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by chiakic 557 days ago
The phrase “All my hats are green” implicitly carries the premise “I have hats” in conversational language. Thus, if this statement were to be expressed as a logical proposition, it should be: “I have hats, and all my hats are green.”

This means there are two potential falsehoods in the statement: 1. “I have hats.” 2. “All my hats are green.”

Therefore, what we can deduce is: • He might not have any hats. • If he does have hats, at least one of them is not green.

However, considering the options provided by the author, it is clear they did not take into account the implicitly stated proposition (1) in conversational language. Instead, the author assumes that if he has no hats, then “All my hats are green” is true.

This interpretation, however, is conversationally unreasonable; otherwise, one could claim something equally absurd, such as “All my houses are worth over 100 million dollars” but actually has no house.
3 comments
8note 557 days ago
I think the implicit premise might come from the logical deduction that "all my hats are green" is false means that "i have hats"

the statement is ambiguous when i have no hats, therefore, i must have at least a hat. weve seen the case so often as to know its true without thinking about it

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poincaredisk 557 days ago
Author was pretty clear about the spirit of the riddle:

>Note: this question was originally set in a maths exam, so the answer assumes some basic assumptions about formal logic.

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MrCheeze 557 days ago
In conversational language, "All my hats..." implies that the speaker has at least two hats, which theoretically means that the sentence could be a lie from them having exactly one hat (even a green one). However, in practice, I don't think anyone would actually call that a lie. I think we treat the "I have hats" part not as part of the sentence itself, but more as an underlying premise.

You could have a similar situation in pure logic or math - if I were to say "the largest prime number is odd", is that false? Or something else entirely? (This is what Hofstadter calls mu, from a related concept in Zen.)

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