Deductive Reasoning

Deductive Logic is the process of taking something that is known to be true and eventually reaching a conclusion of absolute truth. There are different kinds of deductive reasoning. The specific ones we learned today were syllogisms, Modus Ponens, and Modus Tollens.

Syllogisms were invented by Aristotle. It takes the structure of the math transitive property which shows that A=B, B=C, and C=A. These letters represent different terms that are used in the syllogism. In a syllogism, a general characteristic is taken and turned to make a specific point. In it, there are three different statements including the major premise, the minor premise, and the conclusion. There can only be three terms in total, and only two terms in each statement. An example would be:

All babies cry a lot. (B=A) -->Major

Mikey is a baby. (B=A) -->Minor

Mikey cries a lot. (C=A) -->Conclusion

If that didn't make much sense, the other form of deductive logic is much easier to understand. This one is the modus ponens. The formula is: If p, then q. P, therefore, q. An example can make this clearer.

If it is windy outside, then I will have a bad hair day. (p, q)

It is windy outside. (p)

Therefore, I will have a bad hair day. (q)

The last form of deductive logic we learned was modus tollens. The structure is expressed as: If p, then q. Not q, therefore not p. This has a similar structure like the modus ponen but different because of the second line. Instead of using the premise "p" on the second line, it is q. A good statement would be:

If I get an A on the final, I will get an A in the class. (p, q)

I did not get an A in the class. (not q)

Therefore, I did not get an A on the final. (not p)

Finally it all makes sense.