### Logic and sets and sense and nonsense

For one thing, I have this message on my Google blog entry form.
Does anybody see anything wrong with that? It was fixed to (3/26) before the outage, however, they could have been planning a year and a day ahead!

On to the real subject of logic and sets. It is possible to define things which are not resolvable. One of the interesting things about sets is that I think the entire subject is poorly initiated. We can probably thank Zeno and Cantor for that, though many people have contributed.

Nonsense can exist anywhere and any concept taken too far becomes nonsense. I could define the building that holds all buildings and it would be nonsense. I could say there is a building that contains all packages and it has a package that contains all bottles. I could go further and say there is a bottle that holds all buildings and then I would have gone into nonsense.

The idea of the recursive, zero, and the infinite are areas that must be dealt with specially in analysis and methods. I could have a program that defines a number as the product of itself and another number and it would be constantly tested false if measured.

The idea in topology ( which is in a way, a superset of sets ) would preclude an object that contains itself. I can say everything and not be ambiguous and yet I cannot say that I have a set which contains everything, as I have created something outside of the concept to contain even itself. I can see why Cantor spent so much time in the mental recuperation facility.

This type of problem arises when I define lists. I can have a list of all lists, and that can include itself, however I can never know where it is in memory, as its reference is contained in a list without a pointer. So in this case a list of lists is a special case that must be handled differently. The container must precede reference to that which is contained.

It does seem to me that there is hope to resolve the concept of logic rules for dealing with numbers, sets, topology, and the concepts derived from them.

```reflexive
symmetric
transitive
closed under equality
```

These things are true within limits and there is where the real issues come in. If I were using computer programming and object-method terms , I would say that a specific object or group of objects has associated methods and that assigning the wrong methods would lead to undefined behavior. I can store a number as a "float" and use it as an "int", but your mileage could vary.

Personally it seems odd that the ontology of mathematic functions is not questioned when a standard CPU is used. Why would I define a set of numbers that had operations that are indeterminate? For any positive or negative number greater than zero, division is defined and yet, a FPU will try to divide by zero and get NaN ( if I remember correctly), which is "Not a Number". This is the device we use for all our internet access and to run our software.

It isn't an idle thought. It is the fact that some degree of mysticism has crept into the concept of reason. Just because I assign a symbol to represent the ordinal of objects, does not mean that it is anything more than that. If I define the idea of chopping things into parts of a specific size, and then wonder how many parts there would be when the size of the parts does not exist? If I define counting as the continual inclusion of one more object in a set, it could be said that it will find infinity, however that is not a concept that is defined in this context, as the system is designed to perform methods on real symbolic sets.

I have zero friends and I want to divide this candy bar among all of them. What do you suppose I will do, considering it is a NaN?

## Automated Intelligence

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