Wednesday, February 11, 2009

Syllogisms, Modus Ponens and Modus Tollens

Syllogisms Modus Ponens and Modus Tollens are all part of Deductive Logic. But even though they fall onto the same category they are not the same. A Syllogism is the bringing together of two statements to get to a conclusion. There must be three terms. The major premise the minor premise and a conclusion. In the conclusion there is no new information being presented. In the first term you have your A and your B in your second term you repeat the B and have C and in the conclusion you include A and the C
For example: All dogs have tails
Pluto has a tail
Therefore Pluto is a dog

A Modus Ponen is different than a syllogism it begins with the word if and only has two statements. It is if p then q therefore p has to be q. For this type of deductive logic you need to make p statement true and if the p statement is true then q also has to be true.
For example:If i am happy then i smile
I am happy therefore i am smiling
A Modus Tollens is similar to Modus Ponen but the only differences is that if p is not true then p can't be true either. And when you are writing these Modus Tollens you negate and inverse the second part of the statement. If p then q; Not q therefore not p.
For example: If my dog is tired then my dog is sleeping
My dog is not sleeping therefore he is not tired.

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