Logic of opposites

(Picture of Lausanne Park copyright A. Barake)

I recently read a blog quoting E. Wiesel, about how the opposite of love is not hate but indifference. ( I thought it was Dave Pollard, but I can't find the link). In any case, the point is that attention is the commodity being given or withheld. I am severely summarizing, but I tripped on the word "opposite". How do we define it in such a context? Why can't hate be the opposite of love if intimacy or something else defined as the desired commodity?

Math and logic try to resolve these ambiguities by making distinctions between converse, complement, and other technical relationships, that have something to do with oppositions. The usefulness of these constructs depends on their generality and how they fit within the meta-world of math operators and relationships - set theory etc. Why this is satisfying is a mystery. It may be that our minds are happy to tie these loose ends together in a big coherent construct, or it maybe that our world is actually organized in this way, at least physically, but I am not sure.

I think that what the crisis of mathematics that occurred over 100 years ago shows is that as culture and knowledge and philosophy mature, fragmentation inevitably takes hold. Size matters in that holding something too big together takes exponentially increasing effort, and this applies to things both physical like boats and civilizations or entirely platonic - like mathematics.

Words like "opposite" and "similar" can be so misused in important contexts. Mathematics tries to bring precision to them by limiting the context, and some people try to bridge that limited context world with the real one via ideas like AI, but I am not sure that there is a mapping. the computer is a limited for now in its interactions with our reality.

Also, logical operations depend on predicates, and transitivity, and operations that are repeatable and consistent, which means that the environment in which they operate must be stable. This is not a good environmental expectation for non-mathematical reality.

I was attracted to mathematics and computer programming because it gave me this sense of control, but now I realize that as in programming, the real-world intrudes and must really be considered first.