Logic Test - i don't get it

Al Vallario said:
The same way you cannot state, stating only true premises, the falsehood that some racing tracks are not routes of transport.
Click to expand...

I have not stated that, I have said that we cannot decide as we are not furnished with enough information in the two given conditions.

The conclusion is not logically false based on the two given conditions.

It may be absolutely false based on a patent truth, but that is not relevant to the aim of the problem, to determine if a statement is logically correct or not according to two given conditions.

You could have a similar problem with two conditions whereby you could not logically decide if the sky was green or not as they did not provide the relevant information.

a. Water is not green.
b. The sky is not water.
Conc. The sky is green.

Clearly the sky is not green but logically we could not deduce that given only the two conditions above. Equally, that logic does not dictate that the sky is green either, we just don't have enough information there to conclude either way unless we add further knowledge/patent truth/whatever.

Wrong can be Right Logically

Within logical reasoning it can sometimes happen that the premises and conclusion seem obviously wrong, but are logically speaking correct when applying one of the logical reasoning types mentioned above. Be aware that conclusions are drawn based on logical reasoning and not on the validity of the context of certain premises or conclusions.
Click to expand...
(my emphasis)
 
You're missing the point i'm getting at, yet again, and I really do need sleep now, so i'll have to pick this up tomorrow evening unless the debate is concluded for me before then (killerkebab seems to have picked up precisely what I mean, as had several other poster earlier this evening).

Goodnight guys
 
The test is trying to see if you can make deductions from simple statements. The actual truth of the premises in our world here and now is obviously not the object of the test.

Otherwise, why would anyone write the test? If all I had to do to pass the logic test was know that the sky is actually blue and racetracks are transportation routes, then I wouldn't even need to know the axioms, would I? I'd just answer that the conclusions are all false because when I got up this morning the sky didn't look like the grass and smash this test right out of the park :rolleyes:

Kenai, you take over because I'm going to sleep.
EDIT: Damn :p
 
Thanks for the thread Chronictank although I'm sorry if it's not helping you more. I've been reading this morning and this picture keeps appearing in my head...

SomeoneIsWrong.jpg


:D
 
Al Vallario said:
snip
Click to expand...
You are making an assumption where there is a lack of information.
It's not to do with saying "oh, it's obviously that"

Take two *true* premises:
Steve's father is called John
Emma's father is called John

Therefore Steve and Emma are brother and sister.

This is logically similar to your dogs and cats example, but more obvious that you simply can't draw a conclusion. You do not know if the two Johns are the same person, much like from the logic provided you cannot say whether a cat can be a dog or a dog can be a cat. I haven't provided any *false* information, yet the deduction could be either correct or incorrect.
 
TheCenturion said:
In that case, if the word 'all' can be considered a subset of 'some' then the conclusion would be correct. However, it's badly worded. IT would be better written as 'At least some canadians are opticians'
Click to expand...
you're looking at it from the opposite direction for some reason.
The premises lead to all Canadians are Opticians, this does not imply that all Opticians are Canadian so you have no need to question that.

I'd say the only issue was as already raised, whether there are any Canadians at all. It may be possible that there are no canadian opticians if and only if there are no Canadians at all, as we are not given information about the existance of Canadians the deduction that some Opticians are Canadians could be correct or it could be incorrect.
 
Al Vallario said:
The conclusion is definitely false, by the way. See the same question here: http://www.fibonicci.com/logical-reasoning/syllogisms-test/medium/
Click to expand...



1. 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.

answer: Incorrect is correct!

2. a. All men are brothers.
b. All brothers are fathers.
Conclusion is: Some fathers are men.

answer: Correct is correct!

3. a. None of the movie stars is a commedian.
b. All producers are movie stars.
Conclusion is: Some commedians are no producers.

answer: Correct is correct!

4. a. All bikes are transport.
b. Some bikes are hometrainers.
Conclusion is: None of the transports is een hometrainer.

answer: Incorrect is correct!

5. a. None of the addicts is a drug user.
b. None of the drug users is an alcoholic.
Conclusion is: All addicts are alcoholics.

answer: Incorrect is correct!

6. a. All stones are rocks.
b. All rocks are mountains.
Conclusion is: Some mountains are stones.

answer: Correct is correct!

7. a. None of the A’s is a B.
b. None of the B’s are C.
Conclusion is: All A’s are C’s.

answer: Incorrect is correct!

8. a. All mountains are hills.
b. Mount Everest is a mountain.

Answer: Mount Everest is a hill is Correct!

Some hills are mountains
Mount Everest is a hill
Mount Everest is not a hill
Mount Everest is not a mountain

9. a. All houses are residences.
b. All cheds are residences.

Answer: No valid conclusion is possible is Correct!

Some cheds are residences
All houses are cheds
No house is a ched
No valid conclusion is possible

10. a. Some bosses are employees.
b. All employees are elderly.

Answer: Some bosses are elderly is Correct!

All elderly are employees
Some employees are no elderly
Some bosses are elderly
Some bosses are no elderly

11. a. A car is no boat.
b. Some boats are water bicycles.

Answer: Some water bicycles are no cars is Correct!

No boat is een water bicycle
Some water bicycles are no cars
No boat is a car
Some cars are no water bicycles

12. a. A bird is no fish.
b. Some fish are sharks.

Answer: Some sharks are no birds is Correct!

No fish is a shark
Some sharks are no birds
No fish is a bird
Some birds are no sharks

13. a. All divers are adventurers.
b. No diver is a wimp.

Answer: Some adventurers are no wimps is Correct!

No adventurer is a wimp
No wimp is an adventurer
Some adventurers are no wimps
No valid conclusion is possible
 
The answer stated by any of the conclusions whether they be true or false is completely irrelevant. All that matters is whether you can possibly arrive at that conclusion given only the information supplied. If the only conclusion you can prove is still patently false (the sky is green) then it is still the correct answer to the question. These are test questions designed to see whether you can think in a certain way, not to see if you can use deductive reasoning to find out the truth.
 
So we're all in agreement that "the sky is green" can be a correct conclusion given the right set of premises, although it is not necessarily the truth (as in the universal truth).

I don't think anyone's disputing that, we're just arguing semantics now.
 
Al Vallario said:
Wrong. As with a few others here, you're confusing logical validity and falsity.

A conclusion can be false ("cats are dogs") and yet logically valid (reached by valid deductive logic from a set of premises). That appears to be the point you're trying to make.

The point I'm making is that the conclusion of a logically valid argument can never be false if only true premises are supplied. You can reach the false conclusion "cats are dogs" through a valid argument, but only if a sufficiently bonkers false premise has also been included.
Click to expand...
But how is that of any help to the OP?
You keep harping on about it as if it makes you able to give a definitive answer when the premises lead to an inconclusive answer. It's all very well saying "you don't have to assume the sky is blue, it just is" but you're introducing a new premise to the scenario. It's like adding wind resistance and friction to a simple mechanics equation, the question can be sufficiently answered with the information provided, adding in your real world truism doesn't help you, in fact it can lead you to the wrong answer. i.e. you saying it is incorrect to say that dogs are cats, when from the information provided you cannot tell whether dogs are cats.
 
Al Vallario said:
This is one of the more recent mistakes Kenai made. It is not equivalent to adding another premise.

I don't need to add the premise "the sky is not green" to every argument with the conclusion "the sky is green" to make that conclusion false. The conclusion is universally false.

I'm genuinely struggling to understand how you can look at conclusions like "cats are dogs" or "the sky is green" and fail to acknowledge that these conclusions are false statements. Whether they are logically valid conclusions is another matter. They are false statements in any and all contexts.
Click to expand...
Whether they are true or false is irrelevant, it's whether they can be logically deduced from the premises (Correct), Disproved by the premises (Incorrect) or a deduction is not possible from the premises provided (Inconclusive)
Like I say, you're bringing in additional information, regardless of it's truthfullness, that information does not help you to the correct answer of the 3 available options.
Edit: How does it help the OP? It's a sufficient formal proof that the argument is not logically valid.

The conclusion is false, yet both the premises are true. From that you can deduce the argument must be logically invalid. More precisely, the argument is invalid because the false conclusion does not follow from the premises...
Click to expand...
From the premises you can only conclude that it's inconclusive. Whether the statements are true in real life has no bearing on this inconclusiveness.
 
I can't believe you guys are still discussing this.

It's a logic test, a logic test doesn't depend on subjective (external) knowledge about whether a racetrack constitutes a mode of transport. Frankly Al, you should feel a little embarrassed :).

If the logic test was:

All humans can breath underwater,
All things that can breath underwater, are fish.

The answer would be that humans are fish. Not that humans can't breathe underwater, or that things other than fish live underwater...

As Kenai seems to be exhaustively trying to explain, you work within the confines of the logic that you are presented with, that's all.
 
Last edited:
My post seems to have been lost in the woodwork so reposting

Chronictank said:
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 some of z can be x (because we can't say either way with the information given)

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 some of y can be z as its the outer shell?
(based on the previous example)

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 :confused:
Uploaded with ImageShack.us

All examples from:
http://www.fibonicci.com/logical-reasoning/syllogisms-test/easy/
Click to expand...
 
You must log in or register to reply here.
Back
Top Bottom