## Relations & Their Relatives • Discussion 23

Having lost my concentration to another round of home reconstruction disruption, let me loop back to the texts from Roberto and Alex which drew me into this discussion last week.

RR:

What’s your view on:

When to create a greater-than-binary relation rather than a binary relation?

Consider:  You want to represent some information, statement, or knowledge, without necessarily being forced to limit to binary relations.  A common example is when wanting to reference time.  And “between” is greater than binary.  What are other pieces of knowledge that you’d want assert a ternary, or greater than binary relation to capture it accurately?

Do you have any rules of thumb for knowing when to assert n-ary relations greater than binary?

AS:
Let me underline an important point:  first of all, we have found in nature and society one or another relation and ask how many members each example of this relation can have?  i.e. arity is a feature of relation itself.  So […] we come here to the logic of relations and its discovery.  For me, examples of relations of different arity from one or another domain would be great.

I will take up $k$-adic or $k$-ary relations from a mathematical perspective and I will treat them from the standpoint of one whose “customers” over his actually getting paid years were academic, education, health, and research science units or investigators engaged in gathering data by means of experiments, empirical studies, or survey instruments and analyzing those data according to the protocols of qualitative observation methods or quantitative statistical hypothesis testing, all toward the purpose of discovering reproducible facts about their research domains and subject populations.

A sidelong but critically necessary reflection on the research scene comes from the Peircean perspective on scientific inquiry, in which triadic relations and especially triadic sign relations are paramount.  I will develop Peirce’s pragmatic, semiotic, information-theoretic viewpoint in tandem with the treatment of relation theory.

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