‘The madman is not the man who has lost his reason. The madman is the man who has lost everything but his reason.’ Thanks to: Richard van de Lagemaat, Cambridge University Press Downloaded on 12th June 2011
Body in the Park A body is discovered at Jerudong park in the middle of the hot season. It has a fractured skull and many other broken bones, but the cause of death was hypothermia. Can you explain? He was a stowaway hiding in the landing gear of an aircraft. He fell out when the wheels opened for landing at Brunei airport.
Guilty Sister A woman has incontrovertible proof in court that her husband was murdered by her sister. The judge declares, "This is the strangest case I've ever seen. Though it's a cut-and-dried case, this woman cannot be punished." Why? Her sister is her conjoined twin.
Deadly Shoes A woman buys a new pair of shoes, goes to work, and dies. She works as an assistant to a knife-thrower at the circus. The shoes have high heels. The knife thrower blindfolds himself and throws as normal, hitting the woman.
Gavin and Pete Two men enter a bar. They are served identical drinks. One lives; the other dies. The drinks contain poisoned ice cubes. One mans drinks his drink quickly before the ice melts.
Rationalism Rationalists believe that reason is the most important source of knowledge Because it seems to give us some certainty.
Don’t scream! You have 45 minutes to write a short essay entitled – “Which of our faculties is more reliable – reason or perception?”. You must give examples and reasons
Deductive and Inductive reasoning Deductive Reasoning goes from the General to the Particular Inductive Reasoning goes from the Particular to the General
The curious incident An expensive racehorse has been stolen. I’ve been stolen, that’s why I’ve got such a long face!
The curious incident A policeman talks to Sherlock Holmes. Does any aspect of the crime strike you as significant Mr Holmes? Yes constable, the curious incident of the dog in the night.
The curious incident A policeman talks to Sherlock Holmes. The dog did nothing in the night Sir. That is the curious incident!
Holme’s reasoning The solution to the crime hinges on the fact that the guard dog did not bark in the night, and from this Holmes deduces that the thief must have been known to the dog. I know him!
Holmes’ reasoning Holmes’ reasoning can be laid out as follows • Guard dogs bark at strangers • The guard dog did not bark at the thief • Therefore the thief was not a stranger This is an example of gaining knowledge by reasoning. Discuss in your groups the benefits of gaining knowledge by this way.
Syllogisms Holmes reasoning is an example of a syllogism.
The Socrates Syllogism premises • All human beings are mortal • Socrates is a human being • Therefore Socrates is mortal conclusion • Syllogisms contain: • Two premises and a conclusion • Three terms, each must occur twice (“Socrates”, “human being”, “mortal”.) • Quantifiers, such as “all”, or “some” or “no” which tell us of the quantity being referred to Rationalism A branch of philosophy which takes reason as the most important source of knowledge
Truth and validity An argument is valid if the conclusion follows logically from the premises. • All hippopotamuses eat cockroaches • Mr Free is a hippopotamus • Therefore Mr Free eats cockroaches Both premises and conclusion are false, but the argument is valid. Imagine that some strange planet exists where the premises are true
Truth and validity All rats are teachers Mr Free is a rat Therefore Mr Free is a teacher = The premises are both false (although the conclusion is true!) but the argument is still valid.
Deductive reasoning and truth • Just because an argument is valid (Some IB staff are from Scotland All Scots love eating Haggis Therefore some IB staff love eating Haggis) • Does not mean that the conclusion is true.
Deductive reasoning and truth For an argument to be true you must be able to answer “yes” to the following questions: • Are the premises true? • Is the argument valid?
Messi • Messi is a man • All men are mortal • Therefore Messi is mortal The conclusion is only true if the premises are true.
Make up your own VALID syllogisms to illustrate each of the following; • 2 true premises and a true conclusion • 1 true premise, 1 false premise and a true conclusion • 1 true premise, 1 false premise and a false conclusion • 2 false premises and a true conclusion • 2 false premises and a false conclusion
Belief Bias? • Democrats are in favour of free speech • Dictators are not democrats • Therefore dictators are opposed to free speech
Deciding whether a syllogism is valid Trying to decide if a syllogism is valid is not easy. Venn diagrams can help (at last a good use for Venn diagrams!)
Deciding whether a syllogism is valid Mmmm … Hagis! • Some IB staff are from Scotland • All Scots love eating Haggis • Therefore some IB Staff love eating Haggis Is this a valid argument? Typical IB staff from Jerudong International School
Using Venn diagrams • Some IB staff are from Scotland IB Staff who are Scottish IB Staff Scots
Using Venn diagrams • All Scots like eating Haggis Like eating Haggis IB Staff Scots
Using Venn diagrams • Therefore some IB staff like eating haggis Like eating Haggis IBStaff Scots
Another example • All As are Bs • All Bs are Cs • Therefore all Cs are As
Another example • All As are Bs A B
Another example • All Bs are Cs A B C
Another example These Cs are not As • Therefore all Cs are As A The syllogism is not valid B C
Another example! • All As are Bs • Some As are Cs • Therefore some Bs are Cs
Another example! • All As are Bs A B
Another example! • Some As are Cs A C B
Another example! • Therefore some Bs are Cs A C B The syllogism is valid
Now your turn Using Venn diagrams in your notebooks, decide whether each of the following arguments is valid or invalid.
Valid or invalid • All Bruneians eat durian • Kevin eats durian • Therefore Kevin is Bruneian
Valid or invalid • All Year 12 boys are brave • Some brave people are compassionate • Some Year 12 boys are compassionate
Valid or invalid • Some physicists are frauds • Some frauds are not wealthy • Therefore some physicists are not wealthy
Valid or invalid • All Chinese own dogs • No good football players have dogs • Therefore no Chinese are good football players
Valid or invalid • All clever girls are red-headed • All red heads are rich • Therefore all clever girls are rich
Inductive reasoning • All human beings are mortal This statement cannot be proved by logic and reasoning, but is based on experience. This brings us to inductive reasoning
Inductive reasoning Whilst deductive reasoning goes from the general to the particular, Inductive Reasoning goes from the particular to the general Going from “all observed human beings have died” to “all human beings are mortal” is an example of inductive reasoning
Inductive reasoning and generalisations Since inductive reasoning goes from the observed to the unobserved, it enables us to make generalisations about the world • All metals expand • All human beings are mortal
Generalisations Is there a danger to generalisations? Here is a list of 12 generalisations. Put them in order from the most reliable to the least reliable? (you may be asked to justify your order) French people are rude. Water boils at 100 °C. Most graffiti artists are under 25 years old. All generalisations are dangerous. When spelling in English “i before e except after c”. • Dogs eat their own poo. • New Zealanders are good at rugby. • Year 12 students are lazy. • Metals expand when heated. • Chinese students are smarter. • Boys are better at physics than girls. • No-one succeeds without hard work.
Inductive reasoning What makes a good generalisation? You’ve got 5 minutes in your groups to think of “Five rules for making good generalisations”. When you’ve agreed your five rules can you write them in your books?
Inductive reasoning What makes a good generalisation? • Number: You should look at a good number of examples. If you see one dog swimming, this is not enough to decide that “all dogs can swim • Variety: You should look at a variety of circumstances. In the example of dogs swimming, looking at different breeds of dog. • Exceptions: You should actively look for counter examples. Look for dogs that can’t swim! • Coherence: You should look for more evidence to support surprising claims! If somebody suggests that dogs can swim because they have superpowers you may demand greater proof! • Subject area: Generalisations may be more reliable in some subject areas (e.g. science) than in others (e.g. economics or other social sciences).