Hmm.
Hmmm....
I've been trying to capture enormous amounts of data, then to scour the world looking for the rules to process it. This is hard, and this isn't really how people think.
Take induction. "All emeralds are green." Now, we assume this is true because every emerald we've seen has not been green. We don't necessarily hold it to be a law. We may just assume it's a "rule". So, if we find an anomalous instance of a blue emerald, we keep the rule, but adjust our confidence in it.
Now, a logician argues that the rule is derived from the observations of emeralds. We observe one emerald, it is green. We observe another emerald, it is green. And so on, and so forth, and since we know that all emeralds we have seen were green, we assume that the rule "all emeralds are green" is reasonably valid.
BUT, we don't REALLY remember our encounters with MOST individual emeralds. We see an emerald, increment our confidence in the proposition "all emeralds are green" and then promptly forget the particulars of the instance. I can only specifically recall a very few encounters with emeralds, and yet I am confident that they've all been green. My confidence in the rule is held apart from my recollection of the instances which have validated it.
So, is there some way to consider rules apart from the particular components that constitute them?
Let's take the case of an essay Seductotron were reading. The essay would be an object. It would have component pieces called sentences. Those pieces would have component pieces called words. Words would have lateral relations (to one another) and vertical relations (to higher levels (sentences) and lower levels (letters) of structure). We could say of any observed truism that it was potentially a rule. Say it occurred that all sentences beginning with "who" ended with question marks. That would be a true observed proposition. We could then forget the sentence but remember the proposition, and, if the proposition were subsequently validated with some frequency, we could then keep it as a rule. If it never recurred, we would want to toss it in the rubbish heap.
Given any complex observed object, the sum total of potential rules to be derived from the observation is exactly equal to the sum total of true propositions deducible from the observed object. The utility of any potential rule would be derived from the probability of its corresponding proposition's truth.
Recently, a friend brought up the instance of Helen Keller. She was a woman who could neither see nor hear, yet she learned how to speak. From this, it seems reasonable to conclude that communication can occur without any familiarity with the particulars. But in order to learn how to speak, a non-random sequence of experiences had to be forced upon her again and again until she began to observe patternistic relations between the non-random sequence of experiences. Same as how anyone else learns to speak. You keep repeating the same damn thing at the baby until the baby begins to understand the categorical relations of the things you've said....
This is all rather inchoate. I'm trying to articulate it for myself.
Let's go with a sentence - "Pudding tastes best in the morning."
Now, for the word "pudding" we can observe several true propositions.
"Pudding" occurs at the start of a sentence.
"Pudding" occurs directly before the word "tastes"
"Pudding occurs two words before the word "best"
"Pudding occurs in the same sentence as the word "tastes"
"Pudding" occurs in the same sentence as the word "best" (and so on)
hmmm....
This needs fleshing out. There's a thought under all this junk...
