Some thoughts on probability, decision theory, statistical inference…and finally Inductive Reasoning…Part I : How Logicians think about Reasoning

Logic.  It is about good and bad reasoning. Logicians have given precise meanings to some ordinary words, in this first part of my blog dealing with some concepts of probability, statistical inference, decision theory and maybe even “some” inductive reasoning, I review the language of logicians dealing with reasoning…only the examples are original in my blog, the theory is based on Probability and Inductive Logic by Ian Hacking. I give the following title to this blog..

Some thoughts on probability, decision theory, statistical inference…and finally Inductive Reasoning…

Part I of this blog is on: How Logicians think about Reasoning….The theory is borrowed, but the examples are original…

Arguments

Logicians mean by an argument a point or series of reasons presented to support a proposition which is the conclusion of the argument.

An argument thus divides up into:

A point or series of reasons which are called premises,

And a conclusion.

Premises and conclusions are propositions, statements that can be either true or false.

Going wrong: The premises are supposed to be reasons for the conclusion. Logic tries to understand the idea of a good reason.

We find arguments convincing when the premises are true, and when we see that they give a good reason for the conclusion.

Two things can go wrong with an argument

·       The premises may be  false.

·       The premises may not provide a good reason for the conclusion.

The premises could be true and the conclusion false, for any number of reasons.(suppose the 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, but conclusion could be wrong because of the following reason-you sit on your haunches for one hour because *you are given a punishment to that effect by your teacher!!!)

A fallacy is an error in reasoning that is so common that logicians have noted it. Sometimes they give it a name…affirming the consequent..In this fallacy we “affirm” the consequent..

Premise 1-If you love me, you will sit on your haunches Premise 2…you sit on your haunches…Conclusion…you love me.

It is a fallacy to affirm the antecedent..you love me from the consequent you will sit on your haunches..

There are two basic ways to criticise an argument:

#1Challenge the premises-show that at least one is false.

#2Challenge the reasoning-show that the premises are not a good reason for the conclusion.

So we can illustrate #1,  you might question the first premise if sitting on your haunches is a part of your exercise routine, you might also question the second premise…you call that sitting on your haunches???!

#2 Is illustrated by *

Logic is concerned with only reasoning. It cannot in general tell whether premises are true or false. It can only tell whether the reasoning is good or bad.

If the premises that if you love me you sit on your haunches; you sit on your haunches, but the conclusion that you love me is not true, that is an invalid argument…you can sit on your haunches for many reasons…so you don’t necessarily love me…

In logic:

Propositions are true or false

Arguments are valid or invalid…

Now consider this “if-then” proposition…

If every Nepali is Hindu

Manisha is a Nepali

Manisha is Hindu.

To every argument there is a corresponding conditional proposition “if-then” An argument is valid if and only if the corresponding conditional proposition is a truth of logic.

There are many ways to suggest the idea of validity:

The conclusion follows from the premises.

Whenever the premises are true, the conclusion must be true too.

The conclusion is a logical consequence of the premises.

The conclusion is implicitly contained in the premises.

 

Valid argument forms are truth preserving.

“Truth preserving” means that whenever you start with true premises, you will end up with a true conclusion.

When you reason from true premises using a valid argument, you never risk drawing a false conclusion.

Valid arguments are risk-free arguments.

 

WE say an argument is sound when: all the premises are true, and the argument is valid.

Thus an argument may be unsound because:

A premise is false.

The argument is invalid.

Validity has to do with the logical connection between premises and conclusion, and not with the truth of the premises or conclusion.

Soundness for deductive logic has to do with both validity and the truth of the premises.

Validity is not truth:A valid argument can have a false premises but a true conclusion.

 

Every shot that reaches the boundary is a four.

This shot reached the boundary on one bounce.

This shot was a four.

The first premise was false..the shot can be a six….

An invalid argument can have true premises, true conclusion.

This batsman always reaches his century with a six

This batsman hit a six

This batsman has reached his century…

invalid arguement…he my have hit a six and reached any other score so even if the premises and conclusion are possiblty true..the argument is invalid…

To know premises true…you have to know something about the world, about history…

Don’t need to know anything about the world to know whether an argument is valid or invalid. But you need to know some facts to know whether a premise is false or true…

There are two ways to criticise a deduction…

Premise false

Argument is invalid…

Expert on Truth-Detectives,nurses,surgeons, pollsters,astrologers,zoologists,reporters,you and me…

Expert on validity-logician

Logician study the relations between premises and conclusions, but as logicians are not especially qualified to tell whether premises are true or false

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