Originally posted by kaminsky
Both empirical and theoretical probability assumptions seem flawed since they rely on inductive logic , because something has happened before, it will happen again. Im not a mathmatician, but it does not seem very mathmatical to rely on assumed observations of events . The internal maths of probability maybe faultless, its the first principles I'm questioning.
Empirical probability of an event E is defined
to be the number of times E is observed to occur divided by the total number of observations. There is no flaw there, because it's a definition. So if 238 individuals are recorded to be struck by lightning in the U.S. in 2011, then the empirical probability of someone getting struck by lightning is determined to be 238 divided by the population of the U.S. Empirical probabilities, however, are only as good as your data and will (like polls, surveys, and the like) tend to give somewhat varying values as more data is collected.
If n(E) is the number of outcomes of an experiment that are favorable to an event E and n(S) is the total number of possible outcomes of the experiment (also known as the sample space), then the theoretical probability of E is defined
to be given by n(E)/n(S). So, with the roll of a die, the number of outcomes favorable to rolling a five is 1, while the total number of outcomes of the experiment is 6 (i.e. six different numbers could turn up). Hence, the theoretical probability of rolling a five is 1/6.
The only thing that can really get tricky about probabilities -- and in particular theoretical probabilities -- is that they can depend on the amount of information an experimenter knows. A process that appears unpredictable may in fact be merely misunderstood, and additional knowledge about how the process works may alter the probabilities of various events occurring. But that's not a fallacy. It again comes down to what you know about a process.
I'm assuming your problem is with assumptions that are made to compute the probabilities of a physical
process behaving in a certain way. That's certainly a problem for physicists and other researching scientists on the field, but it is not a crisis for the mathematical discipline of probability theory itself since it is a conceptual (i.e. non-physical) construct based on a few basic definitions and axioms. As a system, probability theory is proven to be logically consistent.