Introduction To Propositional Logic PDF

INTRODUCTION TO PROPOSITIONAL LOGIC  WHAT IS AN ARGUMENT? An argument is a unit of thinking that is composed of: Premises [ statement(s) that support a..] Conclusion e.g: P1: Democracy requires an enlightened population that can think critically about the different issues. P2: Education...

INTRODUCTION TO PROPOSITIONAL LOGIC  WHAT IS AN ARGUMENT? An argument is a unit of thinking that is composed of: Premises [ statement(s) that support a..] Conclusion e.g: P1: Democracy requires an enlightened population that can think critically about the different issues. P2: Education plays a key role in teaching critical thinking skills C: Education plays a key role in the successful functioning of a democracy  TYPES OF ARGUMENTS Deductive Inductive A deductive argument is one where the An inductive argument is one where the conclusion follows necessarily ( with conclusion follows contingently certainty) from the premises (probably) from the premises If P is/are true, then C must be true If P is/are true, then C probably is true e.g: Categorical Syllogism, Deductive e.g: causal reasoning, empirical Syllogism, Modus Ponens, Modus Tollens generalizations DEDUCTIVE ARGUMENTS Categorical Syllogism A deductive argument in which all P(s) & C are categorical. Venn diagrams are useful in capturing this logical form. e.g.: P1: All men are mortal P1: All students who attend class regularly will pass P2: Socrates is a man the course. P2: Some in section 3 attends class regularly. C: Socrates is mortal C: Therefore, some in section 3 will pass the course. DEDUCTIVE ARGUMENTS Disjunctive Syllogism A deductive argument in which alternatives are presented. Useful in deducting through exclusion. e.g.: P1: He either owns a cat, or a dog P1: The answer is either A or B P2: He doesn’t own a cat P2: I know it is not B C: The answer must be A C: He owns a dog DEDUCTIVE ARGUMENTS Modus Ponens P1: If X then Y P2: X A conditional deductive argument which affirms the antecedent C: Y e.g.: P1: If I win the lottery, I’ll be rich P1: If it rains, the ground will be wet P2: I won the lottery P2: It is raining C: Therefore, the ground is wet. C: I am rich DEDUCTIVE ARGUMENTS Modus Tollens P1: If X then Y P2: Not Y A conditional deductive argument which denies the consequent C: Not X e.g.: P1: If it rains, the ground will be wet P1: If I win the lottery, I’ll be rich P2: The ground is not wet P2: I am not rich C: Therefore, it did not rain C: I did not win the lottery INDUCTIVE ARGUMENTS Causal Reasoning An inductive argument in which one event is claimed to be caused by another. We see the effect and try to deduce the cause. e.g.: - The universe is probably the result of the Big Bang. - Detectives investigating crimes INDUCTIVE ARGUMENTS Empirical Generalization An inductive argument in which a general conclusion is made about an entire group or population based upon observing a smaller sample. e.g.: P1: Plant A produces oxygen and glucose when P1: Iron conduct electricity exposed to sunlight P2: Copper conduct electricity P2: Plant B produces oxygen and glucose when..etc.. exposed to sunlight..etc... C: All Metals probably conduct electricity C: Photosynthesis  HOW TO EVALUATE A DEDUCTIVE ARGUMENT? Validity: A deductive argument is valid if the conclusion follows necessarily from the premises. Its concern is the form (structure) of the argument, regardless of the truth value of the premises. e.g.: This is a valid deductive P1: All men can fly argument, despite the P2: Socrates is a man ridiculousness of P1 !! C: Socrates can fly  HOW TO EVALUATE A DEDUCTIVE ARGUMENT? An Invalid deductive argument, because the conclusion does not follow from the premises: P1: All men are mortal This is an invalid deductive P2: Socrates is a man argument, despite that P1 P2, and even C are all true!! C: Socrates is a great philosopher  HOW TO EVALUATE A DEDUCTIVE ARGUMENT? Soundness: A deductive argument is sound if a) it is valid and b) the premises are true. Therefore, the “men can fly” argument, is valid, but unsound A sound argument is always valid. An unsound argument e.g. of a sound argument: All examples we saw with can be valid or invalid. types of deduction: categorical syllogism..etc.. HOW TO EVALUATE AN INDUCTIVE ARGUMENT? Strength: An inductive argument is strong if the Strength with inductive conclusion follows with high probability from the arguments corresponds to premises; regardless of the truth value of the validity with deductive ones premises. e.g. P: Zamalek has won the Egyptian league the most This is a strong times in recent years inductive argument despite the false premise C: Zamalek will win the league next season. HOW TO EVALUATE AN INDUCTIVE ARGUMENT? Cogency: An inductive argument is cogent if it is Cogency with inductive strong and the premises are true. arguments corresponds to soundness with deductive ones e.g. of a cogent inductive argument: Replace Zamalek with Ahly ☺ A cogent argument is always strong. An uncogent argument can be strong or weak.