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Lecture Notes Unit 3


  1. Statements, Beliefs and Truth
  2. Knowledge and Justification
  3. Subjectivity and Relativity
  4. Facts and Opinions
  5. Evidence
  6. Reasoning about Causation and Correlation
  7. Reasoning with Statistics: Potential Confusions and Tricks
  8. Hypothetical Reasoning and Science
  9. Open Mindedness
  10. Creativity
  11. Postscript: Russell’s 10 Commandments

Or jump to the unit 1 lecture notes or unit 2 lecture notes.


A. Statements, Beliefs and Truth

Recall these definitions from our first unit.

A statement is a declarative sentence, or part of a sentence, that is either true or false.

The truth value of a statement is its status as true or false.

What is truth? How should it be defined? Philosophers disagree about this, and even about whether or not truth can be defined.

To these, let us add:

Someone makes an assertion when they put forth a statement as true.

Suppose I say:

“Ben Carson believes that the Earth is less than 10,000 years old.”

Here, the statement “the Earth is less than 10,000 years old” is part of what I uttered, but I did not assert it. Perhaps Carson would, but I did not. The whole sentence, however, is something I did assert. I might also assert:

“Ben Carson is not qualified to be HUD Secretary.”

Although truth is hard to define, the following observation seems to give a key insight into truth:


To assert that a statement is true is the same as asserting that statement.

The following all seem to say the same thing.

A belief is a cognitive/psychological attitude to the effect that something is true.

Beliefs are sort of the “inner version” of assertion. Of course, not all assertions actually are true, even though they are presented as such, nor are all beliefs.

If someone does not believe a given statement, this does not mean that they believe the opposite: they may withhold belief, or simply not engage with the issue at all.


Which is more fundamental: the kind of truth we ascribe to beliefs, or the kind we ascribe to statements?

However we answer the question above, it seems clear that there is a close connection between belief and assertion:

  1. Just as belief is a “truth-attitude”, assertion involves making a “truth-claim”.
  2. Unless you have reason to believe that someone is lying, acting, playing some kind of game, you are entitled to think they believe a statement that they assert.
  3. If you have reason to think someone believes something, you should expect that they would assert the statement corresponding to their belief in ordinary circumstances.

B. Knowledge and Justification

Epistemology is the philosophical study of knowledge and the justification of beliefs and related cognitive states.

How would you define knowledge? One popular answer goes roughly like this:

(The tripartite analysis of knowledge*)
A person knows something just in case the following three conditions are met:
(1) The person believes that something.
(2) The something is true.
(3) The person is justified in believing that it is true (in the right way).


It is pretty clear why we need the first two conditions. If someone doesn’t even believe something, they do not know it. Also, you cannot know what is not the case.

But it is also clear that this is not enough: the Venn diagram with the intersection of just those two circles is too simple.

It is possible to believe something true for bad reasons. In that case, you don’t know it. You just got lucky.

Sean believes that all cities whose names begin with ‘P’ are in Pennsylvania. This is his only reason for believing that Pittsburgh is in Pennsylvania. That belief (the one about Pittsburgh) is true, but it is not knowledge.


Here is a taste of some philosophical problems relating to justification and knowledge.

What is justification? How can it be defined? (This too is philosophically debated.)

A lot of the philosophical tradition focuses on these two sources as among the kinds of things that can justify beliefs:

Are these the only kinds of justification?

Foundationalism is the thesis that a belief can only be justified by other beliefs if it can be traced back through a chain of beliefs, similarly so justified, until one comes to a set of foundational beliefs, which are either self-justified or least justified without appeal to other beliefs.

Coherentism is the thesis that a belief is justified when it is a part of a network of mutually supporting beliefs which cohere well with one-another, i.e., not incompatible or inconsistent.

One problem with foundationalism is that it is unclear whether or not any beliefs can be justified directly or immediately. Our senses can be wrong, for example.

One problem with coherentism is it seems that one could have a coherent set or network of beliefs, where many are false.

Is it possible for a justified belief to be false?

The answer would seem to be yes.

elect I believed Clinton would win the election, because that’s what nearly all the polls predicted. I did not have knowledge, because my belief was false, but I still think I was justified in believing it.


But if there is a gap between justification and truth, then it would appear that one could have a justified lucky true belief as well, which poses a problem for the tripartite analysis of knowledge. This is called the “Gettier problem”, after UMass Professor Emeritus Edmund Gettier.

Perhaps the problem could be solved by being more specific about the “in the right way” parenthetical I added to the tripartite analysis above; but it’s hard to know how to be more specific.

sheep Suppose you a driving past a farm. You see in the distance what looks like a sheep. You conclude, and come to believe, that there are sheep on that farm. What you saw, however, was a dog dressed up like a sheep. There are, however, some sheep on the farm, but they’re behind a barn and you can’t see them. So (1) you believe there are sheep on the farm, (2) that belief is true, and (3) you seem to have some justification for believing it, but is your belief knowledge?

C. Subjectivity and Relativity


1. The True-for-Me Phenomenon

Consider claims such as the following:

We discussed statements like these under the category of “argument stoppers” in our first unit: but the point there was merely that these do not constitute refutations of any one particular argument.

What should we make of these kinds of claims? They seem to be more common among college-age students. Instructors sometimes refer to this, perhaps unfairly, as naïve relativism or the true-for-me phenomenon.

I think the issue is more complicated than it might seem at first.

2. Relativity and Indexical Statements

Part of the problem is that people do not always mean the same things by words like “subjective” or “relative”. However, here is a definition of “relative” used by many philosophers:

A property or trait is relative if we cannot say, simply and absolutely, what it applies to without specifying some additional parameter, or filling in another “blank”.

1) Height is relative. Is Yao Ming tall?

Yao Ming is tall for a human / for a basketball player. (true)
Yao Ming is tall for a skyscraper. (false)

2) Direction is relative. Is Sunderland North?

Sunderland is North of Amherst. (true)
Sunderland is North of Greenfield. (false)

3) Tastes are relative. Do Brussels sprouts taste good?

Brussels sprouts taste good to Allyson. (true)
Brussels sprouts taste good to Kevin. (false)

A statement is implicitly relative if it ascribes a relative property or trait to something or someone but without explicitly mentioning the additional parameter or “filling in the missing blank”, leaving it to the audience to determine it from context.

A statement is implicitly speaker-relative if it is implicitly relative, and the missing parameter involves the person speaking.

1) “Yao Ming is tall.” (Implicitly relative)
(In most contexts, this will be interpreted to mean that he is tall for an adult male human.)

2) “Sunderland is North." (Implicitly relative; usually speaker-relative)
(In most contexts, this will be interpreted to mean: Sunderland is North of where the speaker is.

3) “Brussels sprouts taste good.” (Implicitly relative; usually speaker-relative)
(In most contexts, this will be interpreted to mean: Brussels sprouts taste good to the person talking.)

Another way a statement can depend on the identity of the speaker, audience, or context of utterance, comes through the use of indexicals.

An indexical is a word or phrase that is used to refer to different things in different contexts. A linguistic statement is indexical if it employs an indexical word or phrase.

“I” refers to the speaker, which of course is different for different utterances.
“Now” refers to the time at which the utterance is made.
“Here” refers to the place the utterance is made.
The same is true for demonstrative words like “this”, “that” and “there”, and other pronouns such as “you”, “he”, “it” and so on.

It is easy to understand how an indexical or implicitly speaker-relative statement could be “true for me” for me but not for you. But what about others?

It is true for me that coffee tastes good, but it is not true for Emily. (This means: it is true that coffee tastes good to me, but false that coffee tastes good to Emily.)

“I am tired now” is true for me, but perhaps not for you. (This means, if I utter “I am tired now” I am saying something true: that Kevin is tired at 12:02pm on Tuesday, November 13th, but you’d be saying something false if you uttered it instead.)

But what about, “Jupiter is larger than Earth”? Can this be true for me, and not for you?

The suggestion that truth is always relative can come across as quite strange especially when combined with the key insight about truth mentioned above. Thoughts:

These are the kinds of things that lead many thinkers to poke fun at the true-for-me phenomenon.

3. Subjectivity

One proposal about why truth might be thought to be relative, always and generally, involves subjectivity.

Here’s one definition of the notion.

Something is subjective if it is dependent upon the psychological attitudes or mental states of an individual person. It is objective if it is not subjective.


I personally find these definitions to be too obscure to be of much use. What sort of “dependence” is involved? Does it have to depend on minds in general, or does it have to differ for different minds? If the thing in question is complex, and only parts of it depend on the mind, what is it then?

Many philosophers would disagree with me, but I personally think it’s better to avoid the words “subjective” and “objective” altogether. I think they confuse issues more than they clarify them.

It seems clear, however, that belief is relative because it is subjective: different people believe different things. Indeed, the cognitive states of different people differ, because of differences in their personalities, genetics, experience, susceptibility to bias, education, and so on.

But beliefs can be subjective without their contents (i.e., what they’re about) being subjective.

So does that mean truth is relative? What about knowledge, which requires both truth and belief?

(1) It is believed by Copernicus that the Earth revolves around the Sun. (true)
(2) It is believed by Pope Urban VIII that the Earth revolves around the Sun. (false)

(3) It is true-for-Copernicus that the Earth revolves around the Sun. (?)
(4) It is true-for-Pope Urban VIII that the Earth revolves around the Sun. (?)

(5) It was known by Copernicus that the Earth revolves around the Sun. (true)
(6) It was known by Pope Urban VIII that the Earth revolves around the Sun. (false)

Perhaps a charitable understanding of (3) and (4) is that they should be interpreted to mean (1) or (2), respectively. (Or perhaps (5) and (6).)


There are no doubt ways in which belief and even knowledge can be relative, but the suggestion that all truth is relative seems extreme.

But that’s assuming it’s interpreted at face value.

A charitable interpretation of the true-for-me phenomenon: Perhaps it’s not a matter of truth at all, but of how we approach the beliefs of others, especially when they differ from our own. We should be tolerant of differences in beliefs, and keep in mind that when someone’s belief differs from ours, it’s possible that it is our own that is false. Even when it is not, it’s not always a good idea to force or try to bring about agreement. Sometimes it’s best to let different people believe different things.

So interpreted, it’s a principle of tolerance, and I cannot think of any strong objections to it.

What do you think is the most charitable interpretation of the true-for-me phenomenon?

D. Facts and Opinions

Related to this is the distinction often made between facts and opinions.

I frankly think that this distinction is kind of a mess, and runs together a number of different distinctions.

The notion of fact is highly ambiguous; it could mean:
(1) Any true statement (the statement itself);
(2) The feature of the world that makes a statement true (i.e., not the statement, but the part of reality corresponding to it);
(3) A statement or fact in sense 1 or 2 which is objective or non-relative, in some sense of those terms;
(4) A statement or fact in sense 1 or 2 which does not make a value claim or evaluation, or normative or ought-claim;
(5) A statement or fact in sense 1 or 2 which is not controversial;
(6) A statement or fact in sense 1 or 2 which is known or proven, or could be known or proven by some available method;
(7) … etc. …


My advice would be to avoid these terms unless you have a good reason to use them, and if so, make it very clear what you mean by them in that context.

Philosophers most often use “fact” in sense (2). But on that definition, comparing facts and opinions is like comparing apples and oranges. Facts are features of the world, whereas opinions are beliefs/psychological states. They can be related to one another (i.e., a fact can make an opinion true), but they’re not in any interesting way two subgroups of the same kind of things.

They are therefore not two different groups of things within the same category which need distinguishing.

Perhaps one of the other senses would do better here, but notice that we don’t seem consistent in this way. Consider:

1) It is a fact that coffee tastes good to Kevin.
(This seems like a perfectly reasonable thing to say, despite that the claim is subjective, relative and involves a value-claim. The others below seem fine as well.)

2) There is a fact of the matter as to whether or not Tyrannosaurus Rex had feathers, but there’s no way to prove it one way or another, and it remains controversial.

3) It is a fact that white vinegar repels ants better than apple juice does.

We can make similar distinctions among opinions.

The notion of opinion is ambiguous; it could mean:
(1) Any belief;
(2) A belief that is about something subjective or relative, in some sense of those terms;
(3) A statement or belief that makes a value claim or evaluation, or normative or ought-claim;
(4) A statement or belief the truth or falsity of which is controversial;
(5) A statement or belief the truth or falsity of which cannot be proven, or known by some available method;
(6) … etc. …

Again, it is very unclear that there is any consistency in how we talk. Some ways we talk about opinions only make sense under meaning (1), which does not allow a clear distinction from facts.

Consider the examples below:

It is my opinion that 2 + 2 = 4.
It was Copernicus’s opinion that the Earth revolves around the Sun.
It is my opinion that this recycling program is wasting more resources than it saves, and I can prove it!

E. Evidence

1. Overview

There are a number of ways to understand how beliefs can be justified. One way involves evidence.

Evidence is information that points to the truth of a given belief or statement.

The source of evidence is the means or method used to gather the evidence.

sight Right now, I have evidence in favor of the statement “there is a computer on the table”. The source of that evidence is visual perception: I see (what appears to be) a computer on (what appears to be) the table.

When speaking of the source of evidence, how specific should we be?

For example, for the computer, is the source …

A source of evidence is reliable to the extent it provides correct evidence more often than not.


Sources of evidence can be more or less reliable: reliability comes in degrees.

If a source of evidence is not 100% reliable, can it still be a source of knowledge?

In order to know something based on evidence, do we need to know that the source was reliable, or is it enough for it simply to be reliable?

Global skepticism is the belief that genuine knowledge is not possible for any subject matter.

2. Conflicting Evidence

A piece of evidence directly conflicts with another if it points to the opposite conclusion.

A piece of evidence indirectly conflicts with another if it points to the unreliability of the source of the other evidence.

Overriding evidence is directly conflicting evidence that is so strong that it makes it unreasonable or irrational to accept the belief the evidence it conflicts with points to on the basis of that evidence.

late My memory tells me that I mailed my credit card payment last week. My memory provides me with evidence that I in fact did. However, upon arriving home I see the envelope with the check on it still sitting on my desk, and I get a late payment e-mail from the company. These provide conflicting evidence which overrides the evidence from my memory.

Note that this doesn’t mean that my memory isn’t mostly reliable: only that it was wrong on this occasion.

Undermining evidence is indirectly conflicting evidence that is so strong that it makes it unreasonable or irrational to accept the belief the evidence it conflicts with points to on the basis of that evidence.

zodiac After reading an online headline, John comes to believe that Dick Van Dyke was the Zodiac killer. The headline (at least apparently) provided evidence that he was. However, Heather tells John that the headline is from the Onion, which publishes satire. On the basis of Heather’s information, John realizes that his evidence came from an unreliable source, and so stops believing Van Dyke is the killer. The evidence from Heather undermined the evidence from the headline.

Notice that Heather did not provide evidence that Van Dyke is not the killer: she provided evidence that John should not trust the (so-called) evidence that he was.

On some topics we have very little evidence to base our beliefs on. On others, we have a wide variety of sources of evidence, evidence about those sources of evidence, evidence about that evidence, and so on, and we are left with the difficult task of balancing it all.

Keep in mind that sometimes it might be best to suspend judgment: neither believe something nor its opposite, at least until more secure evidence comes along.

3. Kinds of Evidence

Evidence can have many sources. Sources themselves can be placed in broad categories. In the chapter you read for today, Hunter discusses four in some detail: Observation, Memory, Testimony, and Measurement.


Observation is the use of sense perception to collect information.


Important factors that affect the reliability of observation:

  1. The conditions necessary for the sense in question to work properly. (E.g., for sight, having the appropriate amount of light.)
  2. Using the right sense to detect the right things. (E.g., not using taste to detect color.)
  3. The training one has had for making the appropriate kind of observation, especially when it comes to small subtleties. (E.g., the ability of a trained musician to hear specific notes, or someone with a “refined palate” to taste subtle differences in wine.)
  4. The observer's focus, as in this video.
  5. The possibilities of perceptual illusions, cognitive tricks, hallucinations, distortions, and so on.

robot I think I see a robot with a gun! But it’s kind of dark out. Before panicking, I decide to look closer. It’s just a security camera on a pole.


(I’m not going to try defining this. But you know what memory is.)

Important factors that affect the reliability of memory:

  1. How much of the information is truly being recalled, and how much is being “reconstructed” by imagination.
  2. Whether or not the memories could have been affected by suggestion or manipulation.
  3. Any factors that affect the information being remembered. For example, if you are remembering something you saw, then factors relevant to observation are also relevant.

bugs Adults who had visited either Disneyland or Disney World as children were shown a (doctored) photo of Bugs Bunny at one of these locations. They were then asked to recall what they experienced on their visits. A large percentage described a memory involving meeting Bugs Bunny there: which of course never happened, since he is not a Disney character. (Loftus and Pickrell 1995)


Testimony is evidence that comes from what people communicate to us, whether by speaking, writing, or by some other means.

This includes formal testimony by witnesses at trials, but also more mundane reports like your friend telling you she’s already had lunch today.


Important factors that affect the reliability of testimony:

  1. Whether or not the testimony concerns a subject matter or topic the person in question is in a position to know about.
  2. The person’s training and expertise in the subject matter.
  3. Whether or not the subject matter itself is so complex that no one can be considered a reliable authority on it. (E.g., religion, philosophy.)
  4. The person’s access to the relevant information needed to make a judgment in this particular case.
  5. The possibility of a bias or ulterior motive for giving the testimony.
  6. Any factors affecting the witness’ own evidence.

Trusting unreliable testimony is basically the same thing as committing the appeal to unqualified authority fallacy we discussed in our last unit.

Camille Cosby, wife of Bill Cosby, has claimed that he is innocent of the rape charges against him. She claims these encounters were consensual. However, she is not really in a position to know whether or not these encounters were consensual, and she clearly has a motive to protect her husband.


Measurement is the use of tools or instruments that provide information in a quantified way.


“Quantified” information is basically that which takes a numeric format.

Important factors that affect the reliability of measurement:

  1. The clarity of the units employed and what they mean.
  2. The consistency of the measurement tools or instruments.
  3. The ability to provide an independent standard for testing the reliability, accuracy and precision of the measurement or the tools.
  4. Whether or not the scale and measurement process really reflect the thing you are interested in. (For example, IQ tests measure something but it is not clear that this is the kind of intelligence that matters most.)

pain Health professionals often ask patients to rate their levels of pain on a scale from 1 to 10, or similar. But it is unclear what the units are here, and it is unclear if there is an independent way of gauging how consistent or accurate these measurements are. They shouldn’t be dismissed entirely, but should be taken with a grain of salt.

Case in point: I went to my dentist about a sore tooth a few years ago. She did some tests, asking me to rate the pain on a scale. Based on my answers, she decided I did not need a root canal procedure. However, soon after I developed a fistula and had to have the procedure anyway. Apparently, my pain reports were not consistently “calibrated” with those of her other patients.

F. Reasoning about Causation and Correlation

1. Importance

stuDYINGWe care about cause-effect relationships for many reasons.

We also saw in our previous unit that the “false cause” fallacy is a real danger.

It is important to differentiate mere correlation from causation. We want to be able to manipulate effects by manipulating their causes; but this is only possible for true cause-effect relationships.

Despite this chart, Mainers who wish to avoid divorce cannot expect sabotaging the margarine industry to help.
divorce and cheese
Source: Spurious correlation website

2. Categories and Individual Events

One complicating factor in studying causation and correlation is that correlation always deals with kinds of things, whereas we can talk about causes and effects for individual one-time events.

wait line Drinking a lot of water in the morning, in general, does not cause people to fall in love. These are not even correlated.

But this does not mean that an individual drinking too much water one particular morning might not cause them to need to use the bathroom at one particular time, where they just happen to meet their future spouse while waiting in line.

For that one particular event we might say drinking too much water caused someone to fall in love.

This shows it is important to be clear whether we are considering causes and effects in general, or as categories of events, or as specific one-time events.

Individual events are usually the result of many causes (and have many effects), and which one we describe as “the” cause depends on our expectations or interests.

burning house If someone lights a lighter in a house where there’s a gas leak, we wouldn’t hesitate to consider either the gas leak, or the lighter, or both, as causes of the resulting fire, or even “the cause”.

In a case of arson, where someone burns down a house by starting a large pile of papers on fire with a lighter, we probably wouldn’t think to call the presence of oxygen in the room—necessary for the fire to burn—as one of “the causes” in the same way. Yet, probably there is no important difference from a physical point of view.

When we ask about correlations and causations, usually we are interested in categories, or types, or events, not individual ones.

3. Types of Correlations

In Unit 1, we discussed these concepts, which can be applied to types of events.

X is a necessary condition for Y just in case:
(1) Y cannot occur without X; or
(2) if X does not occur, neither can Y; or
(3) if Y in fact occurs, X must have as well.
(These formulations are equivalent.)

X is a sufficient condition for Y just in case:
(1) X cannot occur without Y also occurring; or
(2) X is enough to bring about Y; or
(3) if X in fact occurs, Y will as well.
(These formulations are equivalent.)

Necessary conditions are like requirements; sufficient conditions are like guarantees.

These are the extreme ends of correlation: one kind of thing always goes with the another, at least in one direction or the other.

But even these extreme relationships are not always the result of cause-effect relationships.

The reverse is true as well: not all types of causes or effects are necessary or sufficient conditions. Smoking causes lung cancer, but smoking is neither necessary not sufficient for lung cancer (at least for everyone).

Less extreme correlations are put in terms of probability values.

The correlation coefficient or r-value of two quantities is a measure, from −1 to 1, of the extent to which one can be predicted as a linear function of the other.

If the quantities measured are probabilities of a kind of event which can either occur or not, this is also called a φ value, and measures how strongly correlated events of this kind are.

One thing is positively correlated with another if it (or an increase in it) corresponds to an increase in/increased probability of the other (positive r/φ value).

One thing is negatively correlated or inversely correlated with another if it (or an increase in it) corresponds to a decrease in/decreased probability of in the other (negative r/φ value).

Not all correlated factors are causes, but we call those that are, but are not fully necessary or sufficient, “contributing factors”.

A cause X is a contributing factor for (or against) effect Y if X is positively (or negatively) correlated with Y, but is neither necessary nor sufficient on its own.

A+ grade Taking the exams is a necessary condition for passing this course.
Getting a 100% on every assignment and every exam is a sufficient condition for passing this course.
Attending lecture regularly is a contributing factor for passing this course.

4. Possible Explanations of Correlations

When things X and Y are correlated, there are at least five possibilities to consider.

(1) The correlation is indeed because X causes Y

See How to Verify Actual Causation below.

(2) The correlation is instead because Y causes X

Sometimes the relationship might be the reverse of what one suspected.

louseIn a period in medieval Europe, it was widely believed that lice were beneficial for health, as the more lice someone had, the better health they were observed to have.

In fact, lice prefer to infest the hair of healthy individuals: the temperature and other living conditions for them are better. The health was causing the lice, not the other way around.

In fact, the causation could go in both directions. While an individual event cannot be both a cause and effect of itself, categories of event can be. Poverty can cause crime, and crime can cause poverty, in a cycle.

(3) There is a common cause of both X and Y

It could be that neither is the cause of the other, but that both are caused by the same third thing.

turbulence example In this example, the child thinks that the seatbelt sign being turned on is causing the ride to the bumpy. In fact, turbulence in the flight path is both the cause of the bumps and of turning on the sign.

One study “surprisingly” found a strong correlation between astrological signs and children’s performance in early education, which became less pronounced the more years a child was in school, disappearing by adulthood. But no one should have been surprised. Do you know why?

(4) There is a causal link, but it goes through a side effect

It may not be that X causes Y directly, but only because of a side effect of X or the way X comes about.

acupuncture There are many forms of acupuncture that are widely believed to reduce pain, and many clients of those who sell such services testify that they work. However, many studies show that most forms have the same effect as a placebo pill: people who are told that a pill will reduce pain report pain relief, even if the pill has no real medicine inside. These forms of acupuncture have the exact same level of relief, and likely for the same reasons.

(5) The correlation is accidental

Such is very likely to be the case for those correlations discovered by looking through large bodies of data with many potential correlations and selecting out those which happen to be correlated. With so many potential correlations, it would strange if none of them happened to hold just by coincidence.

Sites like spurious correlations and Google correlate take advantage of the vast amounts of data now available online to do this.

pirate The number of pirates globally is strongly negatively correlated with global warming.

The number of movies starring Nicholas Cage is strongly correlated with the number of fatal drownings in a year.

(The Maine divorce/margarine example above.)

5. How to Verify Actual Causation

So how can we tell if there is actual causation, if correlation is not enough? This is difficult.

Some indicators of actual cause-effect relationships:

  1. Correlations are more likely to be causal when there is covariation or concomitant variation.

    There is covariation (or concomitant variation) between X and Y when there is not only correlation, but changes to the amount or qualities of X are correlated with changes to the amount or qualities of Y.

    headache Sandra notices that she has gotten a headache on the same days she has drunk orange juice. This by itself might not show that the juice is causing the headaches, but she also notices that her headaches are worse on days she drinks a lot, and lighter on days she drinks a little. This is much stronger evidence of a cause-effect relationship.

  2. Correlations are more likely to be causal when the exact mechanism, or chain of processes, leading from cause to effect can be identified.

    If you know how a certain pill has an effect because of its chemical make-up, and not just that it does, it's less likely to be a mere placebo.

    Of course if we already know that mechanism, it may be a moot point, but in cases of uncertainty it makes sense to look for it.

  3. As noted above, correlations are more likely to be causal when the correlation was not discovered by searching through large groups of possible correlations where it would be statistically more likely than not that some accidental correlations would be found.

  4. Correlations are most likely to be causal if the correlation persists when other possible relevant factors are changed. Testing this requires controlled scientific experiments, which cannot always be done for practical or moral reasons.

G. Reasoning with Statistics: Potential Confusions and Tricks


Statistical measures, such as percentages and the like, are a vital and necessary part of reasoning about nearly all subject matters. Of course, UMass has multiple courses dedicated to this subject alone.

For this course, we can only sketch some basics.

Our focus will be on ways statistical information can be misleading, either due to honest confusion, or due to rhetorical tricks which advertisers, politicians or others might employ in order to deceive people.

1. Issues Regarding Statistical Sampling

Many statistics are obtained by forming general conclusions on the basis of a sample of the entire population.

As we saw in our second unit, the hasty generalization fallacy can occur if the sample is not representative.

One of the best ways to ensure that a sample is representative is to ensure that it is random, as much as possible.

A random sample is one in which every member of the larger population has an equal chance of being included in the sample.

Biased Samples Can Be Misleading

roulette Suppose someone wishes to know what percentage of Americans would support legalizing gambling. A survey of randomly “selected” passers-by are asked on the Las Vegas strip. It is not likely that the percentage answering in favor of legalizing gambling represents America as a whole.

Obtaining a truly random sample, however, can be very difficult, depending on the population. It used to be commonplace for phone surveys to select random numbers from the phone book. However, this is biased against people without home phones, people with unlisted numbers, people not home at the time the survey is conducted, etc. In the cell-phone era, this problem is even worse.

Stats based on samples can be misleading because of sample size, margin of error and confidence level

The sample error of a statistic based on a sample is the difference between the frequency of the observed trait in the sample and its frequency in the population as a whole.

The margin of error is the largest possible sample error one can reasonably or confidently expect a certain sampling method to produce.

These issues are all related.

There are many ways therefore for such factors to lead to misleading statistics, even if the sample is representative.

  1. The sample size may be too small for there to be a reasonably small margin of error.
  2. A statistic may be cited without the margin of error, or confidence level for that margin of error being given.

obama Obama’s approval rating is obtained in September (2016) by a random survey, and is given as 64%. It is similarly obtained in October, and given as 67%. Commentators conclude that his approval has gone up. However, the survey is less than 50% likely to have a margin of error below 3%, so it is possible his approval has not increased.

Survey/poll results can be biased by psychological factors

Even if a sample is representative, and sufficiently large to allow otherwise for an acceptable margin of error, data obtained by means of human responses can be biased by psychological factors.

We saw in our previous unit how framing biases can affect survey results.

Other factors become involved when those surveyed have a motive for answering a certain way, or think only certain answers are socially acceptable or desirable.

dt People surveyed about their charitable giving often exaggerate how much, or even whether, they give to charity, compared to the actual numbers.

Things which are illegal or seem “taboo” are underreported, such as illicit drug use and masturbation.

Some have suggested (though this is disputed) that Trump’s poor showing in polling prior to the 2016 election compared to the election results were in part a result of embarrassment, or a reluctance, to publicly voice support for such a controversial figure.

2. Issues Regarding Averages

The word “average” has at least three different meanings:

The mean of a set of values is its arithmetical average, defined by summing the values together and dividing the sum by the number of values.

The median of a set of values is the middle point of the values when arranged in ascending or descending order.

The mode of a set of values is the most frequently occurring or most common value within the set.

kirk Twin toddlers, their parents, and Kirk Douglas are sitting at dinner. The ages at the table are:

2,    2,    27,    29,    99

The mean age is 31.8.
The median age is 27.
The mode age is 2.

Statistics about averages can be misleading if the sense of average isn’t made clear, or the wrong one is focused on

Sometimes one of these is more relevant than another.

bnt Kevin is shopping for new shirts. Only size 3XL fits him; 2XL is too small, and 4XL is too big. He’s told that the average shirt at the local Big and Tall store is 3XL. He gets there and discovers that half of the shirts there are 2XL and the other half 4XL, and so average out to 3XL as a mean. He was hoping 3XL was the mode.

Averages can also be misleading if the dispersion of values (how spread apart they are) is not also considered when it should be

The range of a set of values is the difference between the highest and lowest value.

The standard deviation of a set of values is a measurement of how far the typical value tends to stray from the mean, defined as the square root of the quotient of the sum of squares of the differences of the values from the mean and the number of values.

rory Poor lonely Rory, 32, has just returned to Stars Hallow, and wants to hang around people her own age. She hears that there are two groups of people she could hang out with, both with average ages of 31.8. She figures it doesn’t matter which group she hangs out with.

This is a mistake. One group is the group eating with Kirk Douglas above, none of which are in their 30s. Another is the 30-Something Gang, whose ages are 30, 31, 32, 33, 33. Clearly, she’d be happier with the second group.

At the Kirk Douglas table, there is a 95-year range between the oldest and youngest member, and a relatively large standard deviation (around 35). In the 30-Something Gang, the standard deviation is much lower (around 1), and of course the range is just 3.

3. Issues with Graphs and Diagrams

Graphs, charts and diagrams allow statistical information to be presented in a visually informative way.

Depending on how the information is presented, graphs can be misleading, or even used to deceive.

Some ways these can be misleading:

tax The bar graph on the right represents what would happen to tax rates for the highest bracket if the Obama Bush-era tax cuts expired. Because the y-axis starts at 34, and ends around 42, it is made to appear that the rate would quadruple or more. The difference was actually between 35% and 39%.

innv This line graph represents an increase in innovation over the years 2007 to 2015. What are the units of innovation here? It is entirely unclear.
clicks This chart shows traffic on a certain website, in terms of opens (new visits) and clicks on the page. However, look at the inconsistent way in which the values rise on the y-axis. It is unclear what this graph tells us. The initial value for the green line could be almost anything.
gas Here the x-axis is not spaced apart uniformly: last year is as far away from last week as the current time is, making it seem as if the cost of gas is not rising as quickly as before.
bomb This chart measures the power in kilo/megatons generated by various nuclear explosions. The power is reflected only in changes to the height. However, the larger mushrooms clouds are also wider, giving the illusion of a greater increase. A cloud twice as high would also be twice as wide, making it look 4× as large.

animals This chart represents how many people own certain kinds of animals as pets. Each icon represents 50 owners. Because the horses are much bigger than the cats, it looks as if there are more horse-owners than cats. Of course, however, there are many more cats, so the reverse is the case.
welfare In this graph, the y-axis is unlabeled, and clearly does not begin at 0, which is misleading. What is perhaps worse is that the labels are very misleading in what is being compared. The figure on the left represents anyone living in a household with anyone receiving any kind of welfare benefits. The figure on the right represents individuals with full-time jobs, not including those who live with such individuals. The two groups overlap.

4. Issues with Percentages

Percentages are a very common format for presenting a statistic.

Percentages are obtained by dividing a certain amount by a certain base, and representing the amount as a fraction out of 100. For example, if there are 50 students in the course, 10 of which are getting A’s, I can say that 20% are getting A’s. The amount is the students getting A’s, the base is the number of students in the class.

Percentage statistics can be misleading, especially if the relevant base is different between different statistics, or simply not made clear.

Reasoning about percentages can also be misleading if they are treated as whole numbers rather than as fractions for addition, and the like.

paid Suppose after an economic downturn, your boss tells you your wages will be reduced by 10% for three months, but then increased by 10%. It might be natural to think you will end up back to your current salary. However, this is not so, since the base will change. Suppose you make $12/hour initially. After the decrease, 10% of $12.00 will be subtracted, so you'll make $10.80/hour. When you get the increase, it will be raised 10% of a different base: $10.80, so you'll end up making $11.88/hour.

(For a similar reason, if something is on sale at 50% off, and you get a 30% employee discount, it will only be 65% off total, not 80% off.)

inj This graphic cites percentages for various injuries. But what are these percentages of? Someone might think this suggests that over 5% of children get spinal injuries, but that certainly isn’t true. In fact, it probably really only means that 5.2% of children who get serious orthopedic injuries and need hospitalization have injuries to the spine: a very different statistic.

Suppose someone points out that the number of crimes committed by Latinos has increased over 500% in the US over the last five decades. This might make it appear as if there is a significant new crime problem in the Latino American community. However, the base here is the number of crimes committed by Latinos in the 1960s, and this completely ignores the fact that the population of Latinos has increased around 900% overall, and so there is no reason to think there is a special problem here.

story (A story from a Knowable Listicle, probably ultimately from reddit.)

H. Hypothetical Reasoning and Science

1. Explanations, Revisited

Recall from unit 1:

An explanation is an attempt to shed light on an certain thing, event or fact—an attempt to state why it is the way it is.

The explanandum of an explanation is the thing or fact being explained.

The explanans of an explanation is whatever is used to shed light on the explanandum.

The relationship between explanans and explanandum can often be considered very like the relationship between the premises and conclusion of an argument. Indeed, many philosophers think explanations are nothing more than arguments considered in a different context. (Probably not all arguments can count, however.)

This explains in part why certain words that can also be premise and conclusion indicators are also used in explanations.

broke The window is broken because Isaac threw a baseball as hard as he could right at it from 5 feet away.

This is most likely an explanation. If we know the window is broken but want to know why or how, this tells us.

In a different context, however, it could be an argument. If we know already what Isaac did, but not sure what happened to the window, this reasoning could be used to convince us that it’s broken.

Seeking an explanation for something usually means looking for an explanans for a given explanandum.

Arguments usually have multiple premises, however, and a full explanation usually involves multiple explanans. Background knowledge can supply “implicit” parts of the full explanation, just like it can provide implicit premises in an argument.

Sometimes what we consider “the right explanation” depends on what part of the full explanation isn’t already clear to us.

A chemistry professor mixes H₂O₂ with KI and liquid soap, and it produces a big toothpasty mess. The students know what is being mixed, and ask “why did that happen”. The professor responds “When these chemicals react, it decomposes the H₂O₂ into water and oxygen gas; the water mixes with the soap and the oxygen forms bubbles in the soap, creating a foam. That’s the explanation.”

In this case, the students already know what chemicals were mixed. What they were missing was knowledge about what happens when these chemicals are mixed, so that’s what was considered the important part of the explanation.

Suppose instead that a student does this in the lab when the professor’s back is turned. When she turns around and sees the mess, she says, “explain this please”.

Here, what she wants is something like, “Curt mixed H₂O₂ and KI and soap in that tube”. The professor already knows what happens when those two things are mixed. That’s not the part the professor needs to know.

In both cases, however, the full explanation is basically the same: (1) These things were mixed; (2) when they’re mixed, foam is created; (3) therefore, foam was created. In both cases, the foam was the explanandum, and just different explanans were provided to combine with background knowledge to provide the full explanation.

It is often possible to determine what the best explanation of a given explanandum is.

Abduction is reasoning in which a conclusion is accepted because it, used as an explanans, provides the best explanation for a given explanandum. (C.S. Peirce)

prints I see footprints in the wet sand on the beach. I conclude someone walked by this spot since the last high tide.

(P1) If someone walked by this spot since the last high tide, there are footprints in the sand.
(P2) Someone walked by this spot since high tide.
(C) There are footprints in the sand.

Abductive argument:
I already know the explanandum (conclusion) of the explanation above is true, and this explanation as a whole provides the best explanation. If it is the correct explanantion, then its (P2) must be true. Therefore, someone walked by this spot since high tide.

Is abduction a new form of reasoning, distinct from deduction or induction?

Thoughts on this:

Can everything be explained? Is this the same question as whether or not everything happens for a reason?

2. Hypotheses and Hypothesis Testing

A hypothesis is a statement that is conjectured to be true because it, as explanans, could be part of the explanation of something in need of explaining.

One can think of the thing in need of explaining as providing a “problem” or “puzzle”, or “why is this so?” question the hypothesis is aimed at.

Where do hypotheses come from? Hurley writes that a hypothesis is a “free creation of the mind”. I think this is an exaggeration. However, it is clear that we do not deduce them, and indeed, we do not know whether or not they are true until they are tested.

In most cases, many different hypotheses are possible with regard to the explanation of a given explanandum.

switch You enter the bedroom and flip the switch on the wall. The light does not go on. Here are several possible hypotheses:
(H1) The bulb is burned out.
(H2) The power is off.
(H3) The light fixture is broken.
(H4) The wiring is bad.
(H5) You flipped the wrong switch.
(H6) The switch is not connected.

In order to figure out whether or not any of these hypotheses are correct, you’ll want to test them. This usually involves conducting some kind of experiment.

In the broadest sense of the word, an experiment is the attempt to gather new evidence which would confirm or disconfirm a given hypothesis.

Conducting experiments is something scientists often do, but in this broad sense, this is something people do in their everyday lives as well. It could be as simple as asking a question and listening to the answer.

bulbs In order to test whether or not the bulb is burned out, I replace it with a new bulb. If the light then goes on when I flip the switch again, likely the first bulb was burned out. If it does not, that is unlikely to be the explanation, and I should test others.

Designing an experiment usually involves thinking about what the observable implications of the hypothesis are: that is, what observations the hypothesis suggests you will have in certain situations, and what observations you wouldn’t have in those or other circumstances.

A well designed experiment has certain features:

  1. It should be controlled: different factors should be tested independently from one another, one at a time. Changing the bulb and replacing the fuse at the same time won’t narrow down the correct explanation to just one.
  2. One should not only seek observations that conform with the hypothesis, but also observations that conflict with it.

Unfortunately, this last bit is not something people are always good at. There is a corollary of confirmation bias called congruence bias which leads people to look for evidence in accord with their favored hypothesis, and not actively seek evidence that would disconfirm it, and acting as if the hypothesis is strongly confirmed by this evidence alone.

picard In one study, subjects were given the sequence:

2 4 6

They were told the number sequence followed a certain rule. Subjects were asked to identify the rule, and were allowed to ask whether certain additional number sequences accorded with the rule, and would be given yes or no answers. Most participants theorized that the rule was “increase by 2”, and asked about sequences such as “8 10 12” and “100 102 104”, and were given yes answers. Very few tested sequences that went against the rule, such as “100 101 102” or “10 8 6”. After getting nothing but yes answers, most concluded that their hypothesis was “proven”, In fact, the rule was simply that the numbers had to be in any ascending order, and so they got yes answers, but still got the rule wrong. (Wason 1960)

The example above underscores another point: a hypothesis cannot be “proven” from a single or many positive results. Indeed, if the hypothesis is a general statement, such as a scientific law, it is not clear it can be “proven” at all.

water Suppose I am testing the hypothesis: “At 1013.25 mbar atmospheric pressure, water boils at 212° F.”

Suppose I raise water to 212° F in many different environments, in different containers, using different heating methods, etc., and whenever it reaches 212° F, it boils. I observe water in the same conditions at lower temperatures, and it doesn’t boil. I do this 10,000 times. Isn’t it still possible that the general law isn’t true? At least logically?

It seems a bit easier to disprove the hypothesis: don’t I just need to find a single instance in which it doesn’t boil at 212° F? But even then, if it goes wrong on the 10,001st experiment, it is possible that some other assumption I’m making is wrong instead: perhaps that water sample wasn’t pure (or something else entirely), perhaps my instruments were wrong, perhaps the atmospheric pressure had changed, etc.

Even in science, it’s probably best to speak of a hypothesis having a certain degree of confirmation based on our evidence, rather than its ever have been proven or even disproven.

3. Scientific Hypotheses


Although nearly everyone engages in hypothetical reasoning and hypothesis testing, it is also the main activity of scientists.

There is no clear boundary between “ordinary” hypothesis testing and science itself, but in general science distinguishes itself in the following ways:

  1. In general scientists are interested in hypotheses taking the form of generalizations which might figure not just in the explanation of a single event, but in all events of a certain kind.
  2. Even in those occasions in which scientists seek explanations for particular historical facts (e.g., why did liquid water disappear from the surface of Mars), they do so when particular knowledge of general scientific principles is likely to be of help, and when the results might in principle illuminate similar events discovered later.
  3. Scientists take special precautions to make sure their experiments are controlled, and their data measured in precise and replicable ways.

A law of nature or scientific law is a well-confirmed scientific hypothesis taking the form of a broad generalization.

A scientific theory is a collection of interrelated hypotheses which can together be employed to provide explanations for a wide variety of things or situations within a certain sphere of investigation.

Strictly speaking, a theory is a theory regardless of how well confirmed it is. However, by the time a theory is constructed, it usually contains at least some fairly well confirmed laws as parts; without those, the theory is unlikely to get off the ground.

newton Newtonian mechanics is a scientific theory which involves a number of laws governing motion. These laws could figure in to the explanation of nearly all situations in which something moves. One of these laws is the law of universal gravitation: physical objects attract each other proportionally to their combined mass, and inversely proportionally to the squares of their distances.

Unlike a humdrum everyday hypothesis such as why your light switch doesn’t work today, such a law can be used to explain countless different events, from why your keys fell to the ground when you dropped them, to why the planets orbit the way they do, and so on.

Of course, not all scientific hypothesis are as wide ranging as Newton’s laws of motions, and some take only the form of weak generalizations rather than strong generalizations: e.g., that most humans are subject to the fundamental attribution error in many circumstances, etc. Either way, these hypotheses are tested with experiments.

Criteria Used In Evaluating Scientific Hypotheses and Theories

  1. Adequacy / Fit with Data: The hypothesis or theory must have implications that match what has been observed regarding what it seeks to explain, and must not have implications that have not been observed but would have been if the hypothesis were right.

  2. Predictive power: A general theory must be able to be applied to predict what our observations in the future will be in certain conditions (and these predictions must bear out). The more numerous, precise and accurate its predictions, the better.

  3. Internal unity and simplicity: The various parts of a theory must hang together in a coherent way, and must apply uniformly to all the various things it seeks to explain. The fewer the fundamental laws posited, and the fewer exceptions or complications they involve, the better.
    Occam’s razor is the principle that when scientific theories are equally good according to other criteria, the simpler theory is better, and perhaps more likely to be true.

  4. External consistency: the theory or hypothesis should not conflict with other well established scientific laws or principles.

  5. Fruitfulness: The hypothesis or theory should suggest new lines for future research or technological application.

ngt Newton’s laws did very well at explaining a very wide amount of data collected over decades, if not centuries, to test them. They were also very fruitful and had great predictive power, allowing the creation of new machines and new applications (e.g., explaining the tides in terms of interaction with the moon). Other theories such as Kepler’s laws of planetary motion, and Galileo’s theory of falling bodies made largely consistent predictions and did as well within their particular areas of study. However, Newton’s laws were seen as preferable since they treated both with the same laws, and gave a simpler explanation of the same observations.

albert They were not perfect, however, and some inadequacy was later discovered as scientific observations grew in number and they were applied to new realms. Eventually, Einstein’s theory of general relativity replaced them, although it is largely consistent with their predictions within a certain range, much like they replaced Kepler’s and Galileo’s laws. Einstein’s work also unified the prevalent theories of electricity and magnetism by incorporating Maxwell’s equations and the theory of electromagnetism.

It is possible that Einstein’s theory will be replaced by something yet more uniform and general, especially as there are at least some apparent conflicts between it and the laws of quantum dynamics.

4. Good and Bad Science


Most of us have to rely on scientific results obtained by the work of others. This is true even for scientists, since they cannot do all the studies themselves.

Unfortunately, not all scientific studies are equal, and not everything that masquerades as scientific knowledge really lives up to that label.

Here are some things to think about:

  1. Are the experiments properly controlled? Are distorting variables ruled out?
  2. Is the published work describing the study peer reviewed, anonymously reviewed, and published in a respected scientific venue? Are the authors sufficiently trained in the relevant methodology?
  3. Is the research methodology described in enough detail that the experiments could be replicated by others? Have such replications been done, and what are the results?
  4. Were the researchers likely to personally benefit from a certain result? Was the study funded by individuals or institutions with a vested interest in the results?
  5. If the results are advertised as “groundbreaking” or “revolutionary”, are the results of the now-to-be-considered-obsolete scientific endeavors given a proper explanation? For example, Einsteinian physics did not so much throw out Newton’s as to portray it as a more limited theory valid only under certain conditions.
  6. Were rival hypotheses sufficiently considered and ruled out? Could there be congruence bias?
  7. Are the hypotheses aimed at solving a real problem or explaining something really need of an explanation? Are the claims aimed at filling an emotional need (fear of death, uncertainty, loneliness) by means of a plausible sounding superstition?

I. Open Mindedness

Open mindedness is the ability to consider new possibilities, including those which conflict with your previous beliefs and attitudes, the receptivity to change your mind if situation dictates, and to weigh all evidence appropriately and fairly.

Actively open-minded thinking is thinking that involves self-consciously taking active steps to ensure that you remain open-minded throughout the thought process.

In your reading, Baron advocates actively open-minded thinking, and in general this seems reasonable. But there may be limits.

1. One-sided and Two-sided Thinking


Cognitive biases pose the greatest threat to open-mindedness.

Confirmation bias, also called, “myside bias” can lead us to only seriously consider evidence that favors the position we already hold before our investigation.

Open-minded thinking therefore requires playing devil’s advocate, and actively considering what might lead someone to take an alternative point of view.

This difference between those with different points of view might stem not just from having different beliefs about facts of the matter, but might instead come down to different values or goals.

pento Jordan is an opponent of the death penalty. He thinks punishment is only valuable to the extent it minimizes the criminal behavior it is imposed upon. He also believes that the death penalty does not deter capital crimes such as murder. He realizes however, that proponents of the death penalty might disagree with him either (1) because they think the death penalty does deter murder better than other punishments (a difference in beliefs), or (2) because they think a punishment fitting the crime is valuable in itself (a difference of values or goals).

One-sided thinking is thinking in which only arguments in favor of a given conclusion and against contrary positions are considered.

Two-sided thinking is thinking in which arguments both for and against a given conclusion are considered.

It is fairly obvious that one-sided thinking can be the result of bias, and can lead people to make mistakes or be overly dogmatic about something that is by no means certain.

Is it possible to take two-sided thinking too far?

Baron writes (pp. 202–03)
If most people today were asked to comment on the question “Is slavery wrong?” or “What do you think of the character of Adolph [sic] Hitler?” they would probably not have much to say on the “other side.” In other cases, people have already thought through some position even though others remain on the opposite side. A devout Christian is unlikely to produce a two-sided discussion of the existence of God. Yet such people are not necessarily poor thinkers in general, or even about these issues.
dawkins Some other concerns involve such things as giving “equal weight” to both sides of a controversial issue when the evidence is lopsided. Some critics worry, for example, that media attempts to be “objective” about climate change have led to a distorted perception about the clarity of the evidence.

Evolutionary biologist and atheist activist Richard Dawkins, for example, refuses to debate evolution with creationists because he thinks to do so legitimizes evolution-denial and makes it seem as if it is a position still worthy of serious consideration.

Perhaps even calm consideration of certain perspectives on certain issues is itself harmful.

Perhaps open-mindedness should only be taken to require good judgment about how much two-sided thinking is appropriate, and how much is too much.

Is empathy—the ability to imagine oneself in the position of others and understand their beliefs and feelings—conducive to open-minded thinking?

At first, it might seem as if the obvious answer to this is yes, but in fact, it may be more complicated.

It may depend on whether or not the empathy itself is two-sided. When we emphasize with the pain of another, our own pain-processing neurons fire, and like other negative emotions, this can make us feel more clannish, self-protective, and stubborn. If we only emphasize with those on one side of a dispute, our thinking may even become more narrow-minded or unfair.

empathy In one study, participants were told about someone on a wait-list for receiving treatment for a painful illness. When asked if they would move her up on the wait-list, quite possibly moving her ahead of others with worse conditions suffering for longer, most in the control group said no. Those, however, who were told more about her and asked to empathize with her and think about how she feels were much more likely to say yes. (Batson, Klein, Highberger and Shaw 1995) Would they have done the same if they had been asked to empathize with those ahead of her as well?

According to Baron, the following are among the causes some people resist two-sided thinking, or even treat one-sided thinking as superior:

  1. The influences of institutions: A nation might, through education and government institutions, promote nationalistic ideas about its own greatness, and portray doubts about such things as shameful or treacherous. A religious institution similarly might portray steadfast devotion to and defense of its tenets as virtue and doubts about them as vice.

  2. Emulating experts: People who are perceived as experts about a topic usually make statements and answer questions about that topic without needing to consider many sides, or entertain doubts. (This may be only because they have already done so!) This may create the illusion that knowledge requires rigidity of thought. This tendency may begin with the parent/child relationship.

  3. Confusing the role of thinker with that of an advocate: In debates, and trials, often one side is given the role of promoting that side and that side alone. People who engage in such advocacy—such as lawyers—have a reputation of producing powerful arguments. This way of proceeding, however, only works well when part of a larger process.

2. Openness to Change


Open-mindedness requires the ability or capacity to change one’s beliefs or positions if the evidence demands it.

This means that one must always adopt positions tentatively, and never with complete and certain conviction—at least not of the sort that would preclude rethinking things later.

But this is in direct contrast with the widespread image of changes of mind as a sign of weakness: people often imagine a smart person as one who is determined, committed and steadfast.

Consider the fact that changes of mind, or “flip-flopping”, is usually considered a negative trait in political leaders. (There is more involved here, however.)

The causes of such attitudes likely overlap those that make some prefer one-sided thinking. We associate expertise with confidence, and see confidence as antithetical to tentativity and vacillation. These attitudes too can be harmful.

changes In one of Baron’s studies (1989), participants were first asked about their attitudes about those willing to change their minds about things like religion and politics. Subjects were then asked to consider evidence about a possibly controversial but unfamiliar topic such as whether or not city dwellers should have to play higher auto insurance rates since accidents are more common in cities. Those with an initially more favorable attitude towards changes of mind exhibited more two-sided thinking, and were less prone to confirmation bias.

One potential factor which may contribute to a reluctance to change one’s mind or even seriously consider positions different from one’s own involves the desire to resolve cognitive dissonance.

Cognitive dissonance is the simultaneous holding of incompatible or inconsistent beliefs, often with associated uncomfortable feelings or anxiety.

Dissonance resolution involves adopting cognitive strategies that either eliminate or prevent cognitive dissonance, even when the strategies involve weighing certain evidence more or less than it would otherwise be rational to weigh it.

deepin Angela loves her father, who works as a manager of a meat packing plant. He has worked hard all her life to earn money to help Angela pay for college. Angela is proud of him, and considers him one of the most ethical people she knows. In her ethics class, however, she is exposed to powerful arguments against the morality of eating meat, and in favor of vegetarianism. Although she cannot find logical flaws in these arguments, she discounts them, mainly because if she took them seriously, she would have to rethink the morality of her father’s occupation, and the source of her tuition money. The very prospect of this makes her uncomfortable.

Is it always bad to hold incompatible or inconsistent beliefs? If not, is there any set of beliefs that it is bad to hold?

3. Weighing Evidence Appropriately and Fairly


As we have seen, confirmation bias can lead someone to weigh evidence favoring their prior views more heavily than evidence against them.

It can even lead people to misconstrue neutral evidence (that which is just as likely if their favored hypothesis is true than if it is false) as though it were evidence in favor of their views, and raise their confidence in them.

Moreover, anchoring bias and related effects, can lead us to inappropriately weigh evidence differently depending on the order in which it is received.

This leads us to violate this principle:

The order principle states that if the temporal order in which pieces of evidence are received does not itself affect the strength of these pieces of evidence, then this order should not affect how we weigh this evidence.

In some circumstances, the order does rationally affect the strength and reliability of evidence.

coupleSuppose you first overhear Candace tell Leslie that she loves her. Immediately afterwards, you overhear Leslie tell Candace that she loves her. This provides some evidence that Candace loves Leslie, and some evidence that Leslie loves Candace, but the former evidence is probably stronger, since Candace said it first, and Leslie may have just been responding out of politeness or pressure.

This is the exception rather than the rule, however. Unfortunately, people are often affected by the order of evidence when they should not be.

ginny In a study, some subjects heard someone described as “intelligent, industrious, impulsive, critical, stubborn, envious”. Others heard the person described as “envious, stubborn, critical, impulsive, industrious, intelligent”. (Reversing the order.) Those in the first group responded with much more favorable impressions of the person described than those in the latter group. (Asch 1946)

Remaining open minded requires not letting some evidence overshadow other evidence, or letting earlier evidence color how we understand and weigh later evidence.

4. The Influence of Others


Our ability to remain open-minded can be affected by others, whether through engaging in reasoning as a group, or through our interactions with others, or simply the need to do so.

Working in a group can have a positive effect an open-mindedness, since it can reduce the effects of individual biases, and force reasoners to consider alternative opinions.

However, this depends largely on the attitudes of the people involved, and the dynamics between them. Pressure to conform, and mutual reinforcement of shared presuppositions, and so on, can have the opposite effect.

jfk In a retroactive study (Janis 1982), a comparison was done between the group dynamics of President Kennedy and his advisers (the same group) during two decision-making situations regarding relations with Cuba.

In the build up to the failed “Bay of Pigs” invasion in 1961, the argumentation was described as fairly simplistic and one-sided, with significant pressure evident among advisors and cabinet members to show loyalty and support Kennedy’s own leanings.

During the “Cuban Missile Crisis” of 1962 (widely regarded as having ended with very positive outcomes for U.S. interests), a very different dynamic was reported, with Kennedy actively encouraging advisers to speak their minds, and mention alternative possibilities, regardless of how outlandish.

Groupthink is poor reasoning or thinking produced when a group exhibits poor group dynamic, especially owing to pressure to conform, reduce dissent and disagreement, satisfy leadership, or live up to traditional or preconceived ideas of proper group operation.

On the other hand, individuals often reason better when they know that they will be responsible for explaining or justifying certain claims, assertions or decisions to an audience, at least when that audience or its preexisting attitudes are not known.

Accountability is the necessity of having to justify or defend one’s beliefs, decisions or assertions to others.

In some situations, accountability can improve two-sided and careful reasoning.

acc Studies show that when people are told beforehand that they are going to have to justify their conclusions to an unknown audience beforehand, and then asked to make a decision based on some provided evidence (such as the likely innocence or guilt of someone accused of a crime), they are less likely to be affected by the order of evidence inappropriately, more likely to engage in two-sided thinking, less overconfident, and more likely to consider more complexities in the evidence, than if they were not so told. (Tetlock 1983, 1992)

This result is not found if the reasoner knows what the attitude of the audience is beforehand; in that case, the reasoning can be slanted in order to please the audience.

It has been suggested that the lack of accountability and virtual anonymity of certain online discussion forums explains some of the overly harsh atmosphere and intolerance of different viewpoints sometimes found there.

J. Creativity

No doubt the correct or best definition of “creativity” would itself be a philosophical problem. However, here is a tentative first start.

Creativity is the ability to have original or unique ideas or thoughts that aid in producing something new or solving a problem.


Creativity is important not just for producing works of art and literature, but for everyday problem-solving and forming new hypotheses in science and new methods and views in mathematics, philosophy and similar disciplines.

1. The Creativity Cycle

If there were one process or method that always worked to produce creativity, everyone would already know about it by now.

Perhaps the best we can do is observe the patterns that seem to surround successful creative processes, and see what can be learned from them.

Lau describes the creative process as often taking the form of a cycle, with the following steps.

  1. Preparation: This involves gathering information about your problem or your craft. What is known? What methods currently exist for solving this kind of problem, or creating this kind of thing? What resources do you have access to? What has worked in the past? Talk to others and learn as much as you can. Creativity requires knowledge.

  2. Exploration and immersion: This step involves absorbing everything learned in step 1, and putting it into practice in preliminary studies. Try to find connections between things you haven’t seen before. Write down what you have done and your feelings about it. Devote a lot of time and energy to this, but allow your results to be imperfect, flawed and chaotic.

  3. chickIncubation: This is a period in which you relax, and change your focus away from your creative task. Sleep, take a shower, watch a movie. Allow the ideas from step 2 to settle in your mind without paying deliberate attention to them. It is not really known why, but often the newest and best ideas come either during, or just after, such breaks.

    Of course, the ideas don’t always come. If not, return to step 1 and start afresh.

  4. Verification: Put your ideas into practice, and try to make the final results as best as they can be. Then assess the product. Be open minded as to their success. Sometimes ideas that seem great turn out to be less great than expected. Failure is a possibility, but it can be learned from. Either way, we can return to step 1 for the next cycle.

2. The New Idea Paradox


Is it really possible to have a completely new idea?

The Scottish philosopher David Hume theorized that all our ideas, even things we just imagine, are made up of simpler ideas we’ve previously experienced.

You can imagine a painting with a pattern of colors no one has ever produced before, but all those colors must be ones you have already seen, or combinations of them. It doesn’t seem possible to imagine a completely new (primary) color, nor is there any way to create such a pigment.

But this needn’t make creativity impossible. Perhaps you’ve heard the phrase “Art is theft”. Artists typically borrow from the pre-existing, and modify, twist, change it and make it uniquely theirs. Even outside of art, creativity can take a similar form.

rk Robert Kearns invented the mechanism that first made it possible to have intermittent wipers in automobiles. He was forced to sue auto-manufacturers to maintain patent rights to the mechanism. Lawyers for the automakers alleged that the patent was invalid because all of the parts going in to the mechanism already existed. Kearns successfully responded by asking whether or not the fact that all of the words making up Dickens’s A Tale of Two Cities pre-existed the novel meant that it wasn’t Dickens’s creation.

Shakespeare was not the first (nor the last) to tell the story of Hamlet. Legends with similar plots exist from centuries before. There may even have been a play with that very name with the same basic plot before his, written by Thomas Kyd. But of course, Shakespeare’s is the one that will always be most remembered.

It is very likely that your favorite novel, movie or TV show borrows heavily from earlier works of art, or from history.

This suggests that one way to get new ideas is to deliberately think about taking what already exists and transforming it somehow.

scamper S.C.A.M.P.E.R. is an acronym or mnemonic for a list of strategies for forming creative ideas; it stands for

Substitute something
Combine something with something else
Adapt something to something else
Modify, magnify or minify something
Put something to some other use
Eliminate something
Reverse or rearrange something

(Lau, pp. 224–25, following Michalko 2006)

3. Perspective Shift

If creativity doesn’t come from transforming an external thing, perhaps it can come from transforming your own point of view.

Perspective shift is a deliberate attempt to understand a certain problem or task requiring creative insight differently from how it was previously conceived.


This could take many forms:

  1. Change from thinking about the negatives of a current situation to the potential positives of a new one, or vice versa.
  2. Change from thinking about the way things are to the ways we think they should be, or vice versa.
  3. Change from thinking about the issue from your perspective to attempting to understand it from another perspective, such as a client, or an observer, an alien, or a future anthropologist.
  4. Change from thinking about short term goals to long term, or vice versa.
  5. Reconsider what you would consider a solution, and think about whether a solution could take a different form from what you had originally imagined.
  6. Rethink your level of ambition: could it be greater? Would it help if it were reduced, at least for this project?
  7. Consider the problem from a different intellectual framework or discipline: if you were thinking of it as a matter of psychology, consider it as a biological issue instead, or vice versa.
  8. Consider whether the problem would need to be solved if something else changed to make it unnecessary.
  9. etc.

stand A small business needs new office furniture for its meeting room. The employees cannot agree on any chair design that they all like and which fits their budget. After trying unsuccessfully to find a compromise, they decide to do without sitting meetings, and instead have their meetings standing, or walking. The meetings are shorter and have less filler. They meeting room gets filled with donated exercise equipment. Employees are allowed to discuss business while on treadmills or lifting weights.

4. Potential Hindrances to Creativity

  1. Fear or intolerance of failure: creative endeavors are rarely successful on the first attempt.
  2. Perfectionism.
  3. Groupthink can discourage creativity in group tasks much like it can also discourage open-mindedness.
  4. Not having a well-rounded life: devoting time exclusively to creative attempts; not allowing for incubation.
  5. Impatience or giving up too quickly.
  6. An overly strong desire to get credit or to satisfy our own egos by matching the successes of others or our past selves.
  7. An unwillingness to change from a routine that has worked in the past.

K. Postscript: Russell’s 10 Commandments

Bertrand Russell (1872–1970) is Prof. Klement’s favorite philosopher. He offered the following as a “liberal decalogue”: 10 Commandments that he wished, as a teacher, to pass on to anyone who needed to think and reason well within a complex world. (From “The Best Answer to Fanaticism–Liberalism”, New York Times, 1951)

  1. Do not feel absolutely certain of anything.
  2. Do not think it worthwhile to proceed by concealing evidence, for the evidence is sure to come to light.
  3. Never try to discourage thinking for you are sure to succeed.
  4. When you meet with opposition, even if it should be from your husband or your children, endeavor to overcome it by argument and not by authority, for a victory dependent upon authority is unreal and illusory.
  5. Have no respect for the authority of others, for there are always contrary authorities to be found.
  6. Do not use power to suppress opinions you think pernicious, for if you do the opinions will suppress you.
  7. Do not fear to be eccentric in opinion, for every opinion now accepted was once eccentric.
  8. Find more pleasure in intelligent dissent than in passive agreement, for, if you value intelligence as you should, the former implies a deeper agreement than the latter.
  9. Be scrupulously truthful, even if the truth is inconvenient, for it is more inconvenient when you try to conceal it.
  10. Do not feel envious of the happiness of those who live in a fool’s paradise, for only a fool will think that it is happiness.

© 2024 Kevin C. Klement