## Syllogism problem

What is the basis for reason? And mathematics?

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Jantje7600
Posts: 1
Joined: Fri May 13, 2016 6:34 pm

### Syllogism problem

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

Harbal
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Location: Yorkshire
Contact:

### Re: Syllogism problem

Jantje7600 wrote: 4. Swim Suit can’t swim
How ironic.

Gary Childress
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Joined: Sun Sep 25, 2011 3:08 pm
Location: USA of the UN

### Re: Syllogism problem

Jantje7600 wrote: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

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
Posts: 4197
Joined: Tue Apr 14, 2015 4:48 am

### Re: Syllogism problem

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
Posts: 10658
Joined: Wed Oct 17, 2007 2:31 am

### Re: Syllogism problem

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
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Joined: Tue Apr 14, 2015 4:48 am

### Re: Syllogism problem

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

Arising_uk
Posts: 10658
Joined: Wed Oct 17, 2007 2:31 am

### Re: Syllogism problem

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
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Location: Thin Air

### Re: Syllogism problem

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
Posts: 4197
Joined: Tue Apr 14, 2015 4:48 am

### Re: Syllogism problem

Arising_uk wrote: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
Posts: 10658
Joined: Wed Oct 17, 2007 2:31 am
Give a fuck.

duszek
Posts: 2137
Joined: Wed Jun 03, 2009 5:27 pm
Location: Thin Air

### Re: Syllogism problem

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
Posts: 1660
Joined: Wed Feb 10, 2010 2:04 pm

### Re: Syllogism problem

duszek wrote: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
Posts: 854
Joined: Mon Apr 28, 2014 3:20 pm

### Re: Syllogism problem

Jantje7600 wrote: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

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

surreptitious57
Posts: 1575
Joined: Fri Oct 25, 2013 6:09 am

### Re: Syllogism problem

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
Posts: 2821
Joined: Sat Aug 08, 2015 8:10 am

### Re: Syllogism problem

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.

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