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Probability: A Philosophical Perspective, Part II
In my last essay on probability I highlighted two ways probability can be interpreted. First it can be a measure of uncertainty in a deterministic world. Second it can be viewed as an accurate model of a genuinely ‘non-deterministic world’. This essay will critique both of them, and their implications for God, Scepticism, Science and more.
Um, remind me what this is all about again?
Here’s a brief recap.
A deterministic model might be a system governed by classical mechanics, perhaps a dice roll, but we model it with a non-deterministic model of the world (probability) where the probabilities measure our degree of uncertainty. The non-deterministic model is where there is genuine randomness at play, i.e. multiple observed realities are actually possible. The non deterministic model is essentially the rationale behind the current mathematical foundations of probability.
The Deterministic Model
The deterministic model has conceptual flaws. Identifying uncertainty with a number is not a well-defined concept. The process by which we create such as model is to observe many outcomes and hypothesise a distribution. As mentioned last time, in a deterministic world this model creates astonishingly poor predictions for each individual outcomes; it merely preserves some useful properties for aggregate results. For instance, in the ‘deterministic’ world the dice was always going to roll a 6, but the model only gives it a weighting of 1/6. This is a measure of our uncertainty about the underlying mechanisms: i.e. when we roll a dice, our best estimate given our lack of knowledge is a weighting of 1/6th/
(It is unsurprising that the predictions are poor given the nature of the model and that we assume the world is deterministic!)
Let us review the process by which we created the model. First, we observe. Second, we suppose some ‘likely’ distribution. Third, we check to see if the model seems consistent with the data. This is a process rather similar to Scientific investigations, where we create a mathematical framework which we keep because it is useful (in a very human way!) but where the concepts involved are ill-defined and philosophically un-rigorous. As…
