[Fis] Linking mathematical Indices in the natural sciences. was: Re: Links to YouTube videos of Dec 15 ZOOM session & reminder of meeting on Wed, Jan 19th 2022

[Loet Leydesdorff]

Dear Jerry,

I donwloaded nd read "Syntax, Semantics, and the Problem of Identity of 
Mathematical Items”, but I find it difficult to relate the discussion. I 
guess that I am not the only one needing help.

For example: Can you, please explain
>"the deep tensions between the Rosen - Husserl - C S Peirce 
>philosophies of mathematics."?
It seems to me that all three of them used a definition of information 
which includes meaning.
After Shannon (1948), one can distinguish between information and 
meaningful information.

In my opinion, one can study the dynamics of meaning independent of the 
dynamics of information, and then study the dynamics of meaningful 
information as an interaction term.

[...]

>More specifically, I am referring to the Peircian necessity for 
>indexing symbols prior to creating logical propositions, a consequence 
>of semiosis that is not embraced by Husserl and certainly not addressed 
>by Rosen’s categorical diagrams.
Because the latter two abstracted from the bioogy?

>The indexing of biological symbols denotes the prior indexing of 
>chemical symbols.  The intimate entangling of the indexes of chemical 
>and biologic symbols is a mathematical fact that connects the syntax 
>and semantics of molecular biology.
>
>These indices are essential to connecting the permutation groups of 
>atomic numbers to the physical space groups of X-ray crystallography.  
>These indices are also essential to connecting the electrical 
>attractor/repeller formula of the BZ reaction to the physical 
>attractor-repeller formula such as the Rossler chaotic attractor.  The 
>former comes to equilibrium, the latter does not!
>
>Gian-Carlo Rota (discrete MIT math professor/ philosopher) addresses 
>this syntactical <—> semantic distinction in mathematics in  "Syntax, 
>Semantics, and the Problem of Identity of Mathematical Items” of 
>Chapter 12 of Indiscrete Mathematics (1997). A difficult read to be 
>sure, but extremely relevant to the failures of some FISers to either 
>prehend, apprehend or comprehend the relative propositions of 
>information transmission. Furthermore, this chapter illuminates several 
>foundational issues of physical complexity theory.  After a couple of 
>decades, I just re-read this chapter last evening.  It remains a 
>“thought -energizer” that gracefully transcends academic boundaries 
>from a Husserialian comprehension of mathematics. :-)
Rota is not using this terminology; it is yours. I would particularly be 
interest in "academic boundaries from a Husserlian comprehension of 
mathematics"?
How do you see this? Please, explain. Do not hesitate to be too long. We 
may understand easier when there is some redundancy.

>Cheers
>
>Jerry
Thanks in advance. Best, Loet
>

_______________

Loet Leydesdorff



"The Evolutionary Dynamics of Discusive Knowledge" 
<https://link.springer.com/book/10.1007/978-3-030-59951-5>(Open Access)

Professor emeritus, University of Amsterdam

Amsterdam School of Communication Research (ASCoR)

loet en leydesdorff.net <mailto:loet en leydesdorff.net>; 
http://www.leydesdorff.net/

http://scholar.google.com/citations?user=ych9gNYAAAAJ&hl=en

ORCID: http://orcid.org/0000-0002-7835-3098;


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