I understand how the logic works, and it makes sense that if A most B that B some A since the most can't reverse. However, if A some B's contrapositive is B some A, how can the most statements be equivalent to some statements but only on certain occasions? Are there circumstances where a some statement will have a contrapositive as a most statement, or is there more information needed to make that jump?
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There are not statements where we can derive a most from a some. I'm personally not a big fan of thinking about quantifiers as contrapositives, since it does operate a bit differently from standard if then statements. I think to think about it as follows.
If we know that some Lakers are overrated, we know that there must be at least one overrated player on the lakers. From the statement that some lakers are overrated, we can know for certain that there is at least one overrated laker. This proves that at least one overrated player is also a laker, so some overrated players are lakers.
If we say that most players on the warriors are washed, this does not mean that most players who are washed are on the lakers. The former statement shows that there are at least 7 warriors who are washed. However, we have no idea how many total players are washed! There could be 50 players in the nba who are washed. So, we know only that some players who are washed play on the warriors.
Emil-KunkinFebruary 23, 2024
More information, namely the sizes of the two groups in question, would be needed to prove a most from a most
