# RE5 | perplexity/sonar-pro | run 1

## 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 are compatible with both possibilities: some roses fade quickly, and no roses fade quickly, so the conclusion is *not* guaranteed by the premises.

## Step-by-step explanation

We are given:

1. **All roses are flowers.**  
2. **Some flowers fade quickly.**

Proposed conclusion:

3. **Therefore, some roses fade quickly.**

To see why this is invalid, clarify the quantifiers:

- “All roses are flowers” means:  
  \[
  \forall x\,(R(x) \rightarrow F(x))
  \]  
  Every rose is a flower.

- “Some flowers fade quickly” means:  
  \[
  \exists x\,(F(x) \land Q(x))
  \]  
  There exists at least one thing that is a flower and fades quickly.

The conclusion “Some roses fade quickly” would be:

\[
\exists x\,(R(x) \land Q(x))
\]

From the premises, we only know:

- Roses form a subset of flowers.
- At least one flower fades quickly.

But we are *not* told that the flower (or flowers) which fade quickly are roses. They could all be tulips, daisies, or any other kind of flower. This possibility shows the inference is not logically forced.[1](https://www.reddit.com/r/logic/comments/1f0lehu/teaching_self_logic_and_have_some_specific/)[2](https://stevemehta.wordpress.com/2012/09/05/logic-dictates-the-wrong-answer/)[4](https://askfilo.com/user-question-answers-smart-solutions/5-logical-reasoning-if-all-roses-are-flowers-and-some-3434313539383730)[10](https://www.logicreasoninglab.com/en/logical-reasoning/questions/if-all-roses-are-flowers-and-some-flowers-fade-quickly-what-follows)

## A concrete counterexample

Construct a simple situation:

- There are **roses** and **tulips**.
- All roses are flowers.  
- Only the tulips fade quickly; no rose fades quickly.

Formally:

- Premise 1 is true: every rose is a flower.
- Premise 2 is true: some flowers (the tulips) fade quickly.
- Conclusion is false: no rose fades quickly, so “some roses fade quickly” is not true.

Because there is a possible situation where both premises are true but the conclusion is false, the argument form is **invalid**.[1](https://www.reddit.com/r/logic/comments/1f0lehu/teaching_self_logic_and_have_some_specific/)[2](https://stevemehta.wordpress.com/2012/09/05/logic-dictates-the-wrong-answer/)[5](https://www.goodreads.com/quotes/1403166-all-roses-are-flowers-some-flowers-fade-quickly-therefore-some)

## Why this often *feels* convincing

People often implicitly assume:

- “Some flowers fade quickly” → they imagine typical flowers, including roses.
- So they *intuitively* connect “flowers that fade quickly” with “roses.”

This is a psychological bias: the argument is *plausible* but not *logically valid*. Daniel Kahneman notes that “a large majority of college students endorse this syllogism as valid,” but it is flawed because “it is possible that there are no roses among the flowers that fade quickly.”[5](https://www.goodreads.com/quotes/1403166-all-roses-are-flowers-some-flowers-fade-quickly-therefore-some)

## A similar form that *is* valid

Compare with:

- All roses are flowers.  
- **All** flowers fade quickly.  
- Therefore, all roses fade quickly.

Here the structure is:

- All A are B.  
- All B are C.  
- Therefore, all A are C.

This is a standard valid syllogism (Barbara, AAA-1).[1](https://www.reddit.com/r/logic/comments/1f0lehu/teaching_self_logic_and_have_some_specific/)[8](https://www.letstalkacademy.com/logical-inference-roses-red-flowers-syllogism-exam/)

In contrast, your argument has the form:

- All A are B.  
- Some B are C.  
- Therefore, some A are C.

This is *not* valid, precisely because the “some B that are C” might lie entirely outside A.[1](https://www.reddit.com/r/logic/comments/1f0lehu/teaching_self_logic-and-have-some-specific/)[10](https://www.logicreasoninglab.com/en/logical-reasoning/questions/if-all-roses-are-flowers-and-some-flowers-fade-quickly-what-follows)

Would you like to see how to use a Venn diagram to visualize why this particular syllogism fails?
