Briefly, and in my opinion, mathematics can only make claims like ‘if
A is true then B is true’. To say B is true, you must also say A is
true. Eventually you have to go back to the beginning of the deductive
chain, and the truth of the initial statement is inductive, not
deductive or mathematics. You can predict the time and place of an
eclipse, and this prediction is based on mathematics and a mathematical
model of reality — Newton’s laws in this case. But the truth of this
prediction is inductive since the initial positions and velocities for
the calculation are inductive, as is the applicability of Newton’s
laws to reality, and even the ‘fact’ that mathematics can describe
the universe is inductive.
And Einstein showed that the applicability of Newton’s laws was in
fact wrong and offered a new model — which we inductively accept as
true, if only provisionally.
Mathematics cannot prove any statement about the real world. Any such
statement will depend at some point on an inductive truth or a
definition.
—Barry
On 3 Sep 2021, at 18:10, thompnicks...@gmail.com wrote:
Ok, is mathematics (logic, etc.) a way of arriving at true
propositions distinct from observation or are mathematical truths
different from empirical truths?
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