Inductive+Reasoning

= = = Here we will examine another kind of logic: //inductive reasoning//, in which we reason from = = particular, observed phenomena to generalizations. Note that //deductive reasoning// (a la Sherlock Holmes), in which we reason from general principles to specific conclusions about the world, is often dependent on inductive reasoning to give us the generalizations for our premisses. = = =

** Choose one of the **** GENERALISED STATEMENTS below: **

 * Drivers in Istanbul are dangerous
 * All bachelors are unmarried
 * All libraries have books
 * All metals expand when heated
 * No professional footballers go to university
 * Every night I sleep
 * All dogs can bark
 * No even numbers are prime, apart from 2
 * Every even number greater than two is the sum of two prime numbers
 * An apple a day keeps the doctor away
 * The piece of furniture you eat a meal from is called a "table"
 * Generalisations are always wrong
 * Farmers don't raise pigs in Turkey
 * 1) = Is it true? =
 * 2) = Give a reason for believing it. =
 * 3) = Give some reasons for rejecting its veracity(truth). =

Evaluate the strength of the following inductive logical thoughts:
My neighbor’s dog didn’t bite me in the past, so he won’t bite me today either My chair supported my weight in the past, so it will hold me today Local drivers have driven wildly in the past, so I better be careful today USA has supported only Israel in the past, so they won’t be fair to Palestinians this year either. Girls who are smart are often not very sporty, so the smart new girl in our class won’t be good as sports

= **Inductive reasoning moves from the specific to the general as in the example below:** = = **In history, //every// human I’ve read about has died,and I have never heard of a human who has not eventually died,therefore ALL humans will die.** = **Dead guys I've read about** **All these people will die (if they haven't already)** === **We logically proceed from EVERY human I’ve read about (specific) to All humans will die (a generalization).** ===

= __**Based on a true induction story from history: The Problem of Induction** __ = media type="file" key="The Problem with Induction.mov" width="489" height="489" == However extensive or thorough a person’s research, they can never achieve //absolute certainty// using inductive reasoning. == == This is because some kind of generalization is always made from the observed to the unobserved. ==

=Many Scientific theories are arrived at through Induction (and deduction). So, how reliable is INDUCTIVE REASONING? **When is inductive logic reasonable? When is it not?**=

Induction is more reliable (perhaps we can say more justified?):

 * If you see enough/many examples of something it is more reliable. But what is 'enough'?
 * When your examples look at many different circumstance it is more reliable. But how many?
 * When you look actively for exceptions (counter-examples) to the rule. How?
 * If the statement is unusual, seek more examples. What is unusual?

Consider the area of knowledge: natural sciences may be more reliable than human sciences. But why? =As we have seen, there are some problems with induction:=
 * ** Exceptions: **some particular items don’t fit the patterns: If metal A, and B expand when heated, does that mean that ALL metals expand when heated? ( & does water ONLY boil at 100% centigrade?)
 * ** Novelty: **Could you have predicted a platypus from looking at previous birds/mammals?
 * ** Hasty generalizations: **If the Africans I’ve met are tall, does that mean ALL Africans are tall? If all Asian students I've met are good at maths does that mean that all Asian Students are good at maths.
 * ** Prejudice: **If the Qatari’s I’ve met all shop at fancy stores like Gucci, does that mean they are all fashion snobs?
 * ===__**CONFIRMATION BIAS:**__ WE TEND TO BELIEVE/REMEMBER ONLY EVIDENCE THAT SUPPORTS OUR BELIEFS, AND IGNORE/ FORGET EVIDENCE THAT GOES AGAINST US. Prejudice is reinforced this way - if you have decided that the English are cold, and Qatari’s are lazy, then you LOOK for evidence to support these comfortable beliefs. Define and give an example for GENERALIZATION, PREJUDICE & SCIENTIFIC LAW. Can you find a possible exception of these truths?===

= GENERALIZATIONS ARE NECESSARY! BUT MAKE THEM AS LOGICAL AS POSSIBLE: = =__Some tests for reliability of Induction__=
 * = Look for a Sufficient Number of Observations =


 * =Look for Varying Circumstances=


 * =Look for Exceptions=
 * =Look for Coherence=
 * =Consider the Subject Area=

=== __Conclusions on INDUCTIVE REASONING :__ Inductive reasoning is different from the pure logic of deductive reasoning. We use knowledge claims that we gain from empirical experience and make generalisations. How sound our inductive arguments are depends on the quality of our empirical evidence that we use to make our generalizations. **An inductively strong argument is one in which the evidence, once accepted, establishes a //firm probability//that the conclusion is true.** When judging inductive strength an argument can be considered to be strong if the level of probability established for the conclusion is high.===

=== Advantages: === === Problems: ===

Homework reading: van de Lagemaat p.p. 112-123