Dear Lorraine
>>> ... your essay has not demonstrated a deterministic (i.e. logical) emergence of new function (i.e. new rules) as a consequence of the existing rules/laws-of-nature that control the universe-system.
Two things: I emphasized that the universe is not deterministic, because of quantum effects. And new functions/rules have indeed emerged if you look at the historical development of the universe. Example: processes of Darwinian selection did not exist 15 billion years ago, because there were no living things in existence then. They did exist later, say one billion years ago.
>>> Models show that a system is essentially stagnant without the addition of new rules,
What kind of models? How do you know they correctly represent the real universe in all its complexity?
>> but rules can never deterministically/ logically emerge - there are no models that can show the emergence of new rules in a system controlled by an existing set of rules.
Well then we need to develop such models in order to describe the real universe.
>>> True emergence requires that new rules must be added to the system, and even new initial-values for system variables as a result of quantum randomness counts as adding new (initial-value) rules to the system.
New rules are added to the system as higher levels of emergence come into being. That is the whole point of emergence.
>> The addition of new rules to a system could be due to an algorithm controlling the universe-system, but as you no doubt appreciate, there can be no such algorithm controlling the universe. The real issue is the rules that control the system, not the results of the rules, not what is called "emergence".
The real issue is that the rules that control the universe do indeed allow emergence to occur. That is proven by the historical record.
>> Re "I am open to discussion about numbers... What I have in mind is facts such as the square root of 2 is irrational": I have written a post entitled "Numbers in a universe without a Platonic realm" on my essay page. Essentially I am saying that: numbers always remain relationships - they are never finished products i.e. pebbles;
Numbers are not themselves relationships, in my view. Rather they are abstract representations of physical relationships. I don't know of anyone who talks of them as being like pebbles.
>> numbers are similar types of things to law-of-nature relationships -
Well no, they are independent of the properties of matter, although our understanding of them probably derives from our appreciation of conservation of matter and specifically conservation of physical entities such as cups and spoons
>> if they were like pebbles or like sets, then this would be an anomaly which would have to be explained; numbers ultimately derive from relationships/rules where (if represented mathematically) you can cancel the numerator and denominator categories, and end up with a number i.e. a thing without a category.
Not sure what you mean by `category' here. Are you talking Category Theory?
>> So, I'm saying that the square root of 2, if it is found in nature, represents a hidden relationship between categories, "hidden" because the categories are cancelled out. Categories being essential categories of information from the point of view of the universe, things like mass and charge, or their more primitive antecedents.
I don't understand that.
Regards
George