general category. Inductive inference is a style of defeasible reasoning that has been studied almost as long as deductive forms. Inductive Reasoning and Arguments Inductive reasoning generally involves inferring from the observed to the unobserved. This might mean reasoning from past to the present or future or from the seen to the unseen. This form of reasoning is typically measured probabilistically. In other words, the claims or conclusions are considered likely or less likely true, because the evidence confers some amount of probability for the truth of the conclusion. The most common type of inductive inference is an enumeration of cases. Here are a couple of examples. Each day that I can remember, the sun rose in the morning. I expect that the sun will rise tomorrow morning. In a random sample of 500 voters from our county (composed of 140,000 voters), 60% said that they would vote for a Republican candidate over a Democratic candidate in the next presidential election. This supports the conclusion (with a probability of 0.9) that between 55 and 65% of the county s voters would vote Republican if the next presidential election were held today. The first example seems less formal, but both specify a set of evidential cases that are intended to support the claim or conclusion. In the first instance, we are reasoning from observed cases to the next (unobserved) case; the second argument generalizes from a sample to the population. The second specifies a probability and a margin of error, but we could rephrase the first to make it look similar. For example, the probability might be.999-5-
and no margin of error. The point is that in inductive inferences, the truth of the claim is contingent on the truth of the evidence. It is (logically) possible for the conclusion to be false based on that evidence, but we would be surprised if it were. Inductive arguments are classified in a continuum from strong to weak. An inductively strong argument is one in which the truth of the evidence confers a high degree of probability that the conclusion is likewise true. Inductively weak arguments fail to confer an acceptable degree of probability. Consider the following. I bought two lottery tickets from that vendor and lost each time. The next ticket I buy from that vendor will be another losing ticket. This is a weak inference in spite of the fact based on other considerations the claim might very well be true. Reasoning from two cases is simply too few to warrant such a conclusion. But how many tickets would I have to buy to strengthen the argument: 10, 20, 100, or 1000? The last two seem stronger. However, it is difficult to draw a precise line. Keep in mind that in the last example, our goal is to evaluate the argument and not just the truth- value of the conclusion. The odds on winning a national lottery are very long, so it is very unlikely that a single ticket from any vendor will be the winner. But, this is knowledge not expressed in the argument per se. In this instance, all that we have to go on is two enumerated cases. Unfortunately, there is disagreement among experts who seek to formalize inductive inferences by devising a system of inductive logic. (In other words, the CoA for evaluating inductive inferences is not well defined.) The majority view is that these types of inferences can be explained by means of probability theory (specifically Bayesian conditional probability). The details are highly technical and not intuitive. But, this is an instance when our theories cannot fully explain our practice. We do, after all, use and depend upon inductive inferences everyday. For example, I make an inductive leap of faith every time I choose to eat or drink something. How do I know that it will not poison me? In general, if I ingest the kinds of things that I have eaten before, then I should be safe. Thus, every day we stake our lives on the warrant of inductive inferences even though we lack a complete understanding of how to evaluate them precisely. Abductive Reasoning and Arguments Abductive reasoning is the kind of inference typically used in law, forensics, and scientific theories. We often employ this style of reasoning in ordinary contexts as well. For example, suppose that you are driving and notice that the gas gauge reads Empty. Being a reasonable person, you would plan to stop and buy some gasoline for your automobile. But, this is an inference. What made you decide so? We might reconstruct the argument in this manner. (1) The gas gauge reads Empty. I have no reason to determine that it is malfunctioning. It has been several days since I last put gasoline in the tank. I have good reason to believe that the gas tank is (near) empty. In this instance, the conclusion is inferred because it makes sense out of a collection of facts. In other words, if the conclusion were true, then the evidence would be understandable as a matter of course. If the gas tank were empty then the gas gauge reading would be predictable. Likewise, the fact that I haven t put any gasoline in the tank - 6-
for several days would be consistent with this explanation as well. Furthermore, the claim is more plausible than alternative explanations such as someone secretly filled my gas tank and doctored my gas gauge to read empty. It is also more plausible than I have a faulty gas gauge but plenty of gasoline, because it is a new secret formula gasoline that yields greatly increased mileage. Clearly, these stretch credulity much more than our initial explanation. Thus, the claim seems more warranted as an inference. Abductive arguments contain conclusions that are offered as the best hypothesis or explanation for a set of related facts or details. Here are a couple of other examples. (2) The victim lives alone. The victim arrived at home around 10:00 P.M. There are no signs of forced entry through the doors or windows of the house. It was raining last night around 10:00 P.M., but the only signs of muddy footprints were those matching the victim s shoes. The murderer had ready access to and was already in the house before the victim came home. (3) Fossils that look very much like the remains of modern fishes have been found in this land area. This land area is far inland from any large bodies of water. This land must have been covered by water when the animals that produced these fossils lived. Arguments (2) and (3) differ from the first example in one important respect. Argument (1) has some superficial resemblance to an inductive inference. We could rephrase it to read something like this. (1a) The gas gauge reads Empty. In the past, each time the gas gauge read Empty, the gas tank was (near) empty. I have good reason to believe that the gas tank is (near) empty this time. Thus, we could be reasoning from a sequence of past experiences that correlate these events. Arguments (2) and (3) resist this kind of inductive translation. It is very unlikely that they imply a past experience with either similar murders or fossils. Once more, these demonstrate the explanatory character of abductive reasoning. For instance, in (3) we are presented with an anomaly: literally, fish out of water. The conclusion fills in our gaps of understanding precisely by challenging appearances. The inland area was likely not always inland. The argument (2) represents a common type of reasoning in forensic science as applied in criminal investigations and legal proceedings. (Apologies to Sherlock Holmes.) Both offer a theory to explain the facts at hand. In this respect, abductive reasoning is prevalent in the sciences. While scientific research may employ both deductive and inductive reasoning, theories are explanations that try to interpret a collection of facts or observations in the most plausible way. Theories, of course, are confirmed or disconfirmed. Most theories have predictive power. In other words, a reliable theory is one that can be used to predict additional facts or states- of- affairs are consistent with the theory. For example, in (3), if there was an inland sea on the spot where the fossils are found, then there should be other signs that are typically associated with larger bodies of water. Suppose that we also find sizable areas of - 7-
sandstone rock formations. This is consistent with the hypothesis and helps to confirm it. On the other hand, if we found no such evidence, and in fact geologic formations inconsistent with the presence of an ancient sea, then these observations would disconfirm the theory. As you can see, abductive inferences belong to the category of defeasible reasoning discussed earlier. The merit of an abductive inference can change with the inclusion of additional evidence for better or worse. While abductive reasoning has been studied by some logicians, currently there is no accepted formal system for analyzing types and measuring the reliability of its inferences. Defeasible Reasoning, Again In recent years, logicians (and researchers in Artificial Intelligence) have isolated a very specific form of inference under the label of defeasible reasoning. Defeasible reasoning (in this new, narrower use) supports claims or conclusions only contingently. The argument offers the best evidence available, but future considerations may reverse our acceptance of the conclusion. The standard example of a defeasible argument is Tweety is a bird. Birds fly. Tweety flies. It is defeasible in the sense that if we later find out that Tweety is a penguin, then we would no longer accept the truth of the conclusion based on the evidence. Cast in these terms, defeasible inferences are perhaps better thought as presumptive inferences. Presumptive reasoning amounts to accepting some claim until better evidence comes along that would either corroborate or disconfirm it. The Tweety argument fits squarely into this category. Presumptive reasoning is very different from abductive, for example. Inferring the claim Tweety flies does not somehow make better sense of the premisses. Instead, the argument appears to be more like a faulty (unsound) deductive argument: (All) birds fly. Tweety is a bird. Tweety flies. The problem, of course, is that the generalization about birds flying is faulty. Penguins, ostriches, etc. are technically birds but do not fly. Presumptive arguments amounts to concluding that Given what we know, it is more reasonable to accept claim C than deny it. In other words, the argument rests on the truth of the evidence offered, but it is possible that, in the future, these assumptions may not be adequate. The rational person accepts presumptive reasoning because to do otherwise seems irrational, i.e., believing and acting without any good evidence at all! The point, here, is that there are many different kinds of defeasible reasoning, and presumptive reasoning is one of them. Inductive and abductive reasoning are two other varieties. As arguments or inferences, they share the fact that adding evidence can affect their adequacy. But, they differ in how that adequacy is measured. Whether there are other legitimate forms of reasoning is still an open question. From a practical standpoint, however, it much more difficult proving that something is impossible - 8-
than otherwise. So, smart money would go with the hunch that there may be other legitimate forms. Using and Assessing Arguments When you engage in debates or read or write position papers, it is important to consider the types of arguments or inferences offered. A position paper, for example, should have a clearly expressed claim or conclusion. The paper, however, may offer several arguments in favor of the claim rather than just one. Each of the arguments should be assessed on its own merits. But the moral from the foregoing is a simple one: When evaluating arguments, first, you should identify what type of reasoning is being expressed. Assessing the merit of the argument depends not only on the evidence offered but also the style of reasoning employed. For instance, it may be correct that an argument in a position paper is deductively invalid. But this observation is irrelevant if it was intended as an inductive or perhaps abductive inference instead. In debates and position papers, sometimes evaluating the argument is made more difficult because the reasoning involves either enthymenes and/or argument chains. We saw earlier that enthymenes are arguments with missing but implied elements. An argument chain is an argument whose conclusion is based on a series of connected inferences. In other words, some of the evidence for the claim rests on inferences derived from other evidence. Here is an example. (4) If Candidate X wins the New Hampshire primary, then he/she will likely have an advantage in raising more campaign funds than the opponents. This means that Candidate X would likely win the nomination and be elected in November. Let s restate the argument as a series of conditionals. (4a) If Candidate X wins the New Hampshire primary, then he/she will likely have an advantage in raising additional campaign funds. (4b) If Candidate X raises more campaign funds than the opponents, then he/she will likely secure the party s nomination. (4c) If Candidate X secures the party s nomination, then he/she will likely be elected president. Each of these conditionals expresses an inference. In this instance, most are also enthymenes, that is, having implied premisses. Together, they constitute a series of related inferences that lead to a final conclusion. We could challenge any or all of these inferences. But the credibility of the claim rests on the merit of all of the inferences. If one fails, then the argument chain fails. In some instances, even in editorials written by professionals, there are lots of claims being offered. But when we look for evidence, we may find very little offered. Writings like these may be very formal, but they amount to nothing more than a succession of pronouncements. The fact that something is published carries no extra authority. If the claim is a reasonable one, then there should be some evidence to warrant it. Finally, keep in mind that assessing arguments often depends on some interpretation. Specifically, it is possible that we may disagree about how to express someone s line of reasoning in argument form. The evidence and even the claim might be interpreted - 9-
differently. In these instances, there can be little or no basis for a common evaluation. Like apples and oranges, we are talking about two different things. This provides another practical reason for reconstructing the arguments from their original expression. It is much easier to agree or disagree about the merit of an argument, if we can agree that we are talking about the same thing. Exercises I. Each of the passages below express reasoning. Reconstruct the argument in conventional form by supplying any missing but implied elements. Likewise, identify any argument chains where a premiss for some claim is based on other evidence expressed or implied. 1. Reconstruct the argument chain expressed in specimen (4) above. Specifically, decide on any missing or implied premisses. 2. There is no thunderstorm nearby because we haven t heard any thunder recently. 3. Since Audrey graduated from medical school, her personal income is most likely very high. 4. You should have come to the party. You did promise me that you would. 5. This week I am going all out for the lottery! The law of averages guarantees that I can t keep losing forever. II. Each of the passages below express an argument, that is, each offers evidence for some main claim. Reconstruct the argument in conventional form, identify the type of inference employed, and evaluate its merit. 1. If Mary hit a home run during yesterday s game, her sister would have congratulated her. But her sister did not congratulate Mary. So, Mary did not hit a home run during yesterday s game. 2. Frank is another one of the socialists and liberals who live in our town. All the socialists and liberals in town are at the meeting featuring a speaker who supports universal healthcare. Naturally, Frank is attending the meeting. 3. Your job as a juror is to determine whether the defendant who confessed to fatally stabbing the victim is guilty of first- degree murder or manslaughter. The issue before us is whether the knife blow was of moderate or strong force. The coroner has testified that the knife penetrated only 2 ½ inches and there were no knife marks on the bones of the victim. 4. There are those who say that we should not regulate pornography or any conduct of consenting adults. This is absurd. Like all civilized societies, we have long had rules that attempt to set moral standards and regulate sexual conduct. Regulating pornography is no different. It is no coincidence that societies have decayed and collapsed (viz. the Roman Empire) when moral standards have declined. (based on Alexander Bickel in Pornography, Censorship and Common Sense. ) 5. The materials of nature (the air, earth, water) that remain untouched by human effort belong to no one and not property. It follows that a thing can become someone s private property only if he or she works and labors on it thereby changing its natural state. From this I can conclude that whatever an individual improves by the labor of his hand belongs to him, and to him only. - 10-
(based on John Locke, Of Property. ) 6. No man will take counsel; but every man will take money; therefore money is better than counsel. (Jonathan Swift) 1 Not to be confused with premises, which denotes a location, premiss is used in logic and law. The Oxford English Dictionary defines it as a statement or proposition from which another is inferred or follows as a conclusion. "premise, n.". OED Online. June 2011. Oxford University Press. http://www.oed.com/view/entry/150302?rskey=qew7mt&result=1&isadvanced=false (accessed July 12, 2011). 2 James Hawthorn, Inductive Logic, Stanford Encyclopedia of Philosophy, (2011). http://plato.stanford.edu/entries/logic- inductive/ (accessed July 18, 2011). 3 Charles Sanders Pierce Deduction, Induction, and Hypothesis, Popular Science Monthly Volume 13 (1878), pp. 470-82. 4 Robert Koons, Defeasible Reasoning, Stanford Encyclopedia of Philosophy (2009). http://plato.stanford.edu/entries/reasoning- defeasible/ (accessed July 18, 2011). - 11-