Critical Thinking #11 and #12

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In the eleventh class of the critical thinking course, we saw the movie “Witness For The Prosecution”. It is actually a play written by Agatha Christie. This movie was showed to us so that we understand about evidence. It was good.

The twelfth class was the last day of the course. We took pictures together. We tried solving a few problems. Here are those problems for you to attempt...

The first one is well-known and quite easy.

Q1. Sruti, Keerthanya and Sandhya eat at a eatery. The waiter says the bill is Rs 30 and each of them give Rs 10. When he takes the money to the cashier, the cashier returns Rs 5 as the bill is only 25. The waiter wonders how to distribute 5 between three and being intelligent, decides to keep 2 and return one to each. So each of them paid 9 a total of 27 and the kept 2 so total is 29 whereas they originally paid 30. What happened to the missing rupee?

Q2. At the Secret Convention of Logicians, the Master Logician placed a band on each attendee's head, such that everyone else could see it but the person themselves could not. There were many, many different colors of band. The Logicians all sat in a circle, and the Master instructed them that a bell was to be rung in the forest at regular intervals: at the moment when a Logician knew the color on his own forehead, he was to leave at the next bell. Anyone who left at the wrong bell was clearly not a true Logician but an evil infiltrator and would be thrown out of the Convention post haste; but the Master reassures the group by stating that the puzzle would not be impossible for anybody present. How did they do it?

Q3. The King called the three wisest men in the country to his court to decide who would become his new advisor. He placed a hat on each of their heads, such that each wise man could see all of the other hats, but none of them could see their own. Each hat was either white or blue. The king gave his word to the wise men that at least one of them was wearing a blue hat - in other words, there could be one, two, or three blue hats, but not zero. The king also announced that the contest would be fair to all three men. The wise men were also forbidden to speak to each other. The king declared that whichever man stood up first and announced the color of his own hat would become his new advisor. The wise men sat for a very long time before one stood up and correctly announced the answer. What did he say, and how did he work it out?

Do share your anwers.

Critical thinking #10

In the 10^th class of the course, we moved on to the final part of the course – evaluating arguments, looking at its strength and weaknesses, its success and failure.

The first step is to see in which area the argument lies in the table given below:

	Valid	Invalid
Sound	A	B
Unsound	C	D

If the argument lies in the region ‘A’ then it is a strong argument as it is both valid and sound. 

It is a waste to argue if the reasons are in region 'D' as it is both invalid and unsound.

We learnt that circumstantial evidence is rarely conclusive by itself.

The most reliable evidence from witnesses is a first hand account. Hearsay evidence is not as reliable.

The witness’s credentials(qualification or reputation) are important, but do not guarantee that their evidence is reliable.

Critical Thinking #9

On the 9^th day of the course, we saw the movie “Twelve Angry Men”. I loved the movie. It's about a jury which tries to decide whether a man had committed murder. The first time they vote to check their unanimity, eleven members are convinced that the person in the trial IS guilty and only one is convinced that he MIGHT NOT be guilty. It becomes a eleven-to-one majority. Slowly, the one man convinces all the others with his effective, reasonable, valid and sound counter-arguments. The movie is all about arguments and counter-arguments.

It is a beautiful movie. It is a must watch category.

Critical Thinking #8

In the 8^th class of the critical thinking course we learnt about evidence. We learnt that  stronger the evidence, more confident the conclusion. There are two types of evidence.

 PRIMARY EVIDENCE – what people see (eye witness), hear (ear witness), etc. They give first hand information.

SECONDARY EVIDENCE – hearsay.

We also saw what circumstancial evidence is. Circumstantial evidence consists of facts, or circumstances.

We got to know the important part played by corroboration.

Corroboration means agreement. It helps in evaluating evidence.

We also took a look at the credibility, plausibility and reasonable doubt of an evidence.

Critical Thinking #7

English: inductive and deductive reasoning (Photo credit: Wikipedia)

We discussed about the types of logic in the seventh class of the course. Our teacher said that there are two types of logic– inductive logic and deductive logic.

Deductive logic is always valid. It can either be sound or unsound.

Example for a valid but unsound deductive argument :

R1 : All birds can fly.R2 : Penguin is a bird.C : Peguins can fly.

Example for valid and sound deductive logic:

Nothing that is cheap is good.Therefore, nothing that is good is cheap.

Maths is full of deductive logic. In deductive logic one can be always sure that there is 100% validity.

Inductive logic is stating examples and then generalizing it.

Example for inductive logic:

R1: Satellite picture show a cold front moving eastwards across the Canadian coastline 

R2: It moves with a trough of low pressure along its leading edge. 

R3: It will meet up with a large mass of rotaing wind moving across the Atlantic to scooping down from the easterly-winds sweeping down from the artic.

C: Consequently violent stroms can be expected to develop in the north Atlantic in next 24 hours.

Here, we are stating examples and then concluding. We do not know if its 100% valid in inductive logic, though it may be sound.

We learnt the difference between the two.

Critical Thinking #6

photo credit: http://bit.ly/1cCeT3v

In the sixth class of the critical thinking course, we dealt with assumptions and fallacies. Like the clearly stated reasons, there are also implied reasons which are as important in an argument. They are called assumptions.

Assumptions that have to be made for an argument to work are sometimes called ‘underlying assumptions’. They can also be the missing premise in an argument. It is a premise because it is needed to support the argument. Assumptions can either be opinions or facts.

We also learnt about common fallacies in an argument. Arguments that are unsound are said to contain flaws in the reasoning.

Eg: Beeta passed all her exams without doing any work, so anyone taking exam should stop studying.

This example contains a flaw that makes the conclusion unreliable.

This kind of fallacy is called “generalization”, where we generalize from the particular. Another common type of fallacy is 'composition fallacy'.

Some of the common flaws are :

Ø Arguing from a particular case to a general conclusion

Ø Relying heavily on anecdotal evidence, or past experience

Ø Mistaking a correlation for a cause

There  are many, many more fallacies. We could discuss only this much in one class.