N A G O YA U N I V E R S I T Y L I B R A R Y W O R K S H O P S 2 0 1 5

How to use logic
practically
教養教育院
June 3, 2015

Instructor: Dr. Paul Lai

What is logic?
教養教育院

Logic is the “organon”, or
instrument of thought,
which is specifically usedfor acquiring knowledge.
According to Aristotle,
we would not come toknow anything without
logic.
384-322 BC

KNOWLEDGE ACQUISITION

When you see many people inside asubway station wearing a wet raincoat or
carrying a wet umbrella, what can you tell?

It must be raining outside.

KNOWLEDGE ACQUISITIONINFERENTIAL
R E L AT I O N

Existing information

New information

We c a n n o t g e t a l l t h e
information about the world
through our five senses.

Logical thinking enables us tomake inference (推論)beyond the information
perceived.

Understanding
how to make logical inferenceis vital for understanding logicalthinking

Fun Exercise!!
Solving Logical Puzzles

Puzzle 1:
Who is doing what?

Alonzo, Kurt, Rudolf, and Willard are four creative artists ofgreat talent. One is a dancer, one is a painter, one is a singer,and one is a writer, though not necessarily in that order.
(1) Alonzo and Rudolf were in the audience the night thesinger made his debut on the concert stage.
(2) Both Kurt and the writer have had their portraits
painted from life by the painter.
(3) The writer, whose biography of Willard was a best-seller,
is planning to write a biography of Alonzo.
(4) Alonzo has never heard of Rudolf.
What is each man’s artistic field?

Dancer Painter Singer Writer
Alonzo

YesNoNoNo

RudolfNoNoNoYesWillardNoYesNoNo

By elimination,
Finally,
We alsowe canitknow
is nowknow
thatclear
thatthat
No
Kurt
NoYesNo
AlonzoWillardKurt isisisthe
thepainterDancerRudolftheSingerwriterSome well-known
applications oflogical thinking

Example 1

Courtroom argumentations
exchange between
defense lawyers and prosecutors
based onthe charge(s) against an accusedExample 2

Parliament debate among
members of different political parties
based onsome policy making proposalExample 3

Crime Investigation
conducted by detectives
based on the crime committed

Logic&Knowledge

Logic&EverydayLifeLogic&Profession

Logic &Convincingness

A convincing support for thecentral idea is the one by which
someone can come to believethat the central idea is true.

In order to build aconvincing support, itis necessary to learn
how to build a logicalargument.

LogicalArgument

A logical argument is basically a
combinatorial product of premiseand conclusion, connected in way
that exhibits an inferential relation.

Peter is either at his office or at hisapartment.
Peter is not at his office.
Therefore, Peter is at his apartment.

PremisesPeter is either at his office or at hisapartment.
Peter is not at his office.
Therefore, Peter is at his apartment.
Conclusion

A Conclusion(結論)

A premise (前提)
is a proposition (命題)
upon
which
inference is based;
the proposition thatprovides grounds orreasons for theconclusion.

is a proposition thati s a f fi r m e d o r
supported by apremise or a groupof premises.

I. M. Copi, C. Cohen, 2005. “Introduction To Logic”, p. 7.

Two Kinds ofLogical Argument(Inferential Relation)

Deductive Argument(演繹的論証)In a deductive argument, the inferential
relation between the argument’s conclusion
and its premise(s) exhibits an absolutenecessity.
In other words, the conclusion is claimed tofollow from its premises with 100%
certainty.

Example of a Deductive Argument(1) All human beings are mortal.
(2) Peter is a human being.
(3) Therefore Peter is mortal.
If (1) is true, and (2) is also true,
then (3) must be true.

All human beings are mortal.
Peter is a human being.
Peter is mortal.

Being mortal

Human beingsPeterInductive Argument
In an inductive argument, the inferentialrelation between the argument’s conclusion
and its premise(s) exhibits only a probability.
In other words, the conclusion is claimed tofollow from its premise(s) with less than
100% certainty.

Example of an Inductive Argument(1) Most corporation lawyers are rich.
(2) Peter is a corporation lawyer.
(3) Therefore Peter is probably rich.

If (1) is true, and (2) is also true,
then (3) more likely true than false.

(1) Most corporation lawyers are rich.
(2) Peter is a corporation lawyer.
(3) Therefore Peter is probably rich.

Being richCorporationLawyer

PeterPremise

TrueConclusion

TrueConclusion is true/false
becausethe premises are true/false.

Exercises on
logical inference 1

Logical Inference
PremiseConclusion

Part A of the exercises is designed to train you
how to make a proper inference based on apremise.

Each one of the exercises comes with (i) one statement corresponding to afactual event, and (ii) four inference choices that follow from (i). Althoughmore than one of the four choices might be logical, you need to find outthe one that is most likely / certainly true following from the truth of (i).

e.g.
Ex-1. Paul is in London.
(a) Paul is on a business trip.
(b) Paul will not come back to Japan for a while.
(c) Paul is in England.
(d) Paul likes London.

Ex-2. There is a laptop computer found on a classroom
desk in Nagoya University.
(a) The computer belongs to Nagoya University.
(b) The computer belongs to one of the students whoused the classroom.
(c) Someone has forgotten to take the computer whenleaving the classroom.
(d) Someone came to the classroom with the computer.

Ex-3. A car is found parking in an area with the NO
PARKING sign.
(a) The car’s owner will soon receive an illegal parking
ticket.
(b) The car was driven or transported there by someone.
(c) The car was parked by someone who did not notice
the NO PARKING sign.
(d) The parked car will cause disturbance to the normal
traffic.

Ex-4. Tanaka has a piano in his office.
(a) Tanaka likes to play piano in his office.
(b) The piano is taking some space in the office.
(c) Tanaka’s office is very big.
(d) The piano is used for Tanaka’s work.

Exercises on
logical inference 2

Logical Inference
Conclusion

PremisePart B is designed to train you how to find theproper premise for a conclusion.

Each one of the exercises comes with one
conclusion and four premises. Find out thepremise without which the conclusion is mostcertainly false. Note that your consideration isrestricted to the four possible premises only, andyou are supposed to choose, among the four,
the one that provides the necessary support forthe conclusion. Further note that additional
premise or premises may be needed in order tomake the conclusion true.

Ex-1. Conclusion: Peter is in Nagoya.
(a):Peter is in the central part of the country.

(b):Peter is meeting some people who live inNagoya.

(c):Peter is in Asia.

(d):Peter is in the restaurant called “Nagoya ChickenWings”.

Ex-2. Conclusion: Today is Tuesday.
(a):Today is the second day of the week.

(b):

Today is the day for burnable garbage.

(c):

Today is the day that Paul teaches the AWC.

(d):

Today is not Friday.

Ex-3. Conclusion: Life is found on Mars.
(a):

The planetary environment of Mars is similar toEarth.

(b):Hydrogen is found on Mars.

(c):

The evolutionary history on Mars is similar to thaton Earth.

(d):Some movements are detected on Mars.

Ex-4. Conclusion: Peter submitted his programming
assignment on Monday.
Premise (a):Peter is a hard-working student.

Premise (b):Peter cares about his assignment verymuch.

Premise (c):Peter’s computer was working properly
before the submission.

Premise (d):Peter went to school early on Monday.

Exercises on
logical inference 3