Sunday, October 3, 2010

Talk About Math: Valid vs Invalid

In geometry we're currently discussing Valid Vs Invalid and this is creating some interesting conversations and with it fair confusion. So here's a few ideas for keeping things straight:

Here is a sample valid agrument (using the Law of Detachment):

"Not a wizard gone bad wasn't in Slytherin. That one is a wicked evil wizard, so it only makes sense he was one of them Slytherin." (stolen slightly from Harry Potter)

Let's clean that up and put it into the format we use in class:

If they are a bad wizard, then they were in Slytherin.
That is a bad wizard.
Therefore, they were in Slytherin.

This follows the Valid arguement we call the Law of Detachment and thus is a valid argument.

Now this gets a little tricky because we can argue with someone about whether or not the argument is True. For example, let's say that the second statement is not true. Let's say that due to a case of mistaken identity, we get a good wizard confused for an evil one. Does the conclusion that they were in Slytherin still fit? Of course not, making the statement that he was in Slytherin, and the whole argument overall False.

But it's still a Valid argument.

The hardest thing we face is seperating True conclusions from Valid conclusions. Students frequently focus on True/False (which we also covered in the first few sections) instead of Valid/Invalid which is the newer topic.

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