Presentation on theme: "Discovered or Invented"— Presentation transcript:
1Discovered or Invented MathematicsDiscovered or InventedPowerpoint Templates
2What’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?
3Some people beleive that math could explain everything 2 lions + 2 lambs= how many in morning?(2 + 2) – 2 = 2
4Discovered or invented? EmpiricistsFormalistsPlatonists
5Maths is not true by definition and it is a posteriori EmpiricismMaths is not true by definitionand it is a posterioriNot true by definition– there are elephants in Africaa posteriori– can only be known by experience
6Maths is true by definition and it is a priori FormalismMaths is true by definitionand it is a prioriTrue by definition– all bachalors in UK are singlea priori– can be known without experience
7Maths is not true by definition and it is a priori PlatonismMaths is not true by definitionand it is a prioriNot true by definition– there are elephants in Africaa priori– can be known without experience
8PlatonismNon trivial knowledge about reality that can be proven without experienceIf true – then we can discover truths about the nature of existence by the power of reason alone.
9Platonism Common beleif from Euclid (300BC) until 1800s De Carte (1600s)– cogito ergo sum (axiom)ProblemHow 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
10Discovered or invented PlatonistsMaths is out there waiting to be discoveredFormalistsMaths is defined by us & exists only in the mind
11Discovered or invented Nature of existanceIn order for something to exist, it must be possible to observe it.Agree or Disagree?
12Discovered or invented Does Maths exist?- do maths objects/concepts actually exist?FormalistsNo, it’s invented by us you massive egotist.It is a socio-cultural invention, Hebraic Kabbalah.PlatonistsOf course you fool, it’s all around us.Symetry in nature, the Fibonacci sequence
13Meaning of existance Formalists No, you fool. You cannot draw a perfect circle-it’s never perfectYou cannot draw a line- a lin has length but no breadthYou cannot actually measure things- only to x decimal places
14Meaning of existance Platonists Yes, you fool. You can make real discoveries about themI can prove that a circle has the largest possible area for any given perimeterPlato said they exist ‘out there’ as a unique type of object
15Discovered or invented Meaning of existanceIf Romeo & Juliet are fictional characters, is it true to say Romeo loves Juliet?Does their love actually exist?