1. Hypothetical Syllogism

2. Hypothetical syllogism
-a deductive argument which asserts the sequential relation between the two elements of a hypothetical proposition
-its main premise is a hypothetical proposition

3. Analysis of a hypothetical prop.
If it rains, then the roof is wet
C-consequent
A-antecedent
+ A
+ C
+ C
? A
- C
- A
- A
? C

4. Example
If public officials committed serious lapses, then they will be charged administratively.
Some police officers committed serious lapses.
Hence, they will be charged administratively. +A
Valid +C

5. - C Valid - A +C + A Invalid
Joe will not comeback unless he loves Michelle
Joe will come back
Ergo, he loves Michelle
If you truly love a person, you don’t stifle her growth.
Mickey lets go of Minnie to give her space for growth.
Thus, Mickey truly loves Minnie
- C
Valid
- A
Invalid +C
+ A

6. Types of Hypothetical Syll.
Conditional
Simple Conditional
If… then…
Unless…
Reciprocal Conditional
Only if C, A

7. Types of Hypothetical Syll.
Conditional
Biconditional
If and only if…
Pure conditional
If B, then C
If A, then B
Ergo, if A, then C.

8. Reciprocal conditional
Only if students are treated as mature persons will they act responsibly
But students are treated as mature persons.
Hence, they will act responsibly. +C
Invalid
+ A

9. Biconditional +A +C + C + A - C - A - A - C -A Valid - C
If and only if Perf is a millionaire will Cath marry him
Perf is not a millionaire
Hence, Cath will not marry him. -A
Valid
- C +A +C
+ C
+ A
- C
- A
- A
- C

10. Pure conditional If A is B, then X is Y. If X is Y, then C is D.
Ergo, if A is B, then C is D.
Rule:
The common element must be used once as antecedent and consequent.
If Nolan is honest, then he will tell the truth. If he will tell the truth, then he will implicate the officials behind illegal gambling.
Thus, if Nolan is honest, then he will implicate the officials behind illegal gambling.
_________
Common Element
_________

11. Pure conditional
If the president is sincere in stopping corruptions, she will investigate the COMELEC.
If she will investigate the COMELEC, she will discover the anomalous transactions on election automation.
Hence, if the president is sincere in stopping corruptions, she will discover the anomalous transactions on election automation.
If Filipinos live a truly Christian life, then they will take care of their environment. If Filipinos show true concerns for the environment, then they will take care of their environment. Thus, if Filipinos show true concerns for the environment, then they live a truly Christian life.

12. Disjunctive Syllogism
-a type of hypothetical syllogism whose main premise is a disjunctive proposition (Either… or…)
Types of Disjunctive
Perfect Disjunctive
-the main premise contains alternatives that cannot be both affirmed and denied.
Either he is telling the truth or he is telling a lie.
________________
_____________ +B
- A B +A +A -B
- A +B

13. Perfect Disjunctive Valid Jie’s necklace is either rare or common.
Matt is either a theist or an non-theist.
He is not a non-theist.
Therefore, he is a theist.
Jie’s necklace is either rare or common.
Jie says it is rare.
Hence, it is not common B
+ A
Valid
+ A
- B
Valid

14. Disjunctive Syllogism
Types of Disjunctive
Imperfect Disjunctive
-the main premise contains alternatives that cannot be both denied but can be both affirmed
Either you try or you won’t succeed.
_______
______________ +A ?B +B
? A
- A +B
- B +A

15. Imperfect Disjunctive
Jeff will either return to Malaysia or go to Singapore.
He is not going to Singapore.
So, he will return to Malaysia
Either he will engage in business or he will continue being an employee.
Georg will engage in business.
So, he will not continue being an employee. B
+ A
Valid
+ A
- B
Invalid

16. Conjunctive Syllogism
-a type of hypothetical syllogism whose main premise is a conjunctive proposition (cannot be both… and…)
-the main premise contains alternatives that cannot be both affirmed but can be both denied.
Pierre cannot be both in Albay and in Alcoy atst.
______
________ A ?B +A -B +B
- A B ?A

17. Conjunctive Syllogism
Fred cannot both be a civil servant and a private businessman at the same time.
He is not a civil servant at this time
So, he is a private businessman.
No government prosecutor can both vigorously do his job and receive bribe at the same time.
Some state prosecutors are not doing their jobs vigorously.
Thus, they are receiving bribes. A
+ B
Invalid
- A
+ B
Invalid

18. Valid Invalid Invalid The accused is either innocent or guilty.
Guevarra claims he is innocent.
Hence, he is guilty.
Either the president will not support population control program or Church groups will criticize him.
Many pro-Life Church groups are criticizing the president.
So, he is supporting population control.
One cannot be both a Muslim and Christian altogether.
Derek is not a Muslim.
So, he is a Christian.
+ A
- B
Valid
Perfect Disjunctive
Imperfect Disjunctive
+ A
- B
Invalid
Conjunctive
Invalid
- A
+ B