Isn't the definition given in the first sentence of the paper after the abstract?mathman said:Omniscience principle? Starting with a profound sounding term with no definition! I stopped reading.
Can you explain what you think is interesting about it and why you titled the thread next generation set theory?ShellWillis said:Summary:: A good read needing confirmation
https://www.cs.bham.ac.uk/~mhe/papers/omniscient-journal-revised.pdf
Might be my favorite article I’ve ever came across
I would like to see some interpretations on it to broaden my currently very narrow point of view…
Have fun!
-oliver
define p:
print( yes )define p:
print( no )In logic and foundations, a principle of omniscience is any principle of classical mathematics that is not valid in constructive mathematics. The idea behind the name (which is due to Bishop (1967)) is that, if we attempt to extend the computational interpretation of constructive mathematics to incorporate one of these principles, we would have to know something that we cannot compute. The main example is the law of excluded middle (EMEM); to apply p∨¬pp \vee \neg{p} computationally, we must know which of these disjuncts hold; to apply this in all situations, we would have to know everything (hence ‘omniscience’).
My thoughts as well...Jarvis323 said:Can you explain what you think is interesting about it and why you titled the thread next generation set theory?
Really? Can't or won't?ShellWillis said:I can’t say
Jarvis323 said:Can you explain what you think is interesting about it and why you titled the thread next generation set theory?
Since the paper under discussion is in a peer-reviewed journal, this discussion is re-opened provisionally. @ShellWillis you really need to do a better job of leading this discussion. Please respond to the key questions that @Jarvis323 has asked, or the thread will likely be closed permanently. Thank you.ShellWillis said:I can’t say
"Next generation set theory" is a branch of mathematics that builds upon traditional set theory by incorporating new concepts and techniques. It aims to address some of the limitations of traditional set theory and provide a more comprehensive framework for understanding mathematical structures.
Next generation set theory introduces new axioms and principles that allow for the study of larger and more complex mathematical structures. It also incorporates tools from other branches of mathematics, such as category theory and topology, to provide a more holistic approach to understanding sets and their properties.
"Next generation set theory" has applications in various fields, including computer science, physics, and philosophy. It can be used to study and analyze large data sets, model complex systems, and provide a foundation for understanding the nature of mathematical truth and reality.
There are ongoing efforts to develop new axioms and principles that can further expand the scope of "Next generation set theory". Researchers are also exploring connections between this branch of mathematics and other fields, such as logic and category theory, to deepen our understanding of sets and their properties.
As a foundational branch of mathematics, "Next generation set theory" has implications for various scientific disciplines. It can provide new insights and tools for analyzing complex systems and data sets, as well as help us better understand the nature of mathematical structures and their relationships to the physical world.