[FRIAM] Can empirical discoveries be mathematical?

[uǝlƃ ☤>$]

I feel left out. So I'll plop my 2 cents down, too. EricS' description of consistifying several models to target reality mirrors Nick's original question about the 2 transform requirement. Neither of these imply an overly simplified single point of reality-check/validation. They both imply, to me, an *iterative* (though perhaps not merely sequential) reality-checking method.

So it's not clear to me that we can cleanly separate induction (including abduction) from deduction. What's required are methods by which a little bit's induced, a little bit's deduced, a little bit's induced, etc. [⛤] And it may not need to be a *single* loop, there might be parallel loops, operating at different rates. E.g. the rate at which we learn the symmetries of (embedded) electrons is, I'd bet, slower than the rate at which we learn the symmetries of (embedded) t-shirts. [π]

This argues that our conceptual separation of induction from deduction is an artificial separation ... done to rationalize and model an actual, messy [⛧], learning process. And *that* might argue for a more rare answer to Nick's question. Math and reality are not necessarily the same thing. But they're probably not as distinct as we think they are.


[⛤] It's not quite right to say "Newton's laws are in fact wrong". They're not entirely wrong. But they're a little bit wrong. We can say the same about general relativity and QM ... They're both a little bit wrong. And their wrongness depends fundamentally on when, where, who, what, and why.

[π] Such rates might be a function of the logical depth of the models. Maybe deeper models imply longer cycles through the loop. And, even between deep models, there might be long loops like string theory or biological evolution, with fewer opportunities to error-correct against reality versus long loops like general relativity with more common opportunities to bang up against reality.

[⛧] By messy, including but not limited to para- or non-consistency, [in]completeness, multiple modes, etc.

On 9/6/21 8:13 AM, Barry MacKichan wrote:
> 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? 

-- 
☤>$ uǝlƃ