Logic Test - i don't get it

[D.P.]

You have no information telling you what the interaction between route of transport and race track is though, you could draw multiple completely valid venn diagrams for that particular problem.

On that basis I would say 'not answerable'

Yes it is very true that there is no information on the interaction of the race tracks. I was only looking at the Streets within routes of transport which is correct.

 

[Nanoman]

Sorry I still dont understand you! What's the difference between 'a certain percentage' and 'an undetermined amount'? Sounds the same to me. Whichever your definition, the statement 'some opticians are Canadian' is always logically true. Ah well it's late - gotta be up in... oh crap - 4.5 hours

My previous definition - some could mean that 50% of the opticians were Canadian, which would mean the other 50% would have to be non-Canadian.

Wait, I'm confused.

 

[Liampope]

Say some meant that 50% of the opticians were Canadian, that would mean the other 50% would have to be non-Canadian.

They can be. Of all the opticians, some are right-handed (the rest are not). Of those right-handed opticians, some are Canadian (the rest are not).

In other words, in this strange world, every single Canadian is right-handed. Then every right-handed person on the planet (not just the Canadians!) is an optician. That's a lot of opticians. Could well be that 50% of the opticians are Canadian and then of course the other 50% are non-Canadian.

 

[Al Vallario]

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[Kenai]

Your argument seems to be "The rule of thumb is not useful in all cases, therefore it is not useful in any case", which as I'm sure you'll appreciate has no place in a thread about logic

You're obviously completely missing the point of what i'm saying to you then, as that isn't even remotely my argument, not even close.

I'm saying that using real world interpretations in logic tests such as these is missing the point and will lead to incorrect solutions because you are solving based on content not on logic. The pitbull question above illustrates this perfectly - using your 'rule of thumb' would lead to an incorrect logic solution.

 

[Liampope]

This isn't predicate logic here. The questions are intentionally designed using realistic, real-world examples to aid the person in answering them.

No, I think you'll find more likely the real-world applicability is a red-herring - not designed to assist you at all! I mean all Canadians being right-handed opticians? Seriously?

That's the point Kenai is trying to make to you. You need to ignore the real-world applicability and try to solve only the logic. This is a logic test - not a transport themed general knowledge test (or a Canadian employment demographic general knowledge test).

 

[Al Vallario]

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[Liampope]

The question is apparently tricking you into using your real-world knowledge to fill in missing premises yourself and declare the argument logically valid. I'm not suggesting you fill in any holes with real-world knowledge...

But that's exactly what you were doing when considering whether or not race tracks are transport routes! Logically you cannot construct the set diagram for that problem as you dont have enough information (rather you can construct three valid set diagrams).

 

[Kenai]

That's the point Kenai is trying to make to you. You need to ignore the real-world applicability and try to solve only the logic. This is a logic test - not a transport themed general knowledge test (or a Canadian employment demographic general knowledge test).

Exactly, your solution should be absolutely identical regardless of whether you are answering:

a. All streets are routes of transportation.
b. None of the streets is a racing track.

Conclusion is: Some racing tracks are not routes of transportation.

or

a. All S are R1.
b. None of the S is an R2.

Conclusion is: Some R2s are not R1s.

The logic problem is exactly the same and any answer you reach should be exactly the same, as we are solving the logic.

 

[Al Vallario]

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[Kenai]

The question is apparently tricking you into using your real-world knowledge to fill in missing premises yourself and declare the argument logically valid. I'm not suggesting you fill in any holes with real-world knowledge...

It should be taken as given that all racing tracks are routes of transportation. If you add that as an implicit premise, the conclusion is false.

That is exactly what you WERE doing by adding in your 'taken as given' statement

 

[Kenai]

I know exactly what point you're making, but you're not paying attention to what I'm saying.

In real world examples, where all the premises are real-world facts, yet the conclusion is false in the real-world, that should give you an indication that the conclusion does not follow from the premises. That is true in the original racing track case. All the premises are true in the real-world, the conclusion is false in the real-world. Ergo, the logic is probably bogus, and sure enough, it is. Rule of thumb success.

That's all I'm arguing. I'm not suggesting you use it as a proof. You don't answer the question with "The logic is wrong because the conclusion is false. All racing tracks are routes of transportation."

Without going into the matter of my credentials, I will point out I know a thing or two about logic, and I'm finding your insinuations to the contrary rather insulting.

I don't think you do know what point i'm making, as none of your replies address it, they address a different topic entirely.

We're not talking about real world examples, that is the entire point. You seem to be continually trying to discuss a different topic to everyone else.

 

[Al Vallario]

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[Kenai]

It's constructed around a real world scenario so that the language is more easily digestable that a page of 'If X is Y then Z is R and S is T'.

That's it. The problems are the same whether it's roads and racetracks or railways and tramlines or Xs and Ys.

You shouldn't use external knowledge, such as "It should be taken as given that all racing tracks are routes of transportation" to solve the logic problem because that isn't part of the information you are given. The point of the question is to assess the conclusion vs the two pieces of logic you are given and nothing more. If you reduced the logic to letters as I did a couple of posts ago, you become unable to make that same assertion and thus your solution would change, which it should not.

This is because you are solving the content not the logic.

 

[Nanoman]

nvm

 

[Liampope]

In real world examples, where all the premises are real-world facts, yet the conclusion is false in the real-world, that should give you an indication that the conclusion does not follow from the premises.

Maybe if you're a detective, for example, investigating a real-world case, but not in a pure logic test, it shouldnt. And this entire thread is concerned with a pure logic test. As I said, in a pure logic test such as this, the real-world premises are more likely to be red-herrings than helpful indications - such as the dogs example.

 

[Kenai]

edit - nevermind, you'd apply the same 'rule of thumb' to both of those anyway

 

[Al Vallario]

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[Killerkebab]

In the first example, our conclusion is incorrect. We haven't been told anything about the link between racetracks and transportation routes. We could have no racetracks being a transportation route, or some of them being a transportation route, and our first two statements won't have been contradicted. We need more information.

The the second example, the conclusion given is correct. Here, every single canadian is right handed and every single right handed individual is an optician. It follows therefore that some of our opticians will be Canadian, since all Canadians are opticians

As for the last example I saw in the thread, the brown dog/brown pitbull one (the most interesting one imo) the only conclusion I can draw is 4.
We can't assert any of the other conclusions imo

 

[Liampope]

I'm struggling to understand how this could be correct? Aren't you accounting for non-Canadians, essentially adding premise?

I dont think it's adding information to say things outside the set of canadians are non-canadians. That's just true by definition.

Look at my awesome diagram again...

It's constructed entirely from the two original statements. There is by definition a classification for non-right-handed opticians and also non-Canadian right-handers (who are still all opticians). If you're imagining 'people' in these categories it could be that everyone is in fact a canadian and so there are actually no people in the other two classifications (i.e. the 'some' actually means 'all'). But say you have some additional information, as per your example, that 50% of the opticians are Canadian, then by definition the other 50% of opticians are not Canadian. They must be made up of non-Canadian right-handers and non-Canadian-non-right-handers.