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If I were construct an argument containing the postulation

Men commit more crimes than women.

I would be guilty of a logical fallacy because this statement implies

  1. All men commit crimes.
  2. The man who commits the fewest crimes still commits more than the woman who commits the most crimes.

There is a name of this type of logical fallacy. I think it is a kind of hasty generalization, but I'm not sure which. Can someone please help me find the right term?

EDIT:

So to try to clarify what I'm asking (since I don't have the right lingo apparently), I think I have worked out that there are really two parts to this question.

We can agree that the predicate "Men commit more crimes than women" is ambiguous.

Ambiguity is not a friend of logic; so firstly what might you call a statement that requires disambiguation before it can be considered acceptable in an argument?

Secondly, is there a term that describes the exploitation of ambiguous statements to further an argument? (Is this a logical fallacy? If so, what kind? If not, what else might we call it?)

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    Simply using this statement isn’t necessarily a logical fallacy. A generalisation like “men commit more crimes than women” is ambiguous, and can be taken as meaning several different things, some quite reasonable; the fallacy is in conflating different meanings of it. (For instance, if Prof. X publishes research showing “men on average commit more crimes than women”, journalist Y headlines this as “men commit more crimes than women”, and Prof. Z then cites X’s research to justify that “every man commits more crimes than every woman” — this is a logical fallacy.)
    – PLL
    Commented May 25, 2011 at 13:19
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    The statement implies neither of the conclusions you draw.
    – Colin Fine
    Commented May 25, 2011 at 13:28
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    This seems more on-topic for the philosophy.SE site. They're almost a beta site, so commit to put them over the edge!
    – Mitch
    Commented May 25, 2011 at 13:29
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    It's not a logical fallacy but a linguistic (or more precisely a pragmatic) faulty argument: concluding from a somewhat vague statement a conclusion which follows only from an unlikely reading of the original statement. Not so much a generalisation, as an unwarranted conclusion.
    – Colin Fine
    Commented May 25, 2011 at 14:12
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    @Colin Fine, not even that (in the way I read it); OP claims that there is a fallacy in the postulation (he presents implications, which are indeed incorrect i.e. not implications at all, as proof that there is an error in reasoning).
    – Unreason
    Commented May 25, 2011 at 14:17

4 Answers 4

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From Internet Encyclopedia of Phylosophy 

Faulty Generalization

A fallacy produced by some error in the process of generalizing. See Hasty Generalization or Unrepresentative Generalization for examples.

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    +1 for link, but I still think that no fallacy is presented (though your answer might be exactly what OP wants)
    – Unreason
    Commented May 25, 2011 at 14:09
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First of all, the two conclusions that you draw do not come from

Men commit more crimes than women

but from

Every man commits more crimes than any woman.

Without qualifiers (all, some, none) the proposition can mean that men on average commit more crimes than women.

Secondly, regardless of what is actually the initial phrase, to talk about fallacies you should have some reasoning which you do not present, you only present a simple proposition.

EDIT (after question clarified)

In rhetorics the vice of ambiguity is called simply that - ambiguity (related terms: amphibologia and also ambigua).

In logic the incomplete comparison might be the correct term.

Once you have established a logical fallacy in the premise that should (normally) be enough to classify the conclusion as faulty, too.

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  • Another viable interpretation of this sentence would be "men (as a group) commit more crimes than women (as a group)." This is semantically equivalent to mplungjan's "More crimes are committed by men than by women."
    – senderle
    Commented May 25, 2011 at 17:13
  • @sanderle, true - and in that case it is not ambiguous, but I acceept OPs clarifiction that in his context it is ambigous (by ommital of quantificators).
    – Unreason
    Commented May 25, 2011 at 17:21
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    @Unreason, oh, I agree that it's ambiguous, and I think (after considering the question more) that the terms you've offered are probably right. (However, I prefer the IEP's explanation of Amphiboly. "Elephants, please stay in your car.")
    – senderle
    Commented May 25, 2011 at 17:34
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While reading through some of the other questions on this site, I found this answer, which suggests the word sophistry:

Sophistry: a subtle, tricky, superficially plausible, but generally fallacious method of reasoning.

This term seems very suitable for my purposes. I suggested that the respondent submit it as an answer to this question, but no one has done so. Therefore, I'm submitting it, and accepting it as an answer.

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More a comment than an answer, but too long to fit in as a comment:

Perhaps this is just a flaw in the wording of the question, but there is no logical fallacy in the original statement. It is a statement of fact that can be shown to be true or false statistically. (And any statistics I've seen show it to be true.) If in a particular place in a particular period of time, there are 100,000 crimes committed by men and 50,000 crimes committed by women, then the statement is true.

There is a certain ambiguity in that it is not clear whether you mean "on average" or "total". For example, suppose you said -- and I'm just making this up as an example, these aren't real statistics -- "men with beards commit more crimes than men without". Suppose in the area in question there are 1,000 men with beards and 9,000 men without, and there are 100 crimes committed by men with beards and 450 crimes committed by men without. Then as a total, men without beards commit more crimes: 450 versus 100. But on average, men with beards commit more crimes: 10% versus 5%.

The conclusions you state do not follow logically from the original statement. I think this is a pretty classic case of a "non sequiter". Just because the AVERAGE member of group A does more of something than the AVERAGE member of group B, doesn't mean that EVERY member of group A does more than ANY member of group B. ETc.

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