What are categorical syllogisms and eliminative arguments?

Categorical syllogisms chain class-membership statements ("all/some X are Y"); eliminative arguments rule out alternatives until one remains.

Two further valid deductive forms:

• Categorical syllogism — reasons over categories using "all/some… are…":
  • (P1) All oaks are trees. (P2) All trees are plants. (K) Therefore all oaks are plants.
• Eliminative argument — narrows a set of options by ruling out the others:
  • (P1) Either Hans walked or drove to Rotkreuz. (P2) Hans didn't walk. (K) Therefore Hans drove.
  • A longer murder-mystery version: given the culprit is Andi, Bertha or Claudia, and clues rule out Andi and Bertha, it follows that Claudia did it.

Tip: Eliminative reasoning (the "process of elimination") is only as strong as its opening premise — it must genuinely list all the possibilities. If the disjunction "either X or Y or Z" misses an option, the elimination proves nothing (a "false dilemma").