A categorical syllogism reasons about groups using all, no and some. The classic:
- All humans are mortal.
- Socrates is human.
- Therefore, Socrates is mortal.
Picturing it
Draw a circle for mortal things and put a circle for humans entirely inside it. Socrates sits inside the humans circle, so he must be inside the mortal circle. Circle diagrams like this (Venn or Euler diagrams) make validity visible.
A common trap
- All dogs are mammals.
- All cats are mammals.
- Therefore, all cats are dogs. (invalid)
Sharing a larger group (mammals) says nothing about how the two smaller groups relate. Draw it: two separate circles inside one big circle.
"Some" is not "all"
"Some politicians are dishonest" does not give you "all politicians are dishonest", and it does not tell you anything about any particular politician. Moving from some to all is one of the most common errors in public argument.
Two more valid patterns
Hypothetical syllogism (chaining conditionals): If P then Q. If Q then R. Therefore, if P then R.
Disjunctive syllogism (process of elimination): P or Q. Not P. Therefore, Q.
Disjunctive syllogism is only as good as its "or". If the two options listed aren't the only possibilities, the argument quietly becomes a false dilemma, which you'll meet in level 6.