by Imagine a pure thought experiment: an abstract, logical world where everything is true by definition.In this world, we have a fair dice. The pure mathematical a priori probability of rolling a 6 on this dice is 1/6. That probability has necessary truth – but limited only to the abstract fair game of dice one is imagining. The analytic a priori propositions that express the imaginary world and probability in question do have necessary truth – but limited to this abstract analytic a priori system. This is the epistemological nature of a priori probabilities.But what happens when we step into the real world? As soon as we move to the real world and take any given real world dice, we cannot have apodictic certainty that the dice is not loaded and that the probability 1/6 really applies with necessary truth.Why? Because of (1) the epistemological problems with how we know a posteriori knowledge and (2) Hume’s problem of induction. No matter how much evidence you have that the dice is fair, there is still a tiny possibility you are mistaken. This still holds even if – for good measure – the empirical relative frequency approach to show the probabilities of the outcomes when throwing the dice is used and this shows the dice is fair.
Topics:
Lord Keynes considers the following as important: a priori and a posteriori probability, difference, epistemology
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In this world, we have a fair dice. The pure mathematical a priori probability of rolling a 6 on this dice is 1/6. That probability has necessary truth – but limited only to the abstract fair game of dice one is imagining. The analytic a priori propositions that express the imaginary world and probability in question do have necessary truth – but limited to this abstract analytic a priori system. This is the epistemological nature of a priori probabilities.
But what happens when we step into the real world? As soon as we move to the real world and take any given real world dice, we cannot have apodictic certainty that the dice is not loaded and that the probability 1/6 really applies with necessary truth.
Why? Because of (1) the epistemological problems with how we know a posteriori knowledge and (2) Hume’s problem of induction. No matter how much evidence you have that the dice is fair, there is still a tiny possibility you are mistaken. This still holds even if – for good measure – the empirical relative frequency approach to show the probabilities of the outcomes when throwing the dice is used and this shows the dice is fair.
In short, the belief that the probability that any given dice will roll a 6 is 1/6 has become an a posteriori probability and contingent, not necessarily true.
Most people just take the abstract analytic a priori model first sketched and impose it on the real world, forgetting that this is an epistemological mistake. The difference between
It applies even to probability.(1) abstract a priori truth and
(2) contingent, empirical a posteriori truth is real.
More on this issue here.