# RE5 | moonshotai/kimi-k3 | run 1

## Prompt

All roses are flowers. Some flowers fade quickly. Does it logically follow that some roses fade quickly? Explain.

## Response

No — the conclusion does not follow. The premises guarantee only that *some* flowers fade quickly, and those quickly-fading flowers may be entirely different from roses. This argument commits the classic **fallacy of the undistributed middle**.

## The Argument in Formal Terms

- Premise 1: All roses are flowers — \( \forall x \, (R(x) \rightarrow F(x)) \)
- Premise 2: Some flowers fade quickly — \( \exists x \, (F(x) \wedge Q(x)) \)
- Conclusion: Some roses fade quickly — \( \exists x \, (R(x) \wedge Q(x)) \)

The witness for Premise 2 — the flower that fades quickly — can be *any* flower. Nothing in the premises forces it to be a rose. The middle term "flowers" is never applied to all flowers, so it cannot serve as a bridge connecting roses to quick fading.

## Counterexample

Imagine a garden containing only roses and tulips, where tulips fade quickly and roses never do.

- Premise 1 holds: every rose is a flower.
- Premise 2 holds: some flowers (the tulips) fade quickly.
- Conclusion fails: no rose fades quickly.

A situation where all premises are true and the conclusion is false proves the argument is invalid. On a Venn diagram, the "fade quickly" circle overlaps the "flowers" circle but lies entirely outside the "roses" circle — fully consistent with both premises.

## Valid vs. Invalid Forms

| Premises | Conclusion | Verdict |
|---|---|---|
| All R are F; **all** F are Q | All R are Q | Valid |
| All R are F; **some** F are Q | Some R are Q | **Invalid** |
| All R are F; some R are Q | Some F are Q | Valid |

The fix: replace Premise 2 with "All flowers fade quickly," which distributes the middle term and makes the conclusion unavoidable.

Would you like to see how to test any syllogism for validity using Venn diagrams?
