# RE5 | deepseek/deepseek-v4-pro | 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 that some roses fade quickly. The premises only guarantee that there is at least one flower with the property of fading quickly, but that flower could easily be a type that is not a rose. The argument is deductively invalid because the class of quickly fading flowers might be entirely outside the class of roses.

## The Structure of the Argument
- **Premise 1:** All roses are flowers. (Every rose is a member of the set of flowers.)
- **Premise 2:** Some flowers fade quickly. (There exists at least one flower that fades quickly.)
- **Conclusion:** Some roses fade quickly. (There exists at least one rose that fades quickly.)

This is a syllogism of the form:
- All A are B.
- Some B are C.
- Therefore, Some A are C.

That form is not valid. The “some flowers” in the second premise could refer exclusively to flowers that are not roses. For example, tulips, daylilies, or morning glories might all fade quickly while roses wither slowly. In such a world, both premises remain true, but the conclusion is false.

## Counterexample in Sets
Imagine the Flower universe contains only two kinds: **Roses** and **Tulips**, each with 100 individuals. All roses last a long time (none fade quickly). All tulips fade quickly. Then:
- All roses are flowers ✓ (roses are flowers)
- Some flowers fade quickly ✓ (tulips are flowers that fade quickly)
- Some roses fade quickly ✗ (no roses do)

Thus, the premises are true and the conclusion false, demonstrating invalidity.

## Why It Fails Logically
The term “flowers” is the middle term and appears as the predicate of an A-statement (all roses are flowers) and as the subject of an I-statement (some flowers fade quickly). In traditional logic, the middle term is not “distributed” in either premise — it does not refer to all members of its class in either case, so the premises do not connect roses to fading quickly. The fallacy is sometimes called the **undistributed middle**.

## What Does Follow
A valid conclusion is simply converting the second premise: **Some things that fade quickly are flowers.** No new information about roses is forced by the given statements.

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Would you like to see how adding a premise such as “All flowers that fade quickly are roses” would change the validity of the argument?
