Re: Is {{}} a valid construct?

> > How can I empirically verify {} are valid?
>
> Empirical verification:
> http://en.wikipedia.org/wiki/Axiom_of_empty_set

Sorry Marshall, but this type of "empirical verification" is about the same quality as a religious believer referring to text out of his bible. I can verify the text, but I can't verify what the text says.

As you will recall, Keith (supported by Bob) proposed the string 'bob' can be represented with directly with unordered sets using empty sets (ie {}, {{}}, etc). I questioned the validity of as a construct because a set is defined by its elements, and if there are none, there is nothing, not even an empty set. Then you propsed that if I took all the potatoes out of the sack, the sack would not simply dissappear, therefore one could have an empty set without anything in it. But then when I produced a second empty sack, and asked how can there be two empty sets, you explained I don't know how analogies are supposed to work and there is no concrete connection between abstract and physical world; instead of concluding that sets are defined solely by their content and do not include their container; and when there is nothing, there is no set, not even an empty set.

Things are represented by sets. Nothing is unfortunately and incorrectly represented by the empty set. It should be represented by some other symbol, ie a zero with a slash or simply the word nothing. Using nothing to imply something will lead to propositions that are, at best, unverifiable.

My wife went to the grocery store just before the Super Bowl Party. Upon returning, I asked her if she bought something for the party. She said, she got nothing. So I took nothing out of the car's trunk and put nothing in the fridge. Later, I barbequed nothing on the grill. When the guest arrived, I served them nothing. Everyone had lots of nothing and they even said their stomach's were full of nothing, so I couldn't undetstand why they complained of being hungry :) Received on Sun Feb 04 2007 - 21:24:02 CET