Alex and Lars,
The issues are complex, and they require a major effort to explain in detail. It's not a task that an email list -- such as Ontolog Forum -- can even begin to address. For a start, I recommend 117 slides (with many, many links and references):
https://www.jfsowa.com/talks/vrmind.pdf .
I am not claiming that my 117 slides solve or explain all the issues. But they summarize many issues and point to many more references for further details and explanations.
Alex: I prefer First Order LANGUAGE. As there are so many logics right now. And by the way, the FOL framework (as we discussed after Barwise) does not have numbers of any kind.
Every version of FOL is isomorphic to the versions that were independently discovered by Frege (1879) and Peirce (1885). Nobody but Frege ever used his notation. But everybody adopted Peirce's version with minor changes in the choice of symbols. Most importantly, anything stated in one version can be mapped to and from every other version automatically without the slightest change of meaning.
However, there are various subsets and supersets of FOL. The Object Management Group (OMG) developed the DOL standard for defining the mappings among them. The HeTS system can automatically map any DOL notation to and from equivalent notations. It can also map any notation to any more expressive notation.
As for numbers, they are a family of systems that can be defined in FOL. As soon as the axioms are added to the set of FOL specifications, numbers become available. Please read slides 84 to 105 of vrmind.pdf.
Lars: Information is actually not a good word for what is stored in the brain. Try mneme (as coined and defined by Richard Semon) or (retrievable/mnemic) engram. One reason being - in short - that information (the process) is rather associated with the creation of engrams. And information as the stimulus of perception is also different from engrams.
I agree. I was using the word 'information' for what is stored in computer systems. Please see the 117 slides of vrmind.pdf. I admit that 117 slides require a large amount of reading. But I suggest that you just start at slide 2 and flip through the slides until you find something interesting.
In summary, there are many other groups that do detailed R & D and specifications of standards. As a mailing list that also sponsors various conferences, Ontolog Forum is not a place for developing standards. Anybody who wants to do such work should join a project that does develop standards.
John