[FRIAM] Can empirical discoveries be mathematical?

[Barry MacKichan]

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, thompnickson2 at 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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