Posted by: catindiaonline | October 25, 2008

Critical reasoning: Logic for beginners

Welcome to Logic for Beginners!

Notice how I used a dark blue font for my title? You know I mean business. Seriously though, every person – at one point or another – needs to use logic in order to make decisions that make sense. That’s easy enough. It becomes trickier when you have to search for logical statements and errors in sentences, however. When preparing for your examinations, you want to make sure that the answers you are choosing make sense logically in relation to the statement you are reading. In other words, anything can make sense, but you have to make sure it agrees with your question in order to get a big fat checkmark on your exam.

Type I
“If X is true, then Y must be true. We know that X is in fact true. So Y must be true as well.”
Whenever it’s sunny, I bring my sunglasses to work. It is sunny, so I shall bring my sunglasses to work today.

This sort of logical statement is called modus ponens. If you consider “it is raining” to be X and “I am bringing my sunglasses to work” to be Y, the statement fits the pattern wonderfully. Big, fat checkmark.

A poor example
“The bells you can hear now are always rung during a funeral. Someone must have died!”

Technically it makes sense – if the bells are rung during a funeral and someone usually dead at a funeral, are they not? If you delve a little deeper you will realize this sentence is actually invalid. It doesn’t follow that the bells are only run when there is a funeral. The bells could also be ringing for a wedding, a baptism, etc. If you had said “The bells you can hear now are only rung…”, then this statement would be right. Your invalid statement said that if X is true, then Y must be true. We know Y is true. So X must be true as well. Be careful you don’t mix up the causal effects of X and Y.

Type II
“If X is true, then Y must be true. We know that Y is not in fact true. So X can’t be true either.”
Whenever it’s snowing, I am always in a good mood. I’m feeling quite down today, so the weather can’t be snowing today!

This type of statement is called the modus tollens. X = “The weather is snowing” and Y = “Good Mood”. If X causes Y, and Y is not true – then X cannot be true either. This statement logically makes sense, even though I doubt you’re happy EVERY time it snows! 😛

A poor example
“Wes plays basketball on a team. Winning a basketball game causes him to come into work with cupcakes for everyone the next day. He didn’t win his game yesterday, so I don’t think he will be handing out cupcakes today.”

This might seem like it makes sense at first. But Wes might hand out cupcakes today for any other reason as well – he also handed out cupcakes on his birthday, when he got a promotion and when he got engaged. Just because he didn’t win his game doesn’t mean he won’t give out cupcakes today. This is an incorrect statement – you just said that if X is true, then Y must be true. We know that X is not in fact true. So Y can’t be true either..

But I don’t get it! How can a statement sound totally unrealistic but still be “logically correct”?

For rest go to CAT India Online’s CATclub

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