1. Discovered or Invented
Mathematics
Discovered or Invented
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2. What’s the diff between something discovered and something invented?
What sort of things do we usually say are discovered?
What sort of things are invented?

3. Some people beleive that math could explain everything
2 lions + 2 lambs
= how many in morning?
(2 + 2) – 2 = 2

4. Discovered or invented?
Empiricists
Formalists
Platonists

5. Maths is not true by definition and it is a posteriori
Empiricism
Maths is not true by definition
and it is a posteriori
Not true by definition
– there are elephants in Africa
a posteriori
– can only be known by experience

6. Maths is true by definition and it is a priori
Formalism
Maths is true by definition
and it is a priori
True by definition
– all bachalors in UK are single
a priori
– can be known without experience

7. Maths is not true by definition and it is a priori
Platonism
Maths is not true by definition
and it is a priori
Not true by definition
– there are elephants in Africa
a priori
– can be known without experience

8. Platonism
Non trivial knowledge about reality that can be proven without experience
If true – then we can discover truths about the nature of existence by the power of reason alone.

9. Platonism Common beleif from Euclid (300BC) until 1800s
De Carte (1600s)
– cogito ergo sum (axiom)
Problem
How can we know something by reason alone?
- God, created a harmony between man & existence
- Natural selection, maths is a natural by-product of our early survival skills

10. Discovered or invented
Platonists
Maths is out there waiting to be discovered
Formalists
Maths is defined by us & exists only in the mind

11. Discovered or invented
Nature of existance
In order for something to exist, it must be possible to observe it.
Agree or Disagree?

12. Discovered or invented
Does Maths exist?
- do maths objects/concepts actually exist?
Formalists
No, it’s invented by us you massive egotist.
It is a socio-cultural invention, Hebraic Kabbalah.
Platonists
Of course you fool, it’s all around us.
Symetry in nature, the Fibonacci sequence

13. Meaning of existance Formalists No, you fool.
You cannot draw a perfect circle
-it’s never perfect
You cannot draw a line
- a lin has length but no breadth
You cannot actually measure things
- only to x decimal places

14. Meaning of existance Platonists Yes, you fool.
You can make real discoveries about them
I can prove that a circle has the largest possible area for any given perimeter
Plato said they exist ‘out there’ as a unique type of object

15. Discovered or invented
Meaning of existance
If Romeo & Juliet are fictional characters, is it true to say Romeo loves Juliet?
Does their love actually exist?