What is a logical argument?
What is inductive reasoning?
Fundamentals of Academic WritingLogical relations• Deductive logic– Claims to provide conclusive support for the truthof a conclusion– Valid argument, true premises yield true conclusion• Inductive logic– Arguments support a conclusion, but do not claim
to show that it is necessarily true.
– Strong arguments suggest likely conclusions.

Logical relations• “A great many arguments are not designed todemonstrate the truth of their conclusions[but] to establish them as probable.”– Irving Copi, Introduction to Logic

Inductive logic• Does not seek to prove the conclusion• Offers support for a probable conclusion– Statistical likelihood– Generalization– New data can strengthen (or weaken)

Syllogism• Review: (deductive/categorical) syllogism– All P is M.
– All M is Q.
– Therefore, all P is Q.

• Categorical: Premises are either true or not.
• (Plus, the middle term must be true for “all” inat least one of the premises.)Statistical syllogism• Statistical syllogism– Like a syllogism, conclusion is inferred from twopremises.
– Unlike (deductive) syllogism, the premises are notcategorical.
– X portion of S is Q.
– J is S.
– Therefore, J has X likelihood of being Q.

Statistical syllogism– X portion of S is Q.
– J is S.
– Therefore, J has X likelihood of being Q.

Most* children who survive until their fifth birthday
live to be over 70 years old.
Kobayashi is over five years old.
Kobayashi will most likely live to be over 70.

Statistical syllogism
Most* children who survive until their fifth birthday
live to be over 70 years old.
Kobayashi is over five years old.
Kobayashi will most likely live to be over 70.
*Note that statistical syllogisms don’t have touse numerical statistics. Many use words like“most” or “few”.

Statistical syllogism
Stocks typically outperform bonds during the firstrecovery year after a recession. Japan experienced arecession during 2012-13, but is now experiencing
recovery. Therefore, stocks will probably do better thanbonds in 2014.**This is just an example. It is not actual investment advice.

Statistical syllogism
Ninety-two percent of Nagoya University students arefrom Japan.
Suzuki is a Nagoya University student.
Therefore, Suzuki is likely (92%) to be from Japan.

Statistical syllogism
Only 0.1% of Nagoya University students are fromBrazil.
Silva is a Nagoya University student.
Therefore, Silva is not likely (only 0.1% likely) to befrom Brazil.

Be careful!
• An individual may be a member of manyclasses.
• Arguing from an inappropriate class may yielda conclusion that appears strong, but ismisleading or false.

Be careful!
Ninety-two percent of Nagoya University students arefrom Japan.
Chen is a Nagoya University student.
Therefore, Chen is likely (92%) to be from Japan.
• But Chen is a graduate student, and only 78%
of Mei-Dai graduate students are from Japan.

Be careful!
• Don’t confuse particular (some, most, 92%) for
categorical (all) statements.
Logic looks OK, but
Most birds can fly.
conclusion is false.
This penguin is a bird.
Therefore, this penguin most likely can fly.
• Particular cases may not follow general rule.
• Be careful to account for possible exceptions.

Be careful!
• Don’t confuse particular (some, most, 92%) for
categorical (all) statements.
Only 0.1% of Nagoya University students are from Brazil.
Silva is a Nagoya University student.
Therefore, Silva is not likely (only 0.1% likely) to be fromBrazil.
But Silva is a common name in Brazil, and more Nagoya
students come from Brazil than from other non-Asian countries.

Analogy• Argument from analogy
P is similar to Q regarding property a, b, c
P has property d
Q probably has property dAnalogy• Apples are deciduous trees. Pears are deciduous trees.
• Apple trees flower in spring. Pear trees flower in spring.
• Apples fruit in summer or fall. Pears fruit in summer or fall.
• Apples are cold-hardy. Pears are cold-hardy.
• Apples can grow at high altitude.
• Therefore, it is likely that pears can grow at high altitude.

Analogy
The structure of atoms, with electrons orbiting nuclei,resemble planets orbiting stars. The electrical force that
holds electrons near their nucleus is similar to thegravity that holds planets around their star. Both gravity
and electrical force decrease in strength with the squareof distance.
It follows that electrons should move around nuclei inthe same way that planets move around stars.

Analogy• Evaluating the strength of analogy– Number– More instances strengthen analogy; fewer
instances weaken it.
– More (relevant) similarities suggest stronger analogy.
– Dissimilarities weaken the analogy; fewer
dissimilarities suggest stronger analogy.
– (Deductive reasoning is either valid or not;number doesn’t strengthen it.)

Analogy• Evaluating the strength of analogy– Relevance– Similarities must be relevant to the conclusion.
– Diversity– More variety among instances and similarities
suggests stronger analogy. If the points ofsimilarity are the same type, analogy is less strong.

Generalization• Inductive generalization
S1 is P.
S2 is P.
Therefore, it is likely that S3 is P.
(OR) Therefore, it is likely that all S are P.
– Resembles analogy– Strengthened by repeated measures

Generalization
Twenty-seven patients came to the hospital withyellow fever. Each of the 27 patients was bitten bymosquitoes. Therefore, it is likely that everyone withyellow fever was bitten by mosquitoes.

Generalization• Statistical generalization
X % of S observed are P.
Therefore, it is probable X % of all S are P.

– “Margin of error” – chance conclusion is wrong– Larger observed sample, smaller margin of error

Generalization
A sample of 1,054 voters were asked whether they
approve of the government. Fifty-eight percent of people
surveyed say they approve; 34% say they disapprove.
Therefore, it is likely that most voters approve of thegovernment.
(Given the sample size, the margin of error is about 3%.
For details, take a statistics class.)

Generalization• Beware of hasty generalization: big conclusion
based on a small sample.
Since entering this town, I have seen three people. Allthree were children. Therefore, people in this town areprobably all children.
“Extraordinary claims require
extraordinary evidence.”-Carl Sagan

Be careful!
• How big the sample? Small samples mean lessconfidence, more chance of hasty generalization.
• Is the sample representative (typical) of thepopulation?