User talk:68.49.135.47
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[edit] Peirce's law
Greetings!
You left a note at Talk:Peirce's law back in October, and I hope you get a chance to read this.
(duplicated at Talk:Peirce's law)
Basically, what's going on is that we need to show a contradiction, e.g today is Tuesday and today is Wednesday. It's a bit bizarre. Let's start with these assumptions:
1. Today is Tuesday.
2. We never eat meat on Tuesday.
3. We ate meat today.
Notice that 2 and 3 together mean that today is not Tuesday:
1. Today is Tuesday.
2+3. Today is not Tuesday.
This is a contradiction, so something was wrong. In this case, one of our three assumptions is wrong, but we don't know which. Perhaps today is Wednesday. Perhaps we do sometimes eat meat on Tuesday. Perhaps we ate meat yesterday and not today. All of those are valid ways to fix our assumptions.
Now, in the case of our Pierce's Law example, we have two assumptions and one hypothesis:
1. A line is a glue line if every pear is glued to a kiwi.
2. A glue line has pears.
H. Today, we saw a line without pears.
Through our little mental experiment, that becomes:
H'. Today, we saw a line with every pear glued to a kiwi, but no pears.
So, we combine 1 and H'. Now we know this:
1+H'. Today we saw a glue line, but it had no pears.
2. A glue line has pears.
That gives us our contradiction, and also your confusion. You jumped here to start, and that didn't make any sense. Instead, our contradiction means that something was wrong. We trust our two assumptions, but the hypothesis could be wrong. It was wrong, meaning that the line we saw had pears. So we alter our hypothesis:
1. A line is a glue line if every pear is glued to a kiwi.
2. A glue line has pears.
H. Today, we saw a line with pears.
This is consistent, meaning that there is no contradiction. Notice that we can't combine 2+H:
2+H. Today, we saw a glue line.
is wrong.
Hope that helps! -FunnyMan 20:57, 2 January 2006 (UTC)
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