1. Do now Can you make sure that you have finished your Venn diagrams from last lesson. Can you name 5 famous mathematicians (including one that is still alive)?

2. Deductive reasoning and truth Just because an argument is valid (Some IB students are from Russia, all Russians are good at drinking vodka, therefore some IB students are good at drinking vodka) does not mean that the conclusion is true.

3. Deductive reasoning and truth For an argument to be true you must be able to answer “yes” to the following questions:

4. 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?

5. Socrates Socrates is a man All men are mortal Therefore Socrates is mortal The conclusion is only true if the premises are true.

6. 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

7. 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

8. 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

9. Generalisations Is there a danger to generalisations? Simon is going to give you a list of 14 generalisations. Can you put them in order from the most reliable to the least reliable? (he may ask you to justify your order)