3 ms·

> If all marbles in a bag are black, and you take one marble out, are all marbles in the bag still black? > The only logical answer is yes. The only "logical

> If all marbles in a bag are black, and you take one marble out, are all marbles in the bag still black? > The only logical answer is yes. The only "logical answer" is "there are no marbles in the bag". If this must be cast to a boolean somehow, the only "logical answer" is no. There should be a discontinuity as the last black marble is removed. That isn't absurd at all

jimmaswell 3y ago
Look into formal boolean logic, specifically the "therefore" operator. (T->T)=T,(T->F)=F, but starting with a false premise always results in true. There's good reason for it and it makes other things work out how you'd expect. A marble is in the bag -> the marble is black = True, even if there are no marbles in the bag. You can consider the "all" method as asking for the truth value of "A marble is in the bag -> the marble is black"
- bowsamic 3y ago
  Why should I consider the all function to be like that, rather than actually answering the question “are all the marbles black”? Also, why am I getting downvoted? I’m starting to realise that HN is not the place to come for intellectual discussion anymore if you have anything to say that isn’t immediate agreement. I guess dang has set a flag on my account that encourages others to downvote me, because I’m not sure what other explanation there is for how my comments have been treated recently
  - shadowgovt 3y ago
    With deepest respect: I can't speak to any other comments you've made, but on this thread the downvotes are almost certainly because you've stepped into a philosophical debate that has gone on for over 2,000 years in Western philosophy and more-or-less asserted "If this must be cast to a boolean somehow, the only 'logical answer' is no." I believe the community is interpreting that as a bit dismissive both of the contents of the post and philosophy in general; one of the field's goals is to get past what we feel ought to be the answer to establish some kind of framework where that must be the answer, and your assertion is a bit dismissive of the other viewpoint (which, FWIW, happens to be the modern orthodoxy; IIUC your preferred answer is the old orthodoxy that leads to logical paradoxes and has therefore been put on the shelf as less useful).
  - stOneskull 3y ago
    i think it's a 'black marble bag'. you want to make sure it only ever has black marbles in it. so you do checks on it.. does the bag only contain black marbles? you want to check there's no non-black marbles.
  - 8note 3y ago
    You could define an alternative All where where it means (at least one is true) && (for each n, n is true) But is it useful? Suppose I'm a bus driver and I ask "all aboard?" I'd expect that if the answer is false, I'm missing somebody, and not that the bus is empty
wan23 3y ago
Without knowing how many marbles are in the bag, if you say that not all the marbles in the bag are black, then I'm going to ask you to show me a non-black marble to prove it. Alternatively, I can prove that all the marbles are black by showing you n marbles that are black where n is the number of marbles in the bag. Here you go, zero black marbles!

jimmaswell 3y ago

Look into formal boolean logic, specifically the "therefore" operator. (T->T)=T,(T->F)=F, but starting with a false premise always results in true. There's good reason for it and it makes other things work out how you'd expect. A marble is in the bag -> the marble is black = True, even if there are no marbles in the bag. You can consider the "all" method as asking for the truth value of "A marble is in the bag -> the marble is black"

bowsamic 3y ago
Why should I consider the all function to be like that, rather than actually answering the question “are all the marbles black”? Also, why am I getting downvoted? I’m starting to realise that HN is not the place to come for intellectual discussion anymore if you have anything to say that isn’t immediate agreement. I guess dang has set a flag on my account that encourages others to downvote me, because I’m not sure what other explanation there is for how my comments have been treated recently
- shadowgovt 3y ago
  With deepest respect: I can't speak to any other comments you've made, but on this thread the downvotes are almost certainly because you've stepped into a philosophical debate that has gone on for over 2,000 years in Western philosophy and more-or-less asserted "If this must be cast to a boolean somehow, the only 'logical answer' is no." I believe the community is interpreting that as a bit dismissive both of the contents of the post and philosophy in general; one of the field's goals is to get past what we feel ought to be the answer to establish some kind of framework where that must be the answer, and your assertion is a bit dismissive of the other viewpoint (which, FWIW, happens to be the modern orthodoxy; IIUC your preferred answer is the old orthodoxy that leads to logical paradoxes and has therefore been put on the shelf as less useful).
- stOneskull 3y ago
  i think it's a 'black marble bag'. you want to make sure it only ever has black marbles in it. so you do checks on it.. does the bag only contain black marbles? you want to check there's no non-black marbles.
- 8note 3y ago
  You could define an alternative All where where it means (at least one is true) && (for each n, n is true) But is it useful? Suppose I'm a bus driver and I ask "all aboard?" I'd expect that if the answer is false, I'm missing somebody, and not that the bus is empty

wan23 3y ago

Without knowing how many marbles are in the bag, if you say that not all the marbles in the bag are black, then I'm going to ask you to show me a non-black marble to prove it. Alternatively, I can prove that all the marbles are black by showing you n marbles that are black where n is the number of marbles in the bag. Here you go, zero black marbles!