Here's my simple proof: algebra, or any other formal language for that
matter, is expressible in natural language, if inefficiently.
Words like quantity, sum, multiple, equals, and so on, are capable of
conveying the same meaning that the sentence "x*3 = y" conveys. The rules
for manipulating equations are likewise expressible in natural language.
Thus it is possible in principle to do algebra without learning the
mathematical symbols. Much more difficult for human minds perhaps, but
possible in principle. Thus, learning mathematical formalism via translation
from natural language concepts is possible (which is how we do it, after
all). Therefore, an intelligence that can learn natural language can learn
to do math.
The problem is not to learn the equations or the symbols.
The point is that a system which is able to understand and learn linguistic
knowledge is not necessarily able to use and apply its knowledge to solve
problems.
- Matthias
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agi
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