We homeschool our kids, and "The Great Courses" offers a lot of good intro college classes that are suitable for 6-12th grade as well.
I'm really not into math or logic so please forgive me for the simpleness here. The class is pretty straightforward. In one of the lectures of Categorical Logic, the professor gives 5 rules to ensure a syllogism's validity (apparently to avoid looking up 256 different moods and figures)
1)The middle term is distributed in at least one of the premises.
2) Any term distributed in the conclusion is also distributed in the premises.
3) At least one of the premises must be affirmative.
4) If the conclusion is negative at least one premise must be negative.
5) (Hypothetical mood only) If the conclusion is particular at least one premise must be particular.
Ok, seems straight forward enough (but we're still learning).
To give an example we came up with a simple argument:
- No American is immortal.
- All Idahoans are Americans.
- Therefore no Idahoans are immortal.
I applied all the rules to this and it checked out.
- American (MT) distributed in P1.
- Idahoans is distributed in conclusion and P2.
- P2 is affirmative
- Conclusion is negative and P2 is negative
- Is not applicable bc our syllogism is existential, not hypothetical, and the conclusion is not particular anyway.
-All of the rules checked out. Fair enough.
So, one of the kids says, "it looks to me that if you change the conclusion to 'therefore ALL Idahoans are immortal'
all of the rules still check out". Well, that's OBVIOUSLY not a valid argument, but it seems it passes all the rules regardless. Am I misunderstanding one of these rules, if so, which one?
I did a Venn Diagram (with minor, middle and major term) and verified that it's invalid.
Either I don't understand one of the rules, or the list provided is not complete. Any explanation would be extremely appreciated.
I'm looking like a fool in front of my kids, so thanks in advance!