Logic Test - i don't get it

[Nanoman]

Yea I do get the point you're making.

 

[Kenai]

Every argument with true premises and a false conclusion is invalid. Basic logic.

That is true in this case. The premises are true, the conclusion is false. Ergo, the logic is invalid. Why is the logic invalid? Well, it's a non sequitur. The conclusion simply isn't supported by the premises.

The conclusion is only false judged by conditions external to the original conditions given to you though.

Given only the conditions in the first post, logically the conclusion could be correct or incorrect, we do not have enough information to make a conclusive decision either way.

The conclusion seems ridiculous in real terms but within the purposes of this test, whether it seems ridiculous in real terms is totally irrelevant, it doesn't necessarily contradict the two conditions we are presented with but nor is it completely supported by them so logically it is indeterminable without more information.

 

[Al Vallario]

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[Kenai]

Your judging the content though, not the logic.

Judging purely the logic (which is the entire point of the exercise) there is no false conclusion.

Treat it as S, R and T instead of Streets, Racetracks and Transport Routes. You have to ignore the 'picture' and focus on the mechanics behind it all.

 

[Liampope]

Every argument with true premises and a false conclusion is invalid. Basic logic.

That is true in this case. The premises are true, the conclusion is false. Ergo, the logic is invalid. Why is the logic invalid? Well, it's a non sequitur. The conclusion simply isn't supported by the premises.

So what about false premises and a true conclusion? (e.g. premise 1: All canadians are right-handers, premise 2: all right handers are opticians, conclusion: some opticians are Canadian) . Is that also invalid?

You're taking this a level too high. This is very basic (school level) pure logic. Premises are just premises - statements. They are not either true or false. True or false according to what/whom? in the real world? on Mars? In a particular fairy tale? The premises are simply statements and the conclusion given is either logically true or false depending on whether it follows logically from the premises or not. The factual accuracy (according to somebody's definition of a 'transport route' or whatever) of the premises is completely irrelevant.

 

[Killerkebab]

I'll repeat myself. No valid logical argument can have all true premises and a false conclusion.

Yes, you could reach a false conclusion like the one provided in the question if you had at least one false premise. But you cannot logically reach a false conclusion from all true premises.

What on Earth are you even arguing? There's no such thing as a "true" or a "false" premise here.

 

[Kenai]

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.

All three of those venn diagrams satisfy the conditions a and b without presenting any conflict. Because all three are valid, it means we cannot determine whether the given conclusion is correct or incorrect, it could be either. We need a third condition before we can decide.

edit - ffs I have to be up in a few hours, i'm going to bed now, night guys

 

[Al Vallario]

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[Al Vallario]

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[Kenai]

The content is entirely relevant here.

It's not at all, you should be able to do all of these same problems with only letters to identify conditions, because it is not the content we are trying to resolve here, it is the logic contained behind the content.

All three satisfy the premises of the argument, but neither the second nor third are true conclusions.

They are when judged against the condition presented, they are only false when judged against your external condition that it's a given all racetracks must be routes of transport. This isn't a condition present in the original problem though and is thus entirely irrelevant.

(I am going to bed now).

 

[Scrutinize]

2. a. All Canadians are right handed.
b. All right handed are opticians.

Conclusion is: Some opticians are Canadian.

Is this
Correct
Incorrect

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

Imo, it is incorrect as you are making an assumption that there are any canadian opticians and this assumption, cannot be derived from the statement.

all we know from a and b are that; all canadians are right handed and all right handed are opticians

we do not know if there are any canadian opticians, all it says are ‘all right handed are opticians’ which could be in reference to English, French, Germans and so on. for the conclusion to follow as correct, there would need to be a statement c which says there are some canadian opticians.

 

[Al Vallario]

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[Kenai]

You don't have to explain predicate logic to me. You're barking up the complete wrong tree here.

It's not me barking up the wrong tree, I can assure you of that 110%.

 

[Al Vallario]

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[SuperTronNarwhal]

does this help"?

 

[Kenai]

I can assure you 111% you're wrong

I'm not

You're talking about the content of the statements, we are not, that is where the difference is.

You are deciding certain conclusions are false based on the implications of the content (streets and racetracks), instead of looking purely at the logic presented by the conditions (X is Y, No X is Z, so is 'Some Z are not Y' correct?).

What you are saying is clearly and obviously correct (we're not stupid) but you are addressing the problem on a different level to everybody else.

a. All streets are routes of transportation.
a. All X are Y.
b. None of the streets is a racing track.
b. None of the X is a Z.
Conclusion is: Some racing tracks are not routes of transportation.
Conclusion is: Some Z are not Y.

You are discussing things in terms of the pink 'level' and we are all discussing things purely in terms of the yellow 'level'. On the pink level, real world implications suggest to you that some conclusions must be false. On the yellow level, there is no such external implication involved.

(Now I really have to go to sleep )

 

[Chronictank]

I am really not any the wiser to be entirely honest with you
ok forgetting all the context breaking examples into x,y and z
could you please see if you could spot where i am going wrong


2.
a. All of x are y
b. All of y are z
conclusion: Some z are x

Answer: True

The diagram i get


Uploaded with ImageShack.us


So because Z is the outer shell all of x are z but only some of z can be x

7.
a. None of x is y
b. All of z are y
Conclusion: Some of y are z

Answer: False

My diagram


Uploaded with ImageShack.us
Surely the same is true in this case? all of z are y but only some of y can be z as its the outer shell?

8.
a. None of x is y
b. all of z are x
Conclusion: Some of y are not z

Answer is correct

My diagram

Surely this is incorrect because all of z are not y?

Sorry if i am going in circles i don't get it
Uploaded with ImageShack.us

All examples from:
http://www.fibonicci.com/logical-reasoning/syllogisms-test/easy/

 

[Al Vallario]

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[Kenai]

You're absolutely, categorically wrong

I'm not, telling me I am over and over won't convince me of a lie

 

[Al Vallario]

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