Hypothetical Syllogism

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

Analysis of a hypothetical prop.

If it rains, then the roof is wetA-antecedent C-consequent

+ A+ C

+ C? A

- C- A

- A? C

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

+CValid

Joe will not comeback unless he loves MichelleJoe will come backErgo, he loves MichelleIf 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- A Valid

+C+ A

Invalid

Types of Hypothetical Syll.

ConditionalSimple Conditional

If… then… Unless…

Reciprocal ConditionalOnly if C, A

Types of Hypothetical Syll.Conditional

BiconditionalIf and only if…

Pure conditionalIf B, then CIf A, then BErgo, if A, then C.

Reciprocal conditional

Only if students are treated as mature persons will they act responsiblyBut students are treated as mature persons.Hence, they will act responsibly.

+C

+ AInvalid

Biconditional

If and only if Perf is a millionaire will Cath marry himPerf is not a millionaireHence, Cath will not marry him.

+A+C

+ C+ A

- C- A

- A- C

-A- C

Valid

Pure conditionalIf 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

Pure conditionalIf 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.

Disjunctive Syllogism-a type of hypothetical syllogism whose main premise is a disjunctive proposition (Either… or…)Types of Disjunctivea) 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.

+A-B

________________ _____________

- A+B

+B- A

-B+A

Perfect Disjunctive

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

Disjunctive SyllogismTypes of Disjunctivea) 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

_______ ______________

- A+B

+B? A

- B+A

Imperfect Disjunctive

Jeff will either return to Malaysia or go to Singapore.He is not going to Singapore.So, he will return to MalaysiaEither 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- BInvalid

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

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 timeSo, 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

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

+ A- B

Invalid

Perfect Disjunctive

Imperfect Disjunctive

Conjunctive- A+ B

Invalid