Some contentions:

1. There are no substances.
What does this mean?

1. At the base level (individuals or events or actual occasions) subjects of properties and relations do not persist through time.
2. What persists (enduring objects) through time is classes of individuals.
3. Also predicates or relations (eternal objects) persist through time.
2. There are no essences.
What does this mean?

1. I am no longer sure this is always true.
2. What I think I meant was that the things (enduring objects) above that are classes of individuals may be defined in multiple ways - any one of which is as good as any other. And the equivalence of these is empirical.
3. I think some predicates or relations may be defined in some stronger way in terms of other predicates and relations (and quantifiers and logical connectives) - these definitions might be regarded as giving essences.
3. Names are (at least usually) for universals.
4. Particulars (at least usually) are only described.

Explanation:

1. Whitehead's actual occasions or Russell's events are particulars.
2. A person (an example of something named) is a class of events satisfying a universal.
3. 'Bertrand Russell' is the name of a person - Bertrand Russell - who is the class of events composing him.
4. There are many possible universals - e.g. the events comprising the person called 'Bertrand Russell', or the author of Our Knowledge of the External World which define the class he is.
5. Any of these universals are equally good - none are any more essential than any other.
6. If the universal 'person named "Bertrand Russell"' is used then it will be necessary that that person is named 'Bertrand Russell'.
7. If the universal 'author of Our Knowledge of the External World' is used it will be necessary that that person is that author.
8. We learn names as they apply on more than one occasion.
9. Our minds (via our brains) are adapted to identify future occasions belonging to some natural patterns.
10. re: Wittgenstein - it is natural to continue series of numbers in some ways and not others.
11. It is natural to learn names in certain ways.
12. It is usual that names can be used on more than one occasion.
13. Particulars (events or actual occasions) occur only once - so are not usually named.
14. Particulars are usually described - e.g. my experience now - not named.
15. Particulars do not endure.
16. Classes are defined in terms of predicates - Principia Mathematica.
17. Some predicates are learned more naturally and are more fundamental.
18. The fundamental predicates (and thus classes) can be compounded - but this can only be done in a finite way.
19. Thus the axiom of choice is false.
20. Particulars can have many properties and stand in many relations with other particulars
21. Some of the relations a particular may have with other particulars have a 'vector' character - like a field in physics.
22. I haven't worked out the individuation of events or actual occasions. It is a difficult problem - Whitehead changed his mind about it at times. Russell wrote about it as well.

Comments added 9/21/2008

Consider


[1] (x) P(x) ⇒ Q(x)



1. P(x) might = x is a bachelor
   and
   Q(x) might = x is a unmarried adult male
   in which case [1] would seem to be analytic
   It could be said Q gives the essence of P (but theoretically P is an unnecessary term - it could be eliminated from the vocabulary)
   
2. P(x) might = x is what causes a lightning flash
   and
   Q(x) might = x is what causes a clap of thunder
   in which case [1] would be a (simplified) law of nature
   P and Q have different meanings - correspond to different experiences - we need both to describe our experiences
   in which case [1] would seem to be synthetic - but have some sort of necessity - it is not a perfect example but is seems there must be some universal laws which are not mere definitions, nor merely accidental - or there would be no patterns to our experiences
   
3. P(x) might = x is human
   Q(x) might = x is a featherless biped
   in which case [1] would be true synthetically but seemingly accidentally
   again P and Q have different meanings - correspond to different experiences - we need both to describe our experiences
   
4. The difference between the last two cases is one reason an extensional language must be inadequate for science
   
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