INDUCTIVE LOGIC DECIPHERED-PART II of- Some thoughts on probability, decision theory, statistical inference…and finally Inductive Reasoning…

 

This is an incident which happened with me. You are going to Mussoorie with your aunt and uncle. You meet your pretty classmate Nidhi on the way.She is with her parents. You reach Mussoorie. You guess she will visit Mall Road. You spend all your time in Mall Road,hoping she comes there. You have made a risky argument.She might spend all her time in Company Bagh and you might end up never meeting her.

Valid arguments are risk free.Inductive Logic studies risky arguments.A risky argument can be a very good one and yet its conclusion can be false even when the premises are true. Most of our arguments are risky.

Let us consider a wider view. There is now good evidence that unprotected indiscriminate sex may lead to AIDS, but reasoning from all that to the conclusion that: unprotected, indiscriminate sex causes AIDS is still risky. It might just turn out that people having random sex are also predisposed to AIDS, in which case our inference that indiscriminate sex causes AIDS, would be in question after all.

Here is a typical example of risky arguments-

a)      Abhishek Bachchan  is not a flirt.

So

All (or almost all) stars are decent.

 

The premise is evidence for the conclusion, but not very good evidence, most stars may be flirts.

 

So I take a journalistic random pick from the list of all actors-who do I pick? It turns out to be Imran Khan. He too is not a flirt.So I conclude-

b)      The actor I picked up from the list is not a flirt.

So: All (or almost all) heros are not flirts.

This argument is also risky. But it is not risky as (A)

 

Ila takes six heros at random, she finds only one-Akshay kumar is a flirt,she reasons,c) most (but not all) heros are not flirts.

This is based on more data but still is not a valid argument.

 

a, b and c are arguments with statements about a sample drawn from a given population.

So, statement about population as a whole.

 

I may also reason

I know  almost all actors in this sample are decent.

These four heros taken at random from this list are not flirts.

 

Risky argument

Statement about population

So

Statement about sample.

 

Sample to sample

These four heros chosen are decent.

So next four heros chosen are also not flirts

Statement about a sample.

So, Statement about a new sample.

 

Proportions-

We can try to be more exact, 60 heros in our list

These four heros I chose at random from a list of 60 heros, are decent.

So:

At least 90%(or 54) of heros in my list are decent.

 

At least 90%(or 54) of the heros in our list are not flirts.

These four heros are taken at random from our list:

So these four heros are decent.

Probability-

These four heros, that I chose at random from a list of 60 heros, are decent.

So, probably:

At least 90%(or 54) of the heros in this list are decent.

 

At least 90%(or 54) of the heros in this list are decent.

These four heros are taken at random from this list.

So, probably:

These four heros are not flirts.

 

These four heros I chose at random from this list are decent

So probably:

The next four heros that I draw at random will also be decent.

 

Not all arguments using probability are inductive.

 

There maybe more to a risky argument than inductive logic.

 

Almost all ministers in the cabinet are corrupt

So

The PM is lax

We are offering a hypothesis to explain the observed facts.

There may be other explanations

The PM is corrupt.

The party is very corrupt.

The PM is a bad leader.

There are many inducements in the country which make the ministers corrupt.

 

Remember argument premise 1 is, if you love me you will sit on your haunches for one hour in class tomorrow. Premise 2 is-you will sit on your haunches for one hour tomorrow, Conclusion is-You love me

This is invalid but still an argument, a risky argument.

Each of the arguments we’ve looked at  is an inference to a plausible explanation.

One explanation is much more plausible than any other it is an inference to the best explanation.

Logic is deduction,induction, inference to the best explanation=abduction.

 

Testimony

You believe because someone told you.

 

Sunil Gavaskar says Dilip Sardesai was a gifted batsman.

So,

Dilip Sardesai was a gifted batsman

 Sunil Gavaskar may just be falsely idolising…

Rough definition of inductive logic-Inductive logic analyses risky arguments using probability ideas.