Remember, you can ignore all the hyperlinks in this page. None of them are required. They are just there in case you need a little help.
The aim of this course is to enhance, as much as possible, your ability
to detect, analyze, and critique bad arguments. We are only concerned with
terminology, techniques, fundamental principles and other complicated
matters to the extent that they help you get better at detecting,
analyzing, and critiquing bad arguments.
To explain the title, a marlinspike is a small, spiky tool used by sailors of old fashioned sailing ships to make and unmake knots by applying leverage to ropes and cords. In particular, sailors would often use the point of the spike to work into knots that had tightened-up under tension, separate the cords, and thus make it easier to untie the knot. This course is intended to equip you with a sort of "mental marlinspike" that you can use to work your way into arguments, and thus make it easier for you to analyze, evaluate, and critique those arguments.
To make things as easy as possible, I'm starting with the easiest parts of the material, and moving on to stuff that's progressively a little bit more difficult, on the theory that once you've mastered an easy bit, you'll be better able to master a bit that's slightly less easy, and so on through the course. Deep logical principles, and other arcane matters are held until the end of the course, for when you will be well-used to the practice of logical analysis, and thus you will find those topics much, much easier to understand than if I dropped them on you right away.
I'm also trying to make my readings as short as possible, which makes reading easier, but might not be good for students who need a bit more explanation on certain topics. To make up for this, I'm adding links to optional further reading, marked "optional reading", which you can follow for further explanation of certain topics. (Optional reading.) I'm also making important terms into hyperlinks to Wikipedia and other sources, so you can easily get further explanation of those terms if you need it.
Remember, the optional readings and other links are NOT
REQUIRED. All that is required
for this week's reading is in this main page.
This chapter will cover the following topics:
There's no proof either way
I'm done arguing.
After reading this chapter you should know the technical meanings of the following words
Remember that this discussion is written to be quick and easy to read, so there no extended discussions in the main reading. If there's any bit of it you don't understand, please click on the "optional reading" link for further reading. Remember that there will be an in-class quiz (which will be like the practice quiz at the end of this chapter), so it's best to understand as much as you can before class.
A "claim" (or "proposition") is just something someone says that can be true or false. An "argument" is a claim that comes along with one or more other claims that are supposed to give us reason to believe the first claim. (Optional reading.) "Standardizing" an argument means adding in things assumed or implied by what is explicitly stated ("suppressed premises" and "suppressed conclusions"), and organizing all the claims so that the thing the arguer wants you to believe (the "conclusion") is below a line, and all the arguers reasons ("premises"), stated or suppressed, appear above that line, like so:
|Source||Argument Text||Standardized Argument|
|"Getting your news
from Jon Stewart
is like learning about WWII
from Hogan's Heroes."
1. Getting news from Jon Stewart is like learning WWII from Hogan's Heroes.2. Hogan's Heroes is a very bad source for WWII information
C: Jon Stewart is a very bad source for news
Notice that the argument as stated in the meme is only a partial
argument (technically, this is an "enthymeme"), and that I had to fill in
a suppressed premise and a suppressed conclusion. To reiterate
the important definitions:
"Analysis" means to look closely at something to figure out how all its bits fit together to do stuff. In logic, we analyze arguments in order to be able to figure out if they're good arguments (which can prove stuff), or bad arguments (which can't). There are two parts to argument analysis, "evidence" and "implication". "Evidence" is things that can be seen, heard, touched, or otherwise observe that might tend to prove that something is true or untrue. "Implication" is about the meaning of any given piece of evidence for whether something else is true or false. The kind of evidence that really counts is called "facts". For our purposes, a fact is a claim that is not currently in dispute. Thus a fact is either something everyone agrees is true, or it is something that is so obviously true, that no-one can plausibly dispute it.
Here's an example of evidence.
The above image was created during WWII by inspecting aircraft that had returned to their home airfields after combat, and marking down the specific places various aircraft had been damaged by the enemy. Thus, each red spot represents a place that some particular plane had been hit during combat. This is evidence for something. What it's evidence for remains to be seen.
Figuring out what is implied by a given set of facts is sometimes difficult. Consider the aircraft battle damage diagram given above. It was created to help aircraft designers decide where to install armor on new aircraft. The idea was that if they put the armor in the right places, the armor would prevent enemy bullets from damaging the aircraft at those points, and the aircraft would be more likely to survive the battle. The question is, based on the diagram, where to put the armor? There are two possible answers: 1. Put the armor where the red dots are, and 2. Put the armor where the red dots are not. A fellow called Abraham Wald figured out that the armor should go where there were no red dots in the diagram. His reasoning was that all the aircraft known to have damage in the red dot areas had made it safely back to base, while no aircraft with damage in the other areas had made it back. Thus, he reasoned that any aircraft that had been hit in those areas had been shot down by those hits, and so those were the places to put the armor. (Optional reading.)
Aaaaand, I'll just leave this out here:
This is the process of understanding an argument well enough to figure out whether or not the actual available evidence actually provides compelling support to the given conclusion. It involves looking at all the claims of fact to try to figure out which of the claims actually are facts, and then looking at the actual facts, whatever they turn out to be, and then figuring out what is actually implied by those actual facts. Sometimes this is easy, other times it can be quite difficult.
Many, perhaps most, speakers and writers use analogies merely as a communication tool. An analogy allows a speaker to clarify a new idea by invoking some similarity it has to some idea with which we are already familiar. Sometimes, however, people offer analogies in attempts to change minds. In such a case, the analogy is offered not just to explain, but also to persuade. It is thus then an argument by analogy.
Here are my definitions of the technical terms you are supposed to know
at this point. Memorizing these definitions is okay, but you don't
really understand a term until you are able to put it into your own words,
so practice that too.
Here are links to videos and other online resources that might help if, after following the relevant links, you're still having trouble with some part of the material. I did not create these materials, so some of it may be off-topic, and some may even be wrong! (If anything linked here disagrees with what I say, assume I'm right, or at least remember that I will be the one grading your exam, and notify me of the issue by email, if you can.)
Once you've watched a video, get back here by using your browser's "back" button.
What is a Claim,
Statement, or Proposition?
Premises and Conclusions
The Parts of an
Propositions, premises and conclusions
Evidence: How Do We Know What We Know? | Exploratorium
Argument and Evidence
This is a quiz that you take on your own to prepare for the in-class quiz
you will take before we cover this material in
class. I strongly suggest you take this quiz (several times if
needed) well before class time. You will not be turning
in your answers to this particular quiz. (If there is a BlackBoard or
Canvas site for your class, there may also be an online
quiz in your coursesite. No promises.) Take this quiz closed-book, closed
notes, so you will know what topics you need to study more for the
Even though there's no given answers for these exercises, it's still a
good idea to work through them to improve your skills and better prepare
for all the tests. Check your answers by comparing them to the
examples worked above, and the answers to the previous exercises.
These don't have answers either. However, the more exercises you work
though on your own, the better prepared you will be for the quizzes,
exams, and writing assignments.
Don't look at these answers until you've done the practice quiz.
Finally, if there's anything at all in this reading that you don't think you fully understand, please follow an associated hyperlink to get more information on that particular topic, or email me and I will try to find a way to make the relevant reading easier to understand..
Copyright © 2019 by Martin C. Young
collect reflect suspect reject correct CRSRC
state explain support oppose defend SESOD
"see 'ere, Circe, Sea sod!"
Do as second lecture
defn of fact
A is like B
using "analogy sense" to identify strategies
If you print this page, you can also
download and print the practice/makeup
exercises. (Make sure the document margins are set to 0.5 inches
Analogies are a vitally important and very powerful communication tool, but from a purely logical view, they can be an enormous pain in the fundament. Because analogies are so powerful they can often convince us of things we have absolutely no rational reason to believe. So, before we start, I want to make two things perfectly clear:
1. Analogies are an enormously useful communications tool. If you can work an appropriate analogy into whatever you're writing, that will really help you get your point across. Yea! Go for it!
2. Although there are some good analogy arguments out there, most analogies you see will be horribly misleading. Horribly, horribly misleading. This is because they have an insidious power to make us believe things that have absolutely no basis in fact. (Curse them!)
So, don't be fooled!
Imagine you are a scientist living in the middle of the twentieth century. Imagine that you have just heard that it has been proved that cigarette smoking causes cancer. You understand that cigarette smoking involves burning tobacco so that the smoke may be drawn into the smoker's mouth and lungs. You are aware that cigar and pipe smoking also involves the inhalation of tobacco smoke. From this, you might conclude that there is a strong possibility that cigar and pipe smoking also cause cancer, and that this possibility is strong enough that cigar and pipe smokers should be warned about it, and responsible parties should conduct specific studies to investigate this possibility. If you argue that cigar and pipe smoking probably causes cancer of the basis of the similarity to cigarette smoking, you will be making what is called an "analogy" argument because your whole argument will be based on the similarity between cigarette smoking and cigar and pipe smoking.
Empirical arguments by analogy work the way that stereotyping works. We see something that, in all the ways we can see, is very much like something we've seen before, so we assume that it's like the thing we've seen before in other ways as well. Stereotyping exists because it's worked very well as a survival tool. A neanderthal who'd never seen a sabretooth before might just stand there and be eaten. But if he notices that the sabretooth looks a lot like a weasel (only much bigger) he might assume that it will behave like a weasel, which is to say it will attack anything smaller than it is that looks tasty.
The main reason to use an empirical argument by analogy is that we can't look at the conclusion thingy (the thing the conclusion is about) directly. If we could examine the conclusion thingy all by itself to see if it had the property or not, or if we had any other kind of evidence, we wouldn't bother with an argument by analogy. Thus even the best argument by analogy is fairly weak, and we usually wouldn't use one unless we have no other kind of argument availible.
Empirical arguments by analogy generally have conclusions of the form "object O has feature F " or, less formally, "ferrets are cunning," "pineapples are citrus fruits," "dolphins have gills" or "bats can't fly."
These arguments are inductive because their main premises are basically reports, or summaries of reports, of experiences various people have had. They compare one thing that is known to exist with another thing that is known to exist in an attempt to show that the one has some property that the other is known to have. They deal with physical similarities between objects and situations. They don't deal with imaginary situations. They don't deal with the issue of whether or not some state of a world is logically possible, and they are never deductively valid. Thus, at their very best, they can only give their conclusions a probability of being true, which is what makes them inductive arguments.
Analogy arguments only work when both sides of the analogy are things that are actually known to exist. Imaginary objects, and objects whose existance is in dispute won't work here. You can't ever make a successful empirical analogy argument comparing anything to an object that isn't known to exist. For instance, none of the following arguments could ever work:
A horse is like a hippogriff. Hippogriffs can fly, so horses can fly.
A unicorn is like a horse. Horses have no magical powers, so unicorns have no magical powers.
If you take the time to examine any goblin, you will find that it is very, very similar to you average kobold. And, you have to admit, all kobolds are avid delvers. Kobolds like nothing better than to delve deep into the living rock under the great hall of the mountain king, so clearly goblins must delve like the very devil too!
Vampires are like werewolves. Werewolves don't sparkle, so vampires . . don't . . bloody . . sparkle! Dammit!
The reason is simple. when you're comparing two real things you're comparing things that are both subject to the laws of nature, like physics, chemistry, biology and so on. When a physical analogy argument works, (if any of them ever do), it works because the natural forces forming one object also formed the other one, and if they formed in similar circumstances, then they're likely to be similar in a lot of ways. (For instance, sharks are descended from fish, dolphins are descended from land-living quadrupeds, but the fact that both live by swimming fast means that both need to have the same streamlined, hydrodynamic shape.) When we're talking about things, (like basilisks, mermaids, angels, dragons and so on), whose existance hasn't been documented by science, and which are only really known as hypothetical entities, anlogies to existing physical objects aren't much use.
Unlike real entities, whose properties are known by primarily through observation, the properties of hypothetical entities are specified in their definitions. These definitions may specify an entity that is physically possible, like a unicorn. They may specify an entity that is physically unlikely, like a mermaid, or even an entity that is physically impossible, like the basilisk, which can kill you with a single glance. Again, analogies are not much use in such cases.
Standardizing Analogy Arguments
The basic motor of any analogy argument is a comparison, a claim that one thing is like another thing. (For convenience, and to serve my own bizarre sense of humor, I will refer to these two things as the "premise thingy" and the "conclusion thingy." The "conclusion thingy" is my name for the thing that is mentioned in the conclusion of the argument. The "premise thingy" is the thing that is not mentioned in the conclusion. I call it the "premise thingy" because it is only mentioned in the premises.) The way an analogy argument is supposed to work is that the two things are supposed to be so much alike that if one of them has a certain property (call it "the property,") then the other must have that same property.
Analogy arguments tend to have the following basic logical form:
1. The Premise Thingy is like The Conclusion Thingy
2. The Premise Thingy has The Property
C. The Conclusion Thingy has The Property
Example 1. The war on drugs is like any war. We will not begin to win until we begin to shoot drug dealers on sight.
Since this argument is obviously intended to change our minds about the drug war, the drug war must be the conclusion thingy. The thing it's compared to is a real live shootin' war, so that's the premise thingy. The property is the thing that is known to belong to the premise thingy, and which the arguer wants to convince us also belongs to the conclusion thingy.
Premise Thingy:........Real live war
Conclusion Thingy....The "war" on drugs
Property ..................Can't be won without shooting at somebody
Why is the drug war the conclusion thingy? Because it's the thingy ... er, thing ... that the conclusion is about. another way to look at is, if there's two things being compared, and one of them most definitely has the property in question, then that one is the premise thingy. Real wars can only be one by blood, toil, tears ... I mean shooting. Lots of shooting. With really big guns! Here's how the argument looks when it's all put together.
1. The government campaign against illegal drug use is like a literal war with shooting and bombing and napalm and cool uniforms and so on.
(2. You can't win a real war without shooting at the enemy.)
C. The government won't win the drug war without a "shoot on sight" order against drug dealers.
Notice the comparison is clarified in the first premise.
Here are some exercises. Click on the correct premise thingy, conclusion thingy and property (Or, go to the end of the chapter for the answers.)
1. Dogpatch Community College should not require a freshman writing course. For god's sake, Harvard doesn't require freshman writing!
Premise Thingy: Dogpatch college....Needs freshman writing....Doesn't need freshman writing....Harvard
Conclusion Thingy: Dogpatch college....Needs freshman writing....Doesn't need freshman writing....Harvard
Property Dogpatch college....Needs freshman writing....Doesn't need freshman writing....Harvard
2. I cannot believe they teach socialism in the University. It's like teaching arson in a fireworks factory.
Premise Thingy: Teaching socialism in university....Teaching arson around fireworks....Good idea....Bad idea
Conclusion Thingy: Teaching socialism in university....Teaching arson around fireworks....Good idea....Bad idea
Property: Teaching socialism in university....Teaching arson around fireworks....Good idea....Bad idea
3. Drug use is a matter of behavior control. It's like overeating or gambling. It would be ridiculous to declare war on overeating, so it's ridiculous to declare war on drugs.
Premise Thingy: Drug use....Overeating or gambling....Matter of behavior control....Ridiculous to declare war on it
Conclusion Thingy: Drug use....Overeating or gambling....Matter of behavior control....Ridiculous to declare war on it
Property: Drug use....Overeating or gambling....Matter of behavior control....Ridiculous to declare war on it
4. Saddam Hussein was a lot like Stalin. Both were vicious dictators with their hands on weapons of mass destruction. Both were self-important megalomaniacs. Both were extremely cruel to anyone who comes in their power. And both had absolutely butt-ugly mustaches! Deterrence kept Stalin bottled up behind the iron curtain until he died. We have absolutely no reason to think that deterrence would not have kept Saddam similarly bottled up. Thus we had no reason to go to war when we did.
Premise Thingy: Hussein....Stalin....Dictator....Had nasty weapons....Megalomaniac....Ugly Mustache....Controllable by deterrence
Conclusion Thingy: Hussein....Stalin....Dictator....Had nasty weapons....Megalomaniac....Ugly Mustache....Controllable by deterrence
Property: Hussein....Stalin....Dictator....Had nasty weapons....Megalomaniac....Ugly Mustache....Controllable by deterrence
5. Just as the state has the right to decide who may or may not drive a car, it has the right to decide who may or may not have a baby.
Premise Thingy: Right to drive....Driving a car....Right to have children....Having children....State has the right to decide
Conclusion Thingy: Right to drive....Driving a car....Right to have children....Having children....State has the right to decide
Property: Right to drive....Driving a car....Right to have children....Having children....State has the right to decide
6. Even though God is omniscient, he doesn't know who will repent and who will not because, for him, it's just like tossing a coin.
Premise Thingy: God....God predicting repentance....Repentance....Predicting a coin toss....Can't be done
Conclusion Thingy: God....God predicting repentance....Repentance....Predicting a coin toss....Can't be done
Property: God....God predicting repentance....Repentance....Predicting a coin toss....Can't be done
Vivid vs. Apt Analogies
I'd like to make a distinction here between what I'm calling "vivid" analogies, which have emotional force because they evoke powerful images and ideas in our minds without necessarily referenceing any established real similarities, and "apt " analogies that refer to already established real physical or logical similarities between two objects. (A good rule would be to ask whether a reasonable would think that the analogy made sense even if she did not already believe in the conclusion.) apt analogies can make logically compelling arguments, whether or not they're vivid. But analogies that are merely vivid, without being apt can never make logically compelling arguments.
Just so you know, an argument that uses an analogy that is vivid without being apt commits the fallacy of false analogy.
7. Only one of the following statements is true. Which one is it?
A. Analogies are powerful arguments. The most vivid analogies are very convincing and give good logical reasons to believe the conclusion.
B. The most vivid analogies can also be the most deceptive. An analogy that is vivid without being apt is always a bad analogy.
C. From a logical standpoint, an analogy's ability to grip the imagination is the most important factor. When we are analyzing an argument
we should be prepared to discount the aptness of an analogy whenever that analogy fails to evoke any powerful image in the reader's mind.
For the following arguments, try to determine whether the analogy used is vivid or apt or neither or both. (Answers at end of chapter.)
I would suggest that you start each exercise by thinking about how the image makes you feel. Then give yourself a couple of seconds for the immediate reaction to fade, and then set that feeling aside and think about whether a reasonable person who does not accept the argument's conclusion would accept that the premise thingy and the conclusion thingy really are physically or logically similar.
8. Dogpatch community college should not require a freshman writing course. For god's sake, Harvard doesn't require freshman writing!
9. I cannot believe they teach socialism in the University. It's like teaching arson in a fireworks factory.
10. Drug use is a matter of behavior control. It's like overeating or gambling. It would be ridiculous to declare war on overeating, so it's ridiculous to declare war on drugs.
11. Saddam Hussein was a lot like Stalin. Both were vicious dictators with their hands on weapons of mass destruction. Both were self-important megalomaniacs. Both were extremely cruel to anyone who comes in their power. Deterrence kept Stalin bottled up behind the iron curtain until he died. We have absolutely no reason to think that deterrence would not have kept Saddam similarly bottled up. Thus we had no reason to go to war when we did.
12. Just as the state has the right to decide who may or may not drive a car, it has the right to decide who may or may not have a baby.
13. Even though God is omniscient, he doesn't know who will repent and who will not because, for him, it's just like tossing a coin.
Good and Bad Analogy Arguments
What is special about empirical analogy arguments is that they only work if the similarity between the two objects being compared is extremely strong in areas that are relevant to the issue being settled. Irrelevant similarities don't count. Irrelevant differences don't count either. Relevant similarities make the argument stronger. Relevant differences make the argument weaker. So the thing to do when evaluating an analogy argument is to pay attention to relevant similarities and differences, and ignore irrelevant ones.
Unfortunately, analogies are also a powerful instrument of persuasion, even in instances where they actually carry no weight. Our beliefs about the premise thingy are often so strong that merely associating it with the conclusion thingy can be enough to convince us that the analogy is correct even if the two things actually have nothing to do with each other.
As I've said before, an argument only succeeds if it is clear to you, as a reasonable person, that it presents a clear and compelling logical reason for you to change your mind and agree with the conclusion. If it doesn't seem clear to you that the argument has presented such a reason, then the argument has failed. Since it is usually possible for two things to be very similar in a lot of ways and yet be different in precisely the right way to kill an analogy argument, empirical analogies usually don't present a logically compelling reason to change one's mind, and thus are often not very logically compelling arguments.
To my mind, analogies nicely encapsulate the basic problem of cutting through rhetoric. They often have a powerful effect on our imaginations, but they are also often complete rubbish. Usually, but not always. Once in a while, an analogy argument is actually convincing. So your problem, as a critical thinker, is to ignore the vividness of the image presented by the analogy, and concentrate on whether the facts presented actually comprise a logically compelling argument for the arguers conclusion. Just like critical thinking in general, evaluating analogy arguments requires you to ignore the powerful effect that images can have on your emotions and imagination, and to carefully and impersonally trace out the implications of whatever facts are actually present.
Before you even get into the analogy part of the argument there's a question you should ask. (Remember that the premise thingy is the thing that is known to have the property, and the conclusion thingy is the thing that the arguer wants you to believe has the property.)
1. Does the premise thingy really have the property? If it doesn't, then no amount of similarity between the two things can make the conclusion thingy have the property.
If we're sure that the premise thingy really has the property, then we should next evaluate the strength of the analogy between the two things. The basic way to assess the strength of an analogy is to think about how the conclusion thingy is similar to the premise thingy. If the two things are only similar in a way that has nothing to do with the property, then the analogy is no good. If the two things are similar in a relevant way, but also have some important differences that are relevant to the property, then the analogy is no good. If the two things are relatively similar, and have no relevant differences, you still have to think about whether they are similar enough to make the analogy work. If they aren't, it doesn't. This kind of reasoning is basically a series of judgment calls, and the only way to get good at it is to practice.
Criticizing An Analogy Argument
The most obvious response to an anlogy argument is to try to break the analogy. You succeed in doing so if you can show that the two things compared in the analogy are not similar enough to make the argument work. Here are some examples in which the second arguer offers an anlogy breaker. (Such attempts don't always work, of course, so I'd like you to think a little bit about whether these counter arguments succeed in breaking their respective analogies.)
1. You can't say that letting George W. Bush be commander in chief during a war is like letting a bum off the street coach a Super Bowl team. The U.S. commander in chief makes general policy decisions based on the advice of highly trained and experienced professionals. A Super Bowl coach has to make split-second tactical decisions based entirely on his own judgment.
2. Mountaineering is not like driving. You don't have to climb mountains to get to the grocery store.
Notice that these are both counter arguments because both of them attack parts of other arguments. Okay, I haven't given you those other arguments, but these two above only make sense as attacks on other arguments.
The other way to attack an analogy argument is to argue that the premise thingy doesn't actually have the property, as in this dialog.
A. Tobacco smoking is just like marijuana smoking. Both have heath risks, both can become habitual, and both impose discomfort and risk on the people around the smoker. We know that marijuana should be illegal, and because of this similarity, so should tobacco.
B. But we don't have good reason to think that marijuana should be illegal! The idea that it should be is at least highly controversial, and many health and law enforcement professionals strongly advocate the legalization of marijuana.
Later on, we will worry about which argument is weaker. For now, I just want you to notice that the first argument relies upon the claim that marijuana should be illegal. If this is uncontroversially true, then his argument works. You should also note that he does not support this claim, so if it turns out to be controversial, then his argument will fail. The second arguer is trying to take advantage of this by trying to provide reasons to think that it is not yet proved that marijuana should be illegal.
Now, it should not surprise you to learn that any time an argument has one of these flaws, it is a bad argument, or a "fallacy."
The fallacy of false analogy occurs when an arguer offers an analogy in which the model and the analog are only similar in ways that are not relevant to the property, or in which the model and the analog are clearly different in a way that is very relevant to the property.
Here are some examples of False Analogy. (With reasons why they're false analogies.)
Iraq is a lot like Afghanistan, so the war there will go the same way. (Iraq and Afganistan both have muslim populations, but that's about it. Terrain, population distribution, social structure, form of government and military organization are all different. Since the course of war depends on things like these rather than religion, the analogy is terrible.)
The national debt is like a metastasizing cancer that threatens to destroy our economy from within. (The big difference that I see here is that an economy can recover from just about any kind of "injury," while a living body can be killed by relatively small injuries. The deficit may indeed be dangerous to our economy, but our economy is not enough like an animal body to make the comparison meaningful.)
Just as rain wears down mountains, human problems always yield to perseverance. (Mountains are made of rocks and minerals that have a strictly limited ability to resist water erosion, while human problems are made of things like death, anger, hatred, injury, disease and lots of things that don't get better.)
We should have interventions for coffee drinkers, because they're just like alcoholics. (Yeah, sure, coffee drinkers go on three week binges and wake up in stolen cars on the edge of the Vegas strip unable to remember their own names and the names of the oddly dressed farm animals who are currently singing Christmas carols in the back seat of the car. Yeah, coffee drinkers are juuuuuuuust like alcoholics.)
Finally, follow this link (HGH) to a graphic comparing animal rights activists to Galileo, Frederick Douglass, and women's sufferage activists, on the basis that they were all called fools, blasphemers, troublemakers and lunatics. It may be that animals do indeed have strong moral rights, but this comparison does not logically support that conclusion because the overwheming majority of people who have been called called fools, troublemakers and lunatics were in fact complete fools, unscrupulous troublemakers or raving lunatics.
For each of the following false analogies, see if you can figure out why it's a false analogy.
14. The 40 hour week works very well in modern corporations, so we should use it in farms as well.
15. Just as it is absurd to criminalize the removal of a tumor, it is absurd to criminalize abortion.
16. There's no point in adult literacy programs because there's no point in crying over spilled milk.
17. Coffee and cigarettes should not be illegal, so marijuana should not be illegal.
Begging the Question
The fallacy of begging the question occurs when an arguer offers any argument, of any kind, that relies on a major factual claim that is itself controversial and which is not presently supported by another argument of its own.
Attempts to make analogy arguments can beg the question also. This happens when an arguer offers an analogy in which the premise thingy has not been proved to have the property that is being ascribed to the conclusion thingy. If the arguer just assumes that the premise thingy has the property without good reason to think that it does, then he certainly begs the question, and therefore fails to even get his analogy argument started.
Just like a business, government must first, last and always look to the bottom line. (Nobody has proved that businesses have a moral duty to increase profits above all else. All established moral theories agree that there are some things that businesses shouldn't do, no matter what the profit, so even if government was exactly like business, that analogy wouldn't be enough to prove that government should look to the bottom line.)
Exercise 18. The following argument begs the question. Can you explain exactly how it does so?
Marijuana should be illegal, so coffee and cigarettes, which are at least as unhealthy and addictive, should also be illegal.
The fallacy of red herring occurs when an arguer offers a reason that is not relevant to his conclusion. In terms of analogy arguments, trying to criticize an analogy argument on the basis of an irrelevant difference would be a red herring. In the following examples, the second, red, argument is always a red herring.:
A. Even though God is omniscient, he doesn't know who will repent and who will not because, for him, it's just like tossing a coin.
B. That doesn't make any sense! Deciding whether or not to repent is a process that takes place in a human brain, which sits in a container filled with blood, but coin tosses take place in the open air, with no blood anywhere about!
A. Just as the state has the right to decide who may or may not drive a car, it has the right to decide who may or may not have a baby.
B. Dude, cars are made of steel and plastic, while babies are made of drool and squishy pink stuff. There's no comparison, so your analogy fails!
A. Giving a tax break to the rich is like the government seizing a big stash of stolen money, and then giving some of it back to the bank robbers.
B. But what about the fact that bank robbers wear thos black-and-white banded jerseys, berets and domino masks? And rich people always wear top hats, frock coats and Prince Albert beards?
Exercises . Each of the following argument groups contains one red herring (either A or B). Identify the red herring fallacy and explain why it is a red herring.
19. Promoting a Baha'i society is like promoting Communism. It sounds good until it's achieved, but then it turns into hell on earth.
A. You forget that Baha'i is a doctrine that came out of the middle east, whereas communism originated in France and Germany, so your analogy totally fails!
B. If the only similarity beetween the two is that they both sound good in theory, might I point out that both Christianity and indoor plumbing also sound good in theory.
20. Dogpatch community college should not require a freshman writing course. For god's sake, Harvard doesn't require a freshman writing course!
A. Can you be sure that these two institutions both draw from the same kind of incoming freshman pool? Isn't it possible that Harvard's incoming freshmen are much better prepared than Dogpatch's incomung class?
B. It is abundantly clear that this comparison is logically unsound. It is easy to prove that what goes for Harvard has absolutely no relevance to what goes for Dogpatch, beacuse, ans any educated person knows, the walls of Harvard are covered in the noble and beautiful ivy, while the walls of Dogpatch Community College are covered in base and unsightly Kudzu, which is a completely different kind of plant.
Note for Logic Nerds
If you think about it, false analogy is kind of like red herring because it makes an argument based on irrelevant similarities. However, bad analogies are so common that it's best to have a seperate fallacy name for that kind of failure.
Here's a rule.
If it's a direct analogy argument based on irrelevant similarities, it's false analogy s
If it's a non-analogy counter argument based on irrelevant differences, it's one way of committing red herring.
Fallacy Identification Exercises.
Each of the red arguments in the following dialogs commits a different fallacy. Identify each bad argument as false analogy, begging the question or red herring.
21. A. Drug use is a matter of behavior control. It's like overeating or gambling. It would be ridiculous to declare war on overeating, so it's ridiculous to declare war on drugs.
Don't be an idiot! Drugs enter the body through the mouth, nose and a needle into a vein. Except for some very rare circumstances, food only enters the body through the mouth! Don't you realize what a huge difference that is? It's an enormous differentce, and it means your analogy cannot possibly work!
22. A. Look dude, your dream of forming a hamster precision flying aerobatic team is just not going to work. I've told you a thousand times, hamsters don't fly, and that's it!
Don't be a fool, old man. Don't you know that hamsters are almost exactly like lemmings, and it is well known that the lemming can fly with the agility, grace and power of a F15 Tomcat jet fighter. Since lemmings can fly, it follows that tight formations of hamsters can fly well enough to give aerobatic displays of stunning complexity and precision.
23. A. Is that a Sherman tank you're driving? I thought you were trying to save money. That thing must get terrible gas mileage.
Oh no, it will get great gas mileage, because I got a blue one. My old Pacer got great gas mileage, and it was blue too.
Tactics and Analogy Arguments
Okay, let's say you've got to analyze a set of arguments in which at least one of them is an analogy argument. How do the opposing arguments stand to that analogy argument. The rule is simple. If the opposing argument tries to break the analogy, then it's a counter argument. If it doesn't offer any specific reasons to doubt the analogy, then it's a direct argument.
"Salience" is the property of "stick-outness" something is salient if it it really grabs out attention. Explosions, people who look like movie stars and giant, world-destroying spaceships are really salient. Cars that happen not to be exploding, people who look like everybody else, and small, innoffensive pieces of gravel are not salient. Now, there is a great deal of difference between salience and logical force. This is very like the difference between vividness and congruence. Salient features can catch our imaginations and move us to belief without providing even the beginnings of a logical reason to believe. And salience can, sometimes fatally, distract us from the purely logical features of an issue. Consider the following dialog:
A. Dolphins and sharks have many similarities. They are both shaped very much the same, and are optimized for fast swimming. They are also both built for manuverability in that they both have strong dorsal, ventral and caudal fins. Finally, they both live the same way, by chasing down and eating smaller fish. So the fact that sharks have gills leads inevitably to the conclusion that dolphins must also have gills..
B. Dude, dolphins are mammals, not fish! Mammals have lungs, not gills!
Before you begin a serious analysis, take a moment to think through your own reactions to these arguments. Did you laugh? Did something strike you as especially stupid? Did anything strike you as right on the money? Take a careful inventory of your initial reactions and ideas about this dialog, and write down as much as you can of what you thought.
Then look at the second argument, and ask yourself if it is a counter argument. It's true that the first argument is ludicrous, but that's not the issue here. The question here is whether or not the second argument refers explicitly to the facts and logic that the first argument uses. The second argument is only a counter argument if it actually gets into the nuts and bolts of the first.
Finally, look at the second argument, and ask yourself if it represents good logic. I'm not asking you if it's true, I'm asking if it's good logic. The way to think about this kind of issue is to ask youself if a person who did not already believe the conclusion would rationally have her mind changed by the argument. Here, the issue is whether dolphins have lungs or gills, so I want you to think about whether someone who did not already think dolphins have lungs would get a rational reason to change his mind, and believe that dolphins did have lungs, or to at least believe that the first argument was no good, based on this second argument.
If I've handled this example correctly, you will have been at least mildly surprised by your own responses to these two questions. Because the conclusion of the first argument is so absurd, I expect many people will instinctively tend to feel that the second argument must be either a counter argument or good logic, or both. In fact neither is the case. The second argument is not a counter argument, because it does not refer in any way to the analogy between dolphins and sharks. Furthermore, it is bad logic, committing the fallacy of begging the question. The statements "dolphins are mammals" and "dolphins have lungs, not gills" are pretty much synonymous in this context. If someone believes that dolphins are mammals, he will automatically believe they have believe that they have lungs. If someone doesn't believe that dolphins have lungs, he automatically won't believe that they're mammals, and so the premise "dolphins are mammals" will not be uncontroversial as far as he is conceerned.
Here are some more examples of false analogy, with opposing direct and counter arguments. The counter arguments give reasons why these are false analogies. The opposing direct arguments ignore the analogies.
Iraq is a lot like Afghanistan, so the war there will be a cakewalk, just like Afghanistan.
Direct: The Iraqi resistance is highly motivated and well-funded. They're not going to allow a cakewalk!
Counter: Iraq and Afganistan both have muslim populations, but that's about it. Terrain, population distribution, social structure, form of government and military organization are all different. Since the course of war depends on things like these rather than religion, the analogy is terrible.
We should have interventions for coffee drinkers, because they're just like alcoholics.
Direct: Are you crazy? Coffee drinkers need that black elixir, that steaming java, that jittering caffeine high!
Counter: Yeah, sure, coffee drinkers go on three week binges and wake up in stolen cars on the edge of the Vegas strip unable to remember their own names and the names of the oddly dressed farm animals who are currently singing Christmas carols in the back seat of the car. Yeah, coffee drinkers are juuuuuuuust like alcoholics.
Just as it is absurd to criminalize the removal of a tumor, it is absurd to criminalize abortion.
Direct: Abortion allows women to control their own bodies! We can't have that.
Counter: Tumors don't ever turn into people. Well, except for Glenn Beck.
There's no point in adult literacy programs because there's no point in crying over spilled milk.
Direct: Adult illiteracy is a tragedy for millions of people who would like to read the articles in playboy, but can't.
Counter: Milk can't be unspilled, but illiterate adults can learn to read.
The national debt is like a metastasizing cancer that threatens to destroy our economy from within.
Direct: Rubbish, debt is good for an economy. Debt is what makes this country great!
Counter: An economy can recover from just about any kind of "injury," while a living body can be killed by relatively small injuries. The deficit may indeed be dangerous to our economy, but our economy is not enough like an animal body to make the comparison meaningful.
If I've done this right, you'll be able to look at the examples above and see that the counter arguments all point out differences between the two objects being compared in the analogy argument, while the direct arguments all ignore the analogies.
Exercises For each of the following groups of arguments, identify the argument that is a counter argument to the first argument,
24. I'm tired of those crazy drivers on the 405, so I got myself an old army tank! And I know it will get great gas mileage, because I got a blue one. My old Pacer got great gas mileage, and it was blue too.
A: Pshaw! As if color has anything to do with gas mileage!
B: Um, tanks are lots heavier than cars, so your tank will get lousy mileage!
25. The 40 hour week works very well in modern corporations, so we should use it in farms as well.
A The 40 hour week means weekends off, and crops and animals don't do well when left alone.
B: Corporations usually deal with non-living things, like papers and widgets. Farms deal in living things, like plants and animals.
26. Just as rain wears down mountains, human problems always yield to perseverance.
A: Mountains are made of rocks and minerals that have a strictly limited ability to resist water erosion, while human problems are made of things like death, anger, hatred, injury and disease.
B: Actually no, lots of human problems totally fail to get better, no matter how long and hard people try.
27. Coffee and cigarettes should not be illegal, so marijuana should not be illegal.
A Marijuana makes people happy at low cost. Our corporate overlords cannot profit from that, so it should be illegal.
B: Coffee and cigarettes are way more addictive than marijuana. Neither of them is a serious intoxicant compared to marijuana, so the analogy doesn't work..
28. Given what we know about logic, can you figure out a good counter argument to the "dolphins have gills" argument above?
29. Given what we know about science, can you figure out a good direct argument for the conclusion that dolphins don't have gills?
"SCAEFOD" stands for "Standardize, Context, Analyze, Evaluate, Fist Of Death!" It refers to a process in which an effort is made to clarify arguments and the logical relationships between arguments before any decisions are made about the strength or weakness of any argument.
Here's example of how to "scaefod" (analyze) an analogy argument.
William Bennett holds up an egg. "This is your brain," he says. He cracks the egg, dropping the contents into a hot skillet. The egg cooks. "This is your brain on drugs." Bennett turns to the Emmett, looking very grim. "Any questions?" He asks.
Emmett.Yes Bill, can I have my brain on drugs with bacon and toast?
William Bennett 1. An egg that is cracked open and dropped into a hot skillet will become coagulated and tasty.
(2. It is an extremely bad thing, from the egg's point of view, to become coagulated and tasty.)
(3. The human brain exposed to drugs is like an egg cracked and dropped in a hot skillet.)
C. All drugs are extremely bad. DIRECT
Emmett. No argument, just a sarcastic comment.
William Bennett bears the burden of proof here. Although many people believe drugs are bad, and some recreational drugs have been shown to have some bad effects under some circumstances, all the evidence so far shows that drugs are not seriously damaging for the majority of people who take them.
William Bennett Analogy Argument Emmett. No argument
Analog: brain on drugs
Model: egg on skillet
Property: becomes coagulated and tasty, (and is perhaps served with bacon and toast, and maybe coffee.)
William Bennett: Analogy between brain on drugs and egg on skillet
Most relevant similarities. None.
Most relevant differences. There is no known drug experience that is remotely like hitting oneself in the head with a hard heavy object and then laying one's exposed brain in a hot skillet.
Fist of Death: Based on the conversation between William and Emmett, drugs are not seriously dangerous. Emmett gives no argument, but since he defends the null hypothesis, he doesn't really have to. William gives the analogy between taking drugs and banging oneself in the head, cracking one's head open and dumping one's brains into a skillet. There is no known drug that has this effect, so William's analogy is completely false. Given that we have no anti-drug arguments left here, the proposition that drugs are not seriously damaging carries the day.
(Again, one's pre-existing beliefs about the level of danger attendant on taking illegal drugs cannot be relevant here.)
One last example before the exercises.
Shakira. Marijuana has been proved to cause at least some brain damage, so I think marijuana should be illegal, at least until we can establish exactly how dangerous it is.
Jameson. Rubbish, Red Bull and other "energy drinks" are not illegal, so marijuana should not be illegal.
Shakira. 1. Marijuana causes some brain damage.
2. We're not sure exactly how much.
C. Marijuana should be illegal, at least for the present. DIRECT
Jameson. 1. Red Bull and other "energy drinks" are not illegal.
2. Marijuana is similar in its properties to these energy drinks.
C. Marijuana should not be illegal. DIRECT
Shakira makes a direct argument.
Jameson doesn't talk about the logic of Shakira's argument, so his is also a direct argument.
Shakira is the one arguing that something could be illegal, so she bears the burden of proof.
Shakira. Explanation argument Jameson. Analogy argument.
Based on harm caused by marijuana. Analog: marijuana.
Model: "energy drinks"
Property: should be legal
Jameson. Analogy between marijuana and energy drinks.
Most relevant similarities: Both marijuana and "energy drinks" contain naturally occurring psychoactive chemicals.
Most relevant differences: None that I can think of.
Fist of Death: By the reasoning given above, marijuana should be illegal. I don't think that Shakira's argument is particularly strong, but it doesn't commit any obvious fallacies. The analogy between marijuana and Red Bull-type drinks seems very strong, so if it is the case that these drinks should be legal, it follows that marijuana also should be legal. However, the fact that something is legal doesn't mean it should be legal, so even if marijuana was exactly like these currently legal "energy drinks," that analogy wouldn't be enough to prove that marijuana should be legal. Jameson commits the fallacy of begging the question, because his model, energy drinks, doesn't have the property he thinks it does. So Shakira's argument is the strongest out of these two, and if these arguments were all we had to go on, we would be led to conclude that marijuana should be illegal.
Exercises 30-31. Analyze the following
Carli. Drug use is a matter of addiction and behavior control. It's like overeating or gambling. It would be ridiculous to declare war on overeating, so it's ridiculous to declare war on drugs.
Syed. The war on drugs is like any war. We will not begin to win until we begin to shoot drug dealers on sight.
Based on the discussion between Carli and Syed, it is ridiculous to declare war on drugs.
As Carli says, drug use is like overeating or gambling. (At least, problem drug use is like problem overeating or problem gambling.) These three things are especially similar in terms of addiction, which we can define as the fact that they all involve cravings and involuntary impulses to indulge in the problem behavior. Thus it makes sense that they should be handled in terms of helping individuals gain greater control over their behavior. It would be ridiculous, or at least very counterproductive to try to combat overeating by declaring war on food, and so it is ridiculous to try to combat problem drug use by declaring war on drugs.
Exercise 30. Pick out the best description of Syed's stupid argument.
A. "Syed draws an analogy between the war on drugs and regular wars such as the War of 1812 and World War II. Such wars can only be won by undertaking offensive actions against the enemy, which includes shooting at the enemy on sight. Syed implicitly argues that, since fighting a regular war requires shooting the enemy on sight, fighting the war on drugs requires shooting drug dealers on sight." (Answer)
B. "Syed draws an analogy between the metaphorical "war" on drugs, and the literal meaning of the word "war." He claims that the "war" on drugs is exactly the same as wars such as the War of 1812 and World War II. Syed implicitly assumes that "wars" in the literal sense can only be won by undertaking offensive actions against the enemy, which obviously includes shooting at them whenever such shooting is to our advantage. He also implicitly identifies drug dealers as the "enemy" in the "war" on drugs. Since he says "shoot drug dealers on sight," he is literally advocating that police or anyone else should open fire as soon as they catch sight of anyone they believe to be a drug dealer." (Answer)
C. "Syed draws an analogy between the metaphorical "war" on drugs, and the literal meaning of the word "war." He claims that the "war" on drugs is exactly the same as wars such as the War of 1812 and World War II, at least in terms of how they can be won. Syed implicitly assumes that "wars" in the literal sense can only be won by undertaking offensive actions against the enemy, which obviously includes shooting at them whenever such shooting is to our advantage. He also implicitly identifies drug dealers as the "enemy" in the "war" on drugs. He is saying that the police should undertake offensive operations against drug dealers in the same way as a well-run army undertakes operations against an opposing army. This would presumably include intelligence efforts to correctly identify and locate genuine drug dealers, and careful consideration of when and how to open fire in order to minimize the probability that innocent people would be caught in the crossfire." (Answer)
D. "Syed draws an analogy between the metaphorical "war" on drugs, and the literal meaning of the word "war." He claims that the "war" on drugs is exactly the same as wars such as the War of 1812 and World War II, at least in terms of how they can be won. Syed implicitly assumes that "wars" in the literal sense can only be won by undertaking offensive actions against the enemy, which obviously includes shooting at them whenever such shooting is to our advantage. He also implicitly identifies drug dealers as the "enemy" in the "war" on drugs. Although he says "shoot drug dealers on sight," we don't need to read him as literally advocating that police or anyone else should open fire as soon as they catch sight of anyone they believe to be a drug dealer. Rather we can interpret him as saying that the police should undertake offensive operations against drug dealers in the same way as a well-run army undertakes operations against an opposing army. This would presumably include intelligence efforts to correctly identify and locate genuine drug dealers, and careful consideration of when and how to open fire in order to minimize the probability that innocent people would be caught in the crossfire." (Answer)
Exercise 31. Pick out the best critique of Syed's stupid argument.
A. "Syed's argument does not address the analogy offered by Carli. Since Syed fails to offer a counter argument to Carli's argument, Syed cannot defeat that argument, and it stands. Since Carli's argument stands uncontested, it carries the day, and Syed loses the argument." (Answer)
B. "Syed's argument commits two fallacies. First, he commits the fallacy of assuming that, if the war on drugs really is like a real war, it automatically follows that shooting the "enemy" would be justified. This is an illegitimate assumption because it is simply not the case that all wars are justified. Second, he commits the fallacy of false analogy in that the war on drugs and real warfare are not sufficiently similar to carry his argument. Enemy soldiers are dedicated to shooting us and blowing up our stuff. Drug dealers are dedicated to selling their stuff to people who want to buy it. They only shoot or blow up people who threaten them. Otherwise, they leave us alone. The only justification for shooting at enemy soldiers is that it can prevent them from shooting at us. When shooting them isn't needed to stop them shooting at us, like when they surrender, we stop shooting at them, eventually. Since this difference sits right on the point that Syed needs in order to make his argument work, it kills his argument stone dead." (Answer)
C. "The problem with Syed's argument is that it requires literal warfare against drug dealers. This means attacking them with the most effective weapons in our arsenals. Can you imagine the carnage if your local corner drug dealer suddenly found himself attacked by an armored division operating with air support. Sure, a single hit from the main gun of a modern main battle tank would vaporize the guy, but it would also bring down every nearby building. Cluster bombs and napalm would only make things worse. Undertaking modern warfare in an urban environment would cause untold destruction, so is ridiculous to apply modern warfare to drugs." (Answer)
D. "Syed's argument is a false analogy. There is no way that the war on drugs is anything like a regular war, so things that apply to a regular war do not necessarily apply to the war on drugs." (Answer)
An argument cannot be a bad argument merely because it fails to address some other argument. An arguer can fail because he fails to address some other argument, but that by itself doesn't make his own arguments bad. Taking an uncharitable interpretation of somebody's argument, and then refuting, or ridiculing, that uncharitable interpretation, always fails to refute an argument. In order to really defeat an argument you have to criticize it in its strongest form, and show that even its strongest form cannot stand. Finally, even if your judgment of an argument is exactly right, your clincher will still fail if you do not include the details necessary to allow your readers to understand exactly why the opposition argument fails.
Try to analyze all of the arguments found in each of the following dialogs. Especially figure out which arguments are direct arguments and which are counter arguments. Say which side has the stronger argument(s) and which is weaker. If you can, identify the key fact that unlocks the issue.
32. Kory. I'm taking a political science class at the university. We just started studying socialism, and the professor says that socialism has actually worked in every country where it's been given a fair chance.
Noelia. I cannot believe they teach socialism in the University. It's like teaching arson in a fireworks factory. (Answer)
33. Carli. Drug use is a matter of addiction and behavior control. It's like overeating or gambling. It would be ridiculous to declare war on overeating, so it's ridiculous to declare war on drugs.
Syed. The war on drugs is like any war. We will not begin to win until we begin to shoot drug dealers on sight. (Answer)
34. Catalina. I think it must be pretty boring to be God. After all, he's omniscient, so he already knows how things are going to come out. He can't even make bets on which sinners are going to repent and which are going to burn, because he already knows who is and isn't going to repent.
Jaiden. Even though God is omniscient, he doesn't know who will repent and who will not because, for him, it's just like tossing a coin. (Answer)
35. Clifton. I wish we could stop irresponsible people from having children. It would prevent an enormous amount of suffering, but control over one's own body is a basic human right, and that includes reproduction, so the state will never have the right to control who has children.
Annette. You've got all wrong. Just as the state has the right to decide who may or may not drive a car, it has the right to decide who may or may not have a baby. (Answer)
36. Donavan. I think we should give an enormous tax break to the rich. Both Forbes Magazine and the Wall Street Journal say it will stimulate the economy, increase employment, raise wages, eliminate the deficit, reduce the federal debt and bring peace in the Middle East.
Clifford. That's ridiculous! Giving a tax break to the rich is like the government seizing a big stash of stolen money, and then giving some of it back to the bank robbers. (Answer)
37. Grady. I just spent the last six months researching the Baha'i faith. The Baha'i faith preaches kindness, tolerance and nonviolent social action. I traveled all over the country visiting Baha'i congregations and seeing them in action. I found them all to be composed of gentle and kind people, all doing good work in their communities, and all getting along fabulously with anyone who was willing to get along with them. I think it would be great if we had a Baha'i society!
Kristine Promoting a Baha'i society is like promoting Communism. It sounds good until it's achieved, but then it turns into hell on earth. (Answer)
38. Dimitri. Here at Dogpatch community college we get a lot of incoming freshmen who don't know how to write college-level papers, so we need to have a freshman writing course, and we have to require incoming freshmen to take that course.
Maura. Dogpatch community college should not require a freshman writing course. For god's sake, Harvard doesn't require a freshman writing course! (Answer)
39. Augustus. I really think that the government should put more money into discouraging cellphone use. Cellphones produce microwave radiation, so using a cellphone is literally holding a radiation source right next to your brain. Radiation causes cancer, so it is insane to routinely expose the most important organ in your body to a known carcinogen several times a day. Millions and millions of people use cellphones on a daily basis, so if cellphones cause cancer these people are at a serious risk. We cannot wait for research because waiting could potentially allow thousands of people to contract deadly brain cancers.
Fred. Wait a moment. Cellphones have been around for years and years, so if they caused cancer we would already see a rise in the cancer rates, and this rise would include a correlation between cancer and cellphone use. This is exactly how we found out that cellphone use causes car accidents. There is no rise in the cancer rates, and cancers are not correlated with cellphone use, so cellphone use is not a significant cause of cancer.
Possible Quiz Questions (These you will have to check by looking up the answers in the chapter above!.)
i. Explain the fallacy of false analogy in your own words
vi. Explain the fallacy of begging the question in your own words
viii. In your own words, explain how to argue against an analogy argument.
ix. What do you call an argument that tries to point out a logical problem with someone else's argument?
x. Which kind of argument that doesn't refer to any logical problems in any other argument?
xi. How good is an analogy argument in which the premise thingy bears no useful similarities to the conclusion thingy?
xii. It it's bad, what fallacy does it commit?
xiii. How good is an argument in which the main premise is just the conclusion stated in different words?
xiv. It it's bad, what fallacy does it commit?
xv. How big an idiot is someone who says an argument is bad merely because he thinks the conclusion is false?
xvi. What fallacy is comitted by this kind of idiot?
xvii. How good is an analogy argument in which the premise thingy doesn't even have the property that the arguer is trying to attribute to the conclusion thingy?
xviii. It it's bad, what fallacy does it commit?
xix. Is it good reasoning to try to support one of your premises by citing the conclusion that that premise is supposed to support?
Analogy Quiz (This is an outlink, so enter a fake name, just in
Here are some analogical arguments I'd like to go over in class.
The basic argument given for animal rights is the same as the basic argument given for the rights of women and black people, and the counter arguments against this basic argument are all the same as the arguments against the basic argument for giving rights to women and the basic argument for giving rights to black people. These basic arguments for human rights were eventually (and rightfully) accepted by a majority of the population, and eventually the basic argument for animal rights will be (rightfully) accepted by a majority of the population.
When those two high school students entered the words "big boobs" into an internet search engine and then viewed pornography on the computer, they were doing something that was just as bad as arson and murder. These are very serious crimes, so these students should recieve very serious punishment.
Making alcohol illegal was a social disaster, and that disaster was greatly relieved by legalizing alcohol. Making marijuana illegal has been just about as much of a social disaster, and this disaster can be alleviated by legalizing marijuana.
Allowing gay marriage is like allowing a marriage between a immature pachyderm and a piece of heavy machinery. We would not give legal sanction and protection to a liason between a baby elephant and a steamroller, and so we should not allow a human being to legal sanction and protection to a liason between a fully consenting adult human being and another fully consenting adult human being of the same gender!
More Practice:Identify the weaker argument in each dialog and describe the problem with that argument, including the fallacy name if any. Make sure you include all necessary details, including the "crucial fact," and the precise way the argument goes wrong.
Dexter. I think it's a bad sign when a country is continually starting wars. It's like having a guy in your neighborhood who you have to avoid because he's continually getting into fights with his neighbors.
Kelsi. You don't know what you're talking about. A great nation is like a well-developed human body. The strength and power of human body depends on regular exercise in the form of hard physical activity, so the strength and power of a great nation depends on regular exercise in the form of war.
Pangloss. No, I'm not going to assign The Ominous Parallels in my political science class. I've skimmed through the book and randomly read a few dozen pages. Every page I've looked at, every argument I've looked at, has been just plain silly. Based on this sample of his writing, I would say that the author of this book obviously does not understand political philosophy and obviously has little knowledge of political history. Certainly, I have not seen anything in the book that indicates it would be even the slightest use to a student of political science.
Lemming. Well, but you would happily use the book A Theory of Justice, wouldn't you?
Pangloss. Yes of course. A Theory of Justice is an extremely significant work of political philosophy.
Lemming. Aha, here's where I've got you. Both The Ominous Parallels and A Theory of Justice are hardbound in high-quality paper with rich leather covers. Both weigh about a pound, and both use a 12-point Helvetica typeface. A Theory of Justice is a significant work of political philosophy, so therefore The Ominous Parallels is also a significant work of political philosophy. So you have a very good reason to assign it in your political science class.
More Quiz Preparation
Be able to identify Analogy arguments, and be able to tell when an argument is based on a comparison, and when it is't
Be able to tell when two things are relevantly different, and when they aren't.
Be able to tell when an argument commits false analogy, even if you can't quite explain why.
Be able to tell when an analogy argument commits begging the question, even if you can't quite explain why.
Advanced Topics (These probably won't be on the quiz, though we might talk about them in class.)
Know the difference between false analogy and begging the question.
Be able to standardize analogy arguments. (You can practice on the arguments given above.)
Be able to remember, figure out, or pick out the correct general form for analogy arguments.
1. The Premise Thingy is like The Conclusion Thingy
2. The Premise Thingy has The Property
C. The Conclusion Thingy has The Property
Be able to tell whether an argument is attacking an analogy or not. (A counter argument to an analogy argument will attack the analogy. If an anlogy argument is opposed by an argument that doesn't attack the analogy, then that opposing argument isn't a counter argument.)
1. Premise Thingy: Harvard Conclusion Thingy: Dogpatch college Property Doesn't need freshman writing
2. Premise Thingy: Teaching arson around fireworks Conclusion Thingy: Teaching socialism in university Property: Bad idea
3. Premise Thingy: Overeating or gambling Conclusion Thingy: Drug use Property: Ridiculous to declare war on it
4. Premise Thingy: Stalin Conclusion Thingy: Hussein Property: Controllable by deterrence
5. Premise Thingy: Right to drive Conclusion Thingy: Right to have children Property: State has the right to decide
6. Premise Thingy: Predicting a coin toss Conclusion Thingy: God predicting repentance Property: Can't be done
7. "The most vivid analogies can also be the most deceptive. An analogy that is vivid without being apt is always a bad analogy." is true
8. I don't think this is either vivid or apt. It's certainly not apt! Harvard University has many substantial dissimilarities with any community college.
9. Vivid, but not apt. Someone who already thinks socialism is bad might agree with the conclusion, but there are no significant similarities between the two cases mentioned.
10. Maybe not vivid, but certainly apt. The science of addiction show that people stay on drugs for mostly the same reasons they overeat or gamble.
11. Again apt. The similarities between Saddam and Stalin are well documented, as is the fact that Saddam admired and modelled himself on Stalin! Successful dictators tend to have a lot of features in common.
12. This might be vivid, especially when we think of all the horrible parents out there, but driving is a priviledge while having children is a basic human right, and control of fertility has much more potential for abuse than control of driving licenses, so I think it's not apt.
13. Maybe vivid, but certainly not apt. A human who flips a coin neither controls it's course not has the ability to see it's end, whereas God, if he flipped coins, would be able to do both.
14. Memos won't rot in the fields over a weekend, but crops and animals don't do well when left alone.)
15. Tumors don't ever turn into people. Well, except for Glenn Beck.
16. Milk can't be unspilled, illiterate adults can learn to read.)
17. Coffee and cigarettes are way more addictive than marijuana. Neither of them is a serious intoxicant compared to marijuana.)
18. Has anyone has proved that marijuana should be illegal? This claim is disputed by many reasonable people, and he completely fails to support it himself. It is certainly true that tobacco, coffee and marijuana have many features in common (although marijuana is healthier and less addictive than tobacco), but this similarity, however close it is, doesn't matter when the feature is not uncontroversially associated with the premise thingy.
19. A " . . . Baha'i is a doctrine that came out of the middle east . . ." is the red herring.
20. B " . . . the walls of Harvard are covered . . ." is the red herring.
21. B " . . . Drugs enter the body through the mouth . . . " is a red herring.
22. B " . . . lemmings can fly . . . " begs the question.
23. B " . . . because I got a blue one . . . " is a false analogy
24. A. "Pshaw! As if color has anything to do with gas mileage!" is the counter argument.
25. B. "Corporations usually deal with non-living things, ....." is the counter argument.
26. A. "Mountains are made of rocks and minerals ....." is the counter argument.
27. B: Coffee and cigarettes are way more addictive ....." is the counter argument.
28. Any counter argument here would have to point out a difference between the shape and behavior of an animal and its physiology. If you can figure out a way to show or explain that there's no necessary connection between how and animal looks and behaves, and how it's organized internally, you can show how the analogy fails.
29. Dolphins have been extensively studied, so there should be plenty of reference books with descriptions of dolphin anatomy, which dont include gills. And if you point out that dolphins are mammals, which don't have gills, that can work too.
30. D. This last and most elaborate description od Syed's argument makes it a strong as it reasonably can be made. Notice that this description bends over backwards to as much as possible avoid portraying Syed as saying anything stupid.
31. For my money. B is the best critique because it contains the most purely logical analysis, and it explicitly discusses what drug dealing us really like, what wars are really like, and the morally importand differences between them.
32. Kory. 1. Kory's political science professor says that socialism works.
(2. Systems that work are good systems.)
(C. Socialism is good)
Noelia. 1. Teaching socialism in the University is like teaching arson in a fireworks factory.
(2. Teaching arson in a fireworks factory would have bad consequences that look cool when viewed from a distance.)
(C. Socialism is bad.)
If someone here was arguing that socialism is okay, or that we don't know whether socialism is good or bad, that person would not bear burden of proof. However, we have one person arguing that socialism is good, and another arguing that it is bad, so both sides bear the burden of proof against the null hypothesis.
Both are making direct arguments.
Kory's argument is based on the historical record of socialism. He points out that socialism has worked in all the countries where it's been given a fair chance to succeed or fail on it's own merits, which implies that it's a good thing, since political systems that work are good systems.
Noelia's argument is based on an analogy between socialism lessons in a university and arson lessions in a fireworks factory. It relies on the fact that teaching arson in a fireworks factory would be a very dangerous thing to do, given that fireworks will be very likely to go off if someone is setting fires very close to them. Noelia's argument says that teaching teaching socialism in a university is so similar to teaching arson in a fireworks factory that teaching socialism in a university is just as dangerous as teaching arson in a fireworks factory. Noelia probably doesn't mean that socialism lessons are likely to actually set fire to the univesity. More likely she means that they will result in some kind of unacceptable social cost.
33. Carli. 1. Drug use is a matter of addiction and behavior control.
2. Drug use is like overeating or gambling.
3. It would be ridiculous to declare war on overeating.
C. It's ridiculous to declare war on drugs.
Syed. 1. The war on drugs is like any war.
(2. Wars are only won by shooting people.)
C. We will only win the war on drugs if we shoot drug dealers on sight.
Since we should only ever use violence when we have a clear and compelling reason to do so, Syed bears the burden of proof here because he is the one advocating violence.
Both are making direct arguments.
Carli. Analogy Argument Syed. Analogy Argument
Analog: dealing with the drug problem Conclusion Thingy: dealing with the drug problem (the "drug war")
Premise Thingy: dealing with overeating Premise Thingy: an actual war
Property: should not be prosecuted with unlimited violence. Property: should be prosecuted with unlimited violence.
Carli. Analogy between overeating and taking illegal drugs.
Important similarities: as Carli says, both are matters of addiction and behavior control. Neither intrinsically involves shooting at other people.
Important differences: overeating is always unhealthy, but illegal drug use is not always unhealthy in itself. 35 percent of the American people are obese, but only 6 percent of Americans even use illegal drugs.
Syed. Analogy between making war on America and taking illegal drugs.
Important similarities: none that I can see.
Important differences: people making war on America actively try to destroy American lives and property. People who take drugs don't necessarily destroy anything.
Carli gives a reasonable argument, given the clear similarities between overeating and drug use. Syed seems to think that use of the slogan "war on drugs" means that there is an actual war going on. The problem with this is that it's not clear whether the war on drugs is a real war or a war in name only. After all, we had a "war on poverty," and that didn't require us to shoot anybody. So this argument at least begs the question of whether the drug war is a case of us being attacked by enemies who intend to conquer or dominate us, and who cannot be handled by the normal operations of the police forces. In a real war, we generally encounter the enemy in the form of soldiers who shoot at us or at least try to force us to work for them or give them our stuff. Generally, we have to shoot these guys in order to get them to stop. In the drug war, we generally encounter the "enemy" in the form of people who try to sell us things, or give us things in the hope that we will become hooked and have to buy them later. So if this analogy is good, I will not be able to avoid Jehovah's Witnesses until I start shooting them. Certainly, there are no similarities between the drug war and a real war. Furthermore, the fact that American soldiers shoot people during a real war doesn't mean that such shooting is justified! Syed actually commits three fallacies here. He equivocates on the word "war," he begs the question of whether the shooting in an actual war is justified, and he draws a false analogy between the war on drugs and a real war.
34. Catalina. 1. God already knows how everything is going to come out.
(2. Life is boring if you already know how everything is going to come out.)
C. God's life is boring.
Jaiden. 1. God knowing who will repent is like you knowing how a coin toss will come out.
(2. You cannot predict how a coin toss will come out.)
(3. If there is something god cannot predict, then god will not necessarily be bored.)
(C. God's life is not necessarily boring.)
Catalina bears the burden of proof because he is ascribing a property to God. Jaiden is merely defending the null hypothesis that God's life isn't necessarily boring or non boring.
Both are making direct arguments.
Catalina. Argument Jaiden. Analogy argument
Cites lack of interesting events. Conclusion Thingy: God knowing how repentance will turn out.
Based on perfect predictability Premise Thingy: Someone knowing how a coin toss will come out.
Catalina gives a fairly reasonable argument. Lots of things (like movies and sporting events) would be boring if we knew every little detail before it happened. On the other hand, I don't know if that covers everything. Would our friends amuse us if we knew exactly what they were going to do ahead of time? And maybe God has a high tolerance for predictability. Many TV shows are excruciatingly predictable, and plenty of people watch them. Jaiden's argument relies on a supposed similarity between predicting who will repent and predicting how a coin toss will come out. Actually, I just realized that I misinterpreted Jaiden's argument. I've been talking about it as though it says that god knowing about repentance is like you knowing about a coin toss, but that's not what she said. She said "for him, it's just like tossing a coin," which means that the analogy is really between God predicting repentance and God calling a coin toss. But, if God exists and is omniscient, then he always knows how a coin toss is going to come out! So if that's the analogy, it proves that God will know who will repent and who will not, and Jaiden's argument fails. So Jaiden's argument will be stronger if we take it to rest on a comparison between God calling repentance and you calling a coin toss. Here, the argument is stronger because you, (unless you're God, or some other supernatural being), cannot reliably predict how a coin toss will come out. Furthermore, there is a significant similarity between the two cases in that the outcome of the coin toss is out of your control and, because of free will, the outcome of repentance is out of God's control. However, there is a fatal difference. Humans are not omniscient. They don't know how coin tosses will turn out because they can't see the future. God is supposed to be omniscient. If he or she is omniscient, then he or she can see into the future, and will see how a coin toss will turn out. So even if a repentance decision is like a coin toss, in that God cannot control how it turns out, his or her ability to know everything means that he or she can know how it's going to turn out. The problem with this analogy is that while repentance for God might be analogous to a coin toss for God, God's purported omniscience means that it cannot be analogous to a coin toss for a human. God calling repentance is unlike you calling a coin toss precisely because God is omniscient and you're not. Since omniscience is about predictability, and predictability is precisely what is in question here, Jaiden's argument is a false analogy, so it fails. Big-time.
35. Clifton. 1. Control over one's own body is a basic human right, and that includes reproduction.
2. Control over one's own body includes reproduction.
C. The state does not have the right to control who has children.
Annette. 1. The state has the right to decide who may or may not drive a car.
(2. Driving a car is like having children.)
C. The state does have the right to control who has children.
Clifton is basically saying that the state should leave people alone when it comes to reproduction, while Annette is saying that the state has the right to interfere. Since state interference in people's lives is never allowable without a clear justification, Annette has the burden of proof.
Both are making direct arguments.
Clifton: Argument Annette: Analogy Argument.
Based on control of one's own body. Conclusion Thingy: state control over who has and who doesn't have children.
Premise Thingy: state control over who drives and who doesn't.
Property: state has the right to do it.
Clifton's argument is based on the human right to control what is done with one's body. Reproduction is done with one's body, so it seems to follow that there is a human right to control one's own reproduction, which means that the state doesn't have a right to interfere with one's reproduction. Annette's argument is based on a purported similarity between being allowed to drive a car and being allowed to reproduce. The crucial similarity here is that some people can be identified as very likely to be bad parents just as some people can be identified as very likely to be bad driv ers. The state has a duty to keep bad drivers off the road because bad drivers are a serious, and often deadly threat to other innocent people. If a risk was the only consideration, it would follow that the state has a duty to keep bad parents from reproducing because bad parents are a serious, and often deadly threat to other innocent people, to wit, their children. Indeed, such considerations would imply that the state has more duty to regulate parenting, because most people threatened by bad drivers are drivers themselves, and have some ability to avoid the effect of the bad driving. Children have no ability to avoid the effects of bad parenting.
[Now, if you said that Annette's argument was stronger because of the compelling state interest in preventing harm to children, I would mark that right. If you said that Clifton's argument was stronger because control of one's body is a fundamental right that overrides the state's duty to prevent harm to children, I would mark that right. And if you said that you couldn't tell which argument was stronger because you couldn't decide whether or not individual rights were more important than state duties, I would mark that right also. In fact, any answer that was based on the logical structure of both arguments would be right The important thing here is identifying and clearly stating the logical elements of the issue. Since neither side commits a clear fallacy, and (in my view) it is actually difficult to decide who is right, it is actually possible to do everything you really need to do for this exercise without coming to any particular conclusion. Remember the class is more about understanding and clearly explicating the logical structures of issues than it is about coming to conclusions. When the arguments genuinely add up to logical uncertainty, the most rational thing you can do is say that you are uncertain, and explain why.]
36. Donavan. 1. Forbes Magazine and the Wall Street Journal say an enormous tax break for the rich is a good idea.
C. Giving an enormous tax break to the rich is a good idea.
Clifford. 1. Refunding taxes to the rich is like returning stolen money to robbers.
(2. Giving recovered stolen money back to the people who stole it is not a good idea.)
C. Giving a tax break to the rich is not a good idea.
Donavan bears the burden of proof because, in the absence of an argument to the contrary, our most reasonable conclusion is that everyone is paying the right amount of taxes. If someone thinks that there is something wrong with the current distribution of taxes, it's up to him to prove it. Donavan is such a person, so he has the burden of proof.
Both are making direct arguments.
Donavan. Authority Argument.
Authorities: Forbes Magazine and Wall Street Journal.
Qualifications: popular publications.
Clifford. Analogy Argument
Conclusion Thingy: giving yet another tax break to the rich.
Premise Thingy: recovering stolen money and giving some of it back to the robbers.
Property: not a good idea.
Since Donavan bears the burden of proof, we would assume that his conclusion is wrong if just it turned out that neither argument here was any good. The playing field is tilted against someone who bears the burden of proof since he only wins if his argument is good and the other argument is bad. If both arguments are equally good, or equally bad, the arguer with the burden of proof loses. As an authority argument, Donavan's argument relies on his sources being competent and independent experts. Unfortunately, while they are successful publications, neither the Wall Street Journal nor Forbes Magazine are scientific journals, so they don't count as experts in economics. Furthermore they are owned by rich people, controlled by rich people, and depend on the patronage of rich people for their existence. That is a powerful incentive to say whatever they think will please rich people, so they cannot be assumed to be independent. Clifford's argument relies on the analogy between rich people and robbers. The strength or weakness of this analogy depends on how these rich people got their money. If the vast majority of rich people got their money under conditions of fair competition, then the analogy does not work. However, if the vast majority of rich people got their money from sweetheart deals, favors from government, monopolistic practices, price-fixing, deceptive advertising, corporate welfare and so on, then this analogy works very well. While there is considerable evidence that a large proportion of our rich people got rich through dishonest means, this conclusion is extremely controversial, so the analogy is likewise controversial. Clifford cannot just assume that rich people are like robbers, so his argument is weak also. Given that Donavan bears the burden of proof, the fact that both arguments fail means that the most reasonable conclusion is that the tax break is not a good idea.
37. Grady. 1. Grady spent six months researching the Baha'i faith.
2. The Baha'i faith preaches kindness, tolerance and nonviolent social action.
3. Grady observed Baha'i congregations all over the country.
4. All were composed of good people doing good work and getting along well with others.
(5. Our society would be a good society if it was composed of good people doing good work and getting along well with others.)
C. It would be good if our society was a Baha'i society.
Kristine. 1. Promoting a Baha'i society is like promoting Communism.
2. Promoting Communism sounds good until it's achieved, but then it turns into hell on earth.
(3. It's not good if a society turns into hell on earth. Unless you're SATAN!)
C. It would not be good if our society was a Baha'i society.
Generally speaking, it is well-established that societies where people are nice to each other are good societies, and that creating a good society is usually best accomplished by getting people to be nice to each other. The idea that promoting a good set of values will cause hell on earth is radically counterintuitive and so Kristine bears a heavy burden of proof here.
Both are making direct arguments.
Evaluation: Although it might be a bit awkward, I'm going to interpret Grady's argument as an analogy. If this turns out to make the basic logic of the argument clear, then it's a good idea. If it doesn't help, then it's not a good idea.
Grady. Analogy Argument. Kristine. Analogy Argument.
Conclusion Thingy: a Baha'i America. Conclusion Thingy: a Baha'i America.
Premise Thingy: an individual Baha'i congregation. Premise Thingy: a Communist society.
Property: a good thing. Property: hell on earth.
It might be important to remember that we're not talking just about having a Baha'i society. We're also talking about promoting a Baha'i society. Grady says it would be great to have a Baha'i society, but he can't just wave a magic wand and turn us into a Baha'i society. Turning America into a Baha'i society would be a long, difficult process, even if it can be done at all. So Grady's goal is probably impractical, but that, of course, does not mean it is a bad goal. Since no one has said anything bad about the Baha'i or their values, it seems clear that a Baha'i society would be a good place for Baha'i and non-Baha'i alike. Kristine claims that a Baha'i society would be a bad society based on a supposed analogy with a Communist society. However, the only relevant similarity between people who promote Baha'i and people who promote Communism is that they each promote systems with ostensibly good values. This makes promoting Communism equally similar to promoting libertarianism, promoting Christianity and promoting democracy. So if Kristine has proved that a Baha'i society would be hell on earth, she has proved the same thing about libertarianism, Christianity, democracy and any other belief system with ostensibly good values. If you reject the idea that libertarian societies, Christian societies and democracies are all hells on earth, then you should reject the idea that Kristine's argument proves that a Baha'i society would be hell on earth. Kristine's argument has another problem however. The claim that a Communist society is hell on earth is controversial, to say the least. It is certainly not something that Kristine can assume, so the fact that she does assume it means that her argument also begs the question. Therefore, if this discussion was all we had to go on, it would be clear that Grady is probably right, and Kristine is certainly wrong.
38. Dimitri. 1. Dogpatch community college has a lot of incoming freshmen who don't know how to write college-level papers.
(2. Inability to write college-level papers can really mess up a student's education.)
C. Dogpatch community college should have a required freshman writing course.
Maura. 1. Harvard University doesn't require a freshman writing course.
(2. Harvard University should not require a freshman writing course.)
(3. Dogpatch community college is very similar to Harvard University.)
C. Dogpatch community college should not require a freshman writing course.
Dimitri bears the burden of proof because he is arguing for action whereas Maura is merely arguing for inaction.
Both give direct arguments
Dimitri. Argument Maura. Analogy Argument.
Cites need for course. Conclusion Thingy: Dogpatch community college.
Premise Thingy: Harvard University.
Property: lack of need for freshman writing course.
The aptness of Maura's analogy depends on whether Dogpatch is relevantly similar to Harvard. Size, age, location and prestige are not necessarily relevant. However, there is enough variation among colleges that we should be su spicious of any comparison. Furthermore, Harvard can probably be much more selective than Dogpatch, and thus can probably rely on its students coming in as accomplished writers whereas Dogpatch has no such assurance, so Maura commits false analogy. Since Dimitri gives a concrete reason for requiring the course, and Maura doesn't address that reason, his argument is stronger, and we should here conclude that Dogpatch should have the course.
Clincher: Maura's argument fails because she fails to consider the potential differences between Dogpatch and Harvard. Community colleges like Dogpatch cannot screen their applicants the way prestigious universities like Harvard can, so if Harvard lacks a freshman writing course, it could easily be because they simply do not accept anyone who is not proficient in college level writing. Dogpatch does not have this option, and so very well could have a large infux of students who need help to reach college-level proficiency in writing.
39. The first thing to notice that Augustus has not produced evidence of any correlation between cellphone use and cancer. Instead, his argument is based on what happens in an only vaguely similar situation. This is not a correlation based argument and so, although it is intended to support a causal claim, it is not really a causal argument. Augustus's argument is based on the solidly proven link between one kind of radiation and cancer, but he does not discuss the type of radiation involved in cellphones. This is important because the damaging kind of radiation is ionizing radiation, and cell phones don't give off ionizing radiation. (Also notice that Fred's argument is based on a demonstrable lack of evidence, and we will discuss this kind of argument later on.)
For more practice, you can download and do the practice/makeup exercises. (Make sure the document margins are set to 0.5 inches or narrower.)
Finally, if there's anything at all in this reading that you don't think you fully understand, please follow an associated hyperlink to get more information on that particular topic.
Copyright © 2019 by Martin C. Young