counterargument:
1) let x be a thing
2) I name x "Jeff"
3) all things are nameable (from 1 and 2)
another way to put this is that it's natural to take the paradox as a reductio.
Bhartrhari's Paradox
21–30 of 84 posts
Re: Bhartrhari's Paradox
#22„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.
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Re: Bhartrhari's Paradox
#23How is it a paradox? Isn't this just a proof that there are many unnamed things, but no unnameable ones?
> Isn't this just a proof that there are many unnamed things, but no unnameable ones?
Where is it a proof that there are many unnamed things ? I could only see it as an argument that there are no "unnameable" things.
Re: Bhartrhari's Paradox
#24counterargument: 1) let x be a thing 2) I name x "Jeff" 3) all things are nameable (from 1 and 2) another way to put this is that it's natural to take the paradox as a reductio.
Jeff jeff jeff, jeff jeff jeff jeff! Jeff? Jeff.
Re: Bhartrhari's Paradox
#25c.f. the Berry paradox https://en.wikipedia.org/wiki/Berry_paradox
Re: Bhartrhari's Paradox
#26„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.
I suppose if the number of nameable things is countable (because humans can only enumerate, and it is humans who name), then it trivially follows that some real numbers are unnameable. Which proves the existence of such entities.
This reminds me of a YouTube video I watched this week titled "A counting argument for why mind comes before matter": https://youtu.be/AtduNjJV-6E?is=nBZ9ztZsyeoVhCj1
The argument is something like the set of possible thoughts about physical objects is larger than the physical objects themselves. It feels similar in flavor to the idea of unameable objects.
There's something special about a name. The name of the God of the Bible is special. Christians are to call upon _the name_ of the Lord. We pray, hallowed by _thy name_. It is somehow denotes the summary essence of the thing being named, even if it doesn't give specific details of its characteristics.
Re: Bhartrhari's Paradox
#27counterargument: 1) let x be a thing 2) I name x "Jeff" 3) all things are nameable (from 1 and 2) another way to put this is that it's natural to take the paradox as a reductio.
You proved that definable implies nameable, and also unnameable implies undefinable. Obviously true. However, the idea of undefinable real numbers closely resembles a modern version of the paradox. No surjective function exists from definitions to real numbers.
Really, the blurb about "seems impossible to verify this by giving positive instances" contains the tension between constructive math and non-constructive math. Does an unnameable (and undefinable) thing actually exist? If a tree falls in a forest, but no one can hear it, does it make a sound?
Re: Bhartrhari's Paradox
#28Earlier quoted context omitted.
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 m…
Not a mathematician, so this question may be a bit thick. I see the problem with the set of reals > 0, but is it perhaps that in this case > 0 is the problem and for sets specified as >= 0 it's fine because 0 is a nameable real and the smallest element. Obviously you can't just exclude certain expressions arbitrarily though, so I don't know how you could justify that mathematically.
Re: Bhartrhari's Paradox
#29If 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…
In mathematics, there are infinitely many "computable" numbers. That is, numbers which can be describe using any mathematics available. Then there are far more "non computable" numbers, which can't be described by anything finite.
I think there is some analogy to be made here.
Re: Bhartrhari's Paradox
#30„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.
"Unnameable" and "unnamed" are two different things, in my opinion. Are there real numbers that are unnameable or are those just unnamed?
There are some that unnameable with my mathematical understanding, but that's not saying much.