7 Key Terms
- Deductive reasoning – general to particular
- Inductive reasoning – particular general
- Paradigm – a set of interrelated ideas for making sense of one or more aspects of reality e.g. Euclid Paradigm
- Axioms – starting points or basic assumptions. In Mathematics axioms are like a premise.
- Theorems – in mathematics theorems are like a conclusion.
- Proof – a theorem is shown to follow logically from an axiom.
- Conjecture – is a hypothesis that seems to work but has not shown to be necessarily true.
The Logic of 1 + 1 = 2
One apple plus one apple equals two apples.
Add one lamb to a cage containing one tiger. How many animals will be in the cage the next day?
Join one crowd of people with another crowd of people. How many crowds?
Where else does 1+1 make more than 2?
- —Does teaching maths with apples make maths an empirical subject?
Linking Questions:
- If we grow up speaking Chinese, English seems hard and vice versa. Is this the same for number systems?
- Does base 10 make a cultural difference – how might an alien culture be different?
- How might artists or writers be influenced by the universal acceptance of base 10?
- Would a change in number base affect scientific discoveries?
- Back to main TOK page
How do we count?
Off-Site Links:
- 'The Story of One' - Highly entertaining documentary
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