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Morendil comments on The Universal Medical Journal Article Error - Less Wrong Discussion
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OK, I may be dense today, but you lost me there. I tried to puzzle out how the raven sentences could be put symbolically so that they each corresponded to one of the negations of your original logic sentence, and found that fruitless. Please clarify?
The rest of the post made sense. I'll read through the comments and figure out why people seem to be disagreeing first, which will give me time to think whether to upvote.
You're right! I goofed on that example. I will change it to a correct example.
First, we start with the symbolic statement:
Next, we replace the variables with English names:
Next, we replace the symbols with English phrases:
Then we clean up the English:
We can repeat the process with the other sentence, being careful to use the same words when we replace the variables:
becomes
becomes
and finally:
(I should note that my English interpretation of ∃y P(x,y) is probably a bit different and more compact than PhilGoetz's, but I think that's a linguistic rather than logical difference.)
You certainly gave me the most-favorable interpretation. But I just goofed. I fixed it above. This is what I was thinking, but my mind wanted to put "black(x)" in there because that's what you do with ravens in symbolic logic.
A) Not everything is a raven: !∀x raven(x)
B) Everything is not a raven: ∀x !raven(x)
The new version is much clearer. My interpretation of the old version was that y was something like "attribute," so you could say "Not every black thing has being a raven as one of its attributes" or "for every black thing, it does not have an attribute which is being a raven." Both of those are fairly torturous sentences in English but the logic looks the same.
That's where I don't follow. I read the original sentence as "for every x there is an y such that the relationship P obtains between x and y". I'm OK with your assigning "black things" to x but "raven-nature" needs explanation; I don't see how to parse it as a relationship between two things previously introduced.
The edited version makes more sense to me now.