Originally Posted by
Tiglath
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To predict is to estimate what will happen in the future. Kindly, show how prediction concerning populations works at the individual level, meaning that you show its practical value, if you can. For example:
If you take the prediction that one in seven people will die of heart problems, it is obvious such prediction has a practical value for any endeavor concerning the health care of the entire population, like knowing how many cardiologists will be required and such, but please point out the practical value for the individual.
What does the prediction say about the health of an individual's heart? Apart from regular checks which will already include the heart, what is that he can do after hearing that prediction? Wear an extra sweater? Does it mean that if he knows seven people one of them must have a bad heart? Obviously not. Please explain the, in your own words, "predictive for individual elements," of the 1 in 7 prediction.
Mathematics is a discussion, where one or both persons can learn something. If you want an intellectual contest play Chess or Go. I don't "argue" about math, but I don't mind explaining basic concepts if someone is truly interested.
The prediction says that, without knowing other information, you have a 14.3% chance of eventually dying from heart trouble. This simple datum by itself is of limited utility, except that the individual may realize that with such a high probability for one of many possible causes of death, he can take measures to reduce that number for his own case. He would be best served to survey the medical literature for statistical analysis of specific causes of heart disease, and having taken such measures consider other probable health risks.
The more information you know about the individual, along with associated statistical information, the better and more specific your probabilities become. You're getting sidetracked by wanting certainties, and wanting to reason from specific individual details which are unknowable from a particular data set. A quick general overview. Detailed information, combined with some silogisms, are fundamentals of deductive logic, and you derive some certainty thereby. Within the parameters of your space, or construct. You are essentially demanding that I provide a deductive conclusion about an element of the data set from general knowledge of the data set, and obviously that's not possible, but it's an error to presume that this means that probability is not predictive.
You can still use deductive logic with probability, but it's not a simple boolean statement but rather uses the probabilistic equivalents (of and, or, not etc) and results in a probability and confidence range. So, as with set theory, group theory or any other branch you don't actually give up boolean logic and deductive reasoning, but it does apply in different ways and you must interpret the conclusions within the particular system. Is that more clear?