To me, Hilbert’s Hotel seems like just a modern-day version of the Omnipotence Paradox - “Can God make a stone so heavy that even He cannot lift it?” Both of these thought experiments deal with infinities’ resistance to division and composition. What I think this should tell us is that infinities are “anti-quantities” in terms of real-world quantification.
I was under the impression that the Laws of Thought were about symbols. All words are symbols, but not all symbols are words (unless you equate the two by definition).
People who use the Heisenberg Uncertainty Principle to justify embracing contradictions are making a false analogy. As I understand it, the Heisenberg Uncertainty Principle says nothing about contradictions - it simply says that there are limits to the measurement of interdependent characteristics of a particle (such as position and momentum).
I think we hold similar positions here, although I don’t agree with your apparent implication that reality is no more or less important than any other kind of experience we have. Also, not only am I noncognitive to “ultimate reality” (if I understand what you mean by “noncognitive”), I simply don’t care whether this reality is the “ultimate reality” - this is the only one that seems to have any effect on me.
If they’re equivocating on the meaning of “A”, then they probably don’t really mean “A and not-A”. But I believe you’ve already put forth this notion in another thread.
On the other hand, can you explain what you mean by something meaning nothing to you “in the deepest sense of the word”?
There’s a way to non-arbitrarily label propositions (in the sense of “strings of symbols”) - it’s called logic.
However, I fail to see why the labels “true” and “false” would/should be doubted, and I’m also having trouble with your apparent standard of having to tell one anything about what actions he shoudl take to get what he wants.
