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How
are our natural laws (such as Ohm’s law) put together as a
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matter
of arithmetical structure? How are
the “numbers” in them
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defined? Are these entities “numbers” in the
sense
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mathematicians
refer to numbers?
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When
mathematicians talk about “numbers” what do they mean,
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and
what numbers are they referring to?
How are the numbers the
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mathematicians
use (integers, rationals, irrationals .. etc) defined?
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If we
have to do arithmetic with natural laws as we model, is this
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“mathematics”
in the professional mathematician’s sense? If it
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isn’t,
and the modeling still matters, how do we specify the
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arithmetic
that will represent the physical situations we mean to
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represent?
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