Home > Uncategorized > Foundations of probability 1-3

Foundations of probability 1-3

from Asad Zaman

In this sequence of posts, 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. Based on my paper draft, I estimate that there will be about ten posts of about 1000 words each, though a few of them might be longer.  Here are the first three:

  1. P S BAKER
    December 6, 2019 at 1:55 pm

    Superb – thank you so much for these!

  2. December 6, 2019 at 2:11 pm

    Wow, cool approach! I too think there is an urgent need for getting a handle on precise definitions of uncertainties. We need to converge to a common language in order to progress!
    I’ve got a taxonomy of uncertainties in my book (here is a slide excerpt: https://www.s-e-i.ch/Projects/AssetPrices/Documents/2019_Riga_lkd.pdf ) and there certainly are other options on the table.
    Maybe we should make this issue the topic of a dedicated conference session or conference altogether in order to clarify the various meanings?!?

  3. Ikonoclast
    December 6, 2019 at 10:00 pm

    In other writings you say “The main culprit is logical positivism.” I agree logical positivism has its problems and limitations and is largely philosophically discredited. However, the real culprit is monotheistic thinking which is expressed philosophically (in the West at least) as Cartesian Dualism: essentially the belief that the material and the spiritual co-exist, and somehow interact, in a dualistic universe.

    George Berkeley attempted to solve the problems of Cartesian Dualism with his Monist Immaterialsim. Modern science tends to support the Monist part of the thesis, specifically Priority Monism. Everything in the observable universe is connected and existents appear to be not existent in themselves but existent in relation to everything else. Berkeley’s idealism falls down because after dismissing the term material the term immaterial also has no meaning.

    Logically, if these is no material-ideal duality then there are only existents. One has to dismiss both materialism and immaterialism and talk only of existents and of “existentism”. Existents simply exist (a mere brute fact explanation) and demonstrate some dependable laws of relation but we know nothing of the essential nature of the existent, whether it is material, immaterial or anything else. Indeed, to speak of the essential nature of the existent is to indulge in essentialism or Platonism.

    This renders the cosmos as a profound mystery to us outside of the dependable laws of relation which we can empirically detect. Probability or apparent probability is just another observable law of relation of the cosmos system or parts of the cosmos system. The dependability is not strict one to one, A leads to B causation. The level of dependability is now probable, not certain.

    Others may wish to adopt a faith position to attempt to resolve the cosmic mystery but that leads to no advances in studying things empirically. Indeed, it remains an obstacle to science. One has to admit that applied science certainly needs an obstacle as the blind and selfish application of science is leading us into disaster. We are in the middle of the sixth mass extinction and it is man-made, science-made.

    • December 7, 2019 at 12:57 pm

      Ikoonoclast, for discussion rather than disagreement, you are attempting to smash the material image of immaterial information, denying e.g. the concept of unity, depicted rather better by a closed circuit (or dynamically, by the closure of a circuit) than by the symbol ‘1’.

      A curiosity others have pointed out is that the closed circuit looks more like the symbol ‘0’ and the open circuit a bent ‘1’. In the computing world, conventions differ. However, it was realised that a symbol representing unity is one thing, a symbol representing a symbol of unity another.

      For clarity on this, I find myself turning again to Chesterton’s “Orthodoxy”, written before Hume’s doctrines reappeared as Logical Positivism and forty years before Shannon provided the language enabling us to set aside meaning and focus on information capacity. My original copy is full of underlined aphorisms resolving complex issues in a few words. A couple are particularly relevant here in light of what you say.

      “The insane [materialist] explanation is quite as complete as the sane one, but it is not so large”. (My p.20).

      “If [the ordinary man, a mystic] saw two truths that seemed to contradict each other, he would take the two truths and the contradiction along with them. His spiritual sight is stereoscopic, like his physical sight: he sees two different pictures at once, and yet sees all the better for that”. (My p.27).

      “The whole secret of mysticism is this: that man can understand everything by the help of what he does not understand”. (My p.28).

      So I don’t understand energy; but in the language of geometry I do understand space, time and the evolution of the sub-atomic particles, about which materialists are still scratching their heads! I agree when you say “Logically, if these is no material-ideal duality then there are only existents” [always existing]; but you don’t need to understand the meaning of information, only the idea of the information-representing or carrying capacity of a material channel.

      Likewise, I understand probabilities stereoscopically: both in the language of permutations and combinations (throwing the dice), and in terms of symmetries and possibilities (physical shape and evenness of weight). Digital set logic in the first, topological ordering logic in the second?

  4. ghholtham
    December 6, 2019 at 10:38 pm

    John Kay is correct and attempts at optimisation lose determinacy under radical uncertainty and things like “profit maximisation” have no clear meaning.. Mild uncertainty, however, is different. Bookmakers regularly quote odds on one-off events like horse races and football matches. They make sure the sum of probabilities add up to more than one and lo and behold they make money. Radical uncertainty in the Knightian sense applies to what Donald Rumsfeld called unknown unknowns. They are the things that make the future unfathomable. Once we enter the realm of known unknowns – like who is going to win the 2.30 – we can usually assign some sort of probability. Subjective probabilities will differ but that’s what makes a market. Bookmakers’ prices are driven by the market in expectations. The same applies to the market in financial instruments which exists partly to reconcile diverse expectations.
    In other words probabilities can be assigned to foreseen possibilities. Evidently no probabilities can be assigned to events that have not been foreseen or imagined. As fighter pilots used to say: “it’s the one you don’t see that gets you”.

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