Proving Too Much

Instead I just thought to myself: “Imagine my mother had raped my father, leading to my conception. I cannot will that a policeman had prevented this rape, but I also do not want to enshrine the general principle that policemen in general have no right to prevent rape. Therefore, this argument proves too much.” It took all of five seconds.

At first I thought of this argument as really poor one, but on subsequent thought of it, I guess it really is a perfect proving too much argument according to the first premise.

it can double as a method for creating jelly donuts on demand

For those reading this years later, here's the comic that shows how to make ontologically necessary donuts.

Interestingly, I think that one of the examples of proving too much on Wikipedia can itself be demolished by a proving too much argument, but I’m not going to say which one it is because I want to see if other people independently come to the same conclusion.

For those interested in the puzzle, here is the page Scott was linking to at the time: https://en.wikipedia.org/w/index.php?title=Proving_too_much&oldid=542064614
The article was edited a few hours later, and subsequent conversation showed that Wikipedia editors came to the conclusion Scott hinted at, though the suspicious timing indicates that they probably did so on reading Scott's article rather than independently.

The fallacy of Proving Too Much is when you challenge an argument because, in addition to proving its intended conclusion, it also proves obviously false conclusions. For example, if someone says “You can’t be an atheist, because it’s impossible to disprove the existence of God”, you can answer “That argument proves too much. If we accept it, we must also accept that you can’t disbelieve in Bigfoot, since it’s impossible to disprove his existence as well.”

Wow, I've been looking for a name for this thing for sooo long. Thanks so much. The phrasing here is a bit ambiguous, and can lead to confusion I think.

From the whole of the text, it seems that Scott's view on this is that of the Wiki page, that the fallacy is committed when someone claims a conclusion that is a special case in some category of which there are obviously false instances that would be true if the reasoning was valid. Something like

A) You can (validly) argue that someone else is committing the Proving Too Much fallacy when their argument, were it valid, in addition to proving its intended conclusion, would also prove obviously false conclusions

But 

The fallacy of Proving Too Much is when you challenge an argument because, in addition to proving its intended conclusion, it also proves obviously false conclusions

Can also read (my first understanding of it) as:

B) You commit the Proving Too Much fallacy when you (invalidly) challenge an argument because, in addition to proving its intended conclusion, it also proves obviously false conclusions.

I'm leaning towards A, but would appreciate more info on this. Again, I found this extremely useful.

Funny to see such a highly up-voted post with only one comment. (Of course, he does have his own rather famous blog, and I assume people commented there.) The following are just some musings I had while reading the original post.

I've always had a bit of a problem with claiming things are wrong because they 'prove too much'. The strange thing with 'proving too much' argument, is that it, in itself, also proves too much. Much like it is easy to reduce the use of 'reductio-ad-absurdum' to absurd places, any argument form can be used to prove too much, especially in the colloquial sense.

Let's use logic as an example. In binary logic, they define A->B such that it is only a 'false' statement if 'A' AND 'not B', and that it is 'true' otherwise. This means that every if then statement with a false 'A' is 'true'. Thus the statement 'If I am the king of England, the moon is made of blue cheese' is 'true' (assuming I am not the king of England), and so is the statement 'If I am the king of England, the moon is NOT made of blue cheese'. Thus, 'B' AND 'not B'. Through the 'principle of explosion' we can thus prove anything. Thus the simple construct of 'If A then B' proves too much. In practice, we ignore/ridicule anyone who seriously makes such an argument because we are not first order logic reasoners ourselves, but this same weakness underlies all versions of 'proves too much'.

The obvious reply is 'Who cares? If it's only proven in circumstances inconsistent with the actual state of the world, then what does it matter?' It doesn't usually, but we don't always know in advance that we have contradicting premises. Due to the 'Gödel's second incompleteness theorem' we know that even the natural numbers cannot be fully expressed in arithmetic in a system that can prove it isn't inconsistent. Natural numbers are even a subset of natural language so... we always embed logically inconsistent premises within any argument form, and all argument forms can prove anything, so all forms of argument prove too much.

Then, why do people claim something proves too much as if that means anything? Oh, because it's useful...k, thx. Bye. (*Well I look stupid.*) ;)