Logic Test

Posted by Miss Cellania in Everything Else on January 6, 2009 at 11:30 am

Can you think logically? Take the armchair logic test! There are only 15 questions, and it doesn’t take very long -if you are logical! I scored only 87%, which disappoints me. Link -via the Presurfer

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COMMENT

134 comments to "Logic Test"

Scott-O
January 6th, 2009 at 11:46 am
100% here- although I had to sacrifice a few neurons to get it.
SydneyClaire
January 6th, 2009 at 11:47 am
SydneyClaire scored 100%.
People who score 100% must think logically.
Therefore, SyndeyClaire must think logically.
Valid or Invalid? LOL
coraleaterlinda
January 6th, 2009 at 11:52 am
i scored 93%. that seriously made me think.
canvai
January 6th, 2009 at 11:55 am
the Horse one was a bit of a cheat, but I should have read more carefully.
The water one though, I think remains debatable... If it revealed a different chemical composition, i wouldn't call it water anymore. so of course every observation of water would turn out to be water.
Ken
January 6th, 2009 at 12:04 pm
On the Paris one, did we have to assume it was the same Paris in the two premises? I think it is a flawed syllogism.
xTivo
January 6th, 2009 at 12:06 pm
i messed up on the water one and the murder one. There was nothing to indicate she didn't. there is nothing illogical about saying she did it. Spock would have convicted her.
Leven
January 6th, 2009 at 12:10 pm
The water one is debatable, indeed. Their objections are that it only holds true if water is defined as it is in the first premise (!), and that it only holds true if what we're examining is actually water, which we're told it will be. The conclusion also states that we can make a prediction about future examination of water, not that we can make a prescriptive statement; predictions can be valid and still fail.
Leven
January 6th, 2009 at 12:15 pm
@6: If the question had asked whether or not this evidence would have resulted in a conviction, I'd have said 'yes'. It's logical to say it is highly likely she committed the offense, but it's not a certainty. I gave the answer 'invalid' because it was asking for a logical proof, rather than being beyond reasonable doubt.
Aimi
January 6th, 2009 at 12:21 pm
100% for me
Leif
January 6th, 2009 at 12:23 pm
87%
But I didn't understand some of the questions...and I have a headache so it doesn't count. Oh.,..and the roads were slippery and took a puzzy pink pill before the quiz. ...
IT'S NOT MY FAULT!!!
eni
January 6th, 2009 at 12:23 pm
100%. I took this one before, though, and I remember not liking it because the questions became more bizarre and in some cases (like the "Men are from Mars, Women are from Venus" one) almost irrelevant and stupid.
Namowal
January 6th, 2009 at 12:28 pm
100%
Yet I can't balance my checkbook or remember my phone number. What's going on!?
Mr. Binky
January 6th, 2009 at 12:30 pm
The questions aren't about facts or if men actually ARE from Mars, it's about logic.

And @6: "There was nothing to indicate she didn’t. there is nothing illogical about saying she did it."

There is something illogical about saying she did it, because there was nothing logical that PROVED she did it. There could be a guy with gloves on still in there who killed the victim, and then took the knife and Mary and put her fingerprints on the knife and then got blood all over her. Or it could have been a robot.
Scrabbler
January 6th, 2009 at 12:34 pm
13%
I went with my gut- so if I just go with the opposite of how I feel... I will still do really bad.
Jane Martin
January 6th, 2009 at 12:35 pm
93%. Not too bad
sparge
January 6th, 2009 at 12:39 pm
I also take issue with the water question, particularly with the wording:

Conclusion
Therefore we can predict that every future examination of water will reveal the same chemical composition.

You can predict anything you want. In fact, there's pretty good reason to make that prediction in this case. If (as the site suggests) some not-water should come along, then the prediction is wrong, but the conclusion remains valid.

Other than that, I got them all right.
PAgent
January 6th, 2009 at 12:39 pm
100%

Of course, I took Logic in college, so I had an unfair advantage.
lumpi
January 6th, 2009 at 12:41 pm
Blah. Mostly letter-searching ("Oh, he wrote NOT valid, so the statement is not not not true!").

I still scored 93%
iamevovled
January 6th, 2009 at 12:42 pm
93%. I missed the question on water, although I don't beleive their argument "holds water." (H/T to My Cousin Vinny).
Kent
January 6th, 2009 at 12:43 pm
I am a bit embarrassed to say this, but I took logic 101 in college and what some of you are might not be seeing is that when you judge the validity of the statement groups, you should not bring in any other outside information. You only judge the statements that are there. We have been conditioned from too many years of teachers with "trick" questions that we are always now looking for the trick.
werD
January 6th, 2009 at 12:46 pm
100%. My take on the water question was that future examinations could fail to reveal any chemical composition. Maybe someone slathered pickle relish on my microscope. Everything else was pretty straightforward, if you grok the premise of shutting out common sense.
violet/riga
January 6th, 2009 at 12:51 pm
@19
It's not logical to only go by the information given when you are clearly in possession of further knowledge. By that I certainly disagree with the Paris one - it is not stated that we are referring to the same place. By extension, the given question is flawed insofar as it stupidly assumes simplistic logic.
Kevin
January 6th, 2009 at 1:00 pm
100%, y'all. The interwebs have successfully validated my feelings of superiority.

... suck it dumb-dumbs.
khalid
January 6th, 2009 at 1:03 pm
victory is mine i scored 100 woohoo and I'm not a native speaker of English ....which means that i am a genius valid valid valid valid ...
Idil
January 6th, 2009 at 1:05 pm
100%. YESSSSSSSS
Idil
January 6th, 2009 at 1:06 pm
Khalid, I think it's easier to pass a logic test if you aren't fluent in the language =P Then you only focus on the logic!
Guybrush Threepwood
January 6th, 2009 at 1:07 pm
87%. The "water" and the "men and women test" got me.
Angstrom
January 6th, 2009 at 1:11 pm
I agree with Violet, some of the questions are odd. The paris example is a good one, there needs to be a third clause "3: there is only one place in the world called Paris"

without that clause there can be many places called Paris, one of which is stated as being in New Zealand. So without the limiting clause Jenny could actually live in Paris, Texas, or Paris, France.

In other places the quiz setter makes use of 'unstated evidence' to support a result of 'invalid', for example the murderer is supposedly not Mary because there may be other evidence. Well, if we can't include an un-stated Paris, surely we can't include an un-stated cache of evidence in our deductions.

The use of a fictional character to justify that one is ridiculous "Sherlock Holmes made his name in such cases"

Er, someone better tell the author that Sherlock Holmes is a fictional character !
Alana
January 6th, 2009 at 1:14 pm
100%. But I have an advantage, since I took a logic course in college instead of math.
Ken
January 6th, 2009 at 1:16 pm
The other possibility with the murder one was that there was no murder, but she stumbled on the scene of a particularly gruesome suicide.
Jenny
January 6th, 2009 at 1:18 pm
100% yayayyayayayay
Helgar
January 6th, 2009 at 1:27 pm
got 100% on that one. Just because something is false or defies reason, does not make it illogical.
Corinne
January 6th, 2009 at 1:28 pm
93% Only missed the water one.
Michael Smith
January 6th, 2009 at 1:30 pm
100%!
MadMolecule
January 6th, 2009 at 1:35 pm
100%. But I took logic in college, AND I'm a lawyer.

@6: You're right, there's nothing (given in the facts, anyway) to indicate that she didn't do it, but the question to ask if you're looking for proof is "Given only the facts presented, is it possible, no matter how remotely or implausibly, that she did not do it?" If there's a 0.00000000001% possibility that she didn't do it, then it's not logically "proven." (The O.J. Simpson murder trial is a good example.)
open
January 6th, 2009 at 1:37 pm
Illogical test. All this shows is the universal mind control of the sheeple.
All of these questions can be evaluated to come to a conclusion of both answers and still be logically assessed. For those of you that think this makes you smarter than everyone else you are sadly mistaken and are the ones that are deluded and controlled the most.
k3m15a
January 6th, 2009 at 1:44 pm
100% - WHEEEEEEE!

Too many factored in their own knowledge and experience to answer the questions, and failed to focus on just the situation as presented before them, therefore missing the logic.
giltwist
January 6th, 2009 at 1:49 pm
The one about water is a trick question. As someone who has taken a lot of logic classes.

The problem here is the difference between deductive and inductive logic. The first 14 questions were all deductive. Deductive reasoning means "if all the statements are true, the conclusion has to be true." Inductive reasoning means, "if all the statements are true, the conclusion is probably true based on previous experience."

Side note: science is utterly based on the latter, because it is an empirical system (meaning it relies on observations).

Anyway, while we say deductive reasoning is valid or invalid, we say that inductive reasoning is strong (high likelihood of correctness) or weak (low likelihood of correctness). The argument about water is strong. Any reasonable person is going to say that, if we have to say "valid" or "invalid" we should say "valid" about the water argument. However, given the explanation of why we are wrong, the website is clearly relying on the technical difference between deductive and inductive that a lay person couldn't possibly know.
Skipweasel
January 6th, 2009 at 1:54 pm
100%. Nothing wrong with the water question - it made perfect sense to me. As k3m15a said - it's about disconnecting yourself from everything you know and just living in the universe of information provided by the question /and nothing else/.

Many people have trouble screening off their existing knowledge like this, which is one reason why jury verdicts aren't always sensible. Though to be fair, juries are the least worst system readily available.
dan tacos
January 6th, 2009 at 1:57 pm
wow, open. missing a couple questions really hurt your feelers, huh?
dont
January 6th, 2009 at 1:58 pm
I got the murder one wrong, it seemed illogical, but I decided it might be a trick question thrown in there and went with how I'd decide on a jury instead. I almost failed college logic. This was pretty basic.
Skipweasel
January 6th, 2009 at 1:59 pm
xTivo:- It's utterly wrong to say she did it. The facts presented could, for example, fit an innocent visitor who happened on the dying victim, tried First Aid, then went for help.

As I said above - it's this kind of misunderstanding that leads to flaws in the jury system. Even with a careful explanation by a good defense lawyer you'll find many people think as you do that she's guilty.
Skipweasel
January 6th, 2009 at 2:02 pm
violet/riga:- You're bringing your own pre-existing knowledge to bear on the question - which is exactly what this kind of test is supposed to teach you to eliminate.
If the question had said Splongegorblebrat instead of Paris you wouldn't have got caught. It's because you know that Paris is the name of a place. It might equally have been referring to a product or a person or anything else called Paris. Because it didn't /explicitly/ say that there are more than one entities called Paris is exactly why you assume that there is only one.
Lew A
January 6th, 2009 at 2:13 pm
100% - WOOT!
Lew A
January 6th, 2009 at 2:23 pm
I think what some of you are missing is the fact that a logical statement can be valid and still be false.

For instance:
All Cows are Ducks.
All Ducks are made from Peanut Butter.

Therefore, All Cows are made from Peanut Butter.

That is a logical syllogism. Whether or not it agrees with reality is besides the point.

Lew
SB
January 6th, 2009 at 2:23 pm
93%-much better than I thought I would do! The murder one got me too.
ou812
January 6th, 2009 at 2:24 pm
I agree with Sparge and Leven. As soon as I ran across the word 'predict' then it became valid.

If the statement had read: "Therefore every future examination of water will reveal the same chemical composition.", that would have been invalid.

A very subtle but drastic difference.
Joseph Francis
January 6th, 2009 at 2:25 pm
I got every one but the water one, and I still don't see why I got the water one wrong.

-----------------

*Answer 15. *
a) Water is a molecule composed of two hydrogen atoms and one oxygen atom.
b) Every observation or examination by microscope has confirmed this.

Invalid. Invalid but controversial in philosophical circles. If one defines water as a property that contains two atoms of hydrogen and one atom of oxygen only, then the argument above is valid. However, it is possible also that there may exist a substance that looks like water, boils as water, freezes as water, nourishes plants and life as water, and yet has a different chemical composition to what we know as water. There is nothing that could logically prevent this possibility occurring so the argument then becomes invalid.

------------------------------------------

This question is wrong. What you are asking is this:

a) Water is defined as a substance made from 2 H's and one O.

b) Every past examination of water has confirmed it to be made of molecules consisting of 2 H's and one O.

If you are given a known sample of water and asked to test it, will your observations always confirm that you are in the presence of a substance made from 2 H's and one O?
violet/riga
January 6th, 2009 at 2:26 pm
@44 (Skipweasel)

That's not true actually. I understand how logic questions work but don't accept them as logical. I would still argue the same had it been Splongegorblebrat as it is not implicit enough in the question. It is illogical to assume that there is only one Splongegorblebrat/Paris when that has not been defined.
Persephone
January 6th, 2009 at 2:41 pm
93%. I missed the water one, too. But I agree with canvai that if water is defined as two hydrogen atoms and one oxygen atom, then if you observe a liquid that is said to be water but does not have that molecular makeup, then it is not water.

xtivo, the murder one is invalid because while you have a number of facts, facts which together would probably be accepted in a court of law as beyond a reasonable doubt, it does not logically follow that it is true. It's a logic test, and I had to remind myself of that when I read the question.
Craig
January 6th, 2009 at 2:41 pm
Everyone saying some of the questions were wrong or odd are then saying we who scored 100% are wrong or odd. I reject your reality!
Justin
January 6th, 2009 at 3:05 pm
My gut told me that the last answer was too easy to be valid, but I couldn't figure out how it could be invalid... I should have gone with my gut instead of using logic!

That was the only one I missed.

As for the murder one, I just figured he could have committed suicide or fell on the knife. Mary then tried to save him, and got her fingerprints on the weapon and her DNA on the body. However, maybe I went beyond the scope of the question...
haricotvert
January 6th, 2009 at 3:12 pm
This should be a required test for anyone who is a member of collegiate/high school debate teams.
Goose
January 6th, 2009 at 3:18 pm
100%

These are classic logic puzzles, so don't think about what makes intuitive sense or what the answer SHOULD be.

Only consider what conclusions you can make based on the facts you are given.

As for the water one, in reality scientists would contend that the observed molecule is not water.

But in a broader, logical sense. The question said that that

"we can predict that every future examination of water will reveal the same chemical composition"

very careful wording:

the future examination of the substance which some are claiming would not be water is water by definition in the question ("examination of water")

Since the thing examined is water by definition then it having a different molecular composition would require a broader definition of water.

Tricky, but not unfair. You have to look at the wording closely.

Good Test... I would have missed a couple if I hadn't read the questions twice.
Lala
January 6th, 2009 at 4:15 pm
That was a pretty hard test. Made me think. That dosen't happen very often. I got 93% though.
dgaicun
January 6th, 2009 at 4:19 pm
93%, but not because of logic, but because I was reading and answering very quickly.

Misread 'should' as 'could' on the horse question. The murder and water questions are intuitive if you know that they are distinguishing induction from deduction.
Emmers
January 6th, 2009 at 4:31 pm
100%. Easy as pie.
vero4902
January 6th, 2009 at 4:38 pm
100% - my middle name is "Overanalyze", so I'm not really surprised, lol.
Murmuria
January 6th, 2009 at 4:49 pm
I got 100% too. But now I see that lot of people got the same score, I knew it was an easy one ;(. Anyway, since english is not my first language, I guess the force is with me!
Clotho
January 6th, 2009 at 4:53 pm
there is a difference between "logical" and "rational" - for those with problems with the answers to such questions as the murder one and the water one, you're thinking rationally and not logically.

the biggest problem in the confusion of "logical" and "rational" stems from the so called logical one himself, Spock. He thought rationally, not logically, even though he was telling everyone the conclusions he came up with were logical
Peeves
January 6th, 2009 at 4:57 pm
100%. Interesting use of different types of logic.

The water one, general science rules dictate that theories aren't 100% true because there may be situations in which it is proven false..you can only support a theory 100% but you can't really prove it 100%.

For some questions simple Venn diagrams worked. For the rest situational logic comes in handy, just think like a lawyer/devil's advocate.
violet
January 6th, 2009 at 5:22 pm
Damn water. But even the explanation admitted it's controversial, so I don't know why they didn't just swap it for a question that's Not up for debate...seems illogical.
km
January 6th, 2009 at 5:25 pm
They certainly should have specified that they're using deductive, not inductive, logic. It's implied by their use of the terms "valid" and "invalid," but could still easily cause confusion (as in Q12).

They also don't do a decent enough job of explaining why the water one is invalid, which it is. First off, the language is convoluted, so it doesn't create a syllogism as-written. In fact, a perfectly reasonable syllogistic translation of it would read:

All water molecules have 2 H, 1 O
Some water molecules have 2 H, 1 O*
Therefore, all water molecules have 2 H, 1 O

This is an example of a logical fallacy called "begging the question," in which the conclusion is assumed or stated in one of the premises.

Furthermore, particularly since Hume, deductive logic has typically not been used to make predictive statements. Essentially, the argument in this question says "So far, things have been this way, therefore things will always be this way." That's not a conclusion deductive logic can really come to, at least not on purpose. If nothing else, the phrase "we can predict" should raise a red flag, because it's distinctly out of place in a logical syllogism.

*Since we haven't observed every single water molecule, we can only say that some molecules, namely those we have observed, have this composition.
Skipweasel
January 6th, 2009 at 5:29 pm
violet/riga:- It's not illogical to assume there's only one of something - that's what William of Occam meant when he suggested we not mutiply entities needlessly.
DOJ
January 6th, 2009 at 6:09 pm
After reading all the comments, I still don't see how the water question isn't valid. Premise 'a' would have to be broken for it to be invalid.

"Question 15.
a) Water is a molecule composed of two hydrogen atoms and one oxygen atom.
b) Every observation or examination by microscope has confirmed this.

Conclusion
Therefore we can predict that every future examination of water will reveal the same chemical composition."

If you were to ever examine WATER and find that it did not have "the same chemical composition"(i.e. "two hydrogen atoms and one oxygen atom"), then premise 'a' would be broken. Therefore it is impossible to find a different chemical composition because it is impossible to break a premise.

The reasoning given on the answer page doesn't make any sense for this conclusion. The existence of a substance with identical properties to water, but with different chemical composition, doesn't change the fact that is was WATER that was examined and this other substance.
--------
I also believe the Paris question could be misleading because it in no ways states that the Paris from premise 'b' is the same Paris as in premise 'a'(there could be multiple locations named Paris or perhaps a premise refers to a individual named Paris).
Jose Señaris
January 6th, 2009 at 6:17 pm
I scored 100%, but I´m a really logical guy
DungBeetle
January 6th, 2009 at 6:20 pm
100% - I R shocked!
Even tho' I took the same logic course many of you have taken it has been a loooooong time since then. (Good to know that not all of my brain cells were killed off in the 'shroom wars of '86.)
Arcadion
January 6th, 2009 at 6:22 pm
100% here, but then I did study Logic at university.
ArtR
January 6th, 2009 at 6:42 pm
Question 10. There could be (and there is) more than one city named Paris. It doesn't have to be in New Zealand???
Zane
January 6th, 2009 at 6:44 pm
I has logic, 15 for 15.
Ashley
January 6th, 2009 at 6:52 pm
Despite the defenses here of the water question, I still disagree with it. The first premise is A is B (water is H2O). The conclusion is the same except with the word predict.

A is B.
Some A is B (irrelevant step)
Therefore we predict A is B.

How is that invalid?
bananahammock
January 6th, 2009 at 7:01 pm
100% whatwhat
bananahammock
January 6th, 2009 at 7:03 pm
the use of "every" in the last step ashley.
plus i'm a chem major and i know that water is not always h20 but h30 and oh molecules as well, though still considered water. variants exist. observation, if not proven fact, provides no evidence of future perfect.
bananahammock
January 6th, 2009 at 7:06 pm
"Question 15.
a) Water is a molecule composed of two hydrogen atoms and one oxygen atom.
b) Every observation or examination by microscope has confirmed this.

Conclusion
Therefore we can predict that every future examination of water will reveal the same chemical composition."

it provides that there is a high probability that it will consist only of h20, but not that it is a veritable guarantee
and i retract the previous statement, h30 and oh mean nothing to this question
just a guy
January 6th, 2009 at 7:13 pm
I agree that their water question take is flawed.

Going on their explaination, if we found a substance that appeared to be water in all ways but had a different chemical composition, it wouldn't be water.

The question is:
---------------------
a) Water is a molecule composed of two hydrogen atoms and one oxygen atom.
b) Every observation or examination by microscope has confirmed this.

Conclusion
Therefore we can predict that every future examination of water will reveal the same chemical composition.
-------------------

They are basically saying that:
water = H2O
In the past, we have observered this
therfore,
in the future observation, water = H20.

that's valid. step b just seems like unimportant info.

They claim that "we could look at water in the future and it might have a different chemical compostion", but then we wouldn't be looking at water. They claim this would be only true if we DEFINE water as such, but his #1 statement does just that!

I believe people who got 93% and people who got 100% should consider their scored swapped.
Tweeker
January 6th, 2009 at 7:25 pm
The odds are stupendously low, but it is theoretically possible for a water sample to consist entirely of hydroxide and hydronium ions. Odds are tiny of it happening even with a googleplex samples over a googleplex millenia, but it could.
Tweeker
January 6th, 2009 at 7:26 pm
Well, I suppose the odds arent that terrible if your sample consists of two molecules.
JonathanL
January 6th, 2009 at 8:20 pm
People are missing the point of the water question. It's not a chemistry question it's a logic question. Point A on it's own would make it valid, but Point B means that a scientist can have a substance in front of him that he defines as water and have it turn out to be something else. Logically that substance is still water because it was defined as such and that would make the conclusion invalid. Does it make sense in the real world? No. In the real world it would need to be made of the expected atoms to be water. But like the question about Paris, New Zealand and barking ducks these aren't real world questions.
Skookum
January 6th, 2009 at 8:20 pm
The water question clearly does not say a microscope would be the instrument of every future examination of water. It does not mention the means of examination, therefore it is indeed invalid.

I got 93%, answering the Paris question as invalid. The question did not say where the Paris was that Jenny lived in, only that she lived in Paris. It then said there is a Paris in New Zealand. Therefore my answer, invalid, was valid.
JeffB
January 6th, 2009 at 8:30 pm
I'm with Ken and ArtR, I got 93% because they marked me wrong for the Paris question. There are a TON of places named Paris. Quiz is flizzawed.
JeffB
January 6th, 2009 at 8:42 pm
...which, of course means that me, ArtR and Ken got 100%. The rest of you did not and are in fact illogical.
Wiseguy
January 6th, 2009 at 8:48 pm
I'm very glad I got 100%. I would've been embarrassed if I had scored any lower, being a Computer Scientist and avid logician.

I think the water question may have been a suboptimal example of proving a negative versus proving a positive.

Let's say we know that aliens exist. I claim that all aliens are green. To conclusively prove that all aliens are green, I would have to gather every single alien in the universe and show that each is green. That's really hard. How do I KNOW for sure that I have found every single alien? It's really hard to prove a positive.

On the other hand, I claim that not every alien is green. To prove that, I would only need to find one alien that isn't green. It's much easier to prove a negative.

-----

So maybe this is what they were getting at with the water question. To prove that all water molecules have one oxygen atom and two hydrogen atoms, you would have to example every individual water molecule in existence -- "a lot" or "all but one" does not count as "ALL."
Alex
January 6th, 2009 at 8:51 pm
WooHoo! 100%.

The water one is kind of like the black swan question, which is like this

- a swan is observed to have white feathers
- all observations so far confirm that all swans have white feathers

People in middle age Europe actually believed that ALL swans are white, until someone noticed that there's a black swan outside of Europe.

It's also the title of the book on the economic collapse by Nassim Taleb.
JonathanL
January 6th, 2009 at 8:53 pm
The Paris question is correct as it is as well. Logic questions provide you with the ONLY information that applies to the question.

If it said

a) Jenny lives in Paris.
b) There is a Paris in New Zealand.
c) There is a Paris in France
d) There is a Paris in Vermont

Conclusion
Therefore Jenny lives in New Zealand.

Then it would be incorrect. However all we know is:

a) Jenny lives in Paris.
b) Paris is in New Zealand.

Conclusion
Therefore Jenny lives in New Zealand.
Jon C
January 6th, 2009 at 8:57 pm
93%

Interesting test
cec
January 6th, 2009 at 9:11 pm
Neat test, but poor on the explanation of inductive vs. deductive reasoning.
uh huh
January 6th, 2009 at 9:46 pm
y'all need to learn about truth tables
ted
January 6th, 2009 at 10:10 pm
Messed up the water one, because of the wording that you could predict. I figured it would be wrong before I answered it, but it's only a test.

Also, given the facts about the murder, I thought it would be logical to assume that the chick committed it. Even though I suspected it was wrong when I answered it.
Christophe
January 6th, 2009 at 11:15 pm
93% of the #$%& water question. That's it! I'm done with water! I'll only drink wine!
DOJ
January 7th, 2009 at 12:12 am
but Alex, it doesn't say "water is observed to", it says "water is a"
Aramax
January 7th, 2009 at 12:50 am
The question number 12. ( The murder story ) was open to debate.

Of course it's wrong to assume that she's the murderer but given the incriminating evidences logic implies that she did commit the murder... and this was a logic test.

Question number 12 was my only fault in this test.

NB: All men are from mars and all women are from venus... when you look at the answer and explination they talk about a book... what book are they refering to?
Nathan Miller
January 7th, 2009 at 2:55 am
I'll jump on the 100% bandwagon...

But this isn't 'logic' so much as a simple p->q test. Modus Tollens and what have you. There's a lot more to logic, including logical fallacies, which is what I was expecting.
b°b
January 7th, 2009 at 2:58 am
Is that a serious question, aramax?
clinton labombard
January 7th, 2009 at 4:51 am
Donald Duck is a depiction of a duck. Donald may quack and be vaguely shaped like a duck... but he's only a cartoon character and can just as easily bark. Are you trying to tell me all ducks bark?
Max Power
January 7th, 2009 at 7:34 am
100%

And to the water-question-complainers: It's your logic that's flawed, really. Sorry.
Nick K
January 7th, 2009 at 7:57 am
i think everyone (including the setter) is missing the point with the water question - it has nothing to do with water. forget the water!

there is a vital difference between "therefore we can predict that every future examination will reveal etc." and "therefore every future examination will reveal etc." (the latter being what the revealed answer addresses)

the question in fact asks whether prediction is possible. now there is nothing to stop us predicting anything about anything. but there is nothing in conditions A) and B) which leads to the logical conclusion that this should be so.

therefore the logical answer is that the statement is invalid
Ally
January 7th, 2009 at 9:05 am
I got a 40 on it, and I'm not ashamed to admit it!
Rocky Rook
January 7th, 2009 at 10:17 am
100%. I have some programming experience and I felt those neurons firing when I started thinking about the questions on the quiz.
AnUnSi
January 7th, 2009 at 10:28 am
All you many folks who claimed to get 100% right actually got 93% right, because you answered the final question incorrectly. The quiz-writer's explanation of the final answer is bogus, as at least one person (above) has explained.
Miss Cellania
January 7th, 2009 at 11:15 am
A friend of mine wrote to the creator of the test about the water question, and received this in return. I got permission to post it because he's really busy stamping out all the fires this quiz has set!

Dear Duke

OK take 100%

I receive more emails concerning this question than all the others together.

The answer given on the web site is, as you say, incorrect and needs adjusting, but then it would not be controversial and I would probably not get any feedback.

The syllogism itself is invalid and can only be considered as a strong inductive argument and not deductive. It is the 'we can predict' part of the conclusion which comes from nowhere, so the argument is not strictly formal. Not everyone agrees with this so I will leave you to draw your own conclusions. I discuss these points in my book if I may put in a plug!

However, just as an aside there are other types of water. Heavy water for example is water in which the hydrogen is replaced by its heavier isotope, deuteruim (D2O). It is chemically almost identical to normal water but looks, feels and tastes exactly the same. But don't drink it. This says nothing about the validity but only about the truth of the conclusion.

Thanks again for the feedback and comments,

Colin Beckley
rosekat
January 7th, 2009 at 11:28 am
I got 89%. What?
RobertR
January 7th, 2009 at 11:43 am
I disagree with the stated answer to question 15. As sparge has already pointed out, as the conclusion is worded it is valid as long as we are capable of making that prediction, regardless of whether the prediction itself is valid.

But let's slightly change the conclusion to read, "Therefore we can accurately predict that every future examination of water will reveal the same chemical composition." Then I still disagree with the stated explanation, but I agree that the conclusion is invalid on different logical grounds.

If, as the premise states, water is a molecule composed of two hydrogen atoms and one oxygen atom, then any sample of water examined must, by definition, have that same chemical composition. Otherwise we were not actually examining water, and the conclusion makes no claims regarding the exmaination of a non-water substance regardless of how much it seems like water or how much we believed it was water.

However, there is nothing in the premises or the conclusion to specify that an examination of water will accurately reveal its chemical composition. If I examine a smaple of water with my naked eye, that exmaination will fail to reveal the chemical composition and will invalidate the conclusion.
cec
January 7th, 2009 at 12:02 pm
the explanation for the water question is poor. It's not valid because it depends on inductive reasoning: "all past a's have had property P, so all future a's will have property P"

while there are several notions of validity in inductive arguments, the test was pretty clearly designed to see if you could tell valid from invalid arguments in the main sense - for deductive logic.

A logic text I studied in school said something like "It is important to understand that 'valid' is not a term of praise"
Adrian
January 7th, 2009 at 12:02 pm
To JonathanL (Comment 84) - sorry, not buying that. Your interpretation of the Paris question is now simply incorporating an assumption about how Logic tests work. If such an interpretation is correct, then a similar argument might be used to say that the murder question in the test may offer a Valid conclusion too.

I'm OK with all of the other questions - including the heavily debated water one at the end - but I still reckon the Paris question is missing an important additional statement if you want to guarantee its validity. Either that or you need an explicit statement somewhere saying that all questions are to be answered on the assumption that their written contents express the totality of information relevant to the matter under consideration. (Or something like that.) Unfortunately, I suspect that such an assumption might lead to more complications than it avoids.

Don'cha just love this stuff?
just a guy
January 7th, 2009 at 12:28 pm
Well, Miss C's post from the author has me convinced!
Steve L from NY
January 7th, 2009 at 12:52 pm
Question 15 asks whether we can predict that every future examination of water will reveal the same chemical composition. My dispute is with your choice of the word “predict.” We CAN predict it, we CAN’T conclude it. There’s a big difference. I can predict the weather tomorrow will be rainy… but I might be wrong and the word predict carries with it that meaning. If I could tell you with certainty it would rain tomorrow, without question, I would use a different word like “state that”, “know that”, etc.

Taken from Wikipedia: A prediction is a statement or claim that a particular event will occur in the future in more certain terms than a forecast. The etymology of this word is Latin (from præ- "before" plus dicere "to say"). Niels Bohr stated "Prediction is very difficult, especially if it's about the future."

Nice quiz!

How about this one?

A: Exactly one of Statements B and C (below) is false

B: Statement C is false

C: Statement A is false

Conclusion: Statement B is true.

Invalid or valid?
Charlie
January 7th, 2009 at 1:06 pm
She is just wrong on question 15.

The question is:
a) Water is a molecule composed of two hydrogen atoms and one oxygen atom.
b) Every observation or examination by microscope has confirmed this.

Conclusion
Therefore we can predict that every future examination of water will reveal the same chemical composition.

Her answer is:
Invalid. Invalid but controversial in philosophical circles. If one defines water as a property that contains two atoms of hydrogen and one atom of oxygen only, then the argument above is valid. However, it is possible also that there may exist a substance that looks like water, boils as water, freezes as water, nourishes plants and life as water, and yet has a different chemical composition to what we know as water. There is nothing that could logically prevent this possibility occurring so the argument then becomes invalid.

Let's rephrase the question.
a) Water is a molecule composed of two hydrogen atoms and one oxygen atom.
b) You observe a material that has a different chemical composition but has the same melting point, freezing point, and looks like water.

Conclusion
You are observing water.

Everyone would agree that this is an invalid conjecture.

So what we have here is someone who wrote a book on logic, included a test with a logic error, and is too embarrassed to admit it.
JDexter
January 7th, 2009 at 1:15 pm
100% here, and I think #15 is correct as stated.
Popsi_zen
January 7th, 2009 at 1:26 pm
A: Exactly one of Statements B and C (below) is false

B: Statement C is false

C: Statement A is false

Conclusion: Statement B is true.

Invalid or valid?

Invalid, if Statement B is true then Statement C would have to be false so Statement A would be true - BUT, if statement A is false then Statement C would have to be true and Statement B would be false.
Theo
January 7th, 2009 at 2:37 pm
The water question (15) is poorly written. We define water in A, and then say that we're observing water in the conclusion. If we are observing water, then by definition (A), it is water.

As for the test proposed by Steve L:

A: Exactly one of Statements B and C (below) is false
B: Statement C is false
C: Statement A is false

Conclusion: Statement B is true.

Invalid or valid?

Valid.

The logic for each statement is laid out:
A: True = B or C (but not both) must be false, False = B and C may be both true or both false
B: True = C must be false, False = C must be True (A must be false)
C: True = A must be false, False = A must be True

Now for the combinations:
A: False = B and C may be both true or both false
B: False = C must be true
C: False = A must be true
- C cannot be true and false. Fail.

A: False = B and C may be both true or both false
B: False = C must be true
C: True = A must be false
- All conditions are met. However, the states of B and C make that A true, but it is not. Fail.

A: False = B and C may be both true or both false
B: True = C must be false
C: False = A must be true
- All conditions are met. However, the states of B and C make that A true, but it is not. Fail.

A: False = B and C may be both true or both false
B: True = C must be false
C: True = A must be false
- C cannot be True *and* false. Fail.

A: True = B or C (but not both) must be false
B: False = C must be true
C: False = A must be true
- Given the states of B & C, A cannot be true. Fail.

A: True = B or C (but not both) must be false
B: False = C must be true
C: True = A must be false
- A cannot be true and false. Fail.

A: True = B or C (but not both) must be false
B: True = C must be false
C: False = A must be true
- B is True and C is False, passes condition A. C is false, passes condition B. A is true, passes condition C (as modified by B). All conditions are met. Pass.

A: True = B or C (but not both) must be false
B: True = C must be false
C: True = A must be false
- A cannot be true and False, C cannot be true and false. Fail.

Only one condition passes it's internal logic.
A=True, B=True, C=False. Therefore, the conclusion is valid.
Ralph Beatty
January 7th, 2009 at 3:21 pm
On question 10, there is no evidence that the Paris referred to in the axiom is the only one. Since it is not stated it is a possibility which makes the assertion invalid. The support is the same as the one for the last question.
Lew A
January 7th, 2009 at 4:09 pm
Paris:

1: A is in B
2: B is in C
3: A is in C

Impossible to deny this validity. Forget about the fact that there is a Paris France, or Paris anywhere. The word "Paris" doesn't mean anything and/or it means everything. In this example, Paris could mean "a continent on the planet New Zealand" - it doesn't matter. The form is valid, he did not introduce any known new variables. There is absolutely no justification to believe that "Paris" in premise 1 and 2 are different. If there was, then you surely got almost every other valid questions wrong.

It's like saying this is invalid:
1: All Ducks Quack
2: Donald is a Duck
3: Donald Quacks

Because "Duck" in premise 2 could mean something that the author didn't define and is trying to trick us. Maybe "Duck" means, plastic rubber duckies, aye?

I can understand people being frustrated for not understanding the water one. But to deny the validity of the Paris one is just insane. Chaos even.

i = 1
i + i = 3... the second i really is a 2, tricked you!

Lew

P.S.
Water:
1: A (water) is B (H20)
2: C (every past examination) shows A is B
3: D (every future examination) will show A is B

Too many variables, none of which are connected. That's one reason why it's invalid. There are probably several.
Python
January 7th, 2009 at 4:32 pm
I had to think carefully about the water one and eventually answered it (according to the posted answer) incorrectly. But I technically have to disagree with the posted answer. prediction does not involve certainty. Prediction involves a degree of confidence. Therefore, based on the observed examination we can confidently predict that every future examination of water will exhibit the observed results. However, if you replace the word "predict" with the word "conclude" then "Invalid" becomes the correct answer. Other than that, I aced it.
JW
January 7th, 2009 at 5:40 pm
I assume #6 was meant to be a summary of the OJ trial... I read the first part and thought 'this must be a sneaky way of asking people if they would have convicted OJ' - so I put innocent. I mean invalid. May Cochran rest in peace, the miraculous son of a beach.
JW
January 7th, 2009 at 5:42 pm
I wrote the author about this, but concerning the water question: it's an inductive argument, not a deductive one (it's inductive since you're predicting something outside the scope of the premises). Inductive arguments can't be valid or invalid, they can only be "strong" or "weak" arguments (or "crap" arguments). In other words, the question isn't applicable.
Zach
January 7th, 2009 at 6:05 pm
If you're 12 years old, and got 100% on first try, does it count? I did (and I am 12) and don't find #15 to be poorly written.
Corrie
January 7th, 2009 at 6:30 pm
It is invalid to reason that a substance that behaves in every way as water but has a different chemical composition invalidates that water is comprised of H2O.

The second predicate is: b) Every observation or examination by microscope has confirmed this

The second predicate therefore means that WATER is being observed under a microscope to reveal the chemical composition, not some other substance that behaves and looks like water.
Dark King
January 7th, 2009 at 6:40 pm
I agree with those that dispute the given answer to question 15. The problem is that the question stuffs up on the difference between chemical composition and chemical properties.

Chemical composition is fixed. Water is H2O every single time. The quibble about heavy water is irrelevant - deuterium is still hydrogen. It is just another isotope of hydrogen, just as uranium-235 and uranium-238 are both still uranium. As for "don't drink it" - I've drunk heavy water before. So have you. It is present in almost all water on this planet.

The statements in question 15:
"a) Water is a molecule composed of two hydrogen atoms and one oxygen atom.
b) Every observation or examination by microscope has confirmed this.

Conclusion
Therefore we can predict that every future examination of water will reveal the same chemical composition."

a.) refers to the composition of water molecules
b.) provides supporting evidence for a.)
The conclusion refers to the composition of water molecules.

The given answer then takes a tangent and refers to chemical properties of water, which are not once raised in the initial statements. In point of fact, if I examine water I will always discover H2O molecules. If I examine "water" and do not find H2O, then I am not examining water at all. The chemical properties are irrelevant, water is H2O and nothing else.

To reach the answer given, the conclusion should have read:
"We can predict that if we examine a substance with the same chemical properties as water, that substance will have the chemical composition H2O".
This would also have required some establishing statements regarding the chemical properties of water.

There is also the issue that "we can predict" has no bearing on the accuracy of the prediction. I can predict that the core of the planet Jupiter is made of strawberries. I can also predict that it will snow in the Sahara Desert tomorrow. The accuracy of those predictions is not relevant to the fact that I can actually make those predictions.
Victor
January 7th, 2009 at 8:30 pm
100%. Genius confirmed.

Some of these comments/arguments are priceless. The whole exercise becomes a rorschach if mistakes are made.
Brucifer
January 7th, 2009 at 10:44 pm
100%

#15 - Given that in the Conclusion he just generalized with 'every future examination' I chose to consider the possibility that future examination methods and equipment might reveal a more complex structure to the water molecule than is presently discernible by present examination methods and equipment.

His argument for the possible existence of a 'water-like in every way but composition' substance is irrelevant because the question specifically indicates water as the substance of concern. By saying that a possible substance is water-like, but different in composition, you're by your own description not talking about water, and so not talking about the substance mentioned in the question.
AndrewV
January 8th, 2009 at 9:05 am
100%

But Venn diagrams are named after John Venn, not Charles.

I happen to know this after research for my own book, Venn That Tune: Bringing the Poetry of Maths to the Magic of Pop, which fans of logic might enjoy.

http://www.vennthattune.com
JustinB
January 8th, 2009 at 6:48 pm
Angstrom: The Paris one says "Paris is in New Zealand." not "There is a city in New Zealand called Paris". With the information given, you can not assume there is another Paris somewhere else.

Shenanigans on the water one.
killaseal
January 8th, 2009 at 7:06 pm
15 correct, 100 %.....SWEET!
squishyglobepog
January 9th, 2009 at 4:01 am
15 CAN be valid depending on the assumption(s) you make (does that make it invalid?)

I got a 93%. Guess which question I missed? I was offended. I couldn't be wrong. In the end, we all took either a very poorly written quiz (as per the craptacular explanation given for 15) or a maddeningly deliberate, devilishly clever quiz (ego stroke, I don't like feeling dumb). If the former is the case, I'm mad I wasted my time. If the latter is true, being wrong made me a better person. Screw it, I'm just mad at being a better person minus two hours of sleep.

Here's my take (after looking at all other comments):

I am an objective observer.
I know that (as given by the quiz):

A)Water is made of 2 H and 1 O (fact, as given)

B)Some people (mostly unaware of the above fact, although these people could include you) have consistently observed water to be made of 2 H and 1 O with a microscope (a tool)

Conclusion
Therefore we (I, in my or your case) CAN predict (accurately or not necessarily so?) that every future examination of water (with or without a tool?; naked eye maybe?) will reveal the same chemical composition.

One could argue that by definition (which is subjective), a prediction does not have to be accurate. All done. It's valid. Who cares about the fact that the means of examination are not explained.

What about the word 'can'? I can drive. I can eat. I can even drink (I'm 21, but if I wasn't, I still could). I can do a lot of things.

can-
1. to be able to; have the ability, power, or skill to: She can solve the problem easily, I'm sure.
2. to know how to: He can play chess, although he's not particularly good at it.
3. to have the power or means to: A dictator can impose his will on the people.
4. to have the right or qualifications to: He can change whatever he wishes in the script.
5. may; have permission to: Can I speak to you for a moment?
6. to have the possibility: A coin can land on either side.

'Can' is not a logical verb. 'Is', well, is a logical verb. The statement is invalid because of this, I think. Wait, am I right? Is this logic correct? Does that disqualify the statement? Maybe it doesn't. Does the fact that I am so fixated on the 'can' mean that I was using too much of what I know and not enough simple logic? Are the semantics of a logic question distracting, or the only reason a logic question is what it is?

Is question 15 a philosophical one? Probably not, but it's the only way I can justify spending two hours thinking about this crap question
brent
January 9th, 2009 at 3:33 pm
On the "answers" page to the logic test, http://www.think-logically.co.uk/lt_answers.htm, the Venn diagrams for questions 1 and 2 are grossly incorrect.

For question #1, if all ducks quack, the "D" circle should be completely within the "Q" circle. Showing part of the "D" circle OUTSIDE of the "Q" circle contradicts the first premise, that all ducks quack. We do not have enough information to tell whether the D circle is the same size as the Q circle (which would be the case if ONLY ducks quack) or if the D circle is smaller, but clearly D falls completely within Q. The "DO" circle should fall entirely within the D circle. Since premise A refers to ducks in the plural, and premise B refers to Donald in the singular, we can assume that the DO circle is smaller than the D circle. In either Venn diagram (D the same size as Q, or D smaller than Q), DO would fall within BOTH D and Q, and that is how we know that Donald quacks.

For answer #2, the Female Logicians circle should fall entirely within the "Clear Thinker" circle, under premise A, but again we don't know whether they are the same size, or whether the Female Logicians circle is smaller (we don't know whether all Clear Thinkers are Female Logicians). Similarly, the Lawyers circle should fall entirely within the "Clear Thinker" circle, under premise B, but again we don't know whether they are the same size, or whether the Lawyers circle is smaller (we don't know whether all Clear Thinkers are Lawyers). Since Female Logicians and Lawyers could each be smaller circles, both entirely within the Clear Thinkers circle, we do not even know whether the Female Logicians and Lawyers circles intersect at all. It is possible that NO Female Logicians are Lawyers. All we know is that the premises are clearly not sufficient to support the conclusion that all Female Logicians are Lawyers.
Cardigan
January 10th, 2009 at 4:47 pm
I'm shocked that no one has taken issue with #14. Yes, it is conceivable (though wildly unlikely) that 490 men could outrank 490 of the women on a logic test. As the answer says, you do need the big picture. But consider this: If the top 10 women each scored 100%, the top 490 men each scored 2%, the next 490 women scored 1%, and the bottom ten men scored 0%... the women “win” with an overall higher average score. Also wildly unlikely… but possible.
Chris
January 13th, 2009 at 12:28 pm
I can't believe people were so focused on the water question that it took until Comment 125 for anything to be said about the unbelievable errors in the Venn diagrams. Brent is 100% correct. No excuse for anyone with even a little logic training to get it that wrong. Sorry, but I won't be buying your book. I recommend anything by Raymond Smullyan (e.g. "What is the Name of this Book") for a true and entertaining explantion of logic.
cec
January 15th, 2009 at 1:28 am
The Venn diagram is wrong, yeah, but the test answer is correct - that was an easy question about syllogisms ("All A are B, D is a B...")

This discussion has been so fascinating, and also kind of a mess, because the test is for "validity", undefined in the test instructions, and the questions are from (at least) syllogistic, propositional, and inductive logic. The notion of a valid argument is different for those kinds of logical argument.

I got 100% easily, with very little thought on each question - because I have studied logic in school, and could easily see each question for what it wanted. It is easy to see in the comments how people who haven't had big spoonfuls of university logic would instead think about, e.g, whether all Paris instances had been defined, when the choice of "Paris" instead of "p" or "x" is totally irrelevant

Test takers who had not ever even known the core idea of "validity" - if the premises are true, then the conclusion must also be true - may have fallen prey to the danger from Quine that I mentioned earlier -"remember that valdity is not a term of praise" In propositional logic, validity is formalized first as the tautology - p and q; so, p. That is valid, but not very enlightening....

The converse of Quine's idea is that a praiseworthy and reasonable argument, like the perfectly reasonable #15, need not be VALID.
cec
January 15th, 2009 at 1:33 am
if p, then p is the first tautology
Phil
January 15th, 2009 at 8:18 pm
Here is the e-mail I sent to the test maker :

Not only I think that my answer to the question 15 (valid) was good, I think that the one presented as the "correct one" (therefore, invalid) is clearly wrong.

From the beginning, you give us premises. Some are accurate, some are not but it doesn't change anything for the test (example, question 10 is false : Paris is in New Zealand). Question 10 could have been : "A lives in X" "X is in Y" "Therefore A lives in Y".

The first premise of question 15 is : "Water is a molecule composed of two hydrogen atoms and one oxygen atom.". You give us a definition : Water is THIS. I know it may not be completly accurate in real life (as it was for Paris). Water could be defined otherwise, but in this test, we've gotta think only in function of your premises. It is easier when we use some variables : "Z is a molecule composed of two hydrogen atoms and one oxygen atom", or if you prefer : "Z is D".

The conclusion is : "Therefore we can predict that every future examination of water will reveal the same chemical composition.". My answer is : of course, yes. Because water is D, anytime we examine water it will always be D. If it isn't, that would mean that the substance examined wasn't water, because de premise define it by is chemical composition. See it that way :
a) Z is D
b) Every observations or examination as confirmed that Z is D (superfluous, from the beginning, premises don't have to be confirmed, we're only evaluating their link to the conclusion)

Conclusion : Therefore we can predict that every future examination of Z will reveal that it is D. (of course, conclusion is premise a).

In the explication of your answer, you write : "However, it is possible also that there may exist a substance that looks like water, boils as water, freezes as water, nourishes plants and life as water, and yet has a different chemical composition to what we know as water." Then, it would simply not be water as defined in the premise a). Therefore, it wouldn't be an examination of water (or Z). You use the expression "to what we know as water". As I said, we only know what is in the premise, same thing than Paris in New Zealand.

I strongly suggest that you review your position.
anomdebus
January 16th, 2009 at 8:16 pm
I don't see how both 10 and 15 can both be as evaluated.

In q10, I can see where the supporters are going with this and there is a formalism that I am not familiar with (though I think that makes it more of a shibboleth than a neutral evaluation). I wondered in general how we are supposed to know what hasn't been assumed by the questioner. I fell into that trap. If you don't think the questioner was assuming stuff, go to q15.

For q15, though, many supporters seem to be grasping at stuff that wasn't mentioned either. (deuterium, water-like substance) We are given a straight fact, then essentially asked whether that can change. The same sort of lack of "play" that is in the word "Paris" should apply to "water" was well.

Phil, you said it well, also.
anomdebus
January 20th, 2009 at 1:04 pm
Btw, the naive acceptance of the facts as given reminds me of a description of a peculiar situation:
At the ski resort:
young women were looking for husbands and
husbands were looking for young women

Assuming it were symmetrical would get you in trouble.

Someone cleverer than me could probably put this in the same form as these questions.

(ht K T Cat)
The Chosen One
February 18th, 2009 at 12:26 am
100% i didnt even read any questions...
afra
February 19th, 2009 at 3:08 pm
13 of 15

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