Originally Posted by
wphamilton
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?
Thank you for your thoughtful reply.
I asked a very specific question, and you did not quite answer it, though you managed to include the kitchen sink in your reply.
You need not preface posts with admonitions because I neither seek math instruction nor I believe that asking you to support your statements is looking for a contest. It is what people do in a proper debate, before it degenerates into dog poo as all Internet debates eventually do.
I asked specifically what is the utility of statistics to the the individual that would apply to himself in particular, and by "statistics" I mean also the probabilities derived from them. I assure you I know the difference between statistics and probability. They are both branches of mathematics, one applied the other pure or theoretical, primarily. Statistics analyses the frequency of past events, probability is a way to handle uncertainty.
You seem to resent that I demand certainty for the individual case How not? If a tool to deal with uncertainty can't provide any certainty what good is it?
The problem is that some people believe that the likelihood of future events, derived from population statistics is as useful for the individual as it is for the population, and that is a mistake. Proof of it is in your own very reply. When asked what the 1 in 7 means for the individual, you say that it tells the individual that he has 14.3% probability of dying of heart disease. Well... that adds no new information at all, it just translates the probability from a per-seven to a per-cent. Neat trick though.
Let me clarify my example. If statistics show that in say, New York City one person in seven die of heart disease in 2015, the city mayor will do well to expect one seventh of all deaths to involve heart problems next year, and he should work this likelihood into the city's health plans. The statistic, however, says absolutely nothing about Joe Babaloo at 661 4th Avenue, apartment 16. He may die of cancer, or in a bike accident because he does not wear a helmet, who knows.
In other words, if you cannot find anything that 'statistics' can say for a particular individual, you should concede the point. I grant that knowing that in a statistically significant sample 1 in 7 die of heart problems is far better than knowing absolutely nothing about the lethality of heart disease, but again, it is GENERAL information, not particular. There is a difference, you know. .