05-08-2020, 10:36 PM
(This post was last modified: 05-09-2020, 03:38 AM by Bob Butler 54.)
Just to explain where an idea came from…
Back when I was in college, the Philosophy Department held a small informal meeting to discuss a problem. They described a stone being grue if it was green and observed before a certain time, or blue if it was first observed after. They hypothesize a bag containing unseen stones. They wondered if an inductive proof would be proven invalid at the time specified.
This led to an intense discussion for quite a while. I eventually proposed that if you try to do an inductive proof on the union of two sets, you had best make sure that your inductive proof includes taking samples from both sets. If not, you might well get bogus results.
This absurd logical problem remained buried in my mind for years. Eventually a problem in history reminded me of this rule.
You have four turnings. You have four ages of civilization, which makes 16 combinations. You have a few dozen civilizations, which makes 16 times a few dozen combinations. (Many of these might be invalid as the cultures did not exist in a condition reflecting various ages.)
An inductive proof becomes invalid if all the samples come from only a some of the combinations. They would only be valid in the times and places observed. Perhaps something would become universal if the observations were made on a wide enough set, but you would want to observe all four turnings, all four ages, and a good number of civilizations.
In particular, a prediction made based on observations in the Industrial Age would become invalid in the Information Age. You have to make enough observations during the Information Age to establish the pattern.
Back when I was in college, the Philosophy Department held a small informal meeting to discuss a problem. They described a stone being grue if it was green and observed before a certain time, or blue if it was first observed after. They hypothesize a bag containing unseen stones. They wondered if an inductive proof would be proven invalid at the time specified.
This led to an intense discussion for quite a while. I eventually proposed that if you try to do an inductive proof on the union of two sets, you had best make sure that your inductive proof includes taking samples from both sets. If not, you might well get bogus results.
This absurd logical problem remained buried in my mind for years. Eventually a problem in history reminded me of this rule.
You have four turnings. You have four ages of civilization, which makes 16 combinations. You have a few dozen civilizations, which makes 16 times a few dozen combinations. (Many of these might be invalid as the cultures did not exist in a condition reflecting various ages.)
An inductive proof becomes invalid if all the samples come from only a some of the combinations. They would only be valid in the times and places observed. Perhaps something would become universal if the observations were made on a wide enough set, but you would want to observe all four turnings, all four ages, and a good number of civilizations.
In particular, a prediction made based on observations in the Industrial Age would become invalid in the Information Age. You have to make enough observations during the Information Age to establish the pattern.
That this nation, under God, shall have a new birth of freedom, and that government of the people, by the people, for the people shall not perish from the earth.
