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Powerpoint Templates Page 1 Powerpoint Templates Mathematics Discovered or Invented

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

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Powerpoint Templates Page 4 Discovered or invented? Empiricists Formalists Platonists

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Powerpoint Templates Page 5 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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Powerpoint Templates Page 6 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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Powerpoint Templates Page 7 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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Powerpoint Templates Page 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.

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Powerpoint Templates Page 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

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Powerpoint Templates Page 10 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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Powerpoint Templates Page 11 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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Powerpoint Templates Page 12 Discovered or invented Does Maths exist? - do maths objects/concepts actually exist? Formalists No, its invented by us you massive egotist. It is a socio-cultural invention, Hebraic Kabbalah. Platonists Of course you fool, its all around us. Symetry in nature, the Fibonacci sequence

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Powerpoint Templates Page 13 Meaning of existance Formalists No, you fool. You cannot draw a perfect circle -its 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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Powerpoint Templates Page 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

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

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