3 ms·
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 p
by b450 1mo ago
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.
- crimsonspy 1mo agoJeff jeff jeff, jeff jeff jeff jeff! Jeff? Jeff.
- amavect 1mo agoYou 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?
- onraglanroad 1mo ago> No surjective function exists from definitions to real numbers. I'm not really up on maths so this is possibly a stupid question, but can't any real number be written as an ASCII string, which is basically an integer number, so there is a direct mapping there? Or is it because the ASCII number wouldn't be in order that makes the difference? Or is it that you can't write that mapping as a mathematical function perhaps?
- onraglanroad 1mo agoActually, and perhaps sadly, I asked an LLM and I understand now. But perhaps that's not such a bad thing that I can get answers to my foolish questions!
- amavect 1mo agoguess I won't respond now :( "what is a real number, anyways" is one of my favorite questions, not foolish at all
- quickthrowman 1mo agoIt’s not a foolish question, you got to learn about Cantor’s diagonal argument!
- xelxebar 1mo agoIt's because most real numbers are uncomputable. That means, most of the time, the only way to check that two numbers (i.e. names) are the same is to spend infinite time looking at all their infinite digits. An unknowable name isn't a very good name, IMHO.
- miksteyp 1mo agoThe problem with such sleight of hand counterargument is that you haven't even defined what "a thing" is nor "all things" are in this world. And such discussions will just come back to set theory, ZFC, axiom of choice and real numbers.
- delecti 1mo agoThat isn't a problem with the counterargument, because the "paradox" as-stated also uses the word "thing". For that matter, the paradox is self-resolving. By labeling the entities it is concerned with as "unnameable things", it has named them. As a collection, entities not otherwise named can be simply referred to as "Bhartrhari's things".
- miksteyp 1mo agoAnd this is why analytical philosophy should be kept out of mathematics - Some 18th century mathematician before Cantor