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**Discovered or Invented**

Mathematics Discovered or Invented Powerpoint Templates

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**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?

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**Some people beleive that math could explain everything**

2 lions + 2 lambs = how many in morning? (2 + 2) – 2 = 2

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**Discovered or invented?**

Empiricists Formalists Platonists

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**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

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**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

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**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

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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.

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**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

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**Discovered or invented**

Platonists Maths is out there waiting to be discovered Formalists Maths is defined by us & exists only in the mind

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**Discovered or invented**

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

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**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

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**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

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**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

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**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?

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-Never wrote any records of his own. -Most of what we know is from his pupil Plato. -Did not like the early schools of philosophy=Useless -Declared the.

-Never wrote any records of his own. -Most of what we know is from his pupil Plato. -Did not like the early schools of philosophy=Useless -Declared the.

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