Half of all policemen are thieves and half of all policemen are murderers. Does it follow logically that all policemen are criminals?



Feb 14, 2013

To take the first definition, why "the action or crime of stealing"? Why not just "the crime of stealing"?


Feb 14, 2013

@extremeDating :

 it looks as if deducing analytically that a bald man has no hair isn't without its pitfalls :

Fro the merriam-webster :


 adjective \ˈbȯld\1a : lacking a natural or usual covering (as of hair, vegetation, or nap)b : having little or no tread <bald tires>2: marked with whiteThat leaves some wiggle room for ambiguity about the total lack of hair on a bald man's head.

Feb 14, 2013

^ That's a fair point. The Oxford dictionaries I mentioned give "having a scalp wholly or partly lacking hair."


Feb 14, 2013

i would guess that they're trying to differentiate between ways of using the same noun to indicate two similar but very slightly different things. theft is inherently a crime, but for instance you might wish to indicate that a person, having performed the action of theft, was as a result arrested for/charged with/convicted of the crime of theft.

or to draw a distinction highlighting that, theft being a strictly legal term, an action of taking only becomes a theft retroactively, the fact of criminal taking being proven.

to me it seems more likely to be unnecessary complexity.



Feb 14, 2013

COD/NOAD/(N)ODE: "[theft] the action or crime of stealing"

MWCD: "[theft] 1a: the act of stealing; specifically: the felonious taking and removing of personal property with intent to deprive the rightful owner of it"

AHD: "[theft] 1.a. The unlawful taking of the property of another; larceny"; "[unlawful] 2. Contrary to accepted morality or convention; illicit"

uh, no. those definitions all define theft as a crime. they all make stealing distinct from taking by emphasizing that it is unlawful.

crime of stealing.

stealing is felonious taking.

unlawful taking, where unlawful means illicit and illicit means forbidden by law.

I've looked at this a bit more.

I still believe all three definitions are consistent with the idea of non-criminal theft -- say, the act of stealing in a (hypothetical) jurisdiction in which the act of stealing is not considered a crime.

Already covered COD/NOAD/(N)ODE's "the action or crime of stealing." I don't know whether you're right that it's an unnecessary complexity, but whatever it is, theft as "the action of stealing" is consistent with it.

As for the MWCD definition -- "the act of stealing; specifically: the felonious taking . . ." -- there's an important difference between that and your interpretation of it as "stealing is felonious taking." This is because "the felonious taking . . . " is intended to be "a common but highly restricted meaning subsumed in the more general preceding definition," not an amplification of the more general preceding definition:

Sometimes a particular semantic relationship between senses is suggested by the use of one of four italic sense dividers: especially, specifically, also, or broadly.


The sense divider specifically is used to introduce a common but highly restricted meaning subsumed in the more general preceding definition


So MWCD is making it clear that the act of stealing -- and therefore theft -- isn't limited to felonious taking. Or they've accidentally suggested that.

As for the AHD definition, the problem with "unlawful" is that it allows for a (hypothetical) jurisdiction in which theft is a civil offense but not a criminal one. So the fact that something is "forbidden by law" needn't mean that it's a criminal offense.


Feb 15, 2013

i think at best you've muddied the waters sufficiently that i can't strictly say they're clean.

your interpretation from AHD i think strains the bounds of logic. the question doesn't posit such a jurisdiction, nor does one exist - the world over, theft is either a crime or a nonexistent concept (non-criminal theft not being theft, but simple taking).

as for MWCD, i'd be inclined to apply the "limited" effect of specifically to "felonious," but in a different way than you do. while i hold that theft is inherently criminal, it is not inherently felonious - most thefts are midemeanors.

and in any event, we've both soared far beyond the question's intent. perhaps it would have been better phrased as "can you think well enough to entertain the concept of separate iterated halves?"


Feb 15, 2013

i think at best you've muddied the waters sufficiently that i can't strictly say they're clean.

Good enough for me. I admit the AHD case was a reach, but this whole business is mostly tongue-in-cheek anyway.


Feb 15, 2013



February 4

^ Congratulations; you just flunked Logic 101, despite definitively answering the question:

That means that logically we can make no assumption of the distribution of criminals in the data set based on the information given.



Meh, actually I fail at reading comprehension.  Read it as "Are all policemen are criminals?" instead of the way it is written.


Apr 26, 2013

Consider an extreme case where there are only two policemen.  Policeman A is both a thief and a murderer while Policeman B is not a criminal.  In this situation, half of all the policemen are thieves and half of all the policemen are murderers, but it is not the case that all the policemen are criminals.


Jun 18, 2013

Fundamental theorem of logic: true conclusions can follow from false premises. 


Jun 19, 2013

Someone close this thread... I think 5 years of replies and votes has answered the no longer a user OP's question by now.


Jun 19, 2013

This isn't up for discussion. The answer is straightforwardly no. 


Jul 14, 2013

It's a logic question and a very easy one.


Sep 17, 2014

The answer is no. The way the question was phrased is a bit tricky.

The question here states that Half of all policemen are thieves and half of all policemen are murderers. Does it follow logically that all policemen are criminals?

Now this question can also be phrased like so:

Half of all policemen are either thieves or Murderers. Does it follow logically that all policemen are criminals?

Of course not since the question doesn't apply to all policemen but only half of them.


Sep 17, 2014

The question should rather have been "Half of all C are A, and half of all C are B, does it follow that all C are either A or B?". Even then, it doesn't specify whether it means "exactly half", or "at least half", or "approximately half". Which makes a big difference, what is meant by "half".

I say it should be worded as A, B. and C, because mentioning policemen brings in the much more important social issues implied by the question, which is that if even 1% of policemen are murderers, it is a horrendous intolerable situation. And the fact is, there are way too many policeman who in fact have killed human beings, and are proud of it, and are cruising the streets we live on with loaded weapons and a sense that they have the right to do anything they feel like to anyone they choose, and get away with it.

The recent, much publicized case in a place called Ferguson is merely one example of this, and many more take place all the time without getting any media attention or public scrutiny. So, if you want to discuss Venn logic questions, use impartial symbols like A, B, and C.

If you want to discuss the mentality and behaviors of people who are paid (by your taxes) to wear badges and carry guns and cruise the streets looking for people to harass, then write a question concerning that, leaving out the "logic" element. Because frankly, I would find such a question to be much more useful in rating compatibility than an "A is part of B, is it therefore part of C" question. And anyhow, we already have the some doctors are tall question to do that.

There's no need for 50,000 repetitive questions, in any case. 100 well sorted, well chosen questions would be sufficient and more efficient than this huge random assortment, for the purpose of rating personal compatibility between individuals on this site.


Sep 17, 2014

It doesn't follow from the information given, but that doesn't make it untrue


Sep 17, 2014


you're reading way too much into that question. It's a simple logic question and it can be answered context free, basically.

No need to drag ferguson or whatever into this.


Sep 17, 2014

Since most all murderers start out by stealing, the answer would probably just be half. The have to have been a stealer to escalate to murder.

of course, one may steal without becoming a murderer. 



Sep 17, 2014

How do we know the question doesn't take place in a hypothetical future with drastically different laws, where neither theft nor murder are criminal acts?

It doesn't matter because the answer is no anyway, but what if it's an even weirder future where being a policeman is a crime in itself?


Sep 17, 2014

what if it's an even weirder future where being a policeman is a crime in itself?

Actually, that would be a less weird future. In fact, I think you've just come up with one of the best ideas ever to be suggested on this forum.


It's a simple logic question and it can be answered context free, basically. No need to drag ferguson or whatever into this. 

That's exactly the point I was making in my first two paragraphs. If they wanted a simple logic question, they should have done so using impartial symbols, like A, B, and C, without dragging the concepts of police being criminals into it.

But whoever wrote this question, deliberately wrote it in such a way that brought up the question of criminal behavior among police. They didn't have to do that, but they intentionally chose to do that, and in doing so planted in the minds of the readers the questions relating to criminal police behavior.

Having written the question in that way is designed to divert our thoughts to these questions, and saying at that point "don't drag Ferguson into it" is like explicitly telling people not to think about elephants. You've already set up the situation where they cannot help thinking about elephants.

I did not "drag Ferguson into this", Ferguson was dragged into it by the wording of the question which stated "half of all policemen are murderers". By wording the question in this manner, Ferguson, and every other inexcusable example of murderous actions by police, is automatically implied, and saying "don't drag Ferguson into it" is like trying to shut the barn door after the horses have gotten out.

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