Deductive Arguments

1. Deductive Arguments Syllogisms, Valid and Sound Arguments

2. Deductive Argument Definition • “A Deductive argument is an argument in which the conclusion necessarily follows from its’ premises.” • Deductive arguments sometimes contains words or phrases such as certainly, definitely, absolutely, conclusively, must be, and it necessarily follows.

3. Example of A Deductive Argument • The following is an example of a deductive argument: • “Marilyn is definitely not a member of the swim team, since no freshmen are members of the swim team, and Marilyn is a freshman. “

4. Syllogism • “A Syllogismis a deductive argument presented in the form of two supporting premises and a conclusion.” • Premises and conclusions of a syllogism are presented on separate lines with the conclusion last. • The two premises are always dependent.

5. Example of A Syllogism Premise 1: All men are mortal. Premise 2: All fathers are men. Conclusion: Therefore, all fathers are mortal.

6. Valid and Invalid Arguments • “A deductive argument is validif the form of the argument is such that the conclusion must be true, if the premises are true”. • In logic, Formrefers to the patterns of reasons in a deductive argument.

7. Form of A Deductive Argument All X (men) are Y (mortal). All Z (fathers) are X (men). There, all Z (fathers) are Y (Mortal). Simplified Form All X’s are Y’s All Z’s are X’s Therefore, all Z’s are Y’s

8. Another Example All X (Cats) are Y (mammal)s. All Z (tigers) are X (Cats). Therefore, All Z (tigers) are (Cats).