When a coin is tossed, the mathematician says there is 50% chance it will be head and 50% chance it will be tail. What does it all mean? The outcome is determined to be either a head or a tail, we do not know the outcome prior to the event. If we do not know the outcome, what meaning is there to speak of the unknown by assigning equally meaningless numbers to the unknown outcome.
My understanding is that our description of probability is dependant on our feeling of certainty. In instances when we are very certain of an outcome we say its probability is 100%. when we are more than ordinarily certain, we say its probability is 140%. when we are not sure, we say probability is 50%. however, the probability we assigned has no mathematical basis rather, it is a description of our will to certainty.
My rule is that if we do not know about it meaning it is a unknown, it is meaningless to speak about it, so we ought not to speak about it.
Let’s look at it this way, if there is 50% chance for heads or tails, which one would you pick? Does the ‘50% chance’ say anything, apart from an admission of uncertainty?
(pertaining to the bolded part): I don’t think you can say this in terms of predictive probability. You can say something like… ‘There was a 130% rise in earnings this year’ but I don’t think you can use anything above 100 in the sense you’re talking about… then again I could be wrong.
You’re right that induction is basically a guess… but I mean, in terms of science, it’s worked fairly good so far I’d say.