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It is a fact that the majority of men accused of physical abuse are found to be guilty.
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John X. is a man who has been accused of committing abuse.
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Therefore, it is highly likely that John X. is an abuser.
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4) FROM 3 IT FOLLOWS THAT:   
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Please note that the author does not agree with this argument, but isn't sure exactly why. He invites others to critique this argument which was presented to him recently.
I was not sure how/where to make this remark and I see I can not add critiques to my own argument, so I placed it here.
I feel that this argument is similar to this one, which is clearly false:
Most birds are animals capable of flight.
The Kiwi is a type of bird.
Therefore, it is likely that a Kiwi can fly.
Well, not only is not unlikely that a Kiwi can fly, it is completely impossible. The Kiwi is a small flightless bird from New Zealand (national bird).
So, I have two questions. (1) Is the original argument that was made to me valid, even as a weak (unconvincing?) inductive argument? (2) Is my Kiwi bird argument truly analogous?
What types of logical fallacies are being committed here, if any?
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It's unlikely that the kiwi can fly due to information not given. Namely, that it's a flightless bird. If all we know is that a kiwi is a bird, and that most birds fly, it will be likely that a kiwi can fly. In math:
P(a kiwi can fly|a kiwi is a bird and X% of birds can fly) = X%
P(a kiwi can fly|a kiwi is a flightless bird and X% of birds can fly) ≈ 0
Or to put it another way, if all you know is that a fair coin is flipped, it's just as likely to land on heads or on tails. Once you actually look at the coin, it's near certainty that it landed on whatever you saw.
I suspect the reason you don't feel right about this is that you don't think people should be assuming guilt with out a trial. They indeed should not, for several reasons:
First, suppose 90% of people accused of physical abuse are found guilty. This means that if all you know about John X is that he has been accused, then there is a 90% chance of his guilt. There is likewise a 10% chance of his innocence. Anything you do to him you have a 10% chance of doing to an innocent man.
Second, you can wait until after the trial to do anything. If he's declared innocent, he has a lower probability of guilt. If he's declared guilty, he has an even higher probability of guilt. Somewhere around 99%. If it's not worth the risk of him being innocent after he's declared innocent, you're better of waiting to be more certain.
Third, if all it took for someone to be arrested was them being accused, it would make the system too easy to be taken advantage of by the police. This would result in a high probability of the accused being a political dissident, and even worse to punish than an innocent.
NEW:
"How would anyone know that there is missing information"
There is always missing information. They won't know what it is. The probability for them is given the information that they know.
"I am not sure if your wait-and-see solution will work in all situations of this type."
With criminal proceedings, the wait-and-see solution generally works until all the evidence is presented and discussed. Even if the guilt of the defendant is fairly clear before that, it's most likely worth looking through the rest of the evidence on the off chance that they were wrong. Once they're done with that, getting more evidence usually isn't feasible, and they make their decision based on that probability.
In general, when the cost of gathering more evidence is higher than the expected benefit of greater certainty, you stop gathering evidence and make your decision.
"I am curious if you are a mathematician, or an engineer, or whence comes your authority on the matter."
I'm currently majoring in math. I've taken two classes on statistics.
I'm using something known as Bayesian statistics. This is based on the principle that probability is in the mind. For example, you can get an even bet on whether or not a fair coin will land on heads. You can get an even bet on whether or not it landed on heads, provided neither person saw what it landed on. You can't get an even bet once you see what it landed on. The coin is fair in all cases. The coin has already landed in the second case. The only thing that changes in the third case is what you know about the coin.
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REBUTTAL by
noargument (r2), Dec 30, 2011, 8:28 am GMT
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[This rebuttal addresses an earlier critique version
and has not been revised.]
What I don't get is the part where you say that "[i]t's unlikely that the kiwi can fly due to information not given." How would anyone know that there is missing information at the time they originally assess the argument?
You are correct about my intentions; I wish to spare the accused wrongdoing to him/her regardless of what the end result might be. You said you think I "don't think people should be assuming guilt with out a trial." But the original argument, as stated, never brings up any of these tangential issues, nor does it really aver that X is guilty or not.
I'd like to point out that not every case goes to trial, or even to court. Some cases are settled out of court, and some cases are nailed by DNA. I am not sure if your wait-and-see solution will work in all situations of this type.
At any rate, I am leery of trying to address logical outcomes with social engineering, this case in particular. We are all familiar with the natural tendency to make judgments based on seemingly well-constructed arguments (even if they aren't at all).
BTW, I am curious if you are a mathematician, or an engineer, or whence comes your authority on the matter. Please don't take insult to this inquiry; it's only fair, since you sound knowledgeable on probability.
Anyone else see this issue differently?
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Critique (Rebuttal) history: c1 (r1, r2), c2
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1
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Overall Topic Rating:
As I have not agreed with any critiques:
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