This is the first in sequence of ten posts about Foundations of Probability. I will go through a recent paper of mine, which explains that BOTH of the currently dominant approaches to probability are deeply, fundamentally, and irreparably flawed. The reason for this is that probability is a real-world phenomenon which is unobservable and unmeasurable. The early 20th Century foundations for probability were built at a time when logical positivism was dominant as the philosophy of science. Furthermore, despite its abandonment by philosophers, its central ideas continue to be widely believed, especially among economists. We will see that both frequentism and subjectivism are attempts to reduce the unobservable to the observable, but this is fundamentally impossible, and all such attempts are doomed to failure. Nonetheless, the charm of positivism and empiricism is so strong, that it prevents the formulation of the ideas necessary to see the problems with the current definitions of probability. An alternative method for thinking about probability, based on Critical Realism, will also be offered.
It would be useful to being with a short post from John Kay entitled: “Embrace Radical Uncertainty“.
Between 1920 and 1950, a debate took place which defined the future of economics in the second half of the 20th century. On one side were John Maynard Keynes and Frank Knight; on the other, Frank Ramsey and Jimmie Savage.
Knight and Keynes believed in the ubiquity of “radical uncertainty”. Not only did we not know what was going to happen, we had a very limited ability to even describe the things that might happen. They distinguished risk, which could be described with the aid of probabilities, from real uncertainty — which could not. In Knight’s world, such uncertainties gave rise to the profit opportunities which were the dynamic of a capitalist economy. Keynes saw these uncertainties as at the root of the inevitable instability in such economies.
Their opponents insisted instead that all uncertainties could be described probabilistically. And their opponents won, not least because their probabilistic world was convenient: it could be described axiomatically and mathematically.
It is difficult to exaggerate the practical consequence of the outcome of that technical argument. To acknowledge the role of radical uncertainty is to knock away the foundations of finance theory and much modern macroeconomics. But the reigning consensus is beset with glaring weaknesses. Keynes and Knight were right, and their opponents wrong. And recognition of that is a necessary preliminary to the rebuilding of a more relevant economic theory.
My paper about probability, which I will post here in short segments, one section at a time, is entitled: “Subjective Probability Does Not Exist”. The Abstract for the paper is given below. The next post in this sequence will introduce three different probability concepts which must be kept separate from each other, in order to understand the nature of probability. Unfortunately, logical positivism prevents us from thinking about two of these concepts, which is why those with positivist mindsets cannot see the flaws in the current approaches to probability.
Subjective Probability Does Not Exist
Abstract: Probabilities of one-time events are unobservable and unmeasurable. According to empiricist and positivist principles, they must be meaningless. However, our cognitive limitations do not prevent entities and effects from existing. We show that the argument for existence of subjective probabilities relies crucially on the non-existence of objective probabilities. In this case however, the existence of subjective probabilities reduces to a triviality. When objective probabilities do not exist, we are free to believe whatever we like about these probabilities, without any consequences. The theorems which establish the existence of subjective probabilities are normally interpreted as establishing the existence of beliefs about probabilities. We show that this interpretation is not tenable when objective probabilities do not exist. We establish the validity of an alternative interpretation: in absence of objective probabilities, we are free to choose any arbitrary number as a subjective probability.
Next Post: 2: Three Types of Probability