Other attempts at SRH – 11/09/07 + 30/09/07

Let us define thinghood for a thing x.

1. There is an operator ¬ (not) such that x È ¬x is x (the universal set) for all x
2. x can be replaced existentially by another thing y. (Each thing can be thus be named or represented e.g y = John)
3. x can be essentially replaced by another thing z. (Each thing can thus be referred to by its qualities e.g. z = man)
4. For each x: ¬x is non empty

Explanation of the axioms.

1. Let us take a common “pen”. This pen defines two sets. The set which members itself and the set which members everything else which is not this pen. There is no thing which is neither this pen, nor not this pen; and there is no thing which is both this pen and not this pen.
2. The existence of any thing can substituted by any other thing so that a stone may represent a sheep so that a shepherd may keep a bag of stones to represent his flock. Alternatively we may create a symbol sequence like “PEN” where this thing can be used in place of a pen.
3. The essences of any thing can substituted by any other thing so that a stone may represent a farmer’s wheat and another stone his barley. This way a farmer has a record of crops according to their essence. Alternatively a symbol sequence like “wheat” may be created to replace all the things whose quality is wheat where ¬wheat covers everything else.
4. For any thing the set of things which are not it cannot be empty. Consider: if either the set of pens, or the set of John contained everything we wouldn't know either what a pen was or who John was.

Now is the universal set x a thing itself?

Obviously axiom 4 contradicts such a proposition because ¬x is by definition an empty set.

Let us ignore axiom 4 and phrase another way: is the set of all things a member of itself?

For the purpose of writing and obeying axiom 3 let us refer to the “set of all things” by the symbol x which is also a thing.

x is a non empty set containing all the discrete entities in the universe.

If x is a discrete member of itself then ¬x refers to everything else within x.

Yet for x to be the set of all things ¬x must by definition be empty.

x cannot thus be a member of itself. And x cannot be counted amongst the things.

So what is x?

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There is also this one emailed: 30/9/07 and blogged here

http://riswey.blogspot.com/2007/09/full-outline-of-suggestion-minds-things.html