A Challenge to Mises’s Theory of Probability

0:00This is kind of a boring topic, definition of probability, but hopefully this will interest some people here. The paper that I'm presenting builds upon the paper that I published last year in Libertarian Papers, where I defended the subjective definition of probability against, more in that paper against Richard von Mises. So in this paper I turn more to examine Ludwig von Mises' specific definition of theory of Probability, let's see, so the way that I'd like to proceed is not exactly in the order that I wrote the paper, just because I did not present that paper last year, so I'd like to lay out why I think probability should be defined subjectively and then I can examine and Ludwig von Mises' theory of probability in the light of the subjective definition.

1:19So there's two general ways we can go about defining probability, speaking very generally. We can say that probability is a real physical feature of the world, like the weight of a Like the weight of a chair or the height of something, we can think of it as an actual physical property of the world. And this is the way that Richard von Mises, Ludwig's brother, thought of probability. He speaks of probability in exactly these terms. He says the probability of a six, this is his quote, the probability of a six is a physical property of a given die and is a property analogous to its mass, specific heat or electrical resistance.

2:15Similarly, for a given pair of dice, including of course the total setup, the probability of a 6 is a characteristic property, a physical constant belonging to the experiment, as a whole, and comparable with its other physical properties. So that's the objective, if we were to conceive of probability as an objective physical feature of the world, that's basically the conclusion we would have to draw about probability. But there's another way that we can conceive of probability, and this is the subjective conception of probability. And under this conception, probability is not a physical feature of the world, it's a... it's hard to speak of this, the terms here get confusing, but it's not a physical feature of the world, it's a feature of man, it's something inside man.

3:21It's a consequence of the fact that man is not omniscient. The famous quote from one of the most famous subjectivists is from Bruno de' Finetti, who said that probability does not exist. And he was a probabilist, so he believed in using probability, but he did not conceive a probability as something out there in the world to be measured like Richard von Mises thought probability was. So the question then is, which of these conceptions of probability is correct?

4:09An Objective Physical Feature of the World or a Subjective Quality Inside Man? The answer, I think, comes from the probabilist I.J. Good, who pointed out that the question really depends upon the nature of the world. If the world is deterministic, then we have to say that probability is a measure of something and Man. If, on the other hand, the world is considered indeterministic or random in some sense, then we can define it the way that Richard von Mises defines it. And Richard Ludwig von Mises specifically defines probability as the limit, let's see, he defines it as the limit of the relative frequency of occurrence, he defines it as the limit of the relative Frequency of Occurrence and an indefinite sequence of observations in a collective.

5:29So the question is, is the world deterministic? Does everything that happens in the world have a cause? If I flip a coin, is there something random about the outcome? Or is it just a is a matter of, is it just a collection of various forces acting on the coin that if we knew what all those factors were, we would know the outcome.

6:00And I, of course, take the position that this comes from the paper I published last year, but I take the position that everything that happens in the world has a cause. It's not even really conceivable that something would have, something would occur completely randomly or without a cause. So let me just add as well that even if we did conceive of the world as having a certain amount of randomness in the world, as Richard von Mises did, and Richard von Mises drew Heisenberg established that at certain levels of smallness, things just happen.

7:00I think this is a misreading of Heisenberg, but it was interpreted largely to, especially by Richard von Mises as saying that there's a certain amount of randomness in the world. Even if that's the case, there's still uncertainty in man, in the sense that, even if there's uncertainty about whether a coin will come up heads or tails, we don't know which way So, even in the case that, let me just rephrase this, if the world is deterministic, everything has a cause, then we have to be subjectivist, we have to define probability subjectively.

7:53If the world has an element of uncaused randomness in it, then we can define it as a physical is a fundamental feature of the world, but there's still uncertainty in man, even in that case. So, the central philosophical question then is whether everything in the world has a cause. And for Austrians, this is rather straightforward because, for Austrians who follow Mises because Mises was a determinist and he was very unequivocal that everything has a cause.

8:38And Hans-Hermann Hoppe is the one who really established this as an axiom, but this is This is what Mises himself had to say about this.

9:01This is Mises, Ludwig von Mises. In a world without causality and regularity of phenomena, there would be no field for human reasoning and human action. The world would be a chaos in which man would be at a loss to find any orientation and guidance. Man is not even capable of imagining the conditions of such a chaotic universe. And this is what makes it somewhat difficult to talk about Mises' theory of probability because he discusses probability very much in line with his brother in certain respects. He talks about class probability which is almost identical with his brother's idea of collectives and his brother was a dogmatic frequentist. But on the other hand, Mises This puts his discussion of probability in the section on uncertainty, and as a matter of fact his discussion of probability takes up almost the entire chapter on uncertainty.

10:06So he clearly understood that probability was a problem of human knowledge and not a problem of the natural sciences. And he says specifically that probability is a concern of praxeology and not a concern of the Physical Sciences, whereas Richard thought that it was exclusively the concern of the physical sciences. So the other way that we know that the world is causally deterministic in the sense that everything that happens has a cause, we know this because the relative frequency method for Generating Probabilities relies upon this principle. If it was not the case, if the world was assumed to not be governed by causally determined, the term Hoppe uses is time invariant causal forces. If it was the case that the world operated in that way, that these sorts of Causes did not exist. We could not construct collectives or classes from which we could generate relative frequencies of occurrence. So Richard von Mises' favorite method for – not favorite, he claims it's the exclusive method for generating numerical probabilities

11:40itself relies upon the principle of causality. Governing the phenomena that you're studying, So, given what I've just said, this leads us inexorably to the, I think, to the position that probability must be defined subjectively in the following way. It should be defined as a measure of human uncertainty about the likelihood of occurrence of Events in the World, and this is radically different from the definition that Richard von Mises gave us, and I'd like to say that this is radically different from what Ludwig von Mises gave us in terms of a definition for probability.

12:44And in order to see this, let me just step back and say a few things about how Ludwig von Mises' theory of probability differed from his brother's theory. First on the similarity side, they both were very clear that they thought that numerical Numerical probability only applied to classes of events. Ludwig von Mises uses the term classes, and Richard von Mises uses the term collectives. But essentially what they mean, what they're talking about is the same thing, that unless you can construct a collective or a class of events that are virtually identical in In every way, there can be no numerical probability and this, for both of them, this rules out by definition the possibility of calculating numerical probabilities for singular events like the Super Bowl or events like this where you can't put it into a class, a class of of Similar Events and Generated Relative Frequency of Occurrence, which they called the probability that was generated that way, the numerical probability.

14:15But Ludwig von Mises' theory of probability is different from Richard von Mises' theory in very important ways, I think. In the first place, Richard von Mises was an indeterminist. He was a proponent or he was a disciple of Heisenberg who thought that things could happen in the world that were indeterminate, random, without cause. He felt this not just at the micro level, which is how most people interpret Heisenberg has meaning that at the micro level of smallness, the ultimate level of smallness, things move randomly.

15:01But Richard von Mises went further than that and said that even at the macro level, certain things are indeterminate like length. This is completely different from Ludwig von Mises' position here. This is a determinist, as the quote that I just read indicates.

15:27Another difference between the two is that Ludwig von Mises emphasizes a great deal that probability deals with uncertainty. And this is almost common sense for anybody who hasn't read Richard von Mises anyway. Anyway. But if you read Richard von Mises, you could walk away from his book without even the slightest indication that probability and uncertainty are related to one another. But most importantly, and I think this is the thing to take away from my paper anyway, is that I think that Ludwig von Mises never gave a definition of probability in anything In Human Action, he gives a general definition of the word probable, but he does not give us a definition of the concept of probability.

16:19So, defining the word probable, and really it's just a rehash of a standard dictionary definition of the word probable, that doesn't really clarify anything for us. for us, this is a philosophical problem that you can't really just dispense with by giving the definition of the word probable. So since he lacks an explicit definition of probability, my position is that he ought to have adopted the subjective definition. fits in with the entirety of his philosophical, praxeological, methodological system.

17:06He was a determinist, and I think that he adopted this, his brother's position here because, initially, because he was able to neatly, conceptually integrate class probability and Case Probability into what he thought was a, well, he thought that by integrating class probability into the natural sciences and case probability into the social sciences, that this was a neat separation and an important division. But if we adopt a subjective definition of probability, this is totally arbitrary.

17:55And in addition to this, if we define probability subjectively, this also undercuts entirely the idea that numerical probabilities cannot be applied to singular cases. There's no non-arbitrary reason for us to say that, for example, putting a number of .6 on the NHL finals this year is not a probability just like any other. That makes sense if we adopt Richard von Mises' definition of probability, but if we have a have a subjective definition that's just not defensible.

18:43It's totally arbitrary. And there's no non-arbitrary reason to say that, for example, the terror alert system in the United States is not also a probability. It tells us, it gives us a likelihood of occurrence And that doesn't mean we have to accept it, because in a sense it's an opinion. Probabilities are opinions, but nevertheless it is a probability, if we adopt the subjective definition of probability. And finally, let me just close by talking about these two famous subdivisions that Ludwig von Mises came up with, case probability on the one hand and class probability.

19:44If we adopt a subjective definition of probability, these are totally arbitrary and they are essentially nothing more than methodological subcategories. It's a way of saying some probabilities are generated with the relative frequency approach and some are not, and nothing more than that. So, in conclusion, Mises should have been a subjectivist, I suppose.

20:14Thank you very much.