some peanut butter are dogs (p intersects d, or, d is a subset of p)
some cats are dogs (c and d intersect, or, d is a subset of c)
The first two do not make the third.
You can have:
c is a subset of p,
d and p intersect,
The section of p that intersects with d does not contain any c
To fix this, reverse the first statement.
All peanut butter are cats (p is a subset of c)
some peanut butter are dogs (p intersects d, or, d is a subset of p)
some cats are dogs (c and d intersect, or, d is a subset of c)
Any portion of d that intersects with p (some p is d) must also be c (since all p is in c). Hence some c, but not all c, is in the portion of p that intersects with d (some c is d).
Syllogisms ignore whether each premise is factually true. It focuses on whether it is internally coherent.
If I said:
It would be a valid syllogism (structurally valid). This would mean the premises must be evaluated.
You can test yourself on syllogisms here.
You’ll inherently understand what I’m saying after a few rounds.
Your example is incorrect.
The first two do not make the third.
You can have:
To fix this, reverse the first statement.
Any portion of d that intersects with p (some p is d) must also be c (since all p is in c). Hence some c, but not all c, is in the portion of p that intersects with d (some c is d).
Oops. I fucked up lol. I changed it with your edit :p
Mental note: don’t do syllogisms at 1am.