- 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.
- 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 argument from analogy; 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
Not voting to re-elect Newt Gingrich would be like abandoning your
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 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
- 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
- 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."
- 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.
- 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
|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.
- Disjunctive Syllogism
- If there are only two possibilities, one of which is true, and then, if one is eliminated, the remaining one is true. Hence the following argument form:
Either X or Y
This form of argument is a disjunctive syllogism. It is a syllogism, that is, an argument with two premises, and one of the premises is a disjunction. Here is an ordinary language example:
Either you pass logic or you do not graduate.
You will not pass logic.
Therefore you will not graduate.
Fortunately, the first premise is not true. Hence the argument, while valid is not sound.
- 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
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
- 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
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 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, 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.
- 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
- 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.
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.
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).
- 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
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
- 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.
then s/he is being inconsistent. There is no contradiction here, such as,
Jim Schwartz is a UNC Charlotte student, and
Jim Schwartz is lazy,
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. See
- 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.
- Logic is the study of correct reasoning. It both describes and evaluates the way in which we draw inferences. Inferences are formulated as arguments and then evaluated as to their validity and soundness. The aim is to find generally reliable (see inductive) or always reliable (see deductive) arguments. Although logicians describe our reasoning patterns, this task is more properly the work of psychologists. The logician's primary concern is normative--how we should reason. The value of this ancient enterprise, which can be traced back to Aristotle and his predecessors, notably Zeno of Elea, is well expressed by the British philosopher, Patrick Shaw, in the preface to Logic and Its Limits (Oxford University Press, 1997):
Most of the time, the ordinary person does think straight. In countless ways social life depends on doing so. Balancing the housekeeping money, locating a fault in a wiring system, planning a day out--all involve, tacitly or otherwise, working out what is compatible with what. I cannot spend this pound and save it; if the bulb works in another socket then the fault does not lie in the bulb; either we catch the five o'clock train or we will not be able to get to the concert. These are the kind of commonplaces that underpin any sort of planned, purposive behaviour. They are largely taken for granted, and any mistakes in reasoning quickly run up against the harsh corrective of experience.
Problems arise when the test of experience is neither so immediate nor overwhelming. People speculate on what the facts might be when the facts are not obvious; and they disagree in their speculations. Also people pronounce upon, and disagree about, what ought to be the case, or whether one thing is better than another. They are not disagreeing about what is the case, so they cannot appeal straightforwardly to experience.
When these kinds of disagreement occur, when the competing claims cannot be easily and obviously tested, attention is bound to turn to the route by which a cotnroversial conclusion was reached. We are forced to become self-conscious about the reasoning process. How far reasoning will take us remains to be seen, but so far as it leads we must be sure that it is sound.
- Modus ponens
- A valid argument form, not to be confused with
affirming the consequent, modus ponens consists of
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
If p then q
- Necessary and sufficient
- 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.
- 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
- 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.
- A deductive argument is said to be
sound if it meets two conditions: valid argument form and true premises. (Notice that validity and
premises constitute necessary and sufficient
conditions for soundness.)
- Every proposition is either true or false. This status is called "truth-value".
- 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.
- 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
- Weak Analogy
- An argument that infers that because two objects or situations
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 © 1999, 2000 Michael Eldridge