Philosophy 110:
Practical Reasoning

Definitions of Basic Terminology 

Prepared by T. Gracyk 


 If you only want fallacies, click here.


Analogical
Arguments
 

Anecdotal
Evidence
 

Argument

Affirming the
Consequent
 

Appeal to Fear (Scare Tactics) 

Appeal to Good
Intentions
 

Appeal to Pity 

Argument from
generalization
 

Biased sample 

Categorical
Claim
 

Categorical
Syllogism
 

Causal Argument 

Causal Fallacies 

Chain Argument 

Claim 

Coincidence 

Conditional
Claim
 

Contradiction 

Conclusion 

Confirming
Evidence
  

Controlled study 

Correlation 

Critical Thinking 

Deductive
Argument
  

Denying the 
Antecedent
 

Disjunction

Disjunctive Argument 

Evaluating
Arguments
 

Evaluating Premises 

Evidence 

Excluding
Possibilities
 

Existential
Claim
 

Explicit 

False or faulty
analogy
 

False dilemma 

Generalizations 

Hasty
Generalization
 

Implicit 

Hypothetical
Argument
 

Inconsistency 

Indicator words 

Inductive
Argument
 

Issue 

Modus Ponens 

Modus Tollens 

Overlooking
Common Cause
 

Particular 

Persuasive
definition
 

Post Hoc 

Premise

Principle of
rational
discussion
 

Reductio ad
absurdum
 

Repair 

Reversing 
cause and 
effect
 

Soundness 

Singular claim 

Slippery slope 

Standard form 

Statistical
Syllogism
 

Stereotypes 

Universal claim 

Validity 

Vague sentence  

Wishful Thinking

 


Analogical Argument (Argument by analogy)
An inductive argument, one premise of which is points out a likeness between two kinds of things. Based on the many similarities which are known to hold between the two, the presence of some additional feature in one thing leads to a conclusion that the other kind of thing shares that additional feature.

Not every analogy is offered as an argument. The famous comparison that "A woman needs a man like a fish needs a bicycle" is a fancy way of saying that women don't need men, but it is NOT an argument.

When an analogy is offered as an argument, it can be understood as having this standard form:

Argument Form:

 

  1. A is z.


  2. A is like B: they share 
    w, x, y.

  B is probably z.

 

Here, A and B are the things being compared, z is the feature at issue, and "w, x, y" are other similarities known to hold between A and B.

Example:
  1. The early bird gets the worm.
  2. Birds are like job applicants and worms are like good jobs: the former are many in number and the latter are scarce.

    Early applicants probably
    get the best jobs.

 

 

 

 

Besides considering the truth of the premises, any evaluation of an analogical argument must weigh the strength of the comparison. This is done by considering the possibility of a false or faulty analogy. We can also show them unsound by using a reductio ad absurdum


Anecdotal Evidence 
When generalizing, the fallacy of drawing on limited personal experience or a vivid example as the basis of the generalization. The arguer places too much trust in the example or personal experience even though it is not really representative. Because the sample size will be inadequate and because the sample itself will be chosen to confirm the intended conclusion, anecdotal evidence makes generalizing unsound.

Example: "I don't care what the experts say. Someone who lives in my hometown burned to death in a car accident because he couldn't get out of his seat belt. Anyone who wears a seat belt is just asking for trouble."


Affirming the Consequent 
The invalid argument pattern in which the second premise endorses the consequent of a conditional. This pattern is fallacious (always unsound!) because it is invalid.

 Argument form:

1. If A then B

2. B     

   A

Example:

1. If Sam is tired then he'll fail the exam.

2. Sam failed the exam.   

    Sam was tired.

It's invalid because there might be a different reason why the antecedent fails (in this example, maybe Sam was well rested but didn't study).


 

Argument  
A collection of claims, one of which (the conclusion) is supposed to be shown true by the others (the premises). Arguments are most clearly presented by putting them into standard form.

Pragmatically, the conclusion is what the speaker intends to prove. The premises are the speaker's evidence for the conclusion. 

Successful arguments are classified as either deductive or inductive, which makes a difference in what we look for when we evaluate them. 


Argument from generalization 
(Statistical Syllogism)
An inductive argument, one premise of which is a generalization about a group. From this information about the group, the arguer draws a conclusion about some specific member of that group. This group is technically known as the reference class.

These arguments are strong when the generalization is about almost all members of the reference class, or almost none of them.

Standard Form:

1. Almost all S are P.
   

2. a is S


  a is P

 

 

 

  Example:

  1. Almost all adult men without beards shave regularly.
  2. The President of the U.S.A. is an adult man without a beard.

The President of the U.S.A. probably shaves regularly.

 

Standard Form:

1. Very few S are P.
   

2. a is S.


   a is not P.

 

  Example
  1. Very few toddlers shave regularly.
  2. Bertha is a toddler.

Bertha probably does not shave regularly.

Even if the premises are acceptable, these arguments are frequently weak and therefore unsound. They are weak when the number or statistic deviates much from "almost all" and "very few." And they are weak when the arguer has chosen a poor reference class (often done when the argument only has numerical information about that reference class and no others).

The following argument is weak because the statistic is not clearly at one of the two extremes:

  1. Many American firefighters are of Irish heritage.
  2. My new neighbor is an American and a firefighter.

My new neighbor is probably of Irish heritage.

Evaluation: While there are certainly "many" American firefighters about whom this is the case, there are also huge numbers about whom it is not the case.

The following argument is weak because the reference class is not appropriate to this case:

  1. Almost all U.S. Presidents survive their term in office. 
  2. John F. Kennedy was President of the U.S.A. 

John F. Kennedy probably survived his term in office.

Evaluation: This is a bad reference class because J.F.K. is know by most people to be one of the few Presidents assassinated while in office.

 

Another weak form of the argument parallels the problem of affirming the consequent, that is, reasoning backwards. The following argument form is always weak:

1. Almost all S are P.
   

2. a is P


  a is S

 

 Example:

1. Almost all adult humans can swim.

2. Samantha can swim.


Samantha is an adult human.

In this case, MANY people and animals can swim without being adult humans. Samantha might be a child, or even a pet goldfish.

 

And of course any inductive argument is unsound when evaluation of the premises reveals that one is false or invites us to suspend judgment. 

For a  link to another professor's notes on this topic, click here.


Biased Sample and Overgeneralization 

The problem of generating an unrepresentative sample by using a method of sampling that misrepresents an important subgroup of the population. 

In other words, it involves observing a distinctive subgroup of a larger group, and then mistakenly drawing a conclusion about the larger group instead of the subgroup. It is very easy to do this when you relay on anecdotal evidence. 

Obviously, this is not an issue in a highly homogenous population. Looking at penguins in one location of Antarctica is fine if you just want to know the average height of penguins; where they live in Antarctica probably has no effect on penguin height. But choosing just one place to sample all Americans is going to be biased, because Americans include many, many different subgroups. So going to a shopping mall in Fargo, N.D., is not going to get you a representative sample when trying to determine how many Americans are of Norwegian descent (such a sample will be biased by over-representing that group).

Most bias can be eliminated by stratifying the sample. Stratification is the process of sorting the sample into groups ("strata") that have been identified in advance as highly relevant to the issue being studied. For instance, when the topic is abortion, both a person's sex and religious affiliation will influence his or her position. If we cannot get a highly random sample, then we should stratify our sample for at least these two factors. So in addition to asking them whatever we want to know, we need to determine these additional facts. If we sample more than we really need, we can then sort the sample into the relevant subgroups, see if any are over-represented, and then randomly eliminate samples from the over-represented groups until we reach a sample in which the major sub-groups are represented according to their numbers in the general population. Notice that stratification only works when we already know which subgroups are relevant to the issue and we know their numbers in the general population. 

Confirming evidence is a special case of biased sample. It is the special case of using a method that gets the arguer or researcher a result favorable to his or her desired conclusion. The method can create this bias either intentionally or accidentally. Either way, the fallacy consists in choosing a method that generates a large sample of one very specific, highly unrepresentative group. There are two ways to generate confirming evidence. One is to use a method that initially selects a sample from one particular group. For example, if I want to know how many Americans think that it's time for a woman to become the U.S. President, then I would generate confirming evidence if I only called women. It would be even worse if I only called women whose telephone numbers were provided by N.O.W. (the National Organization for Women). Similarly, if I'm interesting in supporting the idea that video games harm children, I might generate my sample of children by choosing children at a juvenile corrections facility.

The other method to generate confirming evidence is to ask a question that automatically favors one answer over other possible answers. If I want to "discover" strong support for private schools, I might ask people, "Do you favor continuing massive subsidies for our failing public schools or do you support directing some of that money to school vouchers that give parents a choice?" This method involves the fallacy of the leading or loaded question.

If one generates a sample with confirming evidence, stratification is not going to remove the biases from the sample.

Arguments that generalize are unsound when they have a biased sample or involve confirming evidence.


Categorical Syllogism 
Any argument composed of exactly three categorical claims, two of them as premises and one as a conclusion.

Categorical claims are declarative sentences that propose a relationship between two things or types of things. There are six basic types of categorical claim.

S and P usually indicate groups of objects, but they don't have to indicate groups.
( S is the subject, P is the predicate.)

When the subject of the claim is about a group of objects, and it is about EACH AND EVERY one of them, then it is a universal claim. (Example: Every physical object has mass.)

When the subject of the claim is about a group of objects, but only about some of them, the claim is an existential (also called particular) claim. (Example: Some people are unkind.)

When the subject of the claim is an individual object instead of a group, we use a lower case a to stand for a proper name ("Fred Jones") or a description specifying a specific individual ("my mom"). These are singular claims.

In addition, the relationship is either positive or negative, giving us claims of the following types:
S is P (affirmative)
S is not P (negative)

    
The Six Types:
  • All S are P
     Universal affirm.
  • No S are P
     Universal neg.
  • Some S are P
     Particular affirm.
  • Some S are not P
     Particular neg.
  • a is S
     Singular affirm.
  • a is not S
     Singular neg.

 

  
Examples:
  • All cats are felines.

  • No dog is a feline.

  • Some dogs are cute.

  • Some dogs are not cute.

  • Ralph is hungry.

  • Phoenix, Arizona is not a coastal city.

 

Most of the categorical syllogisms that we encounter have at least one premise that is a universal claim (i.e., of the type All S are P or the type No S are P). Categorical syllogisms without a universal premise are always invalid.

It can be quite difficult to tell if a categorical syllogism is valid. For most people, learning to make a diagram of the premises is probably the simplest and most reliable of the available methods.


Causal Argument 

This type of inductive argument has a conclusion that one thing does or does not cause another.

Besides being positive (argument to confirm) or negative (argument to disconfirm), the conclusion may be about a specific case or about what generally happens. The first sort is a cause of a particular case and the second sort is a cause in a population. (Technically, arguments about populations will be a special type of argument that generalizes.) Therefore there are four types of causal arguments:

1. Argument to confirm a particular cause.

Example conclusion: The alarm clock woke Pat.

2. Argument to disconfirm a particular cause.

Example conclusion: The alarm clock did not wake Pat.

3. Argument to confirm a cause in a population.

Example conclusion: Smoking is a cause of lung cancer.

Standard form for this type:

  1. X is correlated with Y.
  2. The evidence is from a controlled/uncontrolled study.

          X is probably a cause of Y.

 

4. Argument to disconfirm a cause in a population.

Example conclusion: Regular exercise is not a cause of lung cancer.

Standard form for this type:

  1. X is not correlated with Y.
  2. The evidence is from a controlled/uncontrolled study.

          X is probably not a cause of Y.

When the correlation is strong and there are no other known causes of the same effect, we can word the conclusion of the third type as "X probably causes Y." We must fully understand the normal background conditions for the cause and effect relationship before we can use this wording. But most causes are not understood well enough to justify this wording.

Evaluation of causal arguments: As with any other argument, first determine whether the premises are true. Since correlations are demonstrated through sampling and generalizing, we should not accept the claim of correlation until we agree that the process of generalizing would be sound. In other words, we must evaluate the claim of a correlation as being an inductive generalization from samples.

But agreeing to the correlation is not enough to make the causal conclusion sound. By itself, a correlation never proves a cause. (Example: The craze for pet rocks may have coincided with the peak year for sales of disco music, but nobody thinks that disco causes pet rocks or that pet rocks cause disco music.) The arguer must take care to rule out the causal fallacies that often lead one to postulate a cause when there's nothing but a correlation.


Causal Fallacies 

Four fallacies pose problems for arguments that try to demonstrate a cause in a population. The presence of any of these four problems will make a causal argument weak. The four are:

The fallacy of reversing cause and effect 

The fallacy of coincidental correlation 

The fallacy of overlooking a common cause 

The fallacy of Post Hoc 


Chain or Hypothetical Argument 
An argument composed entirely of conditional claims (premises and conclusion). When valid, the premises are arranged so that the consequent of one premise becomes the antecedent of the next. (This "linking" by repeating information is why it's often called a chain argument.) The conclusion will then have the antecedent of the first premise and the consequent of the last premise. The argument will have as many premises as there are "links" in the chain.

1. If A then B.

2. If B then C. 

   If A then C.

 

         1. If traffic is really bad then we're late.

         2. If we're late then we'll miss the exam.

If traffic is really bad then we'll miss the exam.

Chain arguments are often set up in order to lead us from one action to another, in order to point out that a seemingly innocent decision will have terrible results. It is assumed that we will not like these results, leading us to add a modus tollens step at the end of the chain. This would give us a valid conclusion that we shouldn't take that first step!

Real example: (Written in response to the question, "Do you think Fargo's Ten Commandments monument should stay on city property?") 

"When you reject the Ten Commandments you are rejecting God. When you reject God you will be rejecting Heaven. Why take hell when you can have Heaven?" 
(September 2003, http://www.in-forum.com/articles/chat/?id=39138)

This chain has two clear steps, then a third step implicit in the question. The resulting argument looks like this:

1. If you reject the Ten Commandments, then you are rejecting God.

2. If you reject God, then you will reject Heaven.

3. If you reject Heaven, then you take Hell.

4. You don't want to go to Hell.

You don't want to reject the Ten Commandments.

Although arguments that follow this pattern are valid, they are frequently unsound due to the fallacy of slippery slope.

A chain can also be formed with universal claims, in which case it is technically a categorical syllogism.

  1. All dogs bark.
  2. All barking is annoying    

     All dogs are annoying.


Claim  
A declarative sentence that we can treat as either true or false.

Example 1: The telephone in Dr. Gracyk's office is bright orange.

Example 2: Tiger Woods can hit a golf ball farther on the moon than on earth.

#1 is false (it's not orange) but it's still a claim. #2 is true, since there is less gravitational force to create drag on a golf ball on the moon.

Questions and commands are not claims.

Claims can be explicit or implicit. The main claim of a piece of writing or speech is often implicit.

It is difficult to determine the truth of a claim if it is unclear in any way. For instance, pronouns can make it unclear about who the claim is about. 

Example: Patricia and Jennifer went to the store for some fruit. She likes oranges and grapes.

In this case, it is not clear who "she" is and we cannot tell what claim is being made. The claim should have been made using a proper name.


Contradiction 
A contradiction is any situation where we have two claims that cannot be true at the same time. 

One claims is the contradictory of another if its truth shows that the other is false.

The contradictory of a conditional claim is the true description of any example where the antecedent is true but the consequent is false. (Such a case is called a counterexample.)

Example: One contradictory of "If you go to college then you will earn lots of money" is "My uncle went to college and then became a priest who lived according to a vow of poverty." Here, the antecedent is true of the uncle (he went to college) but the consequent is false (he didn't go on to earn lots of money).

The contradictory of a universal claim is also any description of a counterexample.

The contradictory of a disjunction will be the information that none of the disjuncts (the choices) is true. This is most easily presented by naming an additional choice which, if selected, will mean that the specified choices are false.

Example: "To have lots of money, you either have to have a successful career or you have to win the lottery" is contradicted by the claim "You can have lots of money by inheriting it from your family."

When a false disjunction is the basis of an argument, it is called a false dilemma.


Controlled Study 
To establish a correlation for a causal argument, the argument needs two different samples: one where the cause is present (the experimental group) and one where it is not present (the control group).

Sometimes we deal with an issue in which it is impossible to totally exclude the cause from the control group. Here, we have a group where the cause is present in higher amounts (the experimental group) and lower amounts (the control group). 

For example, we want to know if smoking is a cause of breast cancer. Since even people who do not smoke are sometimes exposed to quite a lot of second-hand smoke, we have to determine how much exposure to cigarette smoke there has been, and then put people into the high exposure and low exposure groups. (The low exposure group is our control group.) Or we can simply use the cancer rate in the general population and compare it to a sample with high exposure (unless everyone has very high exposure, the general population will have a lower rate of the cause than our experimental group.)

When the researcher introduces the cause into the sample and withholds it from the second sample, thus creating the experimental and control groups, we have a controlled design. This is also known as a randomized experimental design or, more simply, an experiment. The obvious advantage is that the researcher can control other variables that might affect the outcome. It is much less likely to result in a causal fallacy.

An uncontrolled design is used when the researcher cannot run a randomized experimental design (it might be illegal or immoral or just not very practical). In that case, the researcher has to go and find existing cases for the experimental group, and find similar cases where the suspected cause is absent or found at lower rates (the control group). This is also know as a prospective design (the researcher goes "prospecting" for the cause) or it is simply know as a study.

Uncontrolled design is subject to more fallacies than controlled design, particularly the fallacies of reversing cause and effect, of overlooking a common cause, and of Post Hoc

Sometimes the same group is used for both the control and experimental group, by comparing how things were before an event and then again after. To argue that the September 11 terrorist attacks on the World Trade Center in New York caused insomnia in Americans, we could compare insomnia rates in the months before and after the attack. (Yes, there are researchers who track these rates.) Comparing the before and after rates in the same group (Americans) is much easier than trying to find two groups of Americans, those who don't know about the attack and those who know about it! Of course, in this case it is an uncontrolled study and we would have to look for the possible causal fallacies.


Correlation  

A correlation is a measurable relationship between two variables. A correlation can be either positive or negative. Combined with enough other information, correlations play an important role in determining whether one thing is a cause of another.

A variable is an identifiable, changing feature of the world. In other words, it's something that varies! For example, air temperature and humidity are two different variables that affect how hot or cold we feel. 

As the examples of air temperature and humidity suggest, it is important NOT to approach variables with the "false dilemma" thinking that you either have it or you don't. Many variables are present or absent to some measurable degree. If we suspect that something is a variable that has an influence on something else, we will often miss its true significance if we treat it as an "all or none thing." For example, smoking is a variable that is often linked to lung cancer. But we can't just divide the world into smokers and non-smokers. Different smokers smoke in different amounts, and most non-smokers inhale some tobacco smoke sometimes. (For example, non-smokers who live with smokers may actually have a higher exposure to the variable than do smokers who don't smoke very much.)  The lesson here is that SOME variables are "all or none" (an animal is either a wombat or it isn't -- an animal can't be 50% wombat) and some are matters of degree ( whether an animal is dangerous is a matter of degree: pit bulls and fleas are both dangerous, but in very different degrees).

A POSITIVE correlation holds when we have any of the following:

  • If neither variable allows for degrees, a positive correlation is present when one outcome for the first variable is associated with one outcome for the second variable. For example, being pregnant is positively correlated with being female. (However, it does not have to be perfect match! Being a student enrolled at MSUM in 2007 is positively correlated with being female.)
  • If one variable allows for degrees and the other doesn't, a positive correlation is present when one outcome for the first variable is associated with an increase in a particular outcome for the second variable. For example, being male is positively correlated with violent behavior. Being an American citizen is positively correlated with fossil-fuel consumption.
  • If both variables allow for degrees, a positive correlation is present when an increase in one outcome for the first variable is associated with an increase in the presence of a particular outcome for the second variable. For example, literacy is positively correlated with education. Human population density is positively correlated with distance from an ocean.

The positive association can be an overall pattern that does not necessarily occur in all cases. 

FOR EXAMPLE, the height from which an object is dropped is positively correlated with the force of its impact. (The higher the drop point, the higher the force of impact. But not always. Some objects dropped from a height might have parachutes attached to them, so their impact might be more like that of an object dropped from a much lower height.) Observing that being male is is positively correlated with violent behavior DOES NOT MEAN that every male is violent, and it DOES NOT MEAN that women aren't ever violent. 

A NEGATIVE correlation holds when the increase in the presence of one outcome for the first variable  is associated with a decrease in the presence of a particular outcome for the second variable. Again, the association can be an overall pattern that does not necessarily occur in all cases. FOR EXAMPLE, years spent in higher education (beyond high school) is negatively correlated with enjoyment of professional wrestling: the more college credits a person has completed, the less the person enjoys pro wrestling. But not necessarily. A small number of Ph.D.'s go to people who enjoy pro wrestling. ANOTHER EXAMPLE: Regular flossing of your teeth is negatively correlated with gum disease.

There is NO correlation when there are no regular patterns of increase and decrease for pairings of the two variables. FOR EXAMPLE, the number of panda bears living in zoos changes every year, and the total amount of ice sold by Igloo Ice Company changes every year, but the patterns of decline and increase are not associated.  Although the number of panda bears living in zoos has steadily increased every year for the past decade, sales by the Igloo Ice Company have gone up and down from year to year over the same period. So if Igloo Ice sales increase the month that the local zoo gets a new panda bear, we should regard this sequence of events as a COINCIDENCE. 

Although one might ASSUME that "common sense" can tell what variable will be correlated with which other variables, there are often surprises. Many people believe that women talk more than men (that being female is positively correlated with verbosity), but recent studies in several countries reveal no differences in average number of words spoken by men and women on a daily basis. Or, to take another interesting example, one might think that being a member of a church that opposes abortion would be negatively correlated with having abortions. The Roman Catholic church is officially against the practice of abortion. Yet in a recent multi-year period in which 23% of all Americans identified themselves as Roman Catholic, 27% of women receiving abortions in the U.S. identified themselves as Roman Catholic. So being Roman Catholic is positively correlated with abortion in the U.S. (There's an even stronger positive correlation between being an atheist and having an abortion.) There is a negative correlation between being a Protestant and receiving an abortion. However, here is also a negative correlation between being married and receiving an abortion, and it is a much stronger correlation than the negative correlation between being Protestant and abortion.


Critical Thinking 

In response to claims of any kind, a critical thinker demands adequate evidence before accepting or acting on a claim. Essentially, critical thinking is an evaluative stance. The primary characteristics of someone engaged in critical thinking are curiosity, a questioning attitude, a demand for evidence, and suspicion of extreme positions. 


Deductive Argument 

An argument that attempts to guarantee the truth of its conclusion. (Notice that this classification depends on what the arguer intends to do, not on whether the argument succeeds in doing it!)

By "guarantee," we mean that the premises show that the conclusion must be true. An argument that meets this high standard is said to be valid.


Fallacy of coincidence  (Looking too hard)

Coincidence is a fallacy of sampling, but it is mainly a concern when we use sampling to establish a correlation in order to establish a cause. Most of the time, the fallacy consists of extrapolating too quickly. For instance, it happens when a small preliminary study suggests a correlation and thus cause, but the correlation vanishes when we try to replicate the study. Other times, it is the fallacy of putting too much trust in a sample that, due to no other fallacy, fails to represent the general picture. How does this happen? To learn more, click here.


Conclusion  
The claim that an argument tries to establish as true; what the arguer is trying to prove to the audience. The conclusion is supported by the argument's premises.


Conditional Claim  
A claim that says that the truth of one claim depends on the truth of another, or that the situation described in one claim depends on the situation described in the other. For example, the claim "If cows are mammals then cows give milk" is claiming that cows giving milk depends on cows being mammals.

When most clearly expressed, conditionals take the form "If A then B." 
The claim in position A is called the antecedent.
The claim in position B is called the consequent. (That's "consequent," not "consequence.")

Go back to the example about cows and milk. The antecedent is "cows are mammals" and the consequent is "cows give milk." The conditional is claiming that "cows are mammals" is sufficient to claim "cows give milk." The conditional is true when the antecedent is a sufficient condition for the consequent.

But there are many other ways to express a conditional claim besides the form "If A then B." 

Conditionals are the basis of several argument types, most notably modus ponens and modus tollens.


Denying the antecedent 
The invalid argument pattern in which the second premise disagrees with the antecedent of a conditional. This pattern is fallacious (always unsound!) because it is invalid.

Argument form:

1. If A then B

2. Not A     

   Not B

Example:

1. If Sam is tired then he 
   will fail the exam.

2. Sam is not tired.   

   Sam will not fail the exam.

It's invalid because the premises might be true while the conclusion remains false, due to some additional reason making the consequent of the first premise true as it originally stands. (In this example, perhaps Sam is well rested but Sam didn't study for the exam.)


Disjunction  
A claim that offers a choice of alternatives, such as "Either we go to the movies or we stay home." As in this example, we usually create a disjunction by putting two or more choices together with the word or. The choices are called the disjuncts of the disjunction. 

There can be as many disjuncts as there are choices. Here is a disjunction with four disjuncts: "Either we go to the movies or we stay home or we meet friends at the park or we go shopping for a piano."


Evaluating Arguments 

We evaluate an argument when we decide whether it is good (sound) or bad (unsound). This determination requires attention to both the form of the argument (its logical pattern) and to the truth of each of the claims that go into making up the pattern. So evaluating an argument requires evaluating both its type and its premises.


Evaluating Premises 

To decide how strong an argument is, we must evaluate the premises. We consider each premise individually. Each time, we consider three alternatives:

Accept a claim as true.

Reject a claim as false.

Suspend judgment about its truth or falsity.

We should accept a claim (and thus agree that it's true) when one of the following holds:

  1. Personal experience: provided we restrict our belief to the scope of the experience. Example: Youíve eaten one type of Japanese food just one time. You are NOT in a position to agree with the claim that you donít (or do!) like Japanese food. But you've eaten oatmeal many, many times. You ARE in a position to agree with the claim that you like oatmeal.
  2. Someone we personally know has the authority to support the claim, and has supported it.
  3. Someone who is a reputable expert on the subject matter tells us that it is true, and that person has no motive to mislead us.
  4. It is claimed in a reputable reference source (e.g., an encyclopedia).
  5. It is claimed in a reputable media source.
  6. It is the conclusion of a sound argument, all of whose relevant premises are accepted as true because of 1-5 above.

We treat a claim as false when we have personal experience that shows it to be false, or we have agreement among reputable experts saying it is false, or we have another claim that contradicts it (and the one that contradicts it is true because of any of 1-6 above).

Rule of thumb: Never accept any controversial claim from an unknown source. Instead, suspend judgment!

Rule of thumb: Never accept any claim that you do not understand. Instead, suspend judgment!

Many claims can be determined to be true or false through personal experience (e.g., "The sky normally looks green" is false) or because of common knowledge (e.g., "The United States currently has 50 states" is true, but you probably don't know where or when you learned this fact).

The fact that its conclusion is false is NOT a reason to reject its premises.

It is a mistake (a fallacy) to dismiss a premise as false (or an argument as bad) merely because of who gave it. The identity of the arguer is only relevant if their testimony is supposed to be our reason for accepting the truth what is said. But in that case, we must restrict our discussion of the arguer to facts that actually relate to the arguer's reliability on the topic being discussed. To discuss irrelevant facts about the arguer is the fallacy of ad hominem (e.g., "Why should I listen to Professor Oogle's argument about stock market bubbles? Look at the ugly shirts he wears.") 


 

Evidence 
The premises of an argument are the evidence supporting belief in the argument's conclusion

In order to evaluate premises or evidence, a critical thinker must identify the TYPE of evidence that is being offered. The most important kinds of evidence are the following:

  • Personal experience 

  • Unpublished report (hearsay) 

  • Published report 

  • Eyewitness testimony 

  • "Celebrity" testimony 

  • Expert Opinion 

  • Experiment 

  • Statistics 

  • Survey 

  • Formal observation 

  • Research review

Each of these has its drawbacks or weaknesses (i.e., its associated fallacies), and a good critical thinker is familiar with these and is on the look-out for them.


Excluding Possibilities (also called a Disjunctive Argument
An argument with a disjunction as one premise, and one or more additional premises, each of which eliminates one choice (i.e., negates one disjunct). When valid, the conclusion will be a claim containing any choices (disjuncts) that were not eliminated.

The basic standard form for these arguments:

1. A or B

2. Not A    

   B

1. Sam is smart or clever.

2. Sam is not smart.       

    Sam is clever.

Because the order of the disjuncts makes no difference, this version of the
form is equally valid:

1. A or B  

2. Not B   

   A

1. Sam is clever or smart.

2. Sam is not smart.      

   Sam is clever.

It is not valid (invalid) when we agree with a choice and then conclude that the other is false:

1. A or B  

2. A        

   Not B

1. Sam is clever or smart.

2. Sam is clever.   

   Sam is not smart

This last approach is invalid because the statement of choices (the disjunction) failed to say "but not both."

A valid disjunctive syllogism might be a bad argument (i.e., unsound) because it has a false second premise or it poses a false dilemma


Existential Claim (also called a PARTICULAR claim)
A claim about an unspecified number of members of a group or class. Example: "Some cute animals have big eyes" claims that there really is at least one example of the group "cute animal" and it claims that that thing has big eyes. Because the claim affirms that at least one member of the group exists, it is called an existential claim. Because these claims contrast with universal claims, they are also called particular claims.

Existential claims can be affirmative ("Some cute animals have big eyes") or negative ("Some cute animals do not have big eyes").

To demonstrate that a particular claim is false, one must know that a contradictory universal claim is true. 
Example: To prove that "Some cute animals have big eyes" is false, you need evidence that NO cute animal has them. To prove that "Some cute animals do not have big eyes" is false, you need evidence that EVERY cute animal has them.


Explicit claim  
A claim that is actually made by a speaker's declarative sentence.

Example: "Why did you do break the vase? Didn't you know that it's an antique? I can't afford to replace it!"

Here, only "I can't afford to replace it" is an explicit claim of this speaker.


False or faulty analogy

When an argument by analogy overlooks significant differences, it is subject to this fallacy and is inductively weak. When it has a false analogy, it is unsound. Obviously, if you find an analogy but it's not intended as an argument, then it does not commit the fallacy.

To accuse it of false or faulty analogy, one can point to any of several problems with the analogy.

First, one might note at least one significant difference between the things being compared, and must explain how the difference is relevant to the issue being debated.

Example: Some people argue that because alcohol is legal for adults, all other mood-altering substances should be legal for adults. But this is a false analogy, because many mood-altering substances are drugs that permanently alter the pleasure center of the brain, causing strong addictions almost immediately. Alcohol does not work in the same way, so it does not have the same level of addiction that we would get if we legalize many other substances.

Second, one might point out that one of the things being compared is a fiction. It is pure speculation.

Third, we might ridicule the analogy by showing that, when another feature of it is considered, it actually supports the opposite of what it is intended to show. The famous "this is your brain on drugs" can be ridiculed by pointing out that, since hot greased frying pans are desirable objects in some circumstances (like when one wants to fry a meal), it follows that drugs that "fry your brain" are also desirable in some circumstances, such as in a controlled recreational setting. So the anti-drug conclusion is a false analogy.


False Dilemma (Limited Options Fallacy)
The fallacy of arguing by offering someone a false or implausible set of choices. In other words, an excluding possibilities argument with a false disjunction. A false dilemma is always unsound.

We show that the fallacy has taken place by pointing out one or more plausible but overlooked options.

Example: "Either Pat should study harder or take easier classes. Pat won't study harder, so Pat should take easier classes." This argument has a false dilemma because it ignores the plausible alternative that Pat might change majors, or perhaps leave school.

For more information, click here


Generalizations 
These arguments establish that something is true of a group by sampling a portion of that group. The premises give information about the observed cases (the sample) and the conclusion generalizes to the whole group (including both those sampled and those not sampled).

Standard Form 
  1. X percent of sampled A's are B's.
  2. The sample is representative 
    of A's

        Approximately X percent of A's 
        are B's


Example: 
  1.  67 % of sampled airline pilots are bachelors.
  2.  The sample is representative of airline pilots.

       Approximately  67 % of  airline
       pilots are bachelors.

 

An inventory or census is not a sample, for they involve looking at (or at least intending to look at) every case. Sampling is a situation in which there is no attempt to look at every case. When the group is a group of humans, sampling is often done by polling or surveying (that is, though verbal or written communication) rather than by "looking" in the normal sense of the term. Sampling is found in the work of a field anthropologist who visits a tribe in the jungles of South America and then returns and reports on the culture (the anthropologist did not look at all the villages of the tribe). Sampling is also at work when a newspaper reports that the President's approval rating has risen or fallen (the newspaper did not try to talk to everyone in the United States).

Strong versus weak generalizations 

Generalizations are weak when they employ an untrustworthy sample. They are strong if the sampling process has no fallacies. 

Sampling is subject to four fallacies: biased sampling, confirming evidence, hasty generalization, and anecdotal evidence. (The first pair relate to the method used to get the sample. The last two relate to the size of the sample.)


Hasty Generalization 

The fallacy of generalizing from a sample that is too small and failing to take this into account in the conclusion of the argument. "Small" is a relative term here. A sample that is adequate in size when asking people who they plan to vote for will be too small for medical research that looks for low levels of allergic response to a new medication. Basically, the fallacy occurs when we present a conclusion that is more precise than the sample warrants.

The more variety there is in the population, the larger the sample that's needed to generalize with confidence. 

If we can be confident that the population is extremely homogenous (all its members are alike with respect to what we're studying), then a few cases will be sufficient. If we do not have this confidence, then we should be careful to consider how our sample size generates a margin of error.

To be more precise, different sample sizes create different margins of error for the resulting generalization. These margins specify the range within which we can expect to find the correct answer. A 10% margin of error means that the truth is somewhere within a range of 10% on either side of the reported number. A 3% margin of error (commonly found in professional polling) means that the truth is somewhere within a range of 3% on either side of the reported number.

For example, suppose a unbiased sample of 100 Americans gets 55 positive responses to the question "Do you like ice cream with apple pie?" There is no fallacy of hasty generalization if the conclusion is reported as "Approximately 55% of Americans like ice cream with apple pie." There is a fallacy if we report it as "A clear majority of Americans like ice cream with apple pie." This is misleading, because our sample is consistent with the result that as few as 45% agree.


Implicit claims and hidden premises  
A claim that is not actually made by a speaker but that is presupposed by what a speaker says. Pragmatically, it is a claim that we must assume that the speaker agrees with in order to make sense of what the speaker says. When putting an argument into standard form, these often take the form of hidden premises. It is often necessary to supply implicit claims that link the premises to the conclusion. The process is guided by the principle of rational discussion. It is part of argument repair.

How to find a hidden premise: When you have a premise and a conclusion but it's not clear how they are linked, the solution is generally one of three things:

  1. There is information in the conclusion that isn't in the premises. Try to add a premise that focuses on that information. See example 1.
  2. The arguer expects us to react negatively to something in the premises. See example 2.
  3. The arguer has assumed that something is universally true, and the argument's conclusion is just a special case. See example 3.

Example 1: "All Sunday school teachers are good people, so Mayor Krump is a good person."

The argument depends on the hidden premise "Mayor Krump is a Sunday school teacher."

Here's why: In this example there are two explicit claims, but there is nothing in the explicit premise about Mayor Krump. So the information about Sunday school teachers is not relevant to the conclusion unless we link them with the hidden premise that Mayor Krump is a Sunday school teacher. 

Example 2:  Bumper sticker: "America: Love it or leave it." 

Implicitly, we're supposed to conclude that we should love our country. Why? Because the patriot who's showing us the bumper sticker thinks we'll respond negatively to the idea of leaving.

Standard form reconstruction: 

1. We should love America or we should leave America.
2. I don't want to leave.
    I should love America

Example 3: "Joe won't notice my new shoes match my new handbag. After all, he's a jock."

What's the connection here? The arguer seems to be assuming that jocks never notice fashion coordination (i.e., no jocks notice fashion coordination).

Example 4: "Did you really want to go to the movies on Sunday? Don't you remember that you said you couldn't afford any entertainment expenses this month?"

Although there are questions here instead of claims, it is reasonable to interpret this speaker to be making an argument against going to the movies. In standard form, the argument might be this:

1. You  can't afford any more
entertainment expenses this month.
2. A  Sunday movie is another
entertainment expense this month.
You can't afford a movie on Sunday.


Indicator Words 
In addition to the claims made, sentences often have words added to indicate the role that the claim makes in the overall communication. For example, the following sentence makes two different claims: "You should be nice to Larry because he is sick." The word "because" indicates that Larry's being sick is a reason to be nice to him. 

Some words (conclusion indicators) typically indicate that what immediately follows is the conclusion of an argument:

So   Therefore   Hence   Consequently

Some words (premise indicators) typically indicate that what immediately follows is a premise of an argument:

Because     Since

Sometimes whole phrases work as indicators. "It follows that" is a conclusion indicator, while "for the reason that" is a premise indicator.

Example: "Humans are naturally social being, so hermits are practicing an unnatural lifestyle."

In this situation, "so" indicates that the claim about hermits is the conclusion.

Example: "Hermits are practicing an unnatural lifestyle, because after all, humans are naturally social beings."

In this case, we have exactly the same argument, with "because after all" indicating the premise.


Inductive Argument
An argument that attempts to show the conclusion to be likely or probable. (Note the word "attempts." Whether an argument is inductive or deductive depends on what the arguer is intending to prove.) Inductive arguments are always weaker than their deductive counterparts (inductive ones are never valid, which is to say that the truth of the premises cannot guarantee the conclusion). 

But we often lack the information necessary to construct a sound deductive argument. In that case, the best argument strategy is to construct an inductive argument.

Although there is no question of validity with an inductive argument, a properly constructed inductive argument with true premises can succeed in showing that the conclusion is likely. When it succeeds, the argument can be called "sound" in the sense that it is inductively strong. Some people prefer to restrict the word "sound" to successful deductive arguments, but there is an increasing willingness to use "sound" to mean a successful argument of any kind.

Example:

  1. Almost all adult men without beards shave regularly.
  2. The President of the U.S.A. is an adult man without a beard.

The President of the U.S.A. probably shaves regularly.

This example is a case of an argument from generalization.

While I cannot guarantee that the conclusion is true (perhaps he has some other method of removing his facial hair), I am quite sure that both of the premises are true and so it's highly likely that he shaves regularly.

There are four important types of inductive argument:


Issue  
A question that an argument attempts to settle. Except in very complicated issues, it is best to focus the issue by wording it so that it can be answered with a "yes" or "no" response.

Here is an example of a simple argument, "The recession has been going for two years already, so the economy will improve this year."

Now compare these two examples:

Example 1: Will the economy improve this year?

Example 2: What's going on with the economy?

The two examples share the same TOPIC, which is the economy. Example 1 is an issue that can be addressed with an argument (no change in the economy would be included under the "no" response). Example 2 is not the issue of an argument. It calls for an explanation, not an argument. So Example 1 is the issue for our sample argument.

For additional examples of issues for arguments, look at the sample portfolio pages.


Modus Ponens 
An argument with two premises, one of which is a conditional claim and another which endorses the antecedent of that conditional. The valid conclusion of a modus ponens argument will endorse the consequent of the conditional. 

(An English translation of the Latin name "modus ponens" is something like "the direct route" or "direct way.")

Argument Form: 

1. If A then B

2. A           

   B

       An example:

1. If Sam is laughing then he's amused.

2. Sam is laughing.         

    Sam is amused.

Be careful not to confuse modus ponens with the fallacy of affirming the consequent


Modus tollens  
An argument with two premises, one of which is a conditional claim and another which disagrees with the consequent  of that conditional. The valid conclusion of a modus tollens argument will disagree with the antecedent of the conditional.

(An English translation of the Latin name "modus tollens" is something like "the indirect route" or "indirect way.")

Argument Form: 

1. If A then B

2. Not B     

   Not A

 

  An example:

1. If Sam is amused then he's smiling.

2. Sam is not smiling     

    Sam is not amused.

 

Be careful not to confuse modus tollens with the fallacy of denying the antecedent.


Overlooking common cause 

This fallacy is restricted to arguments to establish a cause. It is the mistake of finding a correlation between two things, then drawing a conclusion without checking for other variables that are also correlated with those two. This problem does not occur in a controlled experiment, but it is a common problem in a study of existing behaviors and events.

Let's suppose we correlate two things, A and B. But perhaps A keeps turning up with B because some previous thing, X, is independently causing A and independently causing B. Here, X is the common cause of A and B. 

Failure to screen for such things is the fallacy of overlooking common cause.  

Example: I notice that when I get a sore throat, it will not be long before I get a runny nose. I conclude that sore throats are a cause of runny noses. 

But this overlooks the common cause: I get a sore throat and then a runny nose because I first get a viral infection (a cold). The virus attacks my throat, giving me a sore throat, and it attacks my nasal passages, which respond defensively with mucus. The two things (sore throat and runny nose) are each caused by the virus, not one by the other. 


Persuasive definition 
A speaker appears to make a claim, but on closer inspection it turns out that they are using language in a non-standard way (i.e., assigning their own meaning) in order to get you agree with their position on an issue. The arguer gives words a definition favorable to the argument, but has no good reason for defining things in this way except to advance the argument.

In this way, persuasive definition sneaks assumptions into premises and gives us a version of begging the question. (Click here for an example.)

Persuasive definition is also known as misuse of hypothesis.


Post Hoc 

The full title is Post Hoc, Ergo Propter Hoc. This Latin phrase means "After it, therefore because of it."

It is the fallacy of thinking that if one thing happens and then another thing happens, the first thing was the cause of the second. But time order alone cannot show that something is a cause. At the very least, we also need a control group! The Post Hoc Fallacy occurs when someone does not understand the need for a control group and draws a conclusion based on nothing but the time relationship. A contributing problem is that the time relationship is so obvious that the person jumps to a causal conclusion using only the most anecdotal of evidence.

Many superstitions are based on post hoc reasoning.

Example: I wore my blue sweater when I took that biology test, and I got a 95%! From now on, I'll always be sure to wear my lucky blue sweater when I take an exam.

Example: I'm allergic to scallops. I ate them once and got very sick later that night.

(Yes, but what other seafood did you eat? And did anyone else eat the scallops? Did they get sick? Maybe it was just that batch that was a problem.)

 


Premise 
A claim offered as evidence to support an argument's conclusion; one of the arguer's reasons for the truth of the conclusion. Most arguments have more than one premise.


Principle of rational discussion 
When evaluating an argument, we assume three things about the arguer:

  • The arguer knows about the subject under discussion.
  • The arguer is able and willing to reason well.
  • The arguer is not lying. 

This principle is also known as the principle of charitable interpretation. 

The point of the principle is to guide the interpretation of a vague or incomplete argument. It helps us decide what implicit information to make explicit in our standard form reconstruction. The goal of interpretation is to construct from them the best possible argument, given the author's point of view. We use the principle so that our interpretation and evaluation of another's argument does not commit the fallacy of strawman.

Unfortunately, there are cases where it is perfectly clear that the person giving the argument intends to violate one of the three elements of the principle of rational discussion. (Usually, it will become clear that they don't intend to give a good argument, or they don't care about the truth of what they're saying.) In this case, we simply do our best to capture what the arguer intends to say.

Real example: An advertisement for Mastercard shows Christmas gifts and says, "They'll cost up to 25% less if you buy them with Mastercard." Putting the conditional statement into a correct sequence, we have, "If you buy Christmas gifts with Mastercard, then the gifts will cost up to 25% less."

It is clear from the conditional that an argument is intended here, and the context tells us that the conclusion is that we should shop with Mastercard.

If you buy Christmas gifts with Mastercard, then the gifts will cost up to 25% less.
_______________________________________
I should buy Christmas gifts with Mastercard

 That leaves a hole in the argument (no second premise), so we repair the argument by adding the assumption "Christmas gifts should cost less." This gives us an argument that affirms the consequent, which is invalid:

1. If you buy Christmas gifts with Mastercard, then the gifts will cost up to 25% less.
2. Christmas gifts should cost less.
_______________________________________
I should buy Christmas gifts with Mastercard

Although the goal of interpretation is to construct a strong argument, we must treat this as an invalid and failed argument, because there is no other sensible way to repair it, given the author's point of view. 


Reductio ad absurdum 
Latin for "Reduce to Absurdity"

Also known as the indirect method: you show that a claim is false by initially pretending that it is true and then showing that an absurd result follows from that assumption. It is "indirect" because you do not directly confront their premises. (In its strict form, you show that an actual contradiction follows from the assumption.) 

This technique can be used to respond to an argument. While it does not prove WHICH premise in a group of premises is faulty, if we can show that a set of premises leads to an absurdity, then we have no reason to regard that set as trustworthy. (We know something is wrong with the connection between the premises and the conclusion.) In using the reductio technique, we evaluate an argument by AGREEING with it, then showing that a false conclusion follows just as plausibly as THEIR conclusion does. In this way we have cast doubt on the plausibility of the support the premises give to their conclusion.

This technique is particularly useful for responding to an argument by analogy, where you think the analogy is weak but are having trouble saying just what is not really analogous in the comparison.


Repairing arguments  
When an argument is defective as given, we can repair the argument by adding a premise or conclusion that seems to have been assumed by the person giving the argument. In adding material to repair the argument, we follow the principle of rational discussion. Therefore we only add a premise if it makes the argument stronger and is more plausible than the conclusion. We only add a conclusion if it follows from the premises.

Example: A speaker says "All cute animals have big eyes, so Muzzles has big eyes." This is defective as it stands, because Muzzles could be a threatening, ugly animal like a shark. Or muzzles might not be an animal at all, but the name of a town in North Dakota. The speaker evidently intends for us to understand that there is an implicit premise, "Muzzles is a cute animal." We would add this premise when putting the argument into standard form.

How do we know that this is what the speaker intends? General rule of thumb: Nothing belongs in a conclusion that isn't in the premises. Here, "Muzzles" is in the conclusion but not the premises. So we have a hole in the argument concerning Muzzles. The arguer is obviously making an assumption about Muzzles, and we repair the argument by stating that assumption about Muzzles. General rule of thumb for repairs: Find what's in the conclusion but not mentioned anywhere in the premises. Make that the subject of the repair claim. Finish writing the repair claim by incorporating all information that is in the premises but not mentioned in premises.

Real example: In answering the question, "Do you think Fargo's Ten Commandments monument should stay on city property?", S. Larson replied in this way: " Yes, if we're going to take God from our City then maybe those who have protested this should stop using American money as well, or see if they can get God removed there as well." (September, 2003, at http://www.in-forum.com/articles/chat/?id=39138)

It is clear from the conditional that an argument is intended here, and the "Yes" tells us that the conclusion is that the monument should stay. That leaves a hole in the argument (no second premise), so we repair the argument by adding the assumption "We won't stop using American money or remove God from our money." This gives us a modus tollens argument, which is valid.

Although we try to avoid it, sometimes our goal of capturing what the speaker intends means that we must repair an argument in a way that leaves it as a bad argument. (For an example, click here)


Reversing cause and effect 

This fallacy is restricted to arguments to establish a cause. This problem does not occur in a controlled experiment, but it is a common problem in a study of existing behaviors and events.

The fallacy occurs when we have a genuine correlation, but we have not clearly established which of the two things really comes first. We simply assume we know which comes first, but in reality it is the other way around. If it is plausible that we have turned the time order around, then the argument is unsound due to this fallacy.

Example: Suppose there is a strong correlation between drinking a lot of coffee and being a type A personality. (In the story of the ant and the grasshopper, ants are Type A. Grasshoppers are Type B. Type As work hard to meet goals, are self-critical, have a chronic sense of time urgency and are often impatient, often display  hostility, and usually display fast movements and rapid speech.) We conclude that drinking a lot of coffee is a cause of being a type A. But did we firmly establish that the people in the study were Type A before they started to drink coffee? Perhaps they had this personality type in childhood, long before they started to drink coffee. Perhaps their sense of time urgency and need to meet goals makes them more interested in using stimulants, which attracts them to coffee. So using the correlation to argue that coffee is a cause of personality would be the fallacy of reversing cause and effect.


Singular claim  
A claim about a specific individual that is not a conditional or disjunctive claim. The individual can be any person, place, thing, etc. Most of the time, the individual is specified by a proper name. (Example: Moorhead is a city that gets snow in the winter.) But it can also be done through description. (Example: The city immediately east of Fargo, N.D., gets snow in the winter.)


Slippery Slope 

There are two versions of this fallacy. They are both given this name because they share a common idea that taking a first step will lead us to something we don't want. It is the unjustified assumption of this idea that is the fallacy. (When the assumption is justified, there's no fallacy, even if the argument otherwise looks like any other slope.)

The assumption in question is that choosing one thing leads to, or is equivalent to, choosing a second thing. But the move from the first to the second is not immediate: one leads to the other (or is shown equivalent) by a series of small, plausible steps. The result is then noted to be undesirable, and therefore (by the valid move of modus tollens), we are advised to avoid the first.

For more information and examples, click here. 


Soundness (as in "sound argument" -- has more to do with a "sound" or solid object than with what you hear))
Soundness is an argument's property of being good, that is, of providing premises that really do support the conclusion, and those premises are ones that we (the audience for the argument) can accept as true for good reasons.

Evaluating an argument is the same as determining its soundness.

An argument might be deductively sound or inductively sound. An argument that is not sound is unsound. (Notice that if we apply soundness to both deductive and inductive arguments, then a deductively unsound argument might be inductively sound). 

Some people prefer to restrict the word "sound" to successful deductive arguments, but there is an increasing willingness to use "sound" to mean a successful argument of any kind.

Technical note: Some logicians would object to what I just said about soundness. They use a more technical notion of soundness, according to which a deductive argument is sound if it is both valid and has true premises--rather than (as above) that it be both valid and have premises that we accept as true for good reasons. Under their stricter technical definition, a syllogism is sound even if nobody can tell if it is. But if soundness is the property of proving a conclusion, then it is odd to think an argument is sound when we are unclear about the truth of the premises. Under the more "practical" definition given here, a deductive argument is only sound if we actually know that it is valid and we accept the premises for a good reason.

Example: This argument is valid: "All the cookies James made last week were lemon snaps. Frida does not like lemon snaps. So Frida does not like any of the cookies that James made last week."  Is it sound? If I don't know anything about James and I don't know anything about Frida, then why should I grant that the argument proves its conclusion? I shouldn't. In fact, I just made up those sentences. Why should this argument count as sound if by sheer coincidence there is a James and a Frida who make the premises true? Soundness should not be a matter of good luck. We should regard an argument as unsound when we have good reasons to say that the premises are false, and we should say that it is unsound when we have no good reasons to agree to the premises. Hence the definition of soundness as an argument's property of being good, that is, of providing premises that really do support the conclusion, and those premises are ones that we can accept as true for good reasons.


Standard Form  
An argument arranged with the conclusion below the premises, with premises and conclusion presented as claims. Standard form makes an argument clear to its audience.

Example as done in Epstein's Pocket Guide, page 10:

All cute animals have big eyes.
Muzzles is a cute animal.
So Muzzles has big eyes.

A better way to put an argument into standard form is to number the premises and to replace the conclusion indicator with a solid line.

1. All cute animals have big eyes.
2. Muzzles is a cute animal.
   Muzzles has big eyes.


Stereotypes 

Stereotypes are a special case of generalization. A stereotype is an unjustified judgment that a certain feature is typical or uniform within a specific group. 

Stereotypes are not necessarily negative. For example, one common stereotype about medical doctors is that they are financially well off. One common stereotype of college professors is that they are very intelligent. But stereotypes are often negative: "blond" jokes are based on the stereotype that blonds lack intelligence, and most "lawyer" jokes are based on the stereotype that lawyers are greedy and cruel.

Of course, many stereotypes are very harmful. For example, one common mode of stereotyping combines generalizing about a group of people with an ethnocentric view of their inferiority. Many Americans stereotype the people of eastern Asia as users of chopsticks. (In actuality, some of the cultures of eastern Asia have not adopted the use chopsticks.) This might encourage unsound inferences, such as the unsound inductive argument that, because Piak is from Thailand, which is in Asia, Piak eats with chopsticks.

This stereotype about people from eastern Asia is ethnocentric only if it is combined with the assumption that the American way of eating is superior or "normal" in comparison.  

It is almost impossible to deal with complex information without stereotyping. Many psychologists now believe that concept-formation requires the creation of stereotypes.


Support 

The relationship between premises and conclusion is one of support: the premises are supposed to be the "foundation" that supports agreement with the conclusion.

There are three degrees of support.

A valid argument offers evidence that, if true, guarantees the truth of the conclusion. But with most topics we just cannot find information that will guarantee our conclusion, and we are better off seeking a strong argument rather than a valid one.

A strong argument gives us good reasons to accept its conclusion. There is no plausible reason that the conclusion would be false when the premises are true.

A weak argument gives no good reasons to accept its conclusions. It leaves some "hole" in the argument and we can identify additional information that would easily allow us to avoid the conclusion while accepting the premises. Fallacies always make an argument weak.

The actual truth of the premises is not relevant to the degree of support. We can see how much support they give even if we don't know that they are true. We want to know if an argument is valid or strong so we'll know whether the truth of the premises is worth investigating! 

Example: "All arachnids weigh less than one pound, and spiders are arachnids, so the spider in the bathroom weighs less than one pound." This argument has valid support for its conclusion. I don't actually know whether all arachnids weight less than one pound, but if it IS true, and if spiders are really arachnids, then the one in the bathroom weighs less than a pound! And that's all we are saying when we say it is valid. 


Universal Claim 
A claim that something is true of every single member of a group or class, with no exceptions. Example: "All cute animals have big eyes" claims that every single example of the group "cute animal" is a thing with big eyes. Universal claims are often indicated by such words as "all" and "every," but there are many other ways to convey them (e.g., "The whale is a mammal" is about whales, and says that every single one of them is a mammal). A universal negative claim says that not even one single member of the group has a specified property, as in "No whale is a fish."

Universal claims are most clearly written as 
All S are P
.

Universal negatives are most clearly written as 
No S are P
.

A universal claim is false when just one member of the group or class fails to have the feature in question. So if we found just cute animal with small eyes, we would have a counter-example to "All cute animals have big eyes." A universal negative claim is false if just one member of the group or class has the feature.

Universal claims are a type of categorical claim and they are a necessary component of valid categorical syllogisms.


Validity  
Validity is obtained whenever a conclusion MUST follow from the argument's premises. In other words, an argument is valid when its structure guarantees a true conclusion, provided the premises are true. 

Informally, we say that there are no holes in the argument.

To be more technical, an argument is valid (has validity) when there is no possible way for the conclusion to be false if the premises are true. Arguments are invalid when they aim at guaranteeing the conclusion's truth but fail to do so even when the premises are true. In other words, the structure of the argument allows the conclusion to be false when the premises are true. An invalid argument might still be good by meeting a weaker standard of support, by being strong.

With some arguments, validity is very obvious. One can see that agreeing with the premises will require agreeing with the conclusion.

Example of obvious validity:

1. All rabbits are mammals.
2. All mammals are animals.
  All rabbits are animals.

But in other cases the validity will not be so obvious. The reason is that the issue of validity is independent of the actual truth of the premises. We're evaluating what the connection between premises and conclusion IF the premises are true. The following is valid:

1. Either the first person born in Maine in 2006 will live to be 90 or these words are written in Japanese.
2. The first person born in Maine in 2006 won't live to be 90. 
   These words are written in Japanese. 

Will the first person born in Maine in 2006  live to be 90? I don't know! You don't know, either! We don't even know who that person is. So we don't know if premise 2 is true. And premise 1 is silly. The two parts have nothing to do with each other. Yet the implausibility of premise 1 and the uncertainty about premise 2 cannot deprive the argument of validity: if both premises are true, then the conclusion must be true. This argument is valid but unsound. (It is a valid argument of the excluding possibilities type.)

Look at the conclusion. Are the words written in Japanese? No. But a valid argument can have a false conclusion. (Remember: we don't dismiss an argument as a bad one just because we don't like its conclusion.) If the two premises WERE true, then those words would have to be written in Japanese. So it's valid. Validity is a matter of whether the conclusion would be true when the premises are true. In this case, there is no way the conclusion could be false while the premises are true.

Here is a less silly example of a valid case of excluding possibilities with a false conclusion:

1. Either Fargo is in North Dakota or Fargo is in Manitoba.

2. Fargo is not in North Dakota.

Fargo is in Manitoba.

Think about the premises. If the first one is true (if there are really only these two choices), and the second is also true (we can't find it on our map of North Dakota after checking the name of every town), then we'd better start looking for it in Manitoba.


Vague Sentence 
A sentence is vague if it is unclear what the speaker is claiming to be true. This happens when neither the context nor the speaker indicates what standards are being applied. When Randy Newman sings, "short people got no reason to live," he is vague. It is not clear who he regards as short and there are no established standards for calling someone "short." 

Warning: A sentence is not vague just because you, its audience, can't understand it. The average person doesn't understand what "E=mc2" means, but that doesn't make it vague. Within the context of physics, it is quite clear.

If a sentence is purposely vague, and neither context nor speaker clarifies it, then it should not be counted as a claim within the context of an argument. Example: "Too much TV is bad for children, so you should monitor your child's TV time." The premise of this argument is hopelessly vague unless the speaker clarifies what counts as too much. The argument is automatically weak due to its failure to provide a legitimate claim as a premise.


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Last updated OCT. 22, 2007