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Analyzing Arguments and Evidence

Black, white, and shades of gray

Real world situations always have an effectively infinite number of details. No understanding we have of them will ever be entirely complete. We should always be careful when any issue seems to line up as having two sides which are extreme opposites - right and wrong, good and bad, for us or against us. Almost every situation will have details that we don't know or can't account for. (more)

The dangers of hidden assumptions

Often when we believe something false, that belief is an assumption that we don't even realize we're making. From these we might draw other false conclusions without ever considering whether our original assumption was false. (more)

Cultural assumptions that seem natural

A few hundred years ago it was "obvious" that women were unqualified to vote or hold office. It wasn't an issue that was debated or even questioned. It just seemed natural that men should rule. It was also obvious that educated people should know Latin and a dark suntan was an indication of good health. Some of the hardest assumptions to detect are the ones that are so widely held that they seem natural. We assume these "truths" have been proven over the years. This is not a safe assumption. What false cultural assumptions are we making today? (more)

Testability: is there a way to determine whether a statement is true or false?

Sometimes statements are made that would be very hard to disprove even if they were false. In some cases the statement is so vague that almost anything could happen without our feeling the statement was disproved. Other statements would require impossible effort to prove or disprove. Such statements cannot be considered reliable, since, even if they were wrong, nobody could show it. (more)

Suggestion and perception

Sometimes our conclusions can be wrong even though we seem to have based them on our own observations.  If people have told us a certain food tastes good or certain music sounds good or certain medicine is effective, our own experiences of these things can be influenced by the expectations we have formed, yet we are likely to think our judgment is unbiased.  By the same token, other people who are completely sincere may tell us things they think they have learned by experience when in fact their opinions derive from what other people told them. (more)

Burden of proof

In criminal cases the burden of proof is on the prosecution because we do not want to mistakenly punish people who are innocent. But proving things is hard. As a result, we often find that people debating an issue say the burden of proof is on their opponent. They want the easy job and they want their opponent to have the hard job. If a believer in God debates an atheist, it is likely that the believer will assert the atheist must prove God doesn't exist and the atheist will claim it is the duty of the believer to prove that God does exist. Each wants to claim victory if their opponent cannot accomplish an almost impossible task. Realistically, the burden of proof is on anyone who claims to have certain knowledge one way or the other. The person who claims an issue is in doubt doesn't have to prove anything.

Decisions and alternatives

To evaluate a course of action, we have to consider what would happen if the action were not taken. Should we close nuclear power plants? It depends on what happens instead. Are they replaced by less polluting forms of energy or more polluting forms of energy, or would people just use less energy? We cannot evaluate a decision without evaluating the alternatives. (more)

A shift of perspective can clarify a problem

When it was recognized that the earth goes around the sun instead of vice-versa, the paths of the planets became much more logical. If we look at the flow of goods and services instead of the flow of money, some economic issues become clearer. (more)

Formal Logic and Everyday Reasoning

Formal (mathematical) logic is a system for deduction that is always correct when the hypotheses and axioms are correct. Effectively, all mathematics has this property. If Socrates is a man, and all men are mortal, then we can safely conclude that Socrates is mortal. The trouble with this is that outside of mathematics and physics, it is hard to find generalizations like "all men are mortal" that we can count on, so most practical deductions have some chance for error. In formal logic, statements are either true or false, while in real life even the most truthful statements are rarely 100% true or 100% reliable. (more)


Intuition, for the purposes of this discussion, is the pattern recognition ability of the human mind. Recognizing a familiar face, or noticing that the car engine doesn't sound right, or thinking that a person in a trench coat might be a spy, will all be considered intuition. This type of intuition is the mainstay of most human thinking and action. It even applies to single steps of logic - like recognizing that an equation can be simplified by adding a certain quantity to both sides. Intuition is fast and automatic, but it has weaknesses, like being subject to biases and stereotypes. Much of our concern with responsible thinking is ultimately aimed at avoiding intuition errors. (more)

Note that the word "intuition" as it is used here is not meant to imply any supernatural ability to determine something that cannot be detected by our ordinary senses.

Combining reasoning and intuition

For everyday purposes, using logic means we do some deductions based on logical or mathematical rules. It is easy to make mistakes, since sometimes these rules are "unintuitive". We should always check our logic by using intuition. If Tom has 3 apples and Mary has 4 apples, and we deduce that together they have 34 apples, we should stop and wonder if this is reasonable. When logic and intuition come to different conclusions, we should think about both until we find the logical mistake or conclude our intuition was faulty. (more)

Distorted definitions

A great many disagreements center on how words are words are defined.  Sometimes we spend a lot of effort debating what some word really means, when we should be concentrating on what the world is really like.  After all, unless we are talking about writing or speaking, the world is the same no matter what words we use to describe it.

Since words have multiple definitions, some of which might differ in subtle but important ways, an argument that appears true may actually be false because a statement that is true using one definition may be false using the other.  (more)

Avoiding bias

If we are assigning a grade to a student, we want it to be based on her actual knowledge, not whether we like her or whether she has superficial characteristics which remind us of good or bad students. If we are judging the flavor of a wine, we want to judge only on the flavor, not on the knowledge that it was expensive to produce or that other experts consider it to be extremely good. We don't want to be influenced by propaganda that someone has contrived to deliberately sway our opinion. Typically bias is avoided by objective tests (such as multiple choice tests), in which there is no opinion involved in doing the grading, and by blind tests, where the information that might bias us is kept hidden, for example by tasting wine without seeing the bottle or its label. (more)


When we want to defend an opinion or action that someone disagrees with, we very often don't give the actual reason for what we said or did, but use some other argument that we think will be harder for the other person to challenge. Often we ourselves don't realize that this is not our real motive. We should watch for rationalizations by both ourselves and others, since they interfere with our getting to the root of problems and solving them. (more)


Belief in a superstition may start either by being passed on from someone else or by a coincidence we think might actually be a causal relationship. Typically the prediction, such as good luck or bad luck, is very vague. We might expect good luck if we find a four-leaf clover, but we don't know what kind of luck, how much luck, or when it will occur. As a result, we can usually find some sort of good luck that we can attribute to the clover. If not, we might assume that finding it prevented bad luck, or worse luck than we already had. As a result we can feel like we are accumulating positive evidence for the belief even though the belief is nonsense.  False beliefs like this can be passed from generation to generation because people in each generation feel like they have validated it from their own experience.

The same can occur with situations that would not involve any supernatural effect. We might, for example, decide that a certain food makes us mentally sharper even though it doesn't. We might call such beliefs "stitions" - superstitions without the supernatural. (more)

Be careful of believing aspects of fictional stories

We know fictional stories are not true, but we may assume aspects of them are realistic. A character may quote a "fact" which we think was taken from real life, but there is no guarantee that in fiction this fact is true. We may see aspects of police work that we assume are realistic even if they are not. I suspect that people overestimate the importance of guns for self-defense because gun battles take place so frequently in fictional stories. (more)

Measure where possible, and be aware of the probable error

Since decisions are between alternatives, we normally want to pick the alternative that is "best" in some respect. This implies that we don't just want to know whether a course of action is "good" or "bad", but HOW good or bad, because we may be deciding between two good possibilities or two bad ones. Most of the time this "magnitude" is determined intuitively, and in some cases this may be extremely unreliable. If we have a way to do an objective measure of how good something is, even a very inaccurate measure may be much better than our intuition. Engineers and physicists, who routinely deal with measured quantities, usually include an estimate of the inaccuracy of their measurements: instead of "6" as a value, they may "6 plus or minus 2" or "6 plus or minus .01". Such judgments about accuracy are just as important in human affairs, but are rarely stated specifically. (more)

Self-defeating measurements

It is often impossible, or at least impractical, to measure the quantity we actually care about, like the actual value of an employee's work.  Instead, some relatively easy measurement is made that seems to be closely related to the relevant trait.  This can backfire.

For example, a manager can't easily measure how much useful programming work a computer programmer has done, but she can easily measure the number of lines the programmer has written. Normally the two things are fairly well related, but if the programmer knows the number of lines is being used as the basis for his evaluation, he can easily find ways of adding nearly useless lines to make his performance look better. People being evaluated will often try to make the quantity being measured look good at the expense of other factors that are not measured but may be more important.

Most of the time high quality goods cost more than low quality goods. Sometimes we may choose to buy a more expensive item because we assume it is better quality.  In effect, we are measuring its quality by its price. Merchants know this and can easily raise prices on lower quality goods to take advantage of that assumption. Then the buyer not only gets lower quality, but he pays more.

Other measurements are even more superficial. We may assume that real estate agent we are about to hire is good because she dresses well or drives an expensive car. Many people have learned that such superficial traits help them succeed, but that doesn't mean they will do the best work on the job you need done.

Money as a measure of value

We often think of money as evil, because people's greed is often responsible for evil we see in the world. Money itself is quite neutral - it just sits there and makes no decisions for good or ill. Realistically, money is very useful - it allows people to trade goods and services much more easily than if they were forced to barter, and generally we spend it in order to make our lives happier. 

While many important things, like friendship, cannot be exchanged for money, there is a huge variety of goods and services that can, so money is often the best measure of "value" we have available. We cannot compare apples and oranges directly, but comparing the cost of apples and oranges does let us compare how much people value them. 

Of course when issues involve important factors that can't be bought, we must recognize that alternatives with financial gains are not necessarily better.

Intuition is poor for very large or small quantities

Former Wisconsin senator William Proxmire used to choose a "golden fleece of the month award" to illustrate waste in government spending. One month he talked about the B-1 Bomber, and mentioned a figure of about 5 billion dollars. The next month he chose a research project concerning monkeys clenching their jaws. The cost  was about 180 thousand dollars. As far as I could tell, people were about as upset about one as they were about the other. Both numbers are very large compared to what we deal with on an everyday basis, so our intuition is poor about the magnitude of such numbers. One way to improve our perception of large numbers is to translate them to a personal scale. Since there are about a quarter billion people in the United States, a 5 billion dollar "waste" costs about $20 for every person in the country. A 180 thousand dollar waste costs about one cent for every 14 people. (more)

Counting unequal things

A friend mine recently pointed out that 80% of businesses in the United States are small businesses. I asked if that meant that 80% of people work for small businesses. He started to say yes and then realized what was going on. If a small town had one big business that employed 1,000 people, and 4 small businesses that employed 25 people each, then 80 percent of the businesses would be small, but only 9% (100 out of 1100) of the people would work for the small businesses.

It doesn't usually make sense to count things that are significantly different in size. In the small business example we got the 80% figure by counting businesses that differed greatly in size. Usually when we count things, we're assuming a larger number implies greater importance. But if the sizes of things being counted varies greatly we have no idea how important the total is. There's not much point in counting the number of buildings in an area if an outhouse and a huge hotel each add one to the total. (more)

Don't count data twice

The newscaster might say "Prices are up 3% this month. Worse news - the price of gasoline is up 6%." Since the price of gasoline was reflected in the 3% figure, we have already taken the unpleasantness of this news into account. The fact that this particular product increased by more than the average necessarily implies that other products have increased by less than the average, so the additional news is not necessarily bad.

Zero-sum games

In most games people play for entertainment, from chess to football to monopoly, there is only one winner, so anything that is good for one player is automatically bad (on the average) for the others. These are called "zero sum games" because the sum of all the "good news", totaled over all the players, is zero. This is very clear in gambling, where any money somebody wins must be lost by somebody else. Life in general is not like this - if I give a farmer $5 for a basket of corn, we both come out ahead: I wanted the corn more than the money because I can't eat money, and the farmer, who has plenty of corn, would rather have the money. It is important to differentiate between the situations in life where overall value is increased, and those where value is increased for one person only because it was decreased for others. (more)

Avoiding being fooled by statistics

Make sure you know what the statistic really means, and how it was obtained. If not, don't assume the speaker has a good point. Try to figure out if there is some way the statistic could be true without the thing being implied being true. What does it mean if "9 out of 10 Volvos built in the last 11 years are still on the road?" This is a lot different from saying "9 out of 10 Volvos built 11 years ago are still on the road." Think of what other statistics might have been given relevant to the issue and question why they were not. (more)

Unfair Sampling

Statistics generally involve selecting individual cases from a large group of cases and trying to deduce something about the large group from the small group being examined. For example if a polling organization asks 1000 Americans whether they like a TV show, and 300 of them do, we might assume that 30% of all Americans liked that show. This would be a reasonable assumption if they randomly chose the 1000 people from around the country, but it would not be a safe assumption if they did the poll at a Star Trek convention. (more)


Typically this occurs when someone tries to make news appear much more important than it actually is. It is common for a single incident, which is very dramatic on a personal level, to be publicized nationwide. We are likely to react emotionally because we are as familiar with the details as we might be if this happened to somebody we know, but in reality it tells us little about the state of the world, since it is only a single instance in a national population of more than a quarter billion. (to be expanded)

Emotional manipulation

People who want us to do things will try to get us angry or afraid or feeling sorry for somebody. This distorts our perceptions and makes it difficult to make a fair decision about what is true. (to be expanded)

Seek out the opposing view

People who have some cause to promote, whether for profit or some public issue, can often come up with some very convincing arguments. Sometimes they will tell us the arguments used by their opponents and why they are wrong. We should never make up our minds unless we have heard the opponents' arguments directly, since those promoting the cause aren't likely to represent the other side fairly. We should seek out the best argument each side has to offer, and then decide if one side's case is strong enough for us to form a firm opinion.

This principle also applies on an individual level when someone passes along gossip or relates events that cast others in a negative light.  Often there are surprising differences in the story when heard from the other person's point of view. (to be expanded)

Free Inquiry

In the United States we have "freedom of speech". The idea is that if all sides of an issue are heard, the truth will have an opportunity to be heard. When people become very convinced of a particular belief, they often want to suppress any discussion that calls that belief into question. Unfortunately people who do this are wrong about their position a high percentage of the time, and so the true viewpoint is often suppressed by censorship. (more)

Trying principles on other issues

When an argument involves issues about which we might make assumptions or have biases, we can sometimes try the same argument on a different subject in order to see if it really is valid. (to be expanded)


People trying to manipulate us often try to associate a particular image with a product or person that influences our opinion without suggesting any particular false fact.  For example a politician might distribute pictures of himself enjoying happy times with his family to create the image of being a family man, even though he spends 90% of his time out of town. (to be expanded)

False memory

The fact that someone remembers something does not imply it happened. It is easy for people two confuse things that happened at one time with things that happened at another, or even to visualize something that someone suggests might have happened and confuse that with an actual memory of it happening.  As a result it is common for perfectly intelligent people to "remember" events or details that are false or inaccurate. We should particularly be suspicious of things remembered during hypnosis, since a hypnotized subject is very suggestible. (to be expanded)

Vague claims

When people make vague predictions or claims, they might impress us if their statements turn out to be true. Vagueness, however, allows for many ways in which the statement could be true, and often the confirmation is something that we would not have thought of when we heard the claim. If we allow this much latitude in what we would call a successful outcome, success turns out to be very easy to achieve (more).

Faulty Logic

Often people hear an argument that sounds logical, but they don't really analyze it according to logical rules. Sometimes we have to stop and think very carefully to see if someone's conclusions really follow from their statements. (more)


Open-mindedness is a virtue if it implies a willingness to listen to views that are different from our own. It should not mean believing those views without sufficient evidence. (to be expanded)

Easily checked facts that aren't checked

If we are told there are before and after pictures on record at a certain place of a person who was miraculously healed, we might think of that as irrefutable proof of the miracle, but we should maintain some skepticism if we have not seen the pictures. Sometimes when things like this are checked either the "before" or the "after" picture happens to be lost. Few people follow up on such statements, and even if somebody has shown a statement like this to be untrue, we probably wouldn't hear about it. (to be expanded)

Anecdotal Evidence

Scientists often dismiss reports of remarkable events, saying it is "anecdotal evidence". The problem with anecdotal evidence is that it cannot be checked or reproduced. Stories of personal experiences can turn out to be false or misleading for a variety of reasons. (to be expanded)


Often someone makes a statement that is essentially true, but we notice that there is some special case that is an exception or some interpretation of the words that does not apply. When there is a genuine problem with misunderstanding or the exception is an important one, pointing it out may be valuable. Otherwise nitpicking gets in the way of addressing the real issues, tends to create hostility, and is unlikely to win people over to our position.

Occam's Razor

Named for William of Occam, a fourteenth century English philosopher, it says that if several explanations fit the facts equally well, the simplest is most likely to be true. This makes sense since the more elements that are required for an explanation, the greater the chances that one of them is wrong. (to be expanded)

Love of mystery

It seems that people are sometimes intrigued by mystery and actually prefer an experience or event to be mysterious than to have it be explained in some straightforward way. This may really be a hope for some very exciting explanation, such as that the disk was an alien spaceship rather than a Frisbee. Some people like the idea that human emotions are mysterious and cannot be understood. Clearly if we're searching for truth, we want to solve mysteries, not delight in having them remain unsolved. We can't achieve understanding of an issue if we don't really want to.

Beware of shortcuts to the truth

If we think we have some simple rule that we can count on to tell if something is true, it is probably not valid. We cannot, for example, assume that what somebody says is true because they sound sincere, or have good motives, or are speaking against what would normally be their own interest. At best such factors might improve the odds only slightly. (to be expanded)