by gnramires | 2025-05-15 01:10:39+00:00
I didn't get to read it in its entirety.

I personally think we can view logic(s) as tools. I think in a way Bayesian/probabilistic/fuzzy logics (and extensions) are more useful or appropriate in a greater setting than binary logic. We don't really know anything to absolute certainty in real life, as there may always be interfering things getting in the way of our conclusions and our senses -- and although that's just a theoretical impediment usually (we are quite sure of many things, like say that the set of primes is unbounded), in many real life cases it's very relevant, and we're usually making fuzzy judgements about things (like, the success of a venture, whether we will enjoy one thing or another, which path to take, etc.). But it doesn't make sense to declare binary logic obsolete. Think of it as floats and ints (integers). Although we can represent integers using floating point representation, in many cases representing things as ints is much more efficient and simpler. In the same way boolean logic, perhaps the simplest practical logic, is extremely useful in many cases.

Binary logic (in terms of binary expressions and binary circuits) of course is also universal, as you can represent anything in binary -- so the choice of logic, given several universal choices, comes down to application and setting (including physical realization of the circuits/logic and its match to your application).

For example, analog control circuits were (overwhelmingly up to the 80s perhaps) extremely useful in factories controlling processes, and there are relatively simple physical implementations of linear controls using electronics, and even (mechanical) mechanisms. Then we got really good at building small digital circuits and their analog implementation became mostly irrelevant (but still were an important stage for industrial development). With appropriate non-linearities large analog networks are universal as well though (hence Neural Networks, which happen to be implemented using binary circuits currently, but who knows this might change :) ).

So I think it may be fair to see fuzzy logics as more general and more general in some sense, but they are equivalent in other senses to any universal logic (at least as far as taking computable approximations of continuous quantities).

I read a while ago about Cyc's approach to Ontologies, which I understood to be systems used to prove desired claims. There were hierarchical ontologies, in the sense that if you failed to prove some claim in a certain system, you could resort to a slower, but more powerful system (in the sense that it could decide more claims). I guess you can interpret fuzzy logics as a higher ontology in another sense -- the sense of which our knowledge is really always uncertain and precisely evaluating this uncertainty may be necessary (versus just approximating claims as True/False) -- so probabilistic logics would be higher in both the sense of less efficient and more complete.

Note also how things can change and you may want/need to extend your logic indefinitely! Consider how it may be useful to go beyond a simple uncertainty of a claim, and consider for example how reliable this uncertainty itself is: e.g. it may be useful to distinguish between something you know nothing about, which you might arguably attribute probability 50% to, and something you know for sure has a probability of 50%, like a coin flip -- which in turn seems like a more powerful system to be used when it gives better results than the ones which convey less information.

The view of course that you're just building increasingly sophisticated binary systems that more effectively address your tasks persists valid (and relevant as we still use binary computers), again as the fact that other logics are valid too.