Rule 1: "Most Martians are Green." Rule 2: "Some Green things are
Slime." Can we conclude that "Some Martians are Slime"?
๐ญ How to Think About This
Draw a Venn Diagram in your head. Do the "Martian" circle and the "Slime" circle have to
touch? Or can they stay separate inside the "Green" circle?
Is the conclusion valid?
Imagine a green room. Martians are standing in the left corner (all green). Slime
is in the right corner (all green). Are the Martians touching the Slime? Not
necessarily.
Incorrect.
Just because two groups share a quality (Green), doesn't mean they overlap
with each other.
The term "Green" connects them. But unless we know that "All" green things are
Slime, we can't be sure the Martian part of the green circle touches the Slime
part.
Correct. We cannot conclude that.
The Insight: โข Some + Some = Nothing: "Some A are B" and "Some B are
C" proves nothing about A and C.
โข To connect groups, you usually need an "All"
statement (All Martians are Green, All Green things are Slime -> Martians
are Slime).
Even if "Most" green things are slime, maybe the Martians are in the minority 49%
that aren't slime! "Most" isn't "All". The gap remains.
Still not certain.
"Most" only means >50%. It leaves plenty of room for the groups to stay
separate.
๐ข Strictly Speaking
Some
Means: 1 to 100%.
Does NOT guarantee "All."
Does NOT guarantee "Most."
Most
Means: 51 to 100%.
Does NOT guarantee "All."
Guarantees "Some."
๐ค Which thinking lens(es) did you use?
Select all the lenses you used:
๐จโ๐ฉโ๐ง For Parents & Teachers
๐ฑ Everyday Logic
Politics: "Most of Party A supports Policy X. Some people who support Policy X are
corrupt."
Conclusion: "Party A is corrupt!"
Reality: Invalid logic. The corrupt people might be the ones in Party B who also support
Policy X. Don't let kids make lazy jumps!
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