Uploaded by marcuschan0613

005 Categorical Syllogisms (I)

advertisement
UGED1111C LOGIC:
CATEGORICAL SYLLOGISMS (I)
2021-22, Summer
Sapphires, WONG Sin Ting
Soundness
2

Sound argument
◼
A deductive argument that is valid and has all true
premises.
1. 所有人都有觸手。
2. 所有有觸手的都是殺手。
(F)
(F)
1. All buskers perform in public places.
2. Some buskers are singers.
(T)
(T)
3. 所有人都是殺手。
(F)
3. Some singers perform in public places.
(T)
unsound
sound
Soundness
3
Valid Argument
Invalid Argument
True Premises & True Conclusion
✓
✓
True Premises & False Conclusion

✓
False Premises & True Conclusion
✓
✓
False Premises & False Conclusion
✓
✓
Sound Argument
Arguments, Truth and Validity
4
Recap: Evaluating Arguments
5

Regardless of the type of argument, there are two
steps of evaluation:
◼
◼

How do its premises support its conclusion?
Are all premises true?
How about the inductive arguments?
Inductive Standard
6

Two key concepts:
◼
Strength (Strong/weak)
How do its premises support its conclusion?
◼
Cogency
Are all premises true?
Strength
7

Strong argument
◼

If all its premises are true, it is probable that its
conclusion is true.
Weak argument
◼
Its conclusion does not follow probably from its
premises.
Important Remark
8


Unlike validity, the strength of an inductive argument
is not an all-or-nothing concept.
It is a matter of degree.
30
1. Around 97 percent of CUHK students use a smartphone.
2. Mia is a CUHK student.
3. Mia uses a smartphone.
Cogency
9

Cogent argument
◼
An inductive argument that is strong and has all true
premises.
1. 大部份人從7層樓或以上的高度墮下都會死。
2. 梁振英於2018年8月24日從8樓墮下。
(T)
(F)
3. 梁振英已經死了。
(F)
uncogent
Summary
10
Sound
Valid
Deductive
Argument
Unsound
Invalid
(all are unsound)
Argument
Cogent
Strong
Uncogent
Inductive
Argument
Weak
(all are uncogent)
Agenda
11




Categorical Proposition
Translation
Venn Diagrams
Transformation Procedures
◼
Conversion, Obversion and Contraposition
Categorical Logic
12


This logical system was developed by Aristotle more
than 2000 years ago.
It is the major logical system before the
20th Century.
Categorical Proposition
13

A categorical proposition is proposition that relates
two classes, or categories.
◼
◼
The classes in question are denoted respectively by the
term
subject term and the predicate term.
On top of that, every categorical proposition contains a
quantifier and a copula (which links the terms).
Categorical Proposition
14
Quantifier:
All
Subject term:
CUHK students
Copula:
are
Predicate term:
clever students
Categorical Proposition
15

There are only 4 kinds of categorical propositions:
(A) All S are P.
(E) No S are P.
(I) Some S are P.
(O) Some S are not P.
Aside: The labeling comes from the Latin words Affirmo and Nego, “A” and “I” from the
former and “E” and “O” from the latter.
Quality of Categorical Proposition
16

Every categorical proposition is either affirmative or
negative.
◼
◼
“All S are P” and “Some S are P” are categorical
propositions affirming the class membership between S
and P.
“No S are P” or “Some S are not P” are categorical
propositions denying the class membership between S
and P.
Quantity of Categorical Proposition
17

Every categorical proposition is either universal or
particular.
◼
If a proposition concerns every member of the subject
term, it is a universal categorical proposition.
◼
◼
“All S are P” and “No S are P”.
If a proposition concerns some members of the subject
term, it is a particular categorical proposition.
◼ “Some
S are P” and “Some S are not P”.
Quality and Quantity
18
Affirmative
Negative
Universal
All S are P
(A)
No S are P
(E)
Particular
Some S are P
(I)
Some S are not P
(O)
Remarks
19

“Some” = “at least one”
◼

There are only 4 kinds of categorical propositions.
◼

“Some S are P” means “there exists at least one S that is
also P.”
“All S are not P” and “No S are not P” are not standard
form.
Subject and predicate terms must be plural nouns/noun
phrases as long as they are countable.
Exercise (1)
20









Which of the following categorical propositions is in
standard form?








All students who go to school by bus are LIHKG users.
沒有人是孤獨的。
(A)
Some birds fly south during the winter.
(E)
所有男人都是禽獸。
(I)
Only CUHK students are lunatics.
(O)
阿德是執葉的人。
All animals are not objects.
有些熊貓不是黑白色的動物。
All S are P.
No S are P.
Some S are P.
Some S are not P.
Translation
21

Subject and predicate terms must be both plural
nouns/noun phrases
◼
◼
「沒有人是孤獨的。」
→「沒有人是孤獨的人。」
“All politicians are hypocritical.”
→ “All politicians are hypocrites/hypocritical people.”
Translation
22

Copula must be “are” or “are not”
“Some birds fly south during the winter.”
→ “Some birds are animals that fly south during the
winter.”
◼
◼
「有些人喜歡盲目追隨潮流。」
→「有些人是喜歡盲目追隨潮流的人。」
Translation
23

Every categorical proposition must begin with
standard quantifiers
◼
「阿德是執葉的人。」
→「所有與阿德等同的人都是執葉的人。 」
“Oscar Wilde is a famous English writer.”
→ “All people identical to Oscar Wilde are famous
English writers.”
◼
Translation
24

Adverbs
“You should never read Hegel’s writings.”
→ “No times are times when you should read Hegel’s
writings”.
◼
“Whenever Beerus wants to sleep he sleeps.”
→ “All times Beerus wants to sleeps are times he
sleeps.”
◼
Translation
25

Unexpressed Quantifiers
◼
◼
* Context-dependent *
“Sapphires are blue gems.”
→ “All sapphires are blue gems.”
「獅子住在動物園。」
→ 「有些獅子是住在動物園的動物。」
Translation
26

Definite/indefinite articles
* Context-dependent *
◼
“A cat is a living creature.”
→ “All cats are living creatures.”
◼
“A man is killed in the accident.”
→ “Some men are people killed in the accident.”
Translation
27

Exclusive propositions
◼
◼
“Only CUHK students are lunatics.”
→ “All lunatics are CUHK students”.
「只有偉大的人才能撰寫歷史。」
→ 「所有能撰寫歷史的人都是偉大的人。」
Translation
28

Conditional propositions
◼
“If a man is rich, he is attractive.”
→ “All rich men are attractive men.”
“Unless a boy misbehaves, he will be treated decently.”
→ “All boys who do not misbehave are boys who will
be treated decently.”
◼
Venn Diagrams
29


Venn Diagrams were invented by John Venn.
It is a great tool for representing the relationships
between classes, or categories.
Venn Diagrams
30
All S are P
S
No S are P
P
S
= Emptiness
P
Venn Diagrams
31
Some S are P
S
Some S are not P
P
S
= Existence
P
Singular Propositions
32

「比路斯是破壞神。」
所有與比路斯等同的人都是破壞神。
比路斯等同的人
破壞神

有些與比路斯等同的人是破壞神。
比路斯等同的人
破壞神

If vs Only if
33

If (只要)
◼
只要是億萬富豪,就能娶女神。
所有億萬富豪都是能娶女神的人。
億萬富豪

能娶女神的人
所有能娶女神的人都是億萬富豪。
億萬富豪

能娶女神的人
If vs Only if
34

Only if (只有)
◼
只有是億萬富豪,才能娶女神。
所有億萬富豪都是能娶女神的人。
億萬富豪

能娶女神的人
所有能娶女神的人都是億萬富豪。
億萬富豪

能娶女神的人
Exercise (2)
35

Translate the following proposition to standardized
categorical proposition.
References
36
➢
➢
➢
Copi, I., Cohen, C., & McMahon, K. (2011). Introduction to Logic (14th ed. /
Irving M. Copi, Carl Cohen, Kenneth McMahon ed.). Upper Saddle River, NJ:
Pearson Education.
Hurley, P. (2015). A Concise Introduction to Logic (12th ed.). Australia ; Stamford,
Ct.: Cengage Learning.
Lau, J. (2011). An Introduction to Critical Thinking and Creativity : Think More,
Think Better. Hoboken, N.J.: Wiley.
Download