A Logic Puzzle

Philosophy Forums Philosophy
21

Fuck, I got it wrong.

Basket 1 contains nothing, but has the true note.

Basket 2 contains $1 million, but has the false note.

If basket 1 contains nothing, then the first part of it’s disjunction is true, but the second might not be (the false note basket might contain $1 million). And since both aren’t true the whole statement would be true.

If basket 1 has the true note, then basket 2 has the false note, so it can’t be true that the false note contains nothing and the true note contains $1 million. Thus note 2 is false, but the basket contains $1 million.

22

I’m not quite sure about your logic, but since there have been 2 right answers so far with logic that i didn’t fully understand, I’ll give my logic:

there are only 4 possibilities given the initial criteria: basket 1 has money and is true, basket 1 has nothing and is true, basket 1 has money and is not true, and basket 1 has nothing and is not true. i will go through each one one-by-one to show that only one answer is logically consistent.

Assume Basket 1 is true and basket 1 has nothing. If Basket 1 has nothing and is true, basket 2 must be false and have the money. Both parts of the disjunction of b2 must be false. The first part of the disjunction of B2, “this basket contains $1million and the basket with the false note contains nothing,” is false, because the basket with the false note contains the money. The second part of B2, “this box contains nothing and the box with the true note contains $1million,” is also false because “this box” does contain the money, and the true one has nothing.

So, b1 = true and having nothing is consistent logically

Assume basket 1 is true and has something. basket 2 must be false and have nothing. once again, both parts of the disjunction must be false for b2 to be false. “this basket contains $1million and the basket with the false note contains nothing” ← this is clearly false, as “this basket” does not contain the money. “this box contains nothing and the box with the true note contains $1million.” ← this one, however, is true, making b2 true.

b1 = true and having something is logically inconsistent, as it produces a result of b2 = true and b2 = false.

Assume basket 1 is false and has nothing. the first part of basket 1 states, “this basket contains nothing,” and it does in this case. the second part of b1 states “the one with the false note contains nothing” ← that is also true. b1 ends with “but not both,” so since they’re both true, b1 = false, so far consistent. now to test b2 (which needs to be true if b1 is false): the first part of the disjunction is true, “this basket contains $1million and the basket with the false note contains nothing”, so b2 is true.

b1 = false and having nothing is consistent logically

Assume b1 is false and has something. It’s consistent with both of b1’s standards – they’re both false. b2 has to be true. first part of the disjunction is false, because “this basket” does not contain the money, b1 does. second part is false because the true one does not contain 1million. b2 is false

b1 = false and having something is logically inconsistent, as it produces a result of b2 = true and b2 = false.

There are only 2 logically consistent answers in this (I actually started this thread with the belief that there was only 1, because i hadn’t fully considered the ‘not both’ addendum, but that’s ok), and both of the consistent answers have the money in box 2. So you can safely choose box 2 and expect to be a millionaire. Unless you’re dealing with a liar.

Now, for my promised pic:

23

Way to go, fuse. Still, I think your former solution (and mine) is also correct: it is possible for basket 1 to contain nothing and have the false note attached to it, because then both “this basket contains nothing” and “the basket with the false note contains nothing” are true, which means the “but not both” is false and thereby the note as a whole is false.

24

This would be better expressed in propositional calculus.

AvB
~(A[and symbol]B)

both given?

25

Yeah, but this is ILP. I just assume most people here aren’t going to understand symbolic logic and I don’t feel like giving a course at the moment.

Basket 1: (A v B) * ~(A * B)

v → “or”

  • → “and/but”
    ~ → “not”

A = “this basket contains nothing”
B = “the basket with the false note contains nothing”

Basket 2: (C * B) v (A * D)

A & B are the same as above.
C = “this basket contains $1 million”
D = “the box with the true note contains $1 million”

Then it’s just a matter of plugging in truth values.