Deductive logic...

Today in class we learned about deductive logic. Although there are many types, we learned about the three that were the most important for this unit: Syllogisms, Modus Ponens, and Modus Tollens.

Syllogisms:
Syllogisms are a type of deductive logic thought up by Aristotle, and have three major components: the Major Premise, the Minor Premise, and the Conclusion. In each categorical syllogism, there should be three terms, two terms in each component of the syllogism. The formula for a categorical syllogism is A=B, B=C, A=C. An example of a syllogism would be (B) Humans are (A) mortal. (C) Socrates is (B) human. (C) Socrates is (A) mortal.

Modus Ponens:
A second type of deductive logic would be modus ponens, which is a positive statement with only two terms. The two terms, labeled P and Q, are presented in two statements. The formula for a modus ponens would be "If P then Q. P, therefore Q." An example of a modus ponens would be "If Iran has WMD, then we'll invade Syria. Iran has WMD, therefore we'll invade Syria. "In this example, P would be "Iran has WMD" and Q would be "we'll invade Syria". However, does a modus ponens statement mean "if and ONLY if?"

Modus Tollens:
The third type of deductive logic we learned would be modus tollens, which is a negative statement with two terms. The terms are also labeled P and Q, and this type of deductive logic is very similar to modus ponens. The formula for a modus tollens would be "If P then Q. Not Q, therefore not P." An example of this type of deductive logic would be "If it's raining, it will be cold outside. It's not cold outside, therefore it's not raining." In this example, P would be "raining" and Q would be "cold outside".

As we can see, Modus Tollens and Modus Ponens are very similar, it is just they are the opposite of each other. Tollens is negative whereas Ponens is positive. Both have the same number of terms as well as the same number of statements that make up the whole logical statement. However, both differ from the first type of deductive logic, the syllogism. Ths syllogism has three statements, with three statements that make up the logical statement. The syllogism, so far, is neither negative nor positive, it is just reaching a conclusion from a given truth. The syllogism basically goes from a given truth to something that must be true because of the given truth. However, the Modus Ponens and Modus Tollens statemements are more like cause and effect theories: if this were to happen, then another thing will happen.

Did I spell Ponens right? Is it Ponens or Pones? I'm confused....