Descendants of Aristotle still find limitations of the system amusing, that’s amusing itself.
I hope to live to the day when philosophical advancements of 20th century (or re-discovery of 2500-old Indian logic, if you like), formalized in accessible forms, get widespread acceptance, could leave plenty of people who’se job it to juggle limited abstractions with the need to pick more useful jobs.
No pun intended, these are terribly useful abstractions we’ve built our world on, but they barely hold up against thorough reality check and leave out a lot as ‘paradoxes’.
Please add some substance, or I will make your argument for you.
Yes! We all need to get on board with constructivist mathematics [0][1] already. Construction is very similar to computation, and it is not inconsistent to take "all reals are computable" or "all functions are continuous", the same rules Turing discovered, as axioms if we like. We can therefore move computer science fully onto a foundation that is more rigorous than typical maths.
Keep in mind that Aristotelian logic did not stop with Aristotle. It kept developing through the Middle Ages and even into today. Now, it's called term logic. Fred Sommers made tremendous advances in expanding syllogistic logic into something more versatile than what Aristotle worked on.
Indeed. Yet, it is still based on True/False pair, which does not reflect neither reality or human experience in most cases. Where it is applicable - it perfectly works. But the scope is limited.
1. A "quite a while" is less than a hundred years after Godel and in math? Compared to 2000+ years of Aristotlean logic dominance in hard sciences just because Romans inherited most of their scientific views from Greeks, not from Indians/Chinese?
2. It depends on domains of applicability, if you think of it.
In pure CS and math? Yes, the visible value is limited, because most problems we choose to try to solve can be solved with math apparatus we're armed with. Value I know is mostly limited to optimizing problems that have poor solutions with binary logic.
In practical engineering? ATPG, to my understanding, requires multi-valued logic. Analysis of large phenomena and automated decision making becomes an order of magnitude simpler problems, with better efficiency over chosen metric. Temperature controllers, decisions based on photo-metering (autofocus, exposure adjustment), etc. Somehow, even with lack of readily-available building blocks and tooling, it turns out that there are problems people are motivated to solve from scratch, and MVL/FL comes handy.
It's only stuff I overheard of through my life among bright engineers.
3. Moreover, the biggest impact is not in CS (as original presented paradox isn't, as well), it's on human judgment, decision-making and general assessment of reality, where "neither true nor false" (I don't know) is the first stepping stone to make the world much easier place to live in.
I hope to live to the day when philosophical advancements of 20th century (or re-discovery of 2500-old Indian logic, if you like), formalized in accessible forms, get widespread acceptance, could leave plenty of people who’se job it to juggle limited abstractions with the need to pick more useful jobs.
No pun intended, these are terribly useful abstractions we’ve built our world on, but they barely hold up against thorough reality check and leave out a lot as ‘paradoxes’.