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Let's say that saying 'all my hats' implies that the set of hats is non empty, then you have the two following statements my-hats is not empty for ever
by gpderetta 2y ago
Let's say that saying 'all my hats' implies that the set of hats is non empty, then you have the two following statements
my-hats is not empty
for every hat in my-hats, is-green(hat) is true
We know that the speaker always lies, so both statements must be false: my-hats must be empty, and it must be that it exists at least one hat in my-hat that is not green. This is a contradiction. So either the speaker or the puzzle is not consistent (and uninteresting), or the 'my-hats is not empty' is not a valid assumption.
- rcxdude 2y agoI was initially thinking that, but you can parse it as one statement "my-hats is not empty AND for every hat in my-hats, is-green(hat) is true", in which case it's still consistent for that single statement to be false, and it can be false by my-hats being empty.
- gpderetta 2y agoThat's a very good point!
- nailer 2y agoBut ‘my hats is not empty’ is not a statement being made by the liar.
- gpderetta 2y agoHe said 'all my hats are green' either that statement is to be interpreted to require that the set of hats is not empty or it isn't. In the first case that interpretation would be part of the statement he made.
- nailer 2y agoThis person‘s argument hinges on trying to make two statements rather than one, I’ll illustrate with a quote: > We know that the speaker always lies, so both statements must be false: my-hats must be empty, and it must be that it exists at least one hat in my-hat that is not green. No. Since it is one statement as written, and the rules of common logic are not created by the liar, as I said up in the thread, either possibility is true. The person may have no hats or have one hat that is not green.