Comment by leiz on The Universal Medical Journal Article Error · 2013-04-06T15:29:17.810Z · LW · GW

OK I agree that the word 'inevitably' is ambiguous. Regardless of the accuracy of the literal-to-logical translations, I think the reason the logical expression of the statement of the article does not match that of the final conclusion, as your logical reasoning proves, is that the writer were not doing the very logical reasoning but doing medical research and thus proposing something new, not something of equivalent logical consequences.

Their first statement:

This study tested and rejected the hypothesis that artificial food coloring causes hyperactivity in all children.

only implies that they did not buy the hypothesis, which did not necessarily imply that they accepted the negation of the hypothesis, which corresponds to your first formula:

!( ∀child ( eats(child, coloring) ⇨ hyperactive(child) ) )


∃child !( eats(child, coloring) ⇨ hyperactive(child) )

Even though they actually accepted the negation of the hypothesis, that is to say , accepted your first formula, the final conclusion they got through the research is that:

The results of this study indicate that artificial food colorings do not affect the behavior of school-age children who are claimed to be sensitive to these agents.

whose correspondent logical expression is your second formula:

∀child !( eats(child, coloring) ⇨ hyperactive(child) ) )

This formula seems stronger than the first one:

∃child !( eats(child, coloring) ⇨ hyperactive(child) )

From my point of view, I don't think that the medical researchers were intentionally arbitrarily generalizing their results or just making logical mistakes. They just posed an attitude to an existing hypothesis and give a new one through the article, in this case, a new stronger hypothesis (the word 'stronger' depends on whether they actually just negated the original hypothesis).

I think their only fault is that they failed to keep their own medical views in one article logically identical.

Comment by leiz on The Universal Medical Journal Article Error · 2013-04-06T10:38:45.173Z · LW · GW

I think that the universal quantifier in

!( ∀child ( eats(child, coloring) ⇨ hyperactive(child) ) )

is not appropriate.

The original statement

artificial food coloring causes hyperactivity in all children.

only implicates that artificial food coloring was responsible for all children's hyperactivity, not that children who ever ate artificial food coloring would inevitably have hyperactivity. So the formula without universal quantifier is more reasonable and thus the final statement of the article is without problem.