If we assume the real numbers exist, then perhaps the paradox resolves because there are uncountably many reals and only countably many nameable things, but then perhaps the paradox does not resolve because we assume ZFC is true and we can well order the reals, hence name the first unnameable real.
Bhartrhari's Paradox
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Re: Bhartrhari's Paradox
#12How is it a paradox? Isn't this just a proof that there are many unnamed things, but no unnameable ones?
Re: Bhartrhari's Paradox
#13If you can't name it you can still describe it.
But then by describing it you are committing it to a set of conditions this unnameable thing satisfies.
But then if you go beyond a narrow interpretation of that paradox and accept that naming and describing are both accomplishing the same fundamental thing, that being committing a thing to a condition (like a name) or set of conditions (like a description), you do run into the same problem.
Hmm, interesting. Now back to this E2E testing stuff I've been avoiding.
Re: Bhartrhari's Paradox
#14How is it a paradox? Isn't this just a proof that there are many unnamed things, but no unnameable ones?
Agreed.
This is the stuff of magic and folklore, and neatly resolved by Ursula K. LeGuin in _A Wizard of Earthsea_.
Re: Bhartrhari's Paradox
#15Sounds akin to the complexity inherent in cellular automata. We know via the rules how to mutate successive generations, but backwards propagation, algorithmic simplification, etc may exist but not traceable from any given ruleset.
Re: Bhartrhari's Paradox
#16If we assume the real numbers exist, then perhaps the paradox resolves because there are uncountably many reals and only countably many nameable things, but then perhaps the paradox does not resolve because we assume ZFC is true and we can well order the reals, hence name the first unnameable real.
The reals can be ordered, just use x < y. I think you mean that if ZFC is true, we could enumerate unnameable reals (choose one with the axiom of choice, remove it, choose another one, etc.), but you could not enumerate them all. But it is true that you could get a "first" unnameable real.
Re: Bhartrhari's Paradox
#17If we assume the real numbers exist, then perhaps the paradox resolves because there are uncountably many reals and only countably many nameable things, but then perhaps the paradox does not resolve because we assume ZFC is true and we can well order the reals, hence name the first unnameable real.
The reals can be ordered, just use x < y. I think you mean that if ZFC is true, we could enumerate unnameable reals (choose one with the axiom of choice, remove it, choose another one, etc.), but you could not enumerate them all. But it is true that you could get a "first" unnameable real.
> The reals can be ordered, just use x
That ordering is not a well-ordering, which is what the GP specified. A well ordering requires that every non-empty subset has a smallest element. That's not true for the reals ordered by x 0 has no smallest element.
No one has explicitly shown that the reals can be well ordered, but it's a consequence of the axiom of choice that every set can be well-ordered. So in ZFC there must be a well ordering of the reals, even though no one has found one. Issues like this are why not all mathematicians accept the axiom of choice.
Re: Bhartrhari's Paradox
#18„Wovon man nicht sprechen kann, darüber muss man schweigen“
but if the thing can be interacted with, it can usually be mapped and defined and then named. But there will always be things which do not have names, at least in mathematics -- think of the real numbers.
Re: Bhartrhari's Paradox
#19If you can't name it you can still describe it. But then by describing it you are committing it to a set of conditions this unnameable thing satisfies. But then if you go beyond a narrow interpretation of that paradox and accept that naming and describing are both accomplishing the same fundamental thing, that being committing a thing to a condition (like a name) or set of conditions (like a description), you do run…
Names are like variables in a function. you can name variables anything you want from a human understanding point of view (final cause), but the compiler doesnt care about that. The compiler only cares about the efficient cause of that variable in the sense of what it represents (stack/heap etc).
Re: Bhartrhari's Paradox
#20If you can't name it you can still describe it. But then by describing it you are committing it to a set of conditions this unnameable thing satisfies. But then if you go beyond a narrow interpretation of that paradox and accept that naming and describing are both accomplishing the same fundamental thing, that being committing a thing to a condition (like a name) or set of conditions (like a description), you do run…
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