CT Glossary

Expanded Explanations and Examples

Affirming the consequent

Like denying the antecedent, affirming the consequent is a formal fallacy. The fallacy lies solely in the form itself. It has the following pattern: if p then q, q, therefore p. Any argument that fits this pattern is invalid, that is, even if the premises are true, the conclusion that follows from these premises may not be true. Whereas, a valid form guarantees that, if the premises are true, the conclusion will be true. Indeed, if an argument has a valid form and true premises, then it is impossible for the conclusion to be false.


Alternatives are necessary for critical thinking. By itself a claim is difficult if not impossible to understand or assess. But if one has a rival interpretation one can compare and contrast the two, choosing the better alternative. By generating this second reading the critical reader can then determine which one best fits the text and make an informed judgment. This sort of critical awareness is key to critical thinking. Without relevant choices one cannot make informed judgments.

For instance, in "What the Doctor Ordered" the nurse could have accepted the explanation that the doctor was "weaning" the patient from the respirator but, based on her knowledge of medical procedures, she figured out that the prescribed procedure would result in the patient's death.

Also, by considering alternative interpretations, one can come to understand that an intelligent author made informed choices. She or he did not write down the first thing that came to her or his mind. S/he considered alternatives, choosing the one that best fit her or his purpose. In other words, the text is not sacred. It was constructed. One even can--with practice--recover the choices made by an author and then assess them.


Ambiguity is the use of a term, phrase or statement in two or more distinct senses. If a headline in the University Times were to read:

Chancellor on Drugs

we would probably expect an article about the Chancellor speaking on drugs. (Oops! "The Chancellor speaking on drugs" is also ambiguous.) We would expect an article about a speech on the issue of drugs. But, in a different context, the words, "Chancellor on drugs" could mean something else. Ambiguity can be distinguished from vagueness. See "Who Needs the WWW?" for an example of ambiguity.


Analysis (from a Greek word that means "a loosing") is an intellectual activity much valued by philosophers, which consists of understanding a concept or situation by identifying its constituent parts. Thus a term can be defined by identifying what is implicit in the concept. For instance, "sister" can be defined as "a female sibling." There are two characteristics common to all those we so designate: female and sibling. Again, an object, situation or event can be understood by sorting it into various categories. Buildings on the UNC Charlotte campus can be analyzed in terms of name, use, occupants, type of construction, age, etc. Thus the Winningham Building is used for offices, classrooms and storage, but is occupied by the Department of Philosophy and some members of the art department. Thus Winningham can be analyzed either in terms of name, use or occupancy. The assumption of philosophical analysis is that terms, objects and events can be understood by mentally taking them apart. See necessary and sufficient conditions.

Appeal to authority

If fallacious, an appeal to authority relies on an inappropriate authority, inappropriate because the person appealed to is either insincere (=untruthful) or lacking the necessary expertise. The relevant rule that it violates is: One may rely, to a greater or lesser extent, on the information or advice provided by someone who is truthful and knowledgeable about the issue in question.

Linus Pauling, who won the Nobel Prize for his work in chemistry, advocated the use of megadoses of Vitamin C for controlling the common cold. Therefore you should take lots of Vitamin C for your cold.

Pauling's expertise is not in health care. Causal links are difficult to identify. Even experts in a particular field do not ask us to accept a claim on their authority alone; they cite studies that show causation.

Here is an amusing appeal to authority:

A fellow wanted to take advantage of an advertised special at a fast food place--a hamburger, fries and large drink for $2.50. But instead of a large drink he decided to get a small drink. When he got to the cashier, she charged him for each item separately and the total came to more than $2.50. When he objected, she explained that there could be no changes and, if he wanted the lower price he would have to exchange the small drink for a large one. So he did, noticing, to his dismay, that the counterman dropped the small drink in the trash before giving him a large one. When he returned to the cashier he commented that this made no sense. But she failed to see the problem. She just pointed to the computerized cash register and said, "So how come that's what it says here?" (Adapted from an entry in the Metropolitan Diary section of The New York Times, October 11, 1998).

For another example see "Who's To Say?".

Appeal to ignorance

An argument that reasons that because there is no evidence against a belief, then one is warranted in believing that it is true. The relevant rule that it violates is: Claims should be based on evidence and reasoning.

No one has shown there was no space ship on the other side of the Hale-Bopp comet. So the Heaven's Gate community was justified in believing that there was a space ship hiding behind the comet.

Lack of knowledge enables one to say "I don't know" or even "It's possible" but not "Yes, it's true; there is no proof that it is not true."

See also "Who's To Say?".

Appearance and reality

Awareness of the difference between appearance and reality, or what is and what seems to be, is key to critical thinking. Instead of taking things at face value--what they seem to be--a critical thinker attempts to learn what they are in reality. Sometimes appearance and reality coincide; things are what they appear to be. Sometimes they do not; hence the occasion for critical thinking. It is the sense that something is not what it appears to be that leads one to ask questions. See "What the Doctor Ordered" for an example of a discrepancy between appearance and reality.

The philosopher John Dewey once passed on this story that he had heard from a teacher about a principal's failure to make this distinction:

As a high school teacher in algebra I had what I thought was an unusually successful recitation, because the pupils were doing all the work. I was acting as umpire. The principal came in and did not see me doing anything. He reproved me afterwards, and said that I was lazy. I remedied that immediately. Every time he came into the room after that, I began to lecture to the pupils, and he thought I was a good teacher: Personally I do not think I was teaching so successfully [Middle Works (Southern Illinois Press, 1983), 15:188f].

Clearly, the principal equates lecturing and teaching, thus failing to notice other forms of instruction. The reality, despite appearances to the contrary, is that indirect instruction is still teaching. In the teacher's opinion it is superior to direct instruction.


An argument is a piece of reasoning with one or more premises and a conclusion. Arguments are usually divided into two kinds, deductive and inductive. So defined, an argument is to be distinguished from a disagreement. One may use an argument, in the logician's sense, in order to win an argument, in the everyday sense of a dispute. Clearly the logician's "argument" is not as dramatic as a verbal fight. For an example of an inductive argument see the next entry; for an example of a deductive argument see hard determinism.

Argument from analogy

An argument from analogy is an argument that has the form:

All P are like Q
Q has such-and-such characteristic.
Thus P has such-and-such characteristic.

Thus, for example, a few years ago one Republican congressman, who had been a fighter pilot during the Vietnam War, argued in a caucus prior to the election of the Speaker of the House:

Not voting to re-elect Newt Gingrich would be like abandoning your wingman.
Abandoning your wingman is wrong.
So not voting to re-elect Newt would be wrong.

One evaluates such an argument by examining the analogy. It is a weak analogy, and thus fallacious, if there are not many similarities. For instance, in this example there is some similarity between the two situations. The Congressman no doubt felt that with Speaker Gingrich having been charged with ethics violations that he was under attack as a fighter pilot's wingman could be. But there are also dissimilarities. Voting for Speaker of the House is not a life-or-death situation. Moreover, n combat, one neither gets to choose one's wingman nor one's mission. Yet it is the obligation of a congressman to vote for the officers of the House of Representatives as s/he sees fit.

Here's a stronger analogy:

Premise: Learning logic is like learning a foreign language.
Premise: You can't learn a language by cramming; you have to study it regularly.
Conclusion: You can't learn logic by cramming; you have to study it regularly.

Notice the form is the same for a weak or a strong analogy. What makes a weak analogy fallacious is not the pattern of reasoning but a lack of compelling similarities to warrant the alleged one.


A belief or premise that is understood and is often unstated. For instance, a headline in The Charlotte Observer (June 29, 1998) asked, "Do schools in N.C. favor blacks?" The sub-headline clarified this question by asserting, "5 universities use racial preferences, report says." Only when one read the lead paragraph did he learn that the charge being made was about preferential treatment in the undergraduate application process. Thus the initial headline was ambiguous; it could have meant K through 12 schools, private colleges or public universities. The sub-headline was vague, however, and it is at this point that assumptions come into play. Depending on what one takes the context to be--the schools as wholes or hiring or admission practices or something else--one could think that North Carolina universities were being charged with favoring African-Americans in every aspect or in some limited one. This could then lead to a disagreement in which the disputants were talking past one another. One person could assert that schools favor blacks, meaning in every aspect of the schools' programs; while another person could urge that schools favor blacks, meaning that admissions policies favor blacks.

Begging the question

An argument that assumes in the premises what is at issue; thus the conclusion inferred rests on questionable premises. The relevant rule that it violates is: the conclusion must be inferred from premises whose truth is accepted and does not simply restate what is at issue.

Women should not be given combat roles in the military, because only men should do the fighting.

The issue is the role of women in combat. The claim, or conclusion, is that women should have no role in combat. To justify this claim one should offer reasons, that is, premises that support it. The reason offered, introduced by "because" offers no reason; it simply rewords the conclusion, declaring that "only men should do the fighting." An argument that begs the question thus does not deliver on what it promises. It leads one to think that it is an argument with premises and conclusions, when, in fact, the premises offered are nothing more than a restatement of the claim being made.

See "Ignoring the Constitution" for a possible example of begging the question.


An argument that mistakenly takes as true of the whole what is true of the parts. The relevant rule that it violates is: What is true of the parts is not necessarily true of the whole.

If each stick is breakable, then the whole bundle of sticks is breakable.

It is a fallacy to think that because one can do something with each of the parts, then one can do it with a whole where the whole differs in some relevant aspect from the parts. Sometimes what is true of the parts is true of the whole. For instance, a drop of water is H2O, as is all the water of which the drop is a part. In terms of its chemical composition, there is no difference between parts and wholes of water. But it would be a mistake to infer that since a little bit of water from a lake would present no harm, then a lot of water would also not be potentially harmful. Obviously, a whole lot of water can be harmful, say, through drowning or flooding. The fallacy of composition is structurally similar to division: The movement in composition is from part to whole. In division, there is also a part-whole confusion, but the movement is from whole to part.


A conclusion is the supported claim that is being made. In an argument one expects that a claim will be supported with reasons or premises. Moreover, these premises will be true and will, in fact, lead to the conclusion. Hence arguments can be evaluated as to how well they do this: Are the premises true? Is the reasoning good?


A conditional statement is an if-then statement and consists of two parts, an antecedent and a consequent. The antecedent, or that which goes before, is preceded by the "if"; the consequent, or that which comes after, may be preceded by a "then". English sentences sometimes reverse the order: John studies hard if he thinks that he will do well in a class. But the logic of this sentence is: If John thinks that he will do well in a class, then he studies hard. Here the antecedent is "John thinks that he will do well in a class" and the consequent is "he studies hard".


Consistency is much prized in reasoning. Ideally, one would like for one's beliefs to fit together without any contradictions. Consistency is the intuitive notion that is the basis for the understanding of validity: we expect true premises to lead to a true conclusion. When we find that we have true premises and a false conclusion we lack consistency between premises and conclusion and know that the argument form is invalid.


A contradiction occurs when one asserts two mutually exclusive propositions, such as, "Abortion is wrong and abortion is not wrong." Since a claim and its contradictory cannot both be true, one of them must be false. Few people will assert an outright contradiction, but one may fall into an inconsistency.


A counterexample is an example that runs counter to (opposes) a generalization, thus falsifying it. A TV newscast that limited its coverage of "mayhem and misery" (in Bob Inman's phrase) would falsify a claim that all local TV newscasts focused on crime and disasters. Consequently, careful thinkers avoid rash generalizations (see hasty generalization) by qualifying their generalizations. If there are local TV newscasts that do not focus on "mayhem and misery," one could say, "Most local TV newscasts focus on "mayhem and misery." (For Inman's op ed piece see "Next at 11.)


A criterion (plural: criteria) is a means for judging. The key to evaluation is to be able to identify and use a criterion. If two objects or events are completely dissimilar then they cannot be usefully compared. But if they have something in common, one can ask which one is better in that respect. This limits evaluation, making it less global and more doable. For instance, one can compare pick up trucks and sports cars in terms of their ability to haul things or, alternatively, to make sharp turns at high speeds. Given the criterion of hauling stuff one would expect that a pick up would be better than a sports car in that respect. Similarly one would expect the sports car to out perform the pick up in a road race.

Critical awareness

Critical awareness is necessary for critical thinking, for not every presentation (essay, TV ad, statement by a teacher, information in a reference book, etc.) is as it appears to be.

Here's an example where what appears to be a small change, and is described as such, might actually amount to a deal breaker. Say one had a deal to sell someone something. Let's take as an example a VW camper my wife and I once owned. As it turns out, when we went to sell this camper many years ago, there was quite a bit of demand for it. Let's say (and here I am altering what actually happened) we agreed to sell it for a certain price to someone, but he was having trouble getting a loan from the bank. We had given him a couple of days to come up with the money. So, now, just as this period is coming to a close, he calls to say, "I got the money. Everything's fine. Just one small change. The bank wouldn't loan me the money, but they'll loan it to my father. But the car has to be in his name." This would be no problem, except in the meantime other people had offered more money for the camper. Were we now free to sell to the higher bidder? Was it enough of a change to break the deal? The point is: Oftentimes important matters are not labelled clearly. They may even be misidentified. We have to make judgments about their identity. See appearance and reality.

Other occasions where critical awareness is needed is when two ideas or situations are related, but the relationship is not explicitly stated. These are the sort of situations where we notice a connection and explain to someone, "I just put two and two together." Or, we say to someone who is not noticing a connection, "Come on, think!" For an example of a student not noticing what she should have, see false dichotomy.

Critical thinking

Critical thinking is the practice of thinking things through, in which one carefully describes something (an event, a book, a movie, a person, etc) and evaluates it according to some relevant criterion, considering significant alternatives.


Criticism, like argument, can be emotionally charged. But, also like argument, it can be used in a less passionate way. It is this latter sense that this manual is attempting to promote. If nothing else, I would hope that our rejections of others' beliefs and conduct would be based on a careful consideration of their ideas and behavior. This critical thinking is neither easy nor is it clear to many that it can even be done. That rational criticism can occur--and make a difference in our lives--is a judgment that students should come to as a result of their participation in the course in which this glossary is used.


A deductive argument is one that derives the truth of the conclusion from the truth of the premises. If the argument form, or structure of the argument, is valid, then the conclusion will always follow from the premises. The hard determinism argument below is an example of a deductive argument that makes use of two modus ponens arguments in which the conclusion of the first serves as the premise of the second, or so it appears.


Dictionaries report common usage. Hence they are good sources for learning how a word is ordinarily used or even the history of it use. Ideally, a definition will provide one with a criterion (or rule) that will allow one to pick out all and only those items that fit the definition. For example, understanding "bachelor" to be an adult, unmarried male, one can then rule out all non-adults, married persons and females, leaving only adults, unmarried persons and males. Thus one can use this sort of definition to identify everything (and only those things) that fits the rule provided by the definition. A definition in terms of necessary and sufficient conditions is good or bad depending on how well it performs this function. A definition of "university professor" as "one who teaches" is not very useful because it is too broad. It picks out more individuals, including middle school teachers and perhaps parents, than what should be properly classified as university professors.

The real problem in critical thinking, however, is in knowing which sense is being employed by a writer or speaker and if this sense actually fits what the writer/speaker is talking about.

When someone says that something is such-and-such, s/he is saying that this belongs in that category. Thus to say, "This is a great pencil for working crossword puzzles" is to make several claims:

The second claim is not a definition; rather it is the result of applying a definition. It asserts that a certain object belongs to the pencil category. To determine if it does one would need a description of the object and a specification of the features of pencils (see analysis), then one would apply these specifications to the object in question.

The three claims above illustrate the uses of "is". Not a word that would ordinarily require one to look at a dictionary, "is" can be troublesome if one confuses its various meanings. Let's identify the three uses above, then add a fourth.

Although "an object exists" does not use the word "is", I could have said, "An object is", meaning that it exists. So "is" sometimes asserts existence.

The second one, "this object is a pencil", is the "is" of class inclusion, discussed above.

The third one, "it is great for working crossword puzzles", identifies a feature of the pencil in question. In a way, it is including this pencil in a certain class--great for working crossword puzzles, but more precisely it is is identifying a characteristic of this pencil. (Some pencils because of their soft lead and ability to make a dark line are good for working crossword puzzles in newspapers because they leave a visible image but do not tear the newsprint.)

There is still a fourth sense of "is" that should be noted--the "is" of identity:

This is the pencil I was using yesterday.

Thus "is" is ambiguous; it has multiple but distinguishable senses. Indeed confusion can result if one has in mind one sense when actually another one is being employed. For example, "this pencil is Mike's special crossword puzzle pencil" could mean that the pencil belongs to Mike and is the one he uses to work crossword puzzles or it could mean that it is identical to the one Mike uses.

The Texas Icehouses article nicely illustrates some problems in definition.

Denying the antecedent

Denying the antecedent, like affirming the consequent, is a formal fallacy. Denying the antecedent has the following form, or pattern: if p then q, not-p, therefore not-q, or

if p then q

Both formal fallacies are easily confused with two valid argument forms: modus ponens and modus tollens. Here is an analysis of the four forms according to affirmation-denial and antecedent-consequent:

affirm(1)modus ponens(2)affirm the consequent
deny(3)deny the antecedent(4)modus tollens

(1) and (4) are valid argument forms; (2) and (3) are invalid.


In popular use a dilemma can be almost any sort of difficult choice, but in logic a dilemma is a choice in which there are only two options, attractive or not. One can refute a dilemma, that is, show that is not a real dilemma, by finding a third possibility. A false dichotomy is not a real dilemma; it is only presented as being one.


An argument that mistakenly takes as true of the parts what is true of the whole.

The United States of America is the richest country in the world. So every American is wealthy.

The relevant rule that division violates is: What is true of the whole is not necessarily true of the parts. This is the companion fallacy to composition and is its mirror image. Just because one can't lift a pallet of bricks does not mean that one can't lift each of the bricks on the pallet. Sometimes what is true of the whole is true of the parts. If a toy is made completely of plastic, say, a toy truck or doll house, then each of its parts is made of plastic.

In each case, composition or division, the reasoning is to note something that is true of the parts or the whole and then to assume that the whole or the parts is the same in the relevant aspect and to attribute the characteristic of the one to the other. A little bit of thinking about parts and wholes reveals, however, that sometimes significant differences occur when one moves from one to the other.

To keep the two fallacies straight: Remember that when one is composing something, one is putting things together. Thus the fallacy of composition occurs when one is moving from parts to wholes. Division occurs when one is taking things apart; similarly the fallacy of division occurs when one is moving from consideration of the whole to its parts.

The rule of thinking that is being violated is that one should treat similar things similarly. One violates this rule by treating partially similar things as if they were completely similar. Thus the fallacies of composition and division are like the fallacies of equivocation and weak analogy in this respect. They take what appears to be alike as alike, when in fact they differ in some important respect.


From a Greek word meaning "to experiment," it is used by philosophers to mean that which has to do with sense experience.

Empirical generalization

Empirical (or inductive) generalizations are general statements based upon experience.

Most student desks in older classroom buildings at UNC Charlotte have gum stuck underneath the desk tops.

A good generalization will be developed from a large number of varied experiences. For instance, one could offer as a justification for the previous generalization:

I've looked underneath several desks in several classrooms.

Generalizations drawn from a small number of instances or from anecdotal evidence are said to be hasty generalizations.


An argument which turns on the use of a term in two distinct senses, but treats the term as if it had a single meaning. The relevant rule that it violates is: Terms must be used consistently throughout.

There is a great deal of public interest in the brother of the suspected Unabomber. The media has an obligation to report what is in the public interest. Therefore, the media has an obligation to report information about the brother of the suspected Unabomber.

"Public interest" is ambiguous. In the first occurrence it means curiosity on the part of the public; in the second it means public welfare or benefit. The argument works only if there is a single sense for the key term, "public interest", but since it is used in two senses there are actually two terms with only a verbal similarity. The two terms look alike but they are logically distinct.

Novak's "Most Religious Century" commits the fallacy of equivocation.


An explanation identifies the cause of an event, thus answering the question why something is what it is or why it occurs. Historical explanations show how something came to be what it is. For instance, Old Shell Road in Mobile got its name because at one time the street was paved with shells dredged from Mobile Bay. A scientific explanation identifies the conditions that must be present for something to occur. For instance, an explanation of why matches light would identify, among other things, the presence of oxygen, a phospherous tip, a wooden stick and friction.

The following example, contributed by Lee-Marie Davis, a student in one of my critical thinking classes, explains why a particular explanation is an explanation:

Explanations identify causal relationships. They tell why or how something happens. The following is an example of an explanation:

My father was diagnosed with lung cancer two years ago. Of course, one of the very first questions out of his mouth was, "Why did this happen?" The doctor explained to my dad that he fit into three categories of risk factors that contribute to the onset of cancer in some patients. The first category that the doctor said my did fit into was that he had a history of cancer in his family. The second category was that my dad had smoked for almost 30 years, and the third category was that my dad had gone through a period of high stress.

This is an explanation because the doctor tells my dad why he had cancer. The doctor gives him three reasons that had put my dad at risk for lung cancer. He told him that he fit into the risk categories of family history, high stress and was a smoker. The explanation of the doctor helped my dad better understand why he had the cancer by telling him the cause of the cancer.


A fallacy is an attractive but unreliable piece of reasoning, or argument. It looks good but upon examination it turns out to be undependable.

They are often divided into two kinds--formal and informal. Formal fallacies include affirming the consequent and denying the antecedent. Informal fallacies include begging the question, composition, division, equivocation, false cause, false dichtomy, hasty generalization, personal attack, red herring, slippery slope, straw man and weak analogy. There are many other examples of bad reasoning that have been identified by logicians, but these are enough to illustrate the idea of a fallacy.

I ask students in my critical thinking classes to supply examples of the use of alternatives, definitions, distinctions, such as appearance and reality, explanations, as well as arguments and fallacies.

Chris Earls came up with this imaginative explanation of a false dichotomy:

A false dichotomy is the unnecessary limiting of one's choices.

Last year, while I was sound asleep in my room, one of my suite mates burst into the room with his friends, began talking and laughing loudly, and turned up his stereo. It was 3:00 in the morning and I had to get up at 6. So I walked into my suite mate's room and asked him and his friends very politely to quiet down. He then responded with the statement, "No, this is what college is about. You can either accept it or if you don't like it then go live somewhere else."

This is clearly a false dichotomy because my suite mate had unnecessarily limited my choices. I could have either accepted the fact that he can behave in a manner that disturbs me or I could go somewhere else to stay. It is quite apparent to me however that I have a plethora of choices:

  1. I can beat up my suite mate, along with his friends, and throw his stereo out the window.
  2. I can threaten him verbally so he will keep quiet.
  3. I can complain to the R.A.
  4. I can stay and join the "fun".
  5. I can contact security or campus police to handle the situation.
  6. I can stay in my room, then the next morning request my RC to remove them from the room permanently.
  7. They can find somewhere else to have "fun".
  8. I can tell them that college life is all about studying, going to class, getting to bed on time and getting up early, and that if they didn't agree to that, then they should drop out.

False cause

The wrongful identification of a causal relationship because of temporal or other proximity.

There are more laws on the books today than ever before, and more crimes are being committed than ever before. Obviously, all these new laws are just causing more crimes to be committed.

Examples of false cause, such as the preceding, that depend on temporal succession are called post hoc ergo propter hoc, which is Latin for "after this, so because of this." Superstitions are often examples of this fallacy. A coach who continues to wear the same sweater because his team has been winning is, at least implicitly, committing the fallacy of post hoc ergo propter hoc.

False dichotomy

The unnecessary limiting of one's choices. The relevant rule that it violates is: One's description of a situation should accurately describe the situation.

Either you carry an umbrella or you get wet.

One could choose to stay inside or, if s/he must go outside s/he could wear a rainsuit. Carrying an umbrella or getting wet are not one's only choices.

Here's a true story. I relate it here not only to provide another example of a false dichotomy but also to illustrate the need for critical awareness: After spending several class periods on the fallacies in a logic class one semester, we moved on to the section of the course where I required the students to generate a critical thinking example for the final. They could work it out with me ahead of time, but they had to find some situation or something they had read, identify the reasoning involved and then evaluate it--on the final exam. So one young woman, who had done A work all semester, asked me:

"Are you going to provide us with detailed instructions for the critical thinking examples?"

"No," I replied, explaining, "I have given you guidelines and examples, but no set of instructions. Moreover, I am willing to assist you prior to the final, coaching you on what you can come up with on your own."

"Well," she said, "if you don't give us detailed instructions, then I will be clueless about what to do."

So I said, as I went to the board and began to write, "Either I give you explicit instructions regarding the critical thinking examples or you will not know what to do."

"That's right."

She had no clue that she was employing a false dichotomy. Yet, I bet, if I had given her a quiz on fallacies, she would have been able to pick one out.

For other possible false dichotomies see "Let Parents, not Kids, Make the Choices" and "Who's To Say?".


Arguments often exhibit one or more reasoning patterns. These patterns, such as modus ponens or an argument from analogy, are called forms and are to be distinguished from the content of the actual argument. Just as a coffee cup or mug has a distinctive shape and is distinguishable from what you put it (the coffee or content), so argument forms are identifiable and not to be confused with the actual premises and conclusions used.

Hard determinism

Determinism is the view that all events are caused. One form of determinism, one that pushes the notion of universal causation to unacceptable consequences, is hard determinism. Here, in summary form, is an argument for this extreme view. I offer it as an example of a flawed deductive argument:

1. All events are caused.

2. If all events are caused, then there are no free actions.

3. There are no free actions (from 2 and 1 by modus ponens).

4. If there are no free actions, then there is no personal responsibility.

5. There is no personal responsibility (from 4 and 3, once again, by modus ponens).

There is nothing apparently wrong with the form of this argument, for modus ponens is a valid argument form. Unless one is prepared to accept the consequences that we lack both freedom and responsibility, then one must find some other error.

Hasty Generalization

A generalization based on too little or unrepresentative data. The relevant rule that it violates is: Generalizations should be based on a large number of various representative examples. Here is a note I once received from a student (the names have been changed):

Mr. Eldridge, As you notice, I was not in class Thursday, due to the flu. I gave my paper to Justin because he was going to class. On Sunday, I found out he did not attend class. Here is my revised paper. Let's hope this will work! Now, I've learned not to trust other people. Laura Walker

Hasty generalizations should not be confused with the fallacy of composition. In a hasty generalization one infers a general statement on the basis of an atypical instance; whereas in the fallacy of composition you take something that is true of each of the parts and attribute to the whole. Composition, like division, confuses distribution and collectivity (whether something is considered individually or as a whole); hasty generalizations infer something to be true generally on the basis of a limited number of unrepresentative instances.

Can you specify the ways in which the reading "Student Reactions to Eldridge and his CT Course" commits the fallacy of hasty generalization?


Inconsistency is to be avoided, for it indicates error. It is an implicit contradiction. An inconsistent set of statements will not be an outright contradiction but will lead to one. For example, if one declares:

All UNC Charlotte students are hardworking.
Jim Schwartz is a UNC Charlotte student, and
Jim Schwartz is lazy,

then s/he is being inconsistent. There is no contradiction here, such as,

Jim Schwartz is hardworking and Jim Schwartz is lazy,

but, clearly, there is an inconsistency. For if all UNC Charlotte students are hardworking, then it is impossible for Schwartz to be a UNC Charlotte student and not be hard-working. It is implicitly contradictory to say that Schwartz is UNC Charlotte student (and thus hard-working) and to claim that he is lazy, that is, not hard-working.

A friend once proposed, in reference to the Kosovo-Servian conflict, the principle that homogeneous groups should have co-terminus territories: one people in one place. Then, later in the conversation, she proposed, in reference to the lawsuit then being brought against the Charlotte-Mecklenburg school system, that we should require people to live in assigned, standard-size houses on standard-size lots. The residents would be assigned in such a way as to insure ethnic/racial diversity. In this way there would be no need for busing; we could have integrated neighborhood schools. Of course, once one sets the two proposals alongside one another one can grasp the inconsistency. The second proposal assumes a negation of the first proposal's principle of like people in one place. See consistency.


Unlike deductive arguments, inductive ones promise only probability, not certainty. Thus, if one argues that having watched several different newscasts in several different cities on many different nights one may infer that newscasts emphasize, in Bob Inman's phrase, "mayhem and misery", then one is making an inductive argument. (In this case, an inductive (or empirical) generalization. Another kind of inductive argument is an argument from analogy. Inductive arguments are judged by their reliability, where one expects only a high degree of probability, not one hundred percent reliability as with deduction.

Modus ponens

A valid argument form, not to be confused with affirming the consequent, modus ponens consists of a conditional statement and one other premise. The second premise affirms the antecedent of the conditional, yielding the consequent as the conclusion:

if p then q

Modus Tollens

A valid argument form, modus tollens is not to be confused with denying the antecedent. Modus tollens consists of a conditional statement and one other premise. The second premise denies the consequent of the conditional, yielding the denied antecedent as the conclusion:

If p then q

Necessary and sufficient conditions

If event A must occur for event B to occur, then we say that A is necessary for B. If event A may cause B but there could be some other cause as well, then we say that A is sufficient to cause B.

Personal attack

An argument that wrongly attacks the person rather than what the person is saying. The relevant rule that it violates is: Arguments should be considered on their own merits.

Tom has offered evidence that he was in Milwaukee on January 6. But Tom is not to be believed. He is a drug addict who has been convicted of lots of crimes. All of which are well documented. I don't care what evidence he has; his statement that he was in Milwaukee on that date cannot be believed because he is a terrible person.

The important thing to remember is that the claims about the person making the argument are irrelevant to the argument that the person is making. It should be considered on its own merits. If, however, the person's argument is dependent on his or her character, then his or her character can be considered. For instance, if someone says that you should believe him because he is a person of integrity, then charges against his character are relevant and can be taken into consideration.

So not all personal attacks are fallacious. Only those that inappropriately consider the person making the argument are fallacies.


Statements offered as reasons to support a conclusion are premises. Logicians generally pay more attention to the reasoning, that is, the relationship between premises and conclusion. They rely on scientists to determine the accuracy of the premises.

Red herring

An argument that implicitly shifts the issue. The relevant rule that is violated is: A refutation should stick to the issue or change the subject explicitly.

You say that Hyundais are great cars. But they are not made in the U.S. Given the state of the economy, we shouldn't be buying cars not made in this country. I don't see how you can say that they are great cars.

Red herrings distract the listener from the original issue. It is OK to change the subject, but one should do so openly. Those arguments that disguise the subject shift are unacceptable. In the example above it is true that Hyundais are not made in the U.S. and if the American economy were not doing well one might be able to offer to good reasons to buy only U.S. products. But one has not thereby offered reason to think that Hyundais are not well-made cars offering good value for the money. For one to be persuaded not to buy a Hyundai because it is not a good car, one needs reasons that speak to this claim.

Salva Veritate

A Latin phrase which literally mean "saving truth"; salva veritate is used by logicians to express the concept of truth preservation, which is the test of a valid deductive argument. If a deductive argument does not preserve the truth of the premises (assuming they are in fact true), then it has an invalid argument form. Salva veritate is the necessary and sufficient condition for a valid argument form.

Slippery slope

An argument that wrongly asserts that one situation will necessarily lead to another. The relevant rule that is violated is: A hypothetical syllogism is a valid argument form, but each causal connection must be correct.

You won't catch me calling on a student in class. You call on one student, then another asks a question. Before long they are all asking questions, and you have lost control of the class. Calling on students just leads to chaos.

Notice that a slippery slope is a series of causal statements cast in the form of a hypothetical syllogism (If p then q and if q then r; therefore if p then r). Thus it is not the form of the argument that is the problem; the problem lies in the quality of the causal statements. See false cause.


A deductive argument is said to be sound if it meets two conditions: valid argument form and true premises. (Notice that validity and true premises constitute necessary and sufficient conditions for soundness.)

Straw Man

An argument that distorts an opponent's position in order to make it easier to attack. The relevant rule that it violates is: A refutation should deal with the opponent's position fairly (or in the best possible light).

The textile workers have signed a petition for better ventilation in the work place. Unfortunately, air conditioning is expensive. Air ducts would have to be run throughout the mill, and a massive heat exchange unit installed on the roof. Also, the cost of operating such a system during the summer would be unreasonably expensive. Therefore their request must be denied.

A straw man fallacy is often confused with red herrings. Notice, however, that where red herrings distract the listener, a straw man distorts an opponent's position in order to more easily attack it.

Unstated premises

Not every argument is fully expressed. Sometimes premises or even conclusions are left unexpressed. If one argues that Rover is smart because all dogs are smart, he is leaving unstated that Rover is a dog. Here the unstated premise is no problem; indeed it would probably be obvious in context. But sometimes unstated premises are problematic, particularly if two parties in a discussion are making differing assumptions. If one person thinks violence depicted in the media encourages violent behavior and another does not, then an argument that proceeds as follows will be evaluated differently by the two parties:

There's too much violence on TV.
No wonder we have so much violence among kids these days.

What will appear obvious to the person making these statements will not be so clear to the person who may be wondering what is the connection between the premise--there's too much violence on TV--and the conclusion--no wonder we have so much violence among kids these days. Hence the need for critical awareness. One function of critical thinking is to make the reasoning under discussion explicit.


Vagueness is attributed to terms or statements that are fuzzy or indefinite. Sometimes it is appropriate be vague, sometimes not. For instance, if one says to dump the pail of water on the ground as opposed to the concrete driveway, then one does not have to be precise about the composition of the soil. But if one is thinking about planting azaleas, one needs to know what type of soil one has. Vagueness can be distinguished from ambiguity in that the latter has distinct senses. Vagueness does not; its senses are indistinct from one another. They just shade off into one another.


Validity is a characteristic of good deductive argument forms, those patterns which are one hundred percent reliable. It is impossible for a valid deductive argument with true premises to have a false conclusion. See soundness.

Venn diagrams

Diagrams developed by John Venn, an English logician, in 1881 to represent categorical propositions and categorical syllogisms. They consist of two (for propositions) or three (for syllogisms) overlapping circles and are commonly used in introductory logic courses to represent and test the validity of categorical syllogisms.

Weak Analogy

An argument that infers that because two objects or situations are alike, then what is true of the one is true of the other, yet fails to notice a telling difference between the two objects or situations.

No one objects to a physician looking up a difficult case in medical books. So no one should object to nursing students, when taking a logic exam, being permitted to use their reference materials.

A weak analogy is an argument from analogy; it is just not a very good one.

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Copyright 2000, 2001 Michael Eldridge