Grey Curves on Blankboard

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Mathematics Discovered or Invented
Powerpoint Templates
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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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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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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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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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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, 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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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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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?