Sunday, January 24, 2010

When good arguments go bad...

I enjoy a good argument, I really do.  And not in an uppity, superior, "Look how smart I am" kind of way.  I enjoy presenting my reasoned arguments, and defending my position against other arguments, learning and adjusting my beliefs along the way. 

That's not to say I don't get frustrated dealing with the same, flawed arguments over and over again, such as those made by theists or creationists.  But I can remind myself that while I may have seen the same argument before, each person presenting the argument may never have heard criticism of their ideas.  (Greta Christina turned my attention to this point with a post she wrote a while ago)  And although in most cases my arguments seem to have no effect, I'm at least putting a new idea in someone's head, and in time it may resonate, perhaps with the help of a lot of arguments from encounters with others. 

I can deal with bad arguments and flawed logic.  In fact, I find it helpful to find logical fallacies in others' arguments, because it helps me find them in my own lines of reasoning.  It's often difficult to critically examine your own arguments, because of your own emotional attachment to them.  Critical thinking requires divesting yourself as much as possible, and practicing always helps.

I try my best, whenever I'm in an argument, to deal with the arguments and ideas presented, as rationally as possible.  Part of that means that I have to assume that the person I am arguing with is trying to present a rational argument, and is open to criticism of his use of logic and reason, as I try my best to be.  I know that in practice many people have no intention of even considering my arguments.  And even if they are willing, I am still a disadvantage when trying to change someone's mind, just by normal psychological responses to having your beliefs challenged (e.g., confirmation bias).  But the assumption is necessary in order to hold a reasonable conversation. 

To that end, I am VERY careful about questioning my opponent's willingness to accept new ideas.  I would rather continually explain the problems with an argument, than accuse my opponent of being too stubborn to even consider my arguments.  In fact, if my concern is to arrive at the truth, then I don't even have to concern myself with whether the other person is willing to listen to my arguments. 

I saw an example of making that accusation that really made me shutter the other day.  I was randomly reading a blog post about how to prove that .999... = 1.  That's right, I enjoy both logic and math proofs, that's exactly how cool I am!  Anyway, in the comment section, a commenter with the alias "removed by request" disagreed with the proofs presented, and was having an argument about the consistency of the proofs.  The arugment for the first few rounds were fairly civil, and while I disagreed with removed by request's logic, I had no problem with his argument style on the whole.  Until, that is, he decided he didn't want to play anymore:

I was going to post a rebuttal with complete proof from 2(two) ASU mathematicians (who both agree with me), but upon review of all your posts, I came to the ultimate conclusion that you don't need proof. You will go to your grave believing with the core of your being that .9999999... does, in your mind, equal 1. However wrong I, or anyone else may think you are will not matter. Trying to convince you otherwise is like trying to convince an atheist that God exists.

I leave you now, respectful of your opinion, because whether I agree or not is a moot point. You may choose to use personal attacks, call me a fraud, a liar, and an idiot, but I leave taking the high road. I bid you farewell, good sir.
And just to show you the exchange that prompted that response:

"When you write out .99999999... you are giving it a limit. Once your fingers stopped typing 9s and started typing periods, you gave infinity a limit."

So am I to gather that pi also doesn't exist, or that it also ends, since whenever anyone tries to write it, their fingers have to stop typing?

"Wait, did I see a fraction that equals .9999 repeating? No I didn't. Because it doesn't exist."

Ummm, how about 53/53. that's a fraction that equals .9-repeating.

"And is .99999999... an integer? I thought an integer was a whole number, which .99999999... obviously is not."

If I am claiming that .9-repeating equals 1, then I am indeed claiming that it is a whole number, and I gave a mathematical proof. It's "obvious"ness to you isn't relevant if it's a proof. Numbers can be written in many ways--1, 53/53, .999999....., 83-82, all the same.

"Also, can I see that number line with .999999999999... plotted on it?"
That's actually an argument for my claim, not against it. If that number exists at all (and I'm not 100% sure you think it does, but you haven't explicitly claimed it doesn't), then finding a place for it on the number line is indeed very difficult if you don't think it equals 1. I have no trouble putting it on a number line. It goes halfway between 0 and 2. If you think it exists and doesn't equal 1, then you find a place for it!
"Meanwhile, I'm going to find 10 mathematicians who agree with me."
I give my most solemn word that I will post an explanation on this blog that contradicts my claim if it
a) uses the standard real number system and
b) is verifiably written by a professor of mathematics at an accredited university.
I won't hold my breath waiting for that, though.

Other than the problem I have with criteria (b) above (argument from authority, although "removed" did sort of start that line of argument in an earlier post), I have no issues with this argument.  I see no personal attacks.  You can look at the post and comment thread for yourself here

Not only is it a cowardly way to end an argument, but "removed" really needs to think about what he's claiming.  Don't say things like "You may choose to use personal attacks, call me a fraud, a liar, and an idiot", when I can look back and see that none of those words, or anything like those words, have been used.  

The bit about atheists is equally asinine.  I don't think I need to tell anyone reading my blog regularly that most atheists are willing to have a conversation about the evidence for and against god, and try their best to stick to the arguments.  Even if "removed" had a legitimate point about his opponent, he shows complete ignorance on his part to make that comparison.  

Finally, even if "removed" had a legitimate point, he could still have continued his logical arguments. By saying he won't continue to argue because his opponent is closed-minded, he is showing that he's more concerned with converting someone than finding the truth.  

The more I think about this example, and the issue in general, I think its almost universally a bad idea to accuse your opponent of unwillingness to change one's mind, at least as your only retort to their arguments.  Anyone else have any input on this?

1 comment:

  1. The reason I like the .999... = 1 proof is that so many people aren't willing to accept the fact that it's true, despite all of the proofs out there. It's the same reason I like the Monty Hall problem.