Latin Words?!

So as some of you might now by know, we're learning about modus ponens and modus tollens. Both of those words are Latin; modus ponen meaning "affirms by affirming" and modus tollen meaning "denies by denying." We are also learning about syllogisms, which are another way of coming to a conclusion. All three of these things are commonly used in geometry -_-.

A syllogism is three statements, with each statement containing two terms. It looks something like this.

All people eat food.
Justin eats food.
Therefore Justin is a person.

We first make a general statement, that is followed up by a specific factual statement, and by combining the two we come at a conclusion that is valid. Modus ponen does something similar, as it would looks more like htis.

If Justin eats food, then Justin is a person.
Justin eats food.
Therefore Justin is a person.

This starts with an If, then statement, and then a statement that proves the first part, followed by a conclusion that ends with the last part. Although it is only true if the first two statements are inherently true, it is valid by the way it is proved. Modus tollen is a little different, but once again looks the same way.

If Justin eats food, then Justin is a person.
Justin is not a person.
Therefore, Justin does not eat food.

By using backwards logic and evidence, we can come to the conclusion that Justin is not whatever the first statement says he is; because he isn't the last part, he cannot be the first part. He isn't a person, so he cannot eat food because eating food would make him a person.

Each cna be used to prove a statement true or false, but all three are used similarly and all three are different in their own way. That's all from the desk of Maiyozu-San, see you guys in class tomorrow.