[FRIAM] Can empirical discoveries be mathematical?

Mon Sep 13 13:51:56 EDT 2021

Roger, 

If I weren’t immured with my income tax, I would engage you on this.  I believe that metaphor --  aka “abduction”? – is the root of all evil and the root of all good.  And then I wonder about the connection to the naming fallacy.  The naming fallacy I take to be the idea that if two things have the same name, they have the same properties.  This assertion is absurd as a statement of fact but often useful as a source of hypotheses.  So, on this view, we humans take Adam’s Task very seriously.  We stumble around the world naming every new experience that confronts us and then frantically try to work out how much we can trust the implications of that name.  “My love is … a … rose!  How long are her thorns?”

Ugh!  I now see that I have gone all anthropocentric, here.  What IS the relation between perception (cognition, what-have-you) and naming.  The Whorf hypothesis would have it that all perception is run though a dictionary, but I understand that the Whorf hypothesis is not wearing well, these days, and, more important, animals perceive quite well without dictionaries.  Classical conditioning (a la Pavlov) produces abductions.  (This bell MEANS foodpowder)  Would a dog think, “This bell is … a ….foodpowder!”  Probably not.  It might think “Oh Goody Food Powder!”   So whatever the naming thing contributes, it is layered on to something else, something more fundamental.  (Two bird hunters are walking through the underbrush,  guns ready when, the leader calls out “Duck.”; his companion, stops, raises his gun,  and scans the sky, only to be struck full in the face by a bent hickory sapling.]

These are the things I might have written to you about were I not doing my income tax. 

Nick   

Nick Thompson

 <mailto:ThompNickSon2 at gmail.com> ThompNickSon2 at gmail.com

 <https://wordpress.clarku.edu/nthompson/> https://wordpress.clarku.edu/nthompson/

From: Friam <friam-bounces at redfish.com> On Behalf Of Roger Frye
Sent: Tuesday, September 7, 2021 9:28 AM
To: The Friday Morning Applied Complexity Coffee Group <friam at redfish.com>
Subject: Re: [FRIAM] Can empirical discoveries be mathematical?

Reuben had an article in Issue 65 of Eureka Magazine titled 'Solving Problems by "Cheating": Operational Calculi, Function Theory, and Differential Equations'. The article is a compilation of tricks that he ran across during his career that seemed to apply in a general way to solving problems. The theme is that you doodle with methods that you have no right to assume would work in this particular case, and if you get something worthwhile, then go back and prove it.

Towards the end of his life he became more interested in the metaphors that are at the basis of mathematical thinking, the bodily actions that have been abstracted into mathematical concepts. Yuri I. Manin also spoke of Mathematics as Metaphor is a slightly different way in his essays. 

-Roger

On Mon, Sep 6, 2021 at 8:34 PM Frank Wimberly <wimberly3 at gmail.com <mailto:wimberly3 at gmail.com> > wrote:

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 <mailto: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/>  

On Mon, Sep 6, 2021 at 11:19 AM Barry MacKichan <barry.mackichan at mackichan.com <mailto: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 <mailto: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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