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 wet A-antecedent +A +C +C ?A C-consequent -C -A -A ?C Example If public officials committed serious lapses, then they will be charged administratively. Some police officers committed serious lapses. +A Valid Hence, they will be charged +C administratively. Joe will not comeback unless he loves Michelle -C Joe will come back Valid Ergo, he loves Michelle - A If you truly love a person, you don’t stifle her growth. Mickey lets go of Minnie to give her space for growth. +C Invalid +A Thus, Mickey truly loves Minnie Types of Hypothetical Syll. Conditional Simple Conditional If… then… Unless… Reciprocal Conditional Only if C, A 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. Reciprocal conditional Only if students are treated as mature persons will they act responsibly But students are treated as mature +C Invalid persons. Hence, they will act responsibly. +A Biconditional If and only if Perf is a millionaire will Cath marry him Perf is not a millionaire -A Valid Hence, Cath will not marry him.- C +A + C - C +C + A - A -A -C Pure conditional If A is B, then _________ X is Y. Common Element 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. 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. Disjunctive Syllogism -a type of hypothetical syllogism whose main premise is a disjunctive proposition (Either… or…) Types of Disjunctive a) 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. -B He is not a non-theist. Valid +A Therefore, he is a theist. Jie’s necklace is either rare or common. Jie says it is rare. +A Valid Hence, it is not common - B Disjunctive Syllogism Types of Disjunctive a) 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. -B Valid So, he will return to Malaysia + A Either he will engage in business or he will continue being an employee. Georg will engage in business. + A So, he will not continue being an - B Invalid employee. 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 time -A Invalid +B 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 -A jobs vigorously. Invalid Thus, they are receiving bribes.+ B The accused is either innocent or guilty. +A Guevarra claims he is innocent. Valid Hence, he is guilty.Perfect Disjunctive- B Either the president will not support population control program or Church groups will criticize him. Imperfect Disjunctive Many pro-Life Church groups are criticizing the +A president. Invalid So, he is supporting population control. - B One cannot be both a Muslim and Christian altogether. Conjunctive Invalid Derek is not a Muslim. - A +B So, he is a Christian.