Are Numbers Real?
Lately I have been pondering over numbers, which to the right
kind of mind are a wealth of; interest, mystique, creativity & logic (I
will cover a topic to that of 'the right kind of mind' at a later date under
the name Maths gets a bad press) but a significant question arises when
thinking about maths... Is it real? This question while rhetorical to you has been
on the minds of philosophers for generations, from my deductive work I have
come across three schools of thought on this.
1. Platonism - All numbers are some form of abstract objects
that EXIST as a fundamental part of reality, our use of mathematics can be seen
as a description of how these objects interact. Numbers, functions and any
other form of mathematical expression are discovered NOT invented.
Unsurprisingly Platonism was first conjectured by Plato (of
the famous GCSE a2+b2=c2 in right angle
triangles formula) he tended to treat his maths as a cult with followers who
would publically beat people for not knowing maths. This may seem absurd to
think of at first, thinking there are an infinite amount of all the possible
numbers being stored somewhere abstract can at first seem a copout1 however
as this is philosophy basically anything goes. It is generally not widely
believed today on account of it being a bit out there. (pardon my obvious biases)
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| A description of maths now with added children's toys. |
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| Of course some numbers are more abstract then others... |
2. Nominalism - The real objects in the universe represent all
numbers, maths is an integral part of our universe that is in place to make the
universe work. Numbers, functions and any other form of mathematical expression
are discovered NOT invented .
This may seem a likely alternative to Platonism we can
confidently relate to real word objects more than abstract ones, 'is a bird in
the hand worth two in the brush?' well according to the universe the IS a
greater number of birds in the bush to your hand, likewise for any form of
object; pencils, computers, white boards, sticky notes ect. of course I'm being
somewhat facetious (pardon my obvious biases).What it really means is the universe
is bound by maths at a fundamental level. So a satellite falling from a its
curved geostationary orbit is forced to land the specific way it does due to
the mathematics of the universe preventing it landing via any other; curved, strait
or higgledy-piggledy path.
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| The problem with nominalism depicted in a comic. |
3. Fictionalism - Numbers are concepts invented by humans to
describe the world around us the fabric of reality dose not rest on any type of
numbers actually existing it just does what it does without any laws of mathematics
behind it. Numbers, functions and any other form of mathematical expression are
invented NOT discovered.
It may at first seem like how does this work at all if the
world doesn't have some form of maths embedded into it? But just imagine maths
as the tools we are using to pick apart how the universe is working. We use
this tool to describe and explain just what exactly is going on it has no bias
to exist in the actual universe and just gives us the numbers on what we think
should happen.
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| Every ONE has days like this... *Crickets* |
Now for the conclusion in my opinion fictionalism is the
most accurate definition of what maths is I don't personally believe that we exist
because of maths making everything work and I do believe that when Isaac Newton
invented calculus2 he actually invented it, however I have just
stated my views here to show my biases so you will consider them when reading3.
throughout the descriptions I stated weather mathematicians discover/invent "new"
maths this is an important point as an inventor creates and a explorer
discovers stuff, this is leading to the discussion of weather they are
discovering the mathematics laid down by the fabric of reality4 or if
a new form of maths is created purely by the inventor of that form of maths.
Links to stuff REALLY WORTH WATCHING!
*Warning I found some links try to sway people to their beliefs
mainly by comparing one of the other schools of thought to religion. I have tried
to stay away from this in my description but if you hear this discussed
somewhere they are usually using it as a tactic to discredit that school of
thought by comparison to the illogical, which generally sways an otherwise
overwhelmingly rational audience*
"Is Math a Feature of the Universe or a Feature of
Human Creation? | Idea Channel | PBS" - http://www.youtube.com/watch?v=TbNymweHW4E
"Do numbers EXIST? - Numberphile" - http://www.youtube.com/watch?v=1EGDCh75SpQ
1The image of God with his infinite trophy case
of all numbers, right next to his bookcase containing the elegant solutions to
all possible functions comes into mind.
2 Or Gottfried Leibniz if you are a Leibniz man.
3I don't want to unwitting dupe you into my way
of thinking aren't I good :-)
4 Picking Gods brain for his secrets of how he
made everything work
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