Inductive Generalization (CT-7) is usually how we rationally come to accept a general claim, although we are sometimes in a position to complete an exhaustive tally, such as if I examine my rosters and count 63% of my students are first-year students.

If the generalization comes from a prior inductive generalization, and if that research had a large random sample, we can take the general claim as well established and use it as a premise in a new argument.
If the statistical generalization comes from a complete tally (as with all my current students, for example), it is well established and we can use it as a premise.

Having established a general claim, we can go on to use it as a premise in a new argument.

Any L-argument based on a given general claim (as a premise) to a more specific conclusion is an Argument from a Generalization.

Inductive Generalization (arguing TO a general conclusion)
Premise: A random sample of 3,000 adults found that 9.2% of them are left-handed.
Conclusion: Therefore, approximately 9.2% of all adults are left-handed.

Argument FROM a Generalization
Premise: Since about 9.2% of people are left-handed,
Conclusion: probably about 9 - 10% of the people in my city are left-handed.

General claims are broader, more inclusive, dealing with a whole population. ‘Genus’ is related to ‘general,’ meaning a broad group like canis.

More specific claims deal with a narrower group or an individual within that population. A species is a more specific group, like canis familiaris (dog), within the genus canis.

Statistical/Inductive Argument

If an argument from a general claim is an Argument from a Statistical Generalization (any statistic less than 100%, such as “63% of my students are first-year students.”), it’s an INDUCTIVE ARGUMENT.

An Inductive Argument is any argument claiming that the premises make the conclusion probable, or likely to be true, without guaranteeing the truth of the conclusion.

For example, suppose that

93% of students here (general group) know the capital of Georgia, and
Ella is a student here (particular case within the general group)
It follows, therefore, Ella probably (93% probability) knows the capital of Georgia

OR –

93% of students here (general group) know the capital of Georgia
Therefore, about 93% of my critical thinking students (more specific group within the general group) know the capital of Georgia.

Note that the “statistic” does not have to be presented numerically! Statistical concepts can be expressed in many different ways, such as:

Almost all towns and cities have a public library,
Most college students have downloaded MP3’s,
A large majority of Americans own televisions,
Virtually all Americans approve of the U.S. Constitution,
A majority of U.S. Senators are male.
ETC.

BEWARE:

“Some” does not give us a percentage — it only means “not none.”
“Many” is very vague — it does not have to be a majority, so it does NOT support a strong induction. We need to know how many!
Unquantified general statements, such as “cats are aloof,” do NOT support a strong argument, because they can express only the minimal “some.”

Strong vs. Weak Induction

A STRONG Inductive Argument — the premises make the conclusion more than 50% likely.

Even though the conclusion MIGHT be false with true premises, if it’s more likely true than false, the argument is strong.

With testing inductive arguments, possibility is nothing; PROBABILITY is everything!

A WEAK Inductive Argument — The Premises do not make the conclusion more than 50% likely (i.e., it’s 50% or less). For example, suppose 20% of the city council members are left-handed, and Maria is on the city council. Concluding from just this information that Maria is left-handed would be very weak!

Categorical/Deductive Argument

A DEDUCTIVE ARGUMENT IS ANY L’ARGUMENT CLAIMING THAT:
—IT IS IMPOSSIBLE FOR THE PREMISES
TO BE TRUE WITH A FALSE CONCLUSION
—IF THE PREMISES ARE ALL TRUE, THE
CONCLUSION MUST ALSO BE TRUE
—IF THE CONCLUSION IS FALSE, THERE
MUST BE AT LEAST ONE FALSE PREMISE

An Argument from a Universal Generalization (100% of a group, absolute, categorical) is one type of deductive argument, because it claims that the premises guarantee the conclusion.

For example,

All students here (category 1) are college students (category 2)
All college students are people above the age of seven (category 3)
Therefore, all students here are above the age of seven.
———
[The conclusion follows with certainty if the premises are true.
—This means that if the conclusion is false, there must be a false premise.]

These are sometimes called Categorical Argument (or Syllogism). The categorical (exception-less) statements involved are:

“All S are P”
“No S are P”
“Some S are P”
“Some S are not P”

We can express these using only “All” & “Not”:
All S are P
All S are not P
Not All S are not P
Not All S are P

Examples:

All students are people.
No students are penguins.
Some students are emo (= IT IS NOT TRUE THAT — No students are emo)
Some students are not emo (= NOT All students are emo)

Circle diagrams or Venn diagrams are a natural tool for testing categorical deductions.
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Watch out for some confusing features of ordinary language. For example, “All that glitters is not gold” and “all coffee cups are not recyclable” look like they have to same form. BUT:

All that glitters is not gold = Some glittery things are not gold
All coffee cups are not recyclable = No coffee cups are recyclable

Also, watch out for “only.” Don’t assume an “only” if it’s not stated (see below), but also proceed with caution when it is present. “Only S’s and P’s” does NOT mean “All S are P,” but rather “All P are S”!!
For example, “Only professional players are on the Warriors” = “All Warriors players are professional.”

The Imposters

“Some” and “many” do not support a strong inductive argument from a generalization.
Also, generalizations without any quantifier (“cats are aloof”) do not support a strong argument.

One of the most common mistakes with deductive categorical arguments is to interpret the “all” as “all-and-only.” Repeat after me, “All does not imply only!”

For example,

All members may use the pool
Abernathy was allowed to use the pool
Therefore, Abernathy must be a member
[If the 1st premise said “all and only members,” then the conclusion would follow.]

OR

No notes or books are allowed during the test
Searching the web is not my notes or book
Therefore, searching the web is allowed

These arguments are obviously meant to prove their conclusions absolutely, so they are deductive. But they fail because of a logical mistake.

These arguments are invalid, deductive fallacies.

****************************

And it is irrelevant to think about whether Abernathy is probably a member.

With testing deductive arguments, probability is nothing; POSSIBILITY is everything! It’s possible that Abernathy got in with a guest pass. Hence, the argument is a logically incorrect deduction.

It doesn’t matter if our conclusion is actually true; ‘fallacy’ does not mean false. It is a fallacy simply because the conclusion could be false with the premises still being true.

There are many other common mistakes. Using a diagramming method helps to evaluate the argument more objectively.

FALLACIES FROM STATISTICAL GENERALIZATIONS:

If numbers are used, such as 68%, there can still be a fallacy if the individual or subgroup in the conclusion is likely to be atypical. For example, from the premise “60% of the students here are female,” and the premise “Thomas is a student here,” we do not get a high probability that Thomas is female. You can draw on your background knowledge that someone named Thomas is very unlikely to be female.
Beware of “some” claims used to support an inductive conclusion. For example, “Some students here are socialists” and “Rosa is a student here,” we do not get a conclusion that Rosa is probably a socialist!
Likewise, beware of “many.” “Many students here are socialists” does not support a probable conclusion.
And unquantified generalizations must be presumed weak unless there is clear indication of a majority.

The arguments above, which assume that an all-statement implies all-and-only, is a LOGICAL FALLACY, just as Hasty Generalization is a logical fallacy we looked at in the last chapter.

Hasty Generalization is an INDUCTIVE logical fallacy, intending to make the conclusion likely, but failing.

The argument about Abernathy and the pool is a DEDUCTIVE logical fallacy, intending to prove its conclusion absolutely, but failing.

Fallacies as Thought Illusions

It is useful to compare many logical fallacies to perceptual illusions. Logical fallacies could be called thought illusions.

Even after we have identified them as illusions, they continue to exert a pull on us.
They do not indicate that we are generally incompetent. They are the predictable “glitches in the system” that you would expect in any complex process.
The only way we have to cope with them, since we don’t have a cure, is practice, practice, practice. Become very familiar with their patterns and where they are likely to occur and practice constant vigilance to watch out for them.

Find fun optical illusions at http://brainden.com/optical-illusions.htm. Just for kicks.

See also: https://www.youtube.com/watch?v=2k8fHR9jKVM.
:-/