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
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
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
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.
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
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
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?
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
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
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
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