3 ms·
An alternative way to see why that’s the most logical viewpoint is, that, if you assume not all marbles in an empty bag are black, you can have the following:
by Someone 3y ago
An alternative way to see why that’s the most logical viewpoint is, that, if you assume not all marbles in an empty bag are black, you can have the following:
- Take a bag for which “all marbles in this bag are black” is false
- Add a black marble to that bag
- After that, “all marbles in the bag are black” becomes true
As is often the case in mathematics/logic [1] with these kind of things, you can hold an alternative view where “are all marbles in this bag black” doesn’t make sense for an empty bag or one where it has the answer “yo”, but if you do that, you’ll find that many proofs get more cumbersome because you have to handle that case differently from all other cases.
[1] other examples are the convention that 0⁰ = 1 and the convention that 1 isn’t a prime number (that’s an example where mathematicians (eventually) decided that having 3 kinds of positive integers (prime numbers, composite numbers, and 1) is the better choice)
- marktani 3y agoedit: totally misunderstood parent, my bad. disregard the following. > - Take a bag for which “all marbles in this bag are black” is false > - Add a black marble to that bag > - After that, “all marbles in the bag are black” becomes true This reasoning is not correct. If the bag contains exactly a red marble at the start, "all marbles in this bag are black" is false as you required, but it breaks the claim at the end that "all marbles in the bag are black". There is in fact no bag that fulfills your reasoning, even the empty bag wouldn't (when starting to write my reply I had erroneously assumed so)
- saurik 3y agoIf a bag contains exactly one red marble at the start then all marbles in this bag are black is in fact false, but when you throw in a black marble the value does NOT suddenly become true, as the red marble still exists, which is exactly the point of the scenario: adding a black marble to a bag where that claim is false shouldn't make the bag suddenly become true, and it still didn't in your example... it would, though, if the empty bag were defined to be false (which it should not be based on this argument).
- marktani 3y agothanks, I see my misunderstanding now