Syllogism problem

[Jantje7600]

1. All runners are athletes.
2. Some athletes can’t swim.
3. Swim Suit is a runner.
4. Swim Suit can’t swim

I can't figure out whether it is valid, cogent or ill-formed. I thought it was cogent as it makes you think that because:

All A are B
Some B can't C
x is an A
x can't C

Help please

[Harbal]

4. Swim Suit can’t swim

How ironic.

[Gary Childress]

1. All runners are athletes.
2. Some athletes can’t swim.
3. Swim Suit is a runner.
4. Swim Suit can’t swim

I can't figure out whether it is valid, cogent or ill-formed. I thought it was cogent as it makes you think that because:

All A are B
Some B can't C
x is an A
x can't C

Help please

It's definitely not a "valid" argument because the premises clearly do not support the conclusion in such a way that it is impossible to be otherwise. I would be very reluctant to say it's cogent either because it doesn't seem like a "strong" argument (at least on first glance).

In order to be a "strong" argument I think (but am not 100% sure) it would have to be something along the lines of the following:

All runners are athletes
Most athletes can't swim
Swim Suit is a runner
Therefore Swim Suit probably can't swim

Of course my example above might not be a cogent argument either because premise #2 is maybe false. A cogent argument must BOTH be a strong one AND have true premises. I think your initial argument may have true premises (assuming #3 is referring to a person who is a runner and not to the article of clothing) but it is NOT strong. Therefore I will say it is NOT cogent either.

EDIT: Or perhaps a more cogent version of my example would be:

All runners are athletes
Some athletes can't swim
Swim Suit is a runner
Therefore Swim Suit possibly can't swim

[Dalek Prime]

Superset:athlete contains subset:runner entirely. Swimsuit fits in both categories, and is one that can't swim. He still fits into both categories. If these were factual statements about Swimsuit, they would all be non-contradicting. But if the last statement is a conclusion based on previous statements, it cannot be derived by them, and is therefore unreliable.

[Arising_uk]

I'm with DP here. It's just a set of statement about sets and 4 is just stating that SS is the one that fits the sets 1 and 2. I also agree that if there was a 'therefore 4.' it would be invalid reasoning.

[Dalek Prime]

Oh, I'm so relieved that my explanation met with approval, via repetition...

[Arising_uk]

I wasn't approving I was agreeing. That I also said what I would have said if you hadn't might have been superfluous but up yours.

[duszek]

Does the word runner have the same meaning in the two statements ?

1. All runners are athelets.

runners = all human beings and (possibly some animals) who can run and do it professionally

2. Swim suits are runners.

runners = best-sellers ?

Probably not, so this syllogism is a jest, sir, it is a play on words.

[Dalek Prime]

I wasn't approving I was agreeing. That I also said what I would have said if you hadn't might have been superfluous but up yours.

That's for being a general p.r.I.c.k. As soon as you become reasonable with me, I'll do likewise.

[Arising_uk]

Give a fuck.

[duszek]

Sets and subsets can help, yes.

Do runners (=best-sellers) and runners (=animals moving fast) fit into one set ?

No, they don´t, there is no set then.

If I misunderstand something as a non-native speaker, please explain.

[Impenitent]

Sets and subsets can help, yes.

Do runners (=best-sellers) and runners (=animals moving fast) fit into one set ?

No, they don´t, there is no set then.

If I misunderstand something as a non-native speaker, please explain.

you have the right idea, as some runners are noses

-Imp

[Melchior]

1. All runners are athletes.
2. Some athletes can’t swim.
3. Swim Suit is a runner.
4. Swim Suit can’t swim

I can't figure out whether it is valid, cogent or ill-formed. I thought it was cogent as it makes you think that because:

All A are B
Some B can't C
x is an A
x can't C

Help please

Conclusion is not valid. The premises 1–3 do not provide sufficient information to conclude 4.

[surreptitious57]

On the difference between validity and soundness as pertaining to syllogisms [ and other forms of argumentation too ] A valid syllogism [ or argument ] is one where each premise is a logical consequence of the preceding one and the conclusion is also a logical consequence of the preceding premise. It does not matter if the original premise is actually false. A sound syllogism [ or argument ] however has to have a true
premise. All sound syllogisms [ or arguments ] are valid but not all valid syllogisms [ or arguments ] are sound. So valid is a sub set of sound

[Greta]

1. All runners are athletes.
2. Some athletes can’t swim.
3. Swim Suit is a runner.
4. Swim Suit may or may not be able to swim.

It's impossible to pin down because #2 "Some athletes can't swim" adds no information. Of course some athletes can't swim - diversity dictates so. No doubt some can't play tennis. Some athletes don't watch the World Cup. Some athletes don't like cheese, and so on. So #2 effectively acts as a red herring, directing our thoughts towards the idea of athletes not being able to swim.

This means we base all assumptions on this information:

1. All runners are athletes.
2. Swim Suit is a runner.

So the valid following step is:

3. Swim Suit must be an athlete.