Hmm. Under your definition, “to exist, a thing must directly interact in some fashion with other things which exist”. For this to be non-circular, you must specify at least one thing that is known to exist. I thought, this one certainly-known-to-exist thing is myself. If you say that under your definition I don’t exist, then what can be known to exist and how can it be known to do so?
There is nothing circular about the definition—merely recursive.
Recursive definitions must bottom out at some point. The ones that do not are called circular.
As soon as you observe two things to directly interact with one another, you may safely asssert that both exist under my definition.
You didn’t say so before. Now, we two are interacting now (I hope), so we do exist, after all? And what about the characters in the virtual world of a computer game I mentioned before? I certainly saw them interacting.
This is, frankly, not very complicated to figure out.
Hmm. Under your definition, “to exist, a thing must directly interact in some fashion with other things which exist”. For this to be non-circular, you must specify at least one thing that is known to exist. I thought, this one certainly-known-to-exist thing is myself. If you say that under your definition I don’t exist, then what can be known to exist and how can it be known to do so?
There is nothing circular about the definition—merely recursive. “GNU” stands for “GNU is Not UNIX”.
As soon as you observe two things to directly interact with one another, you may safely asssert that both exist under my definition.
This is, frankly, not very complicated to figure out.
Recursive definitions must bottom out at some point. The ones that do not are called circular.
You didn’t say so before. Now, we two are interacting now (I hope), so we do exist, after all? And what about the characters in the virtual world of a computer game I mentioned before? I certainly saw them interacting.
So sorry for my stupidity.
See Corecursion, Non-well-founded set theory, Barwise&Moss Vicious Circles.
Cool, thanks!