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"implies" and "because" are not equivalent. For example, "x is positive implies x^2 is positive" is true but "x is positive because x^2 is positive" is false.
by tgb 9y ago
"implies" and "because" are not equivalent. For example, "x is positive implies x^2 is positive" is true but "x is positive because x^2 is positive" is false.
- sh87 9y agoexactly what I was trying to point out. It came out wrong I guess. A statement like "if not a, then not b" is not applicable unless a "implies" b and a "is because of" b. Correct me if I got it all wrong somehow.
- yiyus 9y agoI understand the point of your comment. Just the last sentence ("Not being able to...") would have been enough. But your monkey example is confusing, because "=>" usually means "implies", not "because", and with that meaning there is nothing weird about the last statement.
- tgb 9y ago"if not a, then not b" is equivalent to "if b then a" and is neither equivalent to nor the opposite of "a implies b". I'm having trouble understanding your point under these confusions. Is it that being able to explain is a sufficient but not a necessary condition for understanding?
- sh87 9y agoPoint taken. My point is just because I can simply explain it does not imply clear understanding. And not being able to explain isn't a reliable indicator of lack of understanding