# RE5 | z-ai/glm-5.2 | 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. This is a classic example of an invalid categorical syllogism [Logical Fallacy Explanation](https://www.logic-is-not-dead.com).

## The Structure of the Argument

The argument takes this form:

1. All roses are flowers (All R are F)
2. Some flowers fade quickly (Some F are Q)
3. Therefore, some roses fade quickly (Some R are Q)

This conclusion is **invalid** because the premises do not guarantee it [Syllogism Validity Rules](https://www.fallacyfiles.org/).

## Why It Fails

The middle term "flowers" is not distributed in a way that necessarily connects roses to the flowers that fade quickly. The "some flowers" that fade quickly could be entirely outside the subset of roses—they might be tulips, daisies, or lilies. Nothing in the premises requires any overlap between roses and the flowers that fade quickly [Categorical Logic Guide](https://plato.stanford.edu/entries/logic-classical/).

## Visual Illustration

Imagine two circles inside a larger circle labeled "Flowers":

- One smaller circle is "Roses"
- Another smaller circle is "Flowers that fade quickly"

These two smaller circles could be completely separate, partially overlapping, or one inside the other. The premises do not specify which case is true, so the conclusion cannot be drawn with certainty.

## Key Principle

A valid syllogism requires that the middle term be **distributed** at least once—meaning it must refer to *all* members of the category in at least one premise. Here, "flowers" is undistributed in both premises [Distribution of Terms](https://www.britannica.com/topic/syllogism).

Would you like to see a corrected version of this syllogism that produces a valid conclusion?
