Proving a Negative
"There is an
orange crow somewhere in the universe."
The above is a positive statement because it asserts
that something exists. This statement can only be
proven true; it cannot be proven false. To prove it
true, all you have to do is locate an orange crow and
your job is done. Proving that statement false is the
same as proving its negative true. The negative of
that statement is "There is no orange crow anywhere in
the universe" or more simply "Orange crows do not
exist." In order to prove that orange crows do not
exist, you would have to search everywhere in the
universe to make sure an orange crow wasn't hiding
there. And even then, an orange crow might appear some
place you've already searched so even if you've looked
everywhere in the universe and failed to find an
orange crow, that still wouldn't prove that orange
crows don't exist. To prove it, you'd have to be aware
of the contents of the entire universe all at once,
and you'd have to somehow know for a fact that there
aren't any orange crows in it. Clearly, an impossible
task. This is where the notion "you can't prove a
negative" comes from. Basically it states that it's
impossible to prove the non-existence of something.
Meaning, it's impossible to prove that something does
not exist.
First let's prove a negative in the abstract world of
mathematics and we'll move on from there. Let's
consider the integers. An integer is an ordinary whole
number like one (1) or negative five (-5) or seventy
two (72). Does there exist a positive integer that is
less than zero? Of course not, because the definition
of "positive" excludes any number that is less than
zero. It is impossible for a positive integer
to be less than zero if we adhere to the definitions
of "positive", "negative", and "zero".
Therefore, I can confidently state that positive
integers less than zero do not exist.
Now let's move from the abstract world of mathematics
to physical reality. Let "Quiggle" be defined as follows:
Quiggle: (noun) 1. An intelligent life form
that can find a positive integer that is less than
zero.
While it is certainly possible that alien beings exist
somewhere in the universe who are far superior to our
intelligence and mathematical abilities, it's
absolutely impossible for them to find a positive
integer that is less than zero because by
definition, such a number does not
exist. Since Quiggles are defined as beings who
can find such impossible, non-existent numbers,
it logically follows that Quiggles do not exist either. It is
impossible for a Quiggle to exist because a Quiggle is
a being that can perform an impossible task. And
look... I didn't have to search the entire universe to
know for a fact that Quiggles do not exist.
We can build an infinite regress of things that don't
exist based on Quiggles. If a "Quigglatron" is defined
as an electronic apparatus that can locate a Quiggle,
then it logically follows that Quigglatrons do not
exist either. It is impossible to find an object
or being that does not exist, so any device that
supposedly can
find non-existent objects or beings must itself be
either a fraud or... non-existent.