# RE5 | anthropic/claude-opus-5 | 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 follow. The argument is invalid: the premises leave open the possibility that every quick-fading flower is a tulip, daffodil, or some other non-rose, in which case both premises are true while the conclusion is false.

## The Logical Structure

Written in categorical form, the argument is:

- **Premise 1:** All roses are flowers (All R are F)
- **Premise 2:** Some flowers fade quickly (Some F are Q)
- **Conclusion:** Some roses fade quickly (Some R are Q)

Premise 1 places roses *inside* the category of flowers, but it says nothing about *which* flowers they are. Premise 2 identifies an unspecified subset of flowers that fade quickly. Nothing guarantees those two subsets overlap.

## Why It Fails: Undistributed Middle

The shared ("middle") term is *flowers*, and it is undistributed in both premises — neither premise makes a claim about *all* flowers. In "All roses are flowers," the term *flowers* appears as the predicate of a universal affirmative, which only tells us that roses are among the flowers. In "Some flowers fade quickly," *some* explicitly refuses to cover the whole category. A valid syllogism requires the middle term to be distributed at least once, so this commits the classic **fallacy of the undistributed middle** ([Aristotle's Logic, SEP](https://plato.stanford.edu/entries/aristotle-logic/)).

## Concrete Counterexample

Imagine a world with exactly two kinds of flowers: roses (which last two weeks) and poppies (which fade in a day).

- "All roses are flowers" — true
- "Some flowers fade quickly" — true (the poppies)
- "Some roses fade quickly" — false

Since the premises can be true while the conclusion is false, the inference is not valid.

## What Would Make It Valid

| Revised Premise 2 | Conclusion | Valid? |
|---|---|---|
| All flowers fade quickly | Some/all roses fade quickly | Yes (Barbara) |
| Some flowers fade quickly | Some roses fade quickly | No |
| Some roses are flowers that fade quickly | Some roses fade quickly | Yes (but question-begging) |
| No flowers fade quickly | No roses fade quickly | Yes (Celarent) |

Note that the real-world conclusion happens to be *true* — cut roses do fade fairly quickly — but truth of a conclusion is independent of whether the argument establishes it. This is a useful reminder that validity concerns the *form* of the reasoning, not the accuracy of the claim.

Would you like to test a few more syllogisms, or see how these forms translate into predicate logic notation?
