[FRIAM] Can empirical discoveries be mathematical?

[Frank Wimberly]

Our late friend Reuben Hersh was interested in these questions.

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Mon, Sep 6, 2021, 7:58 PM Eric Charles <eric.phillip.charles at gmail.com>
wrote:

> As I said a few days ago: I think traditionally,  "mathematical" would
> have been synonymous with "rigorous deduction from a minimal number of
> axioms", but I doubt that approach is clear cut anymore.
>
> I am pretty confident that modern mathematics is WAY more open-field than
> that.  The Stanford Encyclopedia of Philosophy seems to agree with that
> intuition, though I think it is an even broader topic than implied by just
> this entry:  Non-Deductive Methods in Mathematics (Stanford Encyclopedia
> of Philosophy)
> <https://plato.stanford.edu/entries/mathematics-nondeductive/>
>
>
> <echarles at american.edu>
>
>
> On Mon, Sep 6, 2021 at 11:19 AM Barry MacKichan <
> barry.mackichan at mackichan.com> 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?
>>
>> - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. .
>> FRIAM Applied Complexity Group listserv
>> Zoom Fridays 9:30a-12p Mtn GMT-6  bit.ly/virtualfriam
>> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com
>> FRIAM-COMIC http://friam-comic.blogspot.com/
>> archives: http://friam.471366.n2.nabble.com/
>>
> - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. .
> FRIAM Applied Complexity Group listserv
> Zoom Fridays 9:30a-12p Mtn GMT-6  bit.ly/virtualfriam
> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com
> FRIAM-COMIC http://friam-comic.blogspot.com/
> archives: http://friam.471366.n2.nabble.com/
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://redfish.com/pipermail/friam_redfish.com/attachments/20210906/ad179650/attachment.html>