Deductive Statements

Today we learned about Deductive Logic. The three forms that we learned about were Syllogism, Modus Ponens, and Modus Tollens. These three are different in many ways. First, syllogism was founded by Aristotle. He explains a general term, into a specific using basic math as a guideline. A=B, B=C, therefore A=C. An example of this was All (B)humans are (A)mortals. (C)Socrates is a (B)human. (C)Socrates is (A)mortal. We see that (B)humans is reoccurring through the first two lines. Second, Modus Ponens is using the If P, then Q-P therefore Q. An easier way of looking at this is-If I (P)swim then i am (Q)athletic. I (P)swim, therefore i am (Q)athletic. This is very similar to the Third form mentioned earlier, Modus Tollens. Modus Tollens is basically the contrapositive of the original statement. Modus Tollens states that, If P then Q-Not Q, therefore not P. An example of this would be, If I live in (P)Van nuys, I live in (Q)California-If I dont live in (Q)California, therefore I dont live in Van Nuys. Both Modus Tollens and Modus Ponens have the same original statement, but differ in the follow up statement.