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| 2024-05-13 21:14:56 +0200 | <tomsmeding> | I don't think this discussion was about that :) |
| 2024-05-13 21:14:36 +0200 | <monochrom> | But I guess I am speaking to a community that even refuse to use booleans for logic at all. |
| 2024-05-13 21:14:11 +0200 | <monochrom> | I was just hoping to show that it is beautiful that boolean (==) makes a monoid. |
| 2024-05-13 21:13:50 +0200 | <mauke> | no, a continuum hypothesis |
| 2024-05-13 21:13:48 +0200 | rosco | (~rosco@yp-146-6.tm.net.my) (Quit: Lost terminal) |
| 2024-05-13 21:13:47 +0200 | <ncf> | "this sentence is true" denotes a fixed point of the identity. in classical logic there are two: true and false |
| 2024-05-13 21:13:24 +0200 | <ncf> | do i need to slap you with a fixed point |
| 2024-05-13 21:13:06 +0200 | <mauke> | they are the same world |
| 2024-05-13 21:12:55 +0200 | <ncf> | both worlds are possible |
| 2024-05-13 21:12:50 +0200 | euleritian | (~euleritia@dynamic-176-006-186-214.176.6.pool.telefonica.de) |
| 2024-05-13 21:12:49 +0200 | <ncf> | it can be either |
| 2024-05-13 21:12:47 +0200 | <ncf> | its' not both true and false |
| 2024-05-13 21:12:37 +0200 | <mauke> | "who cares" is not a truth value |
| 2024-05-13 21:12:30 +0200 | <mauke> | in one case, the silver inscription is neither true nor false (paradox), in the other, the silver inscription is both true and false |
| 2024-05-13 21:12:29 +0200 | <tomsmeding> | two possible universes, but the solution of where the portrait is doesn't depend on that choice |
| 2024-05-13 21:12:13 +0200 | <tomsmeding> | there are -- gold is false, silver is either true or false |
| 2024-05-13 21:12:05 +0200 | <ncf> | yes: portrait in gold casket, gold casket lying, silver casket who cares |
| 2024-05-13 21:11:45 +0200 | waleee | (~waleee@h-176-10-144-38.NA.cust.bahnhof.se) |
| 2024-05-13 21:11:41 +0200 | <mauke> | if both inscriptions are required to have a truth value, no solutions are possible |
| 2024-05-13 21:11:27 +0200 | <ncf> | the portrait is in the gold casket |
| 2024-05-13 21:11:18 +0200 | ncf | checks page again |
| 2024-05-13 21:11:00 +0200 | <ncf> | your argument shows that only two universes are possible, and in those two the thing is in the thing |
| 2024-05-13 21:10:59 +0200 | <tomsmeding> | I think doubting the validity of the inscriptions misses the point of the puzzle :p |
| 2024-05-13 21:10:49 +0200 | <ncf> | one bit for the position of the thing, and one bit for the truth of each sentence |
| 2024-05-13 21:10:37 +0200 | <ncf> | mauke: think of it this way: there are 2^3 = 8 universes |
| 2024-05-13 21:10:27 +0200 | <ncf> | (as in, have a truth value) |
| 2024-05-13 21:10:21 +0200 | lisbeths | (uid135845@id-135845.lymington.irccloud.com) (Quit: Connection closed for inactivity) |
| 2024-05-13 21:10:08 +0200 | <mauke> | doesn't affect their contents in any way |
| 2024-05-13 21:10:03 +0200 | <mauke> | but I can write all kinds of things on caskets |
| 2024-05-13 21:09:50 +0200 | <tomsmeding> | "this thing is true but it's also not true" |
| 2024-05-13 21:09:48 +0200 | <mauke> | sure |
| 2024-05-13 21:09:40 +0200 | <tomsmeding> | isn't that kind of the semantical definition of a contradiction |
| 2024-05-13 21:09:23 +0200 | <mauke> | it's a paradox |
| 2024-05-13 21:09:21 +0200 | <ncf> | the hidden piece of information is that both sentences are meaningful |
| 2024-05-13 21:09:05 +0200 | <ncf> | yeah |
| 2024-05-13 21:09:01 +0200 | <tomsmeding> | mauke: isn't a self-refuting statement a contradiction? |
| 2024-05-13 21:08:15 +0200 | <tomsmeding> | now with ambiguity whether the silver one also contains a portrait |
| 2024-05-13 21:08:13 +0200 | <mauke> | if the portrait is in the silver casket, the gold inscription is true and the silver inscription is self-refuting (it is false if assumed to be true and true if assumed to be false) |
| 2024-05-13 21:08:02 +0200 | <tomsmeding> | if you modify the gold inscription to "A portrait" and the proof's conclusion also to "A portrait", I think the result continues to hold |
| 2024-05-13 21:07:47 +0200 | <mauke> | if the portrait is in the gold casket, the gold inscription is false and the silver inscription is self-reinforcing (it is false if assumed to be false and true if assumed to be true) |
| 2024-05-13 21:07:37 +0200 | <tomsmeding> | mauke: the gold inscription talks about "The portrait" |
| 2024-05-13 21:07:04 +0200 | <tomsmeding> | right |
| 2024-05-13 21:06:54 +0200 | <mauke> | anyway, even in the "exactly one" interpretation we're left with two possible outcomes and nothing to disambiguate |
| 2024-05-13 21:05:30 +0200 | <mauke> | consider this situation: there are two caskets, one of which does not contain a portrait |
| 2024-05-13 21:04:58 +0200 | <tomsmeding> | ah, natural language strikes again |
| 2024-05-13 21:04:51 +0200 | <mauke> | one is a subset of two |
| 2024-05-13 21:04:45 +0200 | <tomsmeding> | your third universe is excluded by assumption |
| 2024-05-13 21:04:38 +0200 | <tomsmeding> | one /= two |
| 2024-05-13 21:04:33 +0200 | <tomsmeding> | mauke: "one of which contains a portrait of a lady" |
| 2024-05-13 21:04:32 +0200 | kadir | (~kadir@85.103.183.96) |