# RE5 | moonshotai/kimi-k3 | run 2

## Prompt

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

## Response

No, it does not logically follow. The conclusion "some roses fade quickly" may be true in reality, but it is not guaranteed by the two premises, so the argument is invalid. This is a classic fallacy known as the *undistributed middle*.

## Why the Reasoning Fails

The premises tell us:

- Premise 1: All roses are flowers (the set of roses sits inside the set of flowers).
- Premise 2: Some flowers fade quickly (at least one member of the flower set fades quickly).

The gap: Premise 2 says nothing about *which* flowers fade quickly. The quick-fading flowers could be tulips, lilies, or any other kind — roses might be entirely outside that group. "Some flowers" does not mean "some of every kind of flower."

## Counterexample Proving Invalidity

An argument is valid only if the conclusion is true in *every* situation where the premises are true. Here is a situation where the premises hold but the conclusion fails:

| Entity | Is a flower? | Fades quickly? |
|---|---|---|
| Roses | Yes | No |
| Tulips | Yes | Yes |

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

Since a counterexample exists, the inference is invalid.

## What Would Make It Valid

The conclusion would follow if the second premise were stronger, for example:

- **All** flowers fade quickly → then all roses (being flowers) fade quickly.
- All roses fade quickly → directly entails that some roses do (assuming roses exist).

The original argument mistakes "some members of a broad category have a property" for "this specific subcategory has that property."

Would you like me to map this argument onto a Venn diagram or identify the formal syllogistic mood it violates?
