| I do think you are getting close to the problem.
When you say "One of the
answers, is that math is just a formal system. " then
that is your private
opinion. I don't think it captures much of what Math
is. Math is about
knowledge.
For example, look up wikipedia on math, which starts out
with "Mathematics
(from Greek μάθημα
máthēma,
“knowledge, study, learning”) is the abstract study of topics
encompassing
quantity,[2] structure,[3] space,[2] change,[4][5] and others;[6]
it has no
generally accepted definition.[7][8]"
Not only does this
point out that there is no "generally accepted definition",
but no mention is
made of formal systems. Other sources will be quite
similar.
When
PoiR says "Mathematics is a language" he/she is in the same boat. It
seem
intellectually dishonest not to highlight that math can mean many
things. It
also points to gaps in knowledge not to be aware of how one
structures an
argument.
This is why this whole topic is closer to metaphysics than
being anything
useful.
To suggest "Eliza (being software) is Math" is just
plain silly. It goes beyond
the common meaning of math, and what is commonly
associated with
math.
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