# RE5 | meta/muse-spark-1.1 | 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 may be true in fact, but it is not entailed by those two premises. The quickly-fading flowers referred to in the second premise could be entirely non-roses.

## Logical Form

1.  Premise 1: All roses are flowers. ∀x(Rx → Fx)
2.  Premise 2: Some flowers fade quickly. ∃x(Fx ∧ Qx)
3.  Proposed Conclusion: Some roses fade quickly. ∃x(Rx ∧ Qx)

For the conclusion to logically follow, it would have to be true in *every* situation where the premises are true.

## Why It's Invalid

In Premise 1, the set of roses is a subset of the set of flowers.

In Premise 2, you are told that a subset of flowers has the property of fading quickly, but you are not told *which* flowers. That subset could overlap with roses, but it could also be completely outside the roses subset — for example, tulips and poppies.

This commits the fallacy of the **undistributed middle**. The middle term "flowers" is not distributed in a way that connects roses to quickly-fading things.

A Venn diagram makes this clear:
- Draw a large circle for Flowers
- Draw a smaller circle for Roses entirely inside Flowers
- Draw a third circle for Quickly-Fading Things that overlaps Flowers but does *not* have to overlap Roses

Both premises can be true in that diagram while the conclusion is false.

## What Would Make It Valid

To guarantee the conclusion, you would need a premise that links roses specifically to fading, for example:

*   All flowers fade quickly. (All F are Q) → Then all roses fade quickly.
*   Some roses are among the quickly-fading flowers you identified.

Would you like me to show you the valid syllogism forms that *would* prove something about roses?
