Mei-Writing Academic Writing II(A) - Lecture 3

November 12, 2013

Advanced Logical Thinking Skills (2)A Logical Explanation of Causal Relation
by Paul W. L. Lai

Wednesday, November 20, 13

Group Discussion:
Think about your thesis statement again,
and judge whether it can be best supported
through either(1) a relation from group to individual(2) a relation from individual to individual

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Logic is essentially a study ofan inferential relation
between premise and conclusion.

PremiseWednesday, November 20, 13Conclusion

Consider a typical logical argument:(1) All human beings are mortal. ✔

Wednesday, November 20, 13(2) Peter is a human being.

✔

(3) Peter is mortal.

✔

A logical relation between P
and C is a relation based on
which the truth of C can beinferred from the truth of P.

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Kinds oflogical relation

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Certainty
Vs

Probability

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Two Ways ofbuilding an
inferential relation

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(1) By associating with a group(2) By eliminating possibilities

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(1) By associating with a group

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

Being mortal

Human beings

Peter

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(2) By eliminating possibilities

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e.g. Try the following:
I could not submit my homework on Monday
because my computer broke down on Saturday

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My computer broke down on Saturday.
The assignment must be done on a computer.
No other computer was available during the period.
My computer was not repaired in time.

I could not submit my assignment on Monday.
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How to build anindividual relationthat can belogically related?

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A logical relation between P
and C is a relation based on
which the truth of C can beinferred from the truth of P.

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Let us look at therelation between
P and Cand ask the following
questions:
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What makes P and C related?
What makes P and C unrelated?

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What makes P and C unrelated?

Only two reasons!!

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What makes P and C unrelated?

(1) The possibility for P tobe related to non-C.
(2) The possibility for non-P
to be related to C.
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What makes P and C related?
Eliminate the two possibilities!!!
(1) The possibility for P to
be related to non-C.
(2) The possibility for non-P
to be related to C.
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e.g. Smoking causes heart disease.
What makes smoking and heart diseaseunrelated?

(1) The possibility for smoking tocause non-heart disease.
(2) The possibility for heart disease
to be caused by non-smoking.
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What makes smoking and heart disease
related?

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e.g. Smoking causes heart disease.

Eliminate the two possibilities!!!
(1) The possibility for smoking tocause non-heart disease.
(2) The possibility for non-smoking
to cause heart disease.
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Let us look at therelation between
P and C

Wednesday, November 20, 13Four possibilities between P & C

P e.g. Smoking causes heart disease C
non-Pe.g. Stress causes lung cancer.

CP e.g. Smoking causes lung non-Ccancer.
non-P

non-Ce.g. Non-smoking causes Non-heart disease.
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What makes P and C related?
What makes P and C unrelated?

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What makes P and C unrelated?

P e.g. Smoking causes heart disease C
non-Pe.g. Stress causes lung cancer.

CP e.g. Smoking causes lung non-C
cancer.
non-P
non-C
e.g. Non-smoking causes Non-heart disease.
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What makes P and C unrelated?
(1) The possibility for non-P to be related to C.

non-P
Ce.g. Stress causes lung cancer.
(2) The possibility for P to be related to non-C.

P

non-C

e.g. Smoking causes lung cancer.

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What makes P and C related?
Eliminate the two possibilities!!!
(1) The possibility for P tobe related to non-C.
(2) The possibility for non-P
to be related to C.
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What makes P and C related?
Pnon-P

Wednesday, November 20, 13CCP

non-C

non-P

non-C

A new look at theNecessary & Sufficient
Conditions between P and C
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Sufficient Condition

PP is sufficient for CC

Necessary Condition
P is necessary for C

non-P
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non-CIf P,
Sufficientconditionthen C
Necessarycondition

PWednesday, November 20, 13CSufficient Condition
To say that the occurrence of P is a sufficientcondition of the occurrence of C is just to say:

If it is the case that P, then it is thecase that C.

P, therefore C
P
Wednesday, November 20, 13C

Sufficient Condition
PC“P, therefore C”
suggests that the presence of P guarantees thepresence of C. In other words, it is impossible for thepresence of P without the presence of C. For example, if
there is fire, then there is heat; the presence of fireguarantees the presence of heat. Thus it is impossible forthe presence of fire without the presence of heat.
However, although the presence of P guarantees thepresence of C, the absence of P does not guarantee theabsence of C. Thus it is possible that the presence of C iscaused by the presence of non-P. For, example, heat canbe caused by electricity.

Non-P

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C

If P,
Sufficientconditionthen C
Necessarycondition

Explosion

Fire Heat
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Necessary Condition
To say that the occurrence of P is a necessary
condition of the occurrence of C is just to say:

If it is not the case that P, then it isnot the case that C.

Not P, therefore Not C
non-P
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non-CNecessary Condition“Not P, therefore Not C” non-P

non-Csuggests that the absence of P guarantees the absenceof C. In other words, it is impossible for C to occur
without the occurrence of P. For example, if there is noheat, then there is no fire.
However, it does not suggest that the occurrence of P(alone) is sufficient enough for causing the occurrence ofC. Thus it is possible that the occurrence of C is notfollowed by the occurrence of P. For example, theoccurrence of heat alone cannot cause the occurrence offire.

PWednesday, November 20, 13

non-CIf P,
Sufficientconditionthen C
Necessarycondition

Fire Heat
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Sufficient & Necessary Conditions

P

P is sufficient for C

non-P
PC
non-C

P is necessary for C

non-P
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C

non-C

Sufficient & Necessary Conditions

P

P is sufficient for C

non-P
P

Eliminating the two
possibilities!!!

C

non-C

P is necessary for C

non-P
Wednesday, November 20, 13C

non-CSufficient & Necessary Conditions

P

P is sufficient for CCEliminating the two
P is sufficientandnecessaryforCpossibilities!!!
P is necessary for C

non-P
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non-C

P

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CClasswork:
Try building the premises for the following
conclusion:Peter cannot come to school on Tuesday.

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