Rational Reconstruction II: Identifying Principles

Rational Reconstruction II: Identifying Principles How principles work When the world makes sense to you, it's because it's behaving according to familiar patterns. When it doesn't make sense, it's because familiar patterns have been broken, or because you are dealing with a new subject matter whose patterns you don't understand. In logic we express these patterns, these dependable regularities in the world, as principles. Let's begin by considering a weird example: A beautiful butterfly flutters by and Butch catches it in his hand. A moment later he releases it, screaming that he's been stung. An event like this could precipitate quite a bit of reasoning, both argument and explanation. For example: • • • • • • • • Butch thinks he was stung by a butterfly because he felt a stinging sensation right after a butterfly landed on it. (Explanation) Butch was not stung by a butterfly because butterflies don't sting. (Argument or Explanation) Butch must be pretending to have been stung by a butterfly because he's a practical joker. (Argument) Some butterflies must have stingers. After all, Butch was just stung by one. (Argument) The insect on Butch's finger is not a butterfly. It just stung him, and butterflies don't sting. (Argument) Everyone is laughing at Butch because he's pretending to have been stung by a butterfly. (Explanation) Butch's finger is all swollen because he was stung by a butterfly. (Explanation) Butch shouldn't have smashed the butterfly. That's not funny. (Argument) The event is confusing, and perhaps amusing, because it appears to violate a basic dependable principle: Butterflies are harmless to humans. Principles figure into reasoning by connecting the reason to the conclusion. The easiest way to appreciate this is to consider reasoning that makes no immediate sense to us: • Butch died because he caught a butterfly. The rationale for this would be: We understand what the reason and the conclusion are saying. The reasoning itself makes no sense to us because we don't know any principles concerning death by butterfly. To put it more formally, for the explanation above to make sense we either need to hear a lot more information (e.g. When Butch stopped to catch a butterfly he was hit by a bus.), or we are forced to entertain a principle like: Anyone who picks up a butterfly will die. Put differently: P: If a person catches a butterfly, the person will die. Because we accept no such principle, the reasoning remains mysterious to us. Compare this to the relatively transparent explanation: • Butch died because he was bitten by a rattlesnake. Of course, picking up a rattlesnake doesn't guarantee death, but the connection is familiar and consequently we have a lot less trouble grasping the following rationale and it's corresponding principle. In this diagram we've violated the basic format for rationales in order to show how principles perform their connecting function. In ordinary language this principle might be expressed as: Anyone who is bitten by a rattlesnake will die. However, for the purpose of constructing rationales we will always express principles using an "If...then" form. An "If, then" statement is called a conditional. The "if" part of a conditional is called the antecedent. The "then" part of the conditional is called the consequent. You'll notice that the antecedent of the principle above is a generalization of the reason. In other words, Butch being bitten by a rattlesnake is a specific instance of some person being bitten by a rattlesnake. The principle works the same for anyone. Similarly, the consequent of the principle is just a generalized version of the conclusion. The principle carries out its function in roughly the way a physical connecting device might. In a sense, there is a "loop" on either end of the principle, and if a reason "fits" in one end of the loop and a conclusion "fits" in the other, then the principle can connect the reason to the conclusion. More accurately, a principle is very much like a mathematical function. The function y=x2, for example, takes a number as an input and outputs the square of that number. Similarly, a principle takes a reason as an input, and outputs a particular conclusion. People very rarely state the principles they are using, but it does happen. For example: • You shouldn't lie to me because I'm your friend and you should always be honest with your friends. Here the statement that one should always be honest with ones friends is an explicitly stated principle tying the following argument together. Notice that it would have been very cumbersome to write the principle using standard English. If we had, it would have read something like this: • P: If some person is the friend of some other person that first person should not lie to the other person. That is why we adopt the convention of substituting the letters x,y,u,v,w and z for terms in the principle that are generalizing terms in the conclusion. These function just like algebraic variables and they greatly simplify principles, making them much easier to write and to grasp. Attributing Principles When people don't state the principles involved in their reasoning, then it can become our task to determine what they might be. This can be a pretty thankless affair. From a logical point of view it would be nice if people just told us the principles they were appealing to, but in ordinary contexts this would be impractical. Often the principle is obvious, as when you say: Stop it, that hurts! People tend to grasp that reasoning pretty immediately. You don't need to add: P: If person x is hurting person y by doing action z, then x should cease doing z to y. The reason people do grasp the above reasoning without your having to state the principle is that they belong to the same reasoning community as you. Like you, the principle is encoded in their mind in some form, and they can access it immediately without even realizing it. If they couldn't, then your reasoning simply wouldn't make any sense to them. Other times the principle is not so obvious, but the reasoning is familiar or uninteresting and we just don't care to examine it. It is only when we are examining a person's reasoning for possible problems that we take an interest in the corresponding principles. Unfortunately, for any piece of reasoning there are any number of principles that can perform the connecting function. Let's return to the rattlesnake example subsumed under a different principle: This principle is even more general than the original one because it generalizes not only over Butch, but over rattlesnakes as well. Intuitively, though, we would say that this is not the correct principle, since not all, or even most, reptiles can kill a person. Not even all snakes can kill a person. Identifying a good principle with the proper degree of generality is not at all easy. Consider the following candidate principles all of which would serve to connect the reasoning above: Principle Evaluation 1. If a rattlesnake bites Butch, then Butch dies. 2. If a rattlesnake bites human male This is still too specific. It arbitrarily restricts the principle to male humans. x, then x dies. 3. If a rattlesnake bites person x, then x dies. This is an acceptable level of generality. 4. If a viper bites person x, then x dies. This is a little too general. Vipers are a class of dangerous snakes, but rattlesnakes are particularly deadly. If a rattlesnake bites person x, 5. then x experiences great harm. This is much too specific. It is a conditional but it doesn't generalize the connection at all. It applies to Butch, and Butch alone. This is actually a more reliable principle than the ones above, but death is only one kind of great harm, so it is not strongly connected to the conclusion. 6. If a snake bites person x, then x dies. This is too general, since death does not result from picking up the typical snake. 7. If a reptile bites person x, then x dies. Way to general. 8. If an animal bites person x, then x Way, way too general. dies. The generality of a principle is what makes the rationale to which it applies interesting and useful. Principle (2) is no less reliable than principle (3), but if you thought the reasoning above were connected by principle (2) then you might draw the fatal conclusion that rattlesnakes aren't harmful to females. On the other hand when principles become too general, they can become highly unreliable. Principles 6-8 are so unreliable that they are of little or no value. (It's worth observing, however, that people who are petrified of snakes, seem to live according to something like principle 6. That's probably because they can't tell the difference between a dangerous snake and a benign one, so principle 6, despite it's absurd generality might actually serve to protect them.) Attributing principles with the appropriate degree of generality is difficult because it depends both on guessing at a reasoner's intentions and actually knowing something about the world. For example, to see that principles 4-8 are too general you really have to know a little about snakes. You want to attribute a principle that makes sense in terms of the speakers apparent intentions, but also one that makes sense in terms of what is known about the world. Sometimes you can do this; sometimes you can't. Implication and Metalinguistic Principles When a principle successfully connects a reason to a conclusion we say that the reason and principle jointly imply the conclusion and that the reasoning is valid. These are important logical concepts. To say that reasoning is valid is not to say that it is completely correct, since this ultimately depends on the truth of the reasons and the reliability of the principles. However, validity is an essential condition of correct reasoning. When validity has been established we know that if the reasons and the principles are true, then the conclusion must be true. All valid reasoning depends on principles of some sort. In formal logic these principles are called rules of inference. For example, if you know the first two sentences below are true, you might think that they obviously and immediately imply the third sentence. 1. Frogs are green. 2. Toads are brown. 3. Frogs are green and toads are brown. This reasoning is valid, but its validity is accounted for by the following rule of inference: • If sentence P is true and sentence Q is true, then the sentence (P and Q ) is true. Rules of inference are what we call metalinguistic principles, because they validate certain forms of reasoning by generalizing on the sentences themselves rather than the things the sentences are referring to. Rules of inference actually underwrite all of our valid reasoning, but they are ordinarily hidden even more deeply than the principles that connect reasons to conclusions. Since this is not a course in formal logic, these rules will, for the most part, remain hidden. However, it is important to take a moment to understand how metalinguistic principles function beneath the surface. The rationales we construct can easily be put in the same form as the example above: 1. A rattlesnake bit Butch. 2. Anyone who is bitten by a rattlesnake dies. 3. Butch died. Obviously, sentence 1 is the reason, sentence 2 is the principle (though not in its conditional form) and sentence 3 is the conclusion. Sentence 2 is not a metalinguistic principle, but an empirical one; i.e., it does not describe a logical relation between sentences, but a relation between two things in the world: people and rattlesnakes. There are actually a few different metalinguistic principles needed to license this inference, but the main one is this: • If sentence P is true and sentence (If P, then Q) is true, then Q is true. In the above example, sentence 1 would correspond to P, sentence 2 would correspond to (If P, then Q) and the conclusion, sentence 3, would correspond to Q. So even though we speak as if 2 connects 1 to 3 by itself, in fact this connection depends on more fundamental metalinguistic principles that license this kind of inference in the first place. The logical form of our rationales, while typical of ordinary reasoning, is actually just one of many valid forms of reasoning, and many of these valid forms do not require an empirical principle to connect a reason to a conclusion. (The frog/toad example above involves two premises, both of which are empirical principles, but neither of which connect a reason to a conclusion.) Work So, let's boil this down a bit. When someone gives a reason for a conclusion she becomes committed to a principle that connects the two together, and thereby permits an inference from the reason to the conclusion. People rarely state their principlesthey often do not even know what they are -so you, the logician, have to figure them out. (Yes, you.) Your basic task is to attribute an independently plausible principle that makes the reasoning valid. In other words, the resulting rationale is one in which the reason and the principle, taken together, imply the conclusion. To accomplish this the principle must have all of the following features. 1. It must be written in a conditional (if..then) form. 2. The antecedent must apply to the reason and the consequent must apply to the conclusion. 3. The antecedent must be more general than the reason and the consequent must be more general than the conclusion. 4. The principle must be independently meaningful; i.e., it must make sense as an independent statement. 5. It should be reasonable to claim that the reasoning under consideration is committed to this principle or one that is very similar to it. When the reasoning you are reconstructing is poor the 5th criterion will often be difficult to satisfy. This is because poor reasoning often results in a commitment to unreliable principles, and reasonable people do not endorse unreliable principle. Hence, the failure to satisfy criterion 5 will always indicate some problem with the reasoning itself. Now let's look at some typical problems with identifying principles. In each of the following examples, a mistake is made in attributing the principle. Try to figure out what the mistake is before reading the rap to find out. Example 1 I think my husband Mike must be cheating on me. He's just been so nice lately. Rap: There are two problems here. (1) The principle does not hook up to the reasoning in the proper way. The antecedent applies to the conclusion and the consequent applies to the reason. Hence, no deductive relationship is established. (2) The principle contains the name of a particular individual, Mike, so it lacks generality. A better principle would be: Example 2 Homosexuals seem to be just as good at parenting as heterosexuals. It turns out that children of homosexual parents are as psychologically healthy as those who were raised in traditional families. Rap: This is a good example of a principle gone bad. If you read it objectively, you can see that it makes no sense, which means that it violates criterion 4. The reason it makes no sense is that the variables z and w could be anything at all. People typically write principles make no sense when principle is hard to figure out. A good principle here would be: Example 3 The reason prostitution should not be legal is that only women in desperate economic circumstances become prostitutes. Rap: This principle is actually logically equivalent to the correct one, but it does not follow our guidelines. Specifically, the antecedent "If person x is a prostitute" does not generalize the reason, and the consequent "then x is poor and prostitution should therefore be illegal" does not generalize the conclusion. The word "therefore" does not belong in a principle; its primary function is as a conclusion indicator. A better principle would be: This, of course, is a pretty implausible principle, but it satisfies conditions 1-4 and its failure to satisfy 5 is because the reasoning itself is problematic. Example 4 In strict Islamic societies women must not reveal their bare skin in public because it is very distracting to men. Rap: This is a well written principle, but it does not fit the conclusion. The conclusion simply tells us that Islamic societies forbid women from showing their skin; it does not contain the evaluative phrase "should not." (If it did, then of course the rationale would have to be an argument.) The principle is also a little too general, since the variables are entirely unrestricted, and this rationale is pretty clearly restricted to Islamic culture. Here is a better one: Example 5 Jasper seems to think he knows logic pretty well. He is always offering to help me with it. Rap: The problem here is simple. The consequent does not connect to the conclusion because the conclusions says that Jasper thinks he knows logic well. The consequent says "x knows subject z well". If you are inclined to think this is a pretty unimportant difference, get over it, because it's huge. If you say: Sharene thinks she's a hottie, you are not saying that Sharene is a hottie. In fact, you are probably suggesting that she isn't. (You should also notice that this really is an argument. The reasoner is trying to convince us that Jasper thinks something about himself.) Example 6 Leslie must have a key to the apartment because it was locked and otherwise how could she have gotten in? Rap: This is actually a good principle given the corresponding rationale. The easily overlooked problem is that the principle violates criterion 5. It is actually not reasonable to attribute this principle to the speaker. Why? It is a very weak principle, because it does not require that x actually did y. Of course, this is really not the fault of the principle, because the reason itself does not say that Leslie got into the house. However, the rhetorical question strongly suggests that Leslie did get into the house. So the whole rationale should be rewritten as follows: What makes this example different from any that we have encountered previously is that the reason is compound; i.e., it contains two complete sentences. This is permissible. Later on you'll see that sometimes we will write a single compound reason and other times we will simply separate them into two distinct reasons with two distinct principles. Example 7 I think Adam is going to win the lottery because he bought a ticket, and only people who buy a ticket can win. Rap: Try to ignore the stupidity of this reasoning for a moment. This is actually a particularly vexing example given our analytical guidelines. The principle written does connect the reason to the conclusion very effectively. But this is actually one of those rare occasions when the reasoner states the intended principle, and the principle stated simply does not translate into the one above. The principle stated, "Only people who buy a ticket can win" actually conditionalizes as follows. This principle is highly reliable, but it doesn't connect the reason to the conclusion; i.e., the antecedent applies to the conclusion and the consequent applies to the reason. So you have to decide whether to use the reliable stated principle which does not make the connection, or a really unreliable principle, which is contrary to the one stated, but which does not make the connection. This is pretty much your call. Example 8 Trees have a right to life because all living things have a right to life. Rap: This is another weird example. The problem here is that the reasoner explicitly stated a principle as if it were a reason, and we ended up putting that in the reason box and writing a meaningless principle as a result. The unstated reason is simply: Trees are living things. This is best viewed as an argument because the claim that something has a right to life is a value judgment.