The field of logic is concerned with arguments, in
which two or more statements (called premises or propositions) are presented in order to
assert a new claim (the conclusion). Logic is the means by which reliable conclusions are
drawn and verified from the stated premises.
Logic makes use of two types of reasoning: inductive and
deductive. Inductive reasoning starts with specific facts and tries to create general
conclusions, while deductive reasoning starts with general concepts and works toward
Inductive reasoning is based upon arguments which do not contain categorical
support for a conclusion. Rather, they confer only probability on the conclusion, which
means that it is possible for premises to be true and the conclusion false.
premise that "Most people like ice cream" is true, as is the premise that
"Mary is a person". The conclusion that follows, "Mary likes ice
cream" is logically correct, but may not be true. The reason for this is that while
we have stated that most people like ice cream, Mary may not be one of them.
Because inductive reasoning is based upon probabilities, conclusions are considered to be cogent,
rather than true. This is because the probability exists that the two accepted premises
may not truly lead to the acceptable conclusion.
When developing or listening to an
argument, words such as "Most" or "Some" are a tipoff that inductive
reasoning is being applied. There are two significant ways in which the conclusion
can be wrong:
- It may fall outside of the probability range of the premises,
as in the example above.
- The premise itself may be inaccurate -- Words such as
"many" and "some" could be nothing more than editorializing or wishful
thinking by the presenter.
If possible, try to
turn "Most" into a specific amount, e.g., "80%." Doing so will provide
a more accurate framework in which to assess the argument, while not being able to do so
is cause for skepticism.
Unlike induction, deductive arguments provide absolute support for a conclusion. Deductive
reasoning makes the strong assertion that the conclusion must follow the premises
out of strict necessity. Denying the conclusion means that at least one of the premises is
self-contradictory and thus not true.
From the statements "All creatures need water to live" and "I am a
creature" follows the conclusion that "I need water to live" Note that the
critical difference between this line of reasoning and the previous inductive example is
the word "All" rather than the word "Most".
Because deductive conclusions must be true if the premises
are true, a logically correct deductive argument is termed valid. (Note also that
deductive reasoning takes arguments from very general to very specific outcomes.)
The key to the credibility of a
deductive conclusion lies in the premises. Since the conclusion must follow from
the premises, the only way for a deductive argument to be considered invalid is if one of
the premises is proven false. Make sure that the word "All" truly applies to
the premise in which it is used. Otherwise, the argument will fall apart.
One of the most basic and powerful types of logic is the syllogism, which is a
simple form of deductive reasoning. Syllogisms consist of a minor premise, a major
premise, and a conclusion, and are of the form If A=B; and B=C; then A=C.
|Murphy is a dog.
|All dogs can bark.
||Murphy can bark.
There are at least three ways in which syllogisms and
their conclusions can produce faulty conclusions:
The Undistributed Middle
This fallacy occurs when the middle term is undistributed, meaning
that it doesn't take into account all of the members of the group being described. An
undistributed term makes generalizations invalid, since it doesn't allow for all
conditions to be considered. The Undistributed Middle is probably the most common type of
|The Fallacy of the Undistributed Middle
|Oak trees are fast growing plants.
|Some fast-growing plants don't need much water.
||Oak trees don't need much water.
In this example, the conclusion cannot be
supported by the facts, thanks to the word "Some" in the second premise. It is
possible for the oak tree to be a plant species that is fast growing and requires a
great deal of water. In fact, it may be that oak trees grow quickly because they
consume large amounts of water!
This example is very similar to the one used above in the Inductive Reasoning section above. Again, words like
"some," "many" and "most" are clues that the logic must be
The Illicit Major
An Illicit Major fallacy occurs when the predicate (last part) of the conclusion is
broader than the premises allow:
"Dolphins are mammals, not fish. Dolphins swim in the ocean. Therefore, fish don't
swim in the ocean." In this case, the premise that "dolphins are mammals, not
fish" is undistributed, but ends up (illicitly) as part of the conclusion. The part
of the conclusion that's wrong is the predicate "don't swim in the ocean."
The Illicit Minor
An Illicit Minor fallacy occurs when the subject (first part) of the conclusion is
broader than the premises allow:
"Dolphins are mammals. All dolphins swim. Therefore, all mammals swim." Here,
the premise of swimming is undistributed, but ends up in the conclusion. The part that's
wrong is the subject "All mammals."
There are many, many other types of reasoning
fallacies. Here are some of the most common:
Conclusion (ignoratio elenchi)
This type of fallacy occurs when an argument is directed at proving an irrelevant or wrong
legislator is trying to argue about the merits of her welfare reform bill. Instead of
talking about the specific points in the bill, she bases her presentation on the premise
that "every American is entitled to a decent standard of living." While the last
point may be true, it does not logically make the case that the bill in question will lead
to the desired outcome.
There are quite a few variations of the Irrelevant
Conclusion, including personal attacks and emotional
Arguing from Ignorance
A fallacy of this type is based on the supposition that failing to disprove an argument
means that the premise must be true. Believing in ghosts because it has not been proven
that they do not exist is a prime example, as are other forms of superstition.
After This, Because of That
(post hoc, ergo propter hoc)
This fallacy is also a cause of much superstition, as two independent occurrences become
linked in an erroneous cause-and-effect relationship.
black cat runs in front of you on the way to work. After you arrive at the office, you
spill coffee on your boss and believe that the black cat brought you bad luck.
This may sound silly, but post hoc, ergo propter hoc
fallacies are not uncommon in scientific experiments in which the data point to
statistical correlations that may not really exist:
survey indicates that the bird population in a certain area is declining, and is
statistically correlated with increases in the human population. There may be a
correlation, but without looking at other factors including predator/prey populations and
rainfall, a valid case cannot be made that the decline in the bird population is due to
increases in the human one.
The Personal Attack
The Ad Hominem fallacy creates an irrelevant conclusion by attacking the person rather
than the argument.
"Thomas Edison couldn't have possibly invented the light bulb because he failed at so
many of his other inventive endeavors."
Ad hominem fallacies are very common in political fights,
where candidates attack each other's character, rather than their platform or
accomplishments. Sometimes, these type of arguments make sense -- If a candidate has a
long record of reneging on promises, it is reasonable to argue that future promises may
not be kept. However, it is not valid to argue that a candidate's broken promises in the
past indicate that his or her position on welfare reform is untenable.
Composition and Division
Fallacies of composition involve applying standards from a small set to a much
"If a few ladybugs help control insect pests, a huge number of them will be even more
beneficial." This may turn out to be anything but the truth!
Fallacies of division result when we assume that the value of the whole will be
distributed to the parts:
"The Rolling Stones were one of the most successful rock and roll groups of the
Century. Therefore, each of the members will be highly successful when the band splits
up." Not necessarily!
These two fallacies can be summarized as follows: If a little is good (bad), a lot is
better (worse); or if a lot is good (bad), a little will also be good (bad). Watch out for fallacies of composition and division when reviewing
arguments related to issues of risk, economics
Arguing that "if a very large dose of a certain drug or chemical is harmful, a small
one will be harmful, too" may be a fallacy of division. Conversely, arguing that
"if a small amount of a drug or chemical is safe, a large amount will also be
safe" may be a fallacy of composition.
Begging the Question
Otherwise known as a circular argument, the conclusion also appears as an assumption and
creates a faulty line of logic, as follows:
Ann: "To approve your application, we
need a reference."
Sam: "Why not talk to my friend Bill?"
Ann: "OK, but how do I know that Bill is trustworthy?"
Sam: "I'd be happy to vouch for him."
The Slippery Slope
This fallacy occurs when, without sufficient evidence, an idea is criticized because it
will inescapably lead to a cataclysmic result. It is assumed that once a proposal is set
in motion, results slide down an unrecoverable slippery slope.
"Television is a powerful medium that allows people to view horrible acts of
violence. Viewing horrible acts of violence will make people more violent themselves. The
next thing you know, the murder rate will skyrocket and we'll all be forced to barricade
The Complex, or Loaded,
This fallacy is based upon a question in which the answerer who responds directly will
automatically become committed to its presuppositions, which are usually very unfavorable.
The classic situation is:
Yes or no professor, have you stopped
beating your wife?
Not matter if he answers 'yes' or 'no', the professor will be
considered to have beaten his wife at some point in time.
This trick is used often, as in "When did your firm
first learn that it was polluting the environment?" or "Have you told the
members of the group that you have been illegally using hard-earned donations from
thousands of contributors to pay for your personal expenses?"
"It's not just what
you say, but how you say it."
If logic tells us what to say, rhetoric tells us how.
Such familiar linguistic
terms as the metaphor,
simile and euphemism ; as
well as irony,
are all rhetorical tools.
Rhetoric can be used to increase the
power of logic. Going back to the concept of the syllogism, there is a short form known as
"You can't create a successful program without a lot of money, and we certainly have
a long way to go before we can call ourselves successful." The audience is left to
figure out that there isn't a lot of money available.
This approach draws the audience into the presentation by
making them actively involved. This cooperative understanding helps provide the speaker
with a greater level of credibility, which is a very valuable commodity, especially if the
next part of the presentation involves fund raising.
But rhetoric can also be used to confuse or offset logic,
either through word play or emotional appeal.
Wordplay can be especially hard to decipher, especially when it's used in advertising
(which it frequently is).
An aspirin manufacturer claims that "when it comes to pain relief, there's nothing
better than our Blaxo."
At first glance, most people will think this means that Blaxo
is the best product on the market. A closer look tells a different story: By stating that
there is nothing better, what is really being said is that Blaxo and its competitors
There are four common appeals which can legitimately be called logical fallacies as well
as rhetoric. They are listed here rather than in the logic section because of their
emotional nature, as well as the fact that, in some cases, they actually may be valid
Logic and rhetoric
together form the basis of reasoning, making them essential to the
process of critical thinking. A thorough understanding of both will significantly increase
the chances of making good decisions and decrease the chances of being fooled by faulty
arguments or clever use of words.
Here are concepts to consider when being asked to agree or
disagree with a particular statement or point of view:
Reasoning Crib Sheet
- Break arguments down into easy-to-understand steps of the
A=B, B=C variety. If arguments seem too complex to be broken down, treat them with
- Be careful about drawing firm conclusions when the premises
include words like "some", "many" or "most." These words
signal the use of inductive reasoning, which means that conclusions are based upon
probabilities, and are not certain.
- Be sure that premises using the word "All" are
true and not merely hyperbole. Also, clarify statements that lead you to assume the
word "All", such as "Trees need lots of light." It's possible that
some trees can grow well in the dark, making airtight conclusions impossible.
- Avoid other overly conceptual generalizations, such as
"science has discovered that..." or "from history, we have learned
that..." No one person can speak for all of science, history, medicine, etc.
- Appeals based upon emotion, not facts, are cause for
skepticism. The lack of hard data or evidence indicates that the presenter is on shaky
- Make sure that authorities are speaking within their areas
of expertise. An economist is not an expert on ecology any more than an ecologist is
an expert on the economy.
- Make sure that authorities truly are authorities. Like
the rest of us, actors, musicians, politicians and sports figures cannot usually be
counted upon to truly understand fields outside of their own. Unless talking about their
particular expertise, their opinions are worth no more or less than yours.
- Be wary of claims stating that if a little of something is
good, than a lot will be great; or if a lot of something is bad, a little of it also will
be bad. There are very few linear relationships in the real world. Complex
interactions are characterized by thresholds of change and not by ongoing, straight-line
- Trust your instincts. If the presented case doesn't
seem to make sense, or defies common sense, get more information or ask to have the
- Ask for help. Very few people can effectively think
through complex issues by themselves. Don't be afraid to get additional help or advice!
References On the Net...
compiled by Lee Honeycutt at Iowa State
Composition, a large database at Carnegie Mellon University
Stephen's Guide to the
References Off the Net...
(Clicking on the link will take you to the appropriate
catalog page of Amazon.com, where you can learn more about the book and/or order it.)
Thinking, Hy Ruchlis (Prometheus Books, 1990).
- The Elements
of Logic, Stephen F. Barker (McGraw-Hill, 1989).
Logic, Douglas N. Walton (Cambridge University Press, 1989).
- The Logic of
Failure, Dietrich Dorner (Perseus Press, 1997).
- The Power of
Logical Thinking, Marilyn vos Savant (St. Martin's Press, 1997).
- The Realm of
Rhetoric, Chaim Perelman (University of Notre Dame Press, 1980).
"Reason sits firm and holds the reins, and she will not
let the feelings burst away and hurry her to wild chasms. The passions may rage furiously,
like true heathens, as they are; and the desires may imagine all sorts of vain things: but
judgement shall still have the last word in every argument, and the casting vote in every
-- Charlotte Brontė
©1998 The Center for Informed Decision Making