Anon writes:
Mr. Briggs,
I am trying to understand the statement in the title.
It [probability] is a measure of uncertainty. It is a measure of what we know or do not know. It is epistemic, not ontic. We are saying something about ourselves or our own knowledge, not something about the world.
It is more like saying an argument is sound and valid than saying anything about reality itself.
But I come back to games of chance and the idea that there is a kind of probability built into them that influences their outcomes.
Is not the world something like this, too? Where the way it is can lead to different results and a real probability might exist in the sense that there is a 1/4 chance of x and a 3/4 chance of y in certain real situations so that if we knew everything, we would still not know whether the 1/4 or 3/4 would come back?
And yet this idea that if we really knew everything we would not need probability has power.
I am not sure.
I did just read your very good article on p values and that is wonderfully helpful. I had read a book called Stats.con years ago, where the author suggested statisticians did not themselves understand p values and the author did not seem sure there was a valid definition, if I remember correctly (not wanting to mis-represent him).
I will continue to work on this.
Something near to this pops up, too. Chance is not a cause. I agree. That is a concept, not an agent.
But is there not some chance involved in some way in terms of causal lines intersecting or are we to say there was an agent or cause behind all of that, too?
And, if life has real probability built into it the way a game of chance is set up, there would need to be some sense in which chance is a reason for results or outcomes, even if it could not be a cause or agent.
Or, maybe I am still in the dark, trying to find my way?
Could you toss anything my way or recommend anything further?
Thanks,
[Anon]
Random, and its synonym chance, only means unknown. As in unknown cause. That’s it, nothing more.
Take a game of “chance” like poker. The cards are riffled shuffled once—and stop right there.
Now my old advisor Persi Diaconis proved that if you do just one riffle shuffle, and you know where the cards in the deck started, you know where they end, too. This is easy enough to see, too. The shuffling only interleaves the cards, leaving the order of the shuffled halves untouched.
This makes it easy to guess who has what cards, if they are dealt after only one shuffle. What’s surprising is that if you do this six or fewer times, you could pull off some astonishing magic tricks. (Here’s a pdf which explains all.)
Because you are taking the known properties of riffle shuffling, and what can be deduced from that, the whole becomes more known, i.e. less random.
So, to those who know the trick, the order is not unknown, and therefore not “random”.
Same kind of thing fools people about the so-called Monty Hall problem. Turns out people turn a blind eye to relevant information, or don’t even know it’s there. And some can be become downright surly when you point out what they don’t want to see.
Other things, like dice throws, are similar. Turns out the causes of what side is face up are many, so many it’s hard to control throws, and therefore exceedingly difficult to predict. But it can be done, say, with enormously sophisticated measurements of the initial conditions of the throw and so on, and some subtle physics. That transforms the “random” to known.
Same is true everywhere. It’s just that some things, like quantum mechanics, no one knows what causes are there. Or, that is, not all the time. But things are changing even in that quarter, because some people are allowing themselves to consider the information that they didn’t at first see, or acknowledge. Sort of a grand Monty Hall elevation.
Now to your more subtle question, repeated here: “But is there not some chance involved in some way in terms of causal lines intersecting or are we to say there was an agent or cause behind all of that, too?”
Let me answer by quoting from St Thomas Aquinas, who in turn quotes The Philosopher (as they called him), i.e. Aristotle.
11 But this way of arguing, as Aristotle says in Physics [II, 4], was used by some of the ancients who denied chance and fortune on the basis of the view that there is a definite cause for every effect. If the cause be granted, then the effect must be granted. Thus, since everything occurs by necessity, there is nothing fortuitous or by chance.
12 He answers this argument, in Metaphysics VI [2-3], by denying two propositions which the argument uses. One of these is: “if any cause be granted, it is necessary to grant its effect.”
Indeed, this is not necessary in the case of all causes, for a certain cause, though it may be the direct, proper and sufficient cause of a given effect, may be hindered by the interference of another cause so that the effect does not result.
The second proposition that he denies is: “not everything that exists in any way at all has a direct cause, but only those things that exist of themselves; on the other hand, things that exist accidentally have no cause.”
For instance, there is a cause within a man for the fact that he is musical, but there is no cause for the fact that he is at once white and musical. As a matter of fact, whenever plural things occur together because of some cause they are related to each other as a result of that cause, but whenever they occur by accident they are not so related to each other. So, they do not occur as a result of a cause acting directly; their occurrence is only accidental. For instance, it is an accident to the teacher of music that he teaches a white man; indeed, it is quite apart from his intention; rather, he intends to teach someone who is capable of learning the subject.
13 And thus, given a certain effect, we will say that it had a cause from which it did not necessarily follow, since it could have been hindered by some other accidentally conflicting cause. And even though it be possible to trace this conflicting cause back to a higher cause, it is not possible to trace this conflict, which is a hindrance, back to any cause. Thus, it cannot be said that the hindrance of this or that effect proceeds from a celestial source. Hence, we should not say that the effects of celestial bodies come about in these lower bodies as a result of necessity.
And here is another article, exploring all these in more depth. And here is another on Aristotle and chance.
There is still the idea of coincidence—-two more more incidents occurring together or in some kind of sequence, in which it appears, or there is, direction. That is to say, a master cause.
Here proof often escapes us, and we have to rely on faith or weaker forms of induction.
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Either one believes that effects have causes, or one does not. If one does not believe that for every effect there is a cause, then, perforce, the world (or at least that portion of it not due to cause) runs on magic, and is unknowable. Chaos and chance rule, and their whimsy is law. This logically follows, as water runs downhill.
If one does believe that every effect has a cause, then the world (and thus, eventually, the will of God) is knowable, however imperfect our knowledge must be on any subject at any time. Just because there is a cause, it does not follow that we must necessarily be able to determine that cause to the exclusion of all others. This logically follows, as day banishes the night.
It seems there is a lot of truth in what Briggs is saying.
One does wonder if a game could be created where ‘chance really was built into it’ such that knowing all the causes, one could still end up with different results that had certain probabilities given a full knowledge of the situation. If we had something like a true random number generator (is this possible? for it is really programmed and the program can be known) where we could not get to the bottom of it, no matter how much we knew, even if we knew everything, then probability would still be a calculation and not real in the sense that agents are real, but it would say something about the actual world, not just our knowledge of it. Knowing everything, could some things still happen causally by a kind of chance? Not in the sense that chance causes anything but in the sense that there is real indeterminism built into the causes or between the causes and their effects. Then, could we not speak of two kinds of probability: one kind that really is a matter of our uncertainty or lack of knowledge (where, if we knew everything, we would not need probability calculations) and another kind that could exist even if we had full knowledge of all causes (where probabilities were saying something about the objective world and not just about our ignorance or knowledge or lack thereof or uncertainty)?
Chance required God because random functions must be designef by an advanced mathematician.
Welcome to the multifactorial physical part of the universe, where everything is more or less mutable. While every effect does have one or more causes, conflicts or accidents can and do occur. Conditions matter, folks. We have limited knowledge. Our physical lives are finite. We *cannot* know everything that is possible while in this physical world that is changing to a greater or lesser degree. Certainty or uncertainty are statements about our limited knowledge, and thus, statements about us; and not necessarily statements about the rest of the physical world.
The easiest way to recouncile competing views of Prob is to eschew causality entirely and believe, instead, that
P(E) is a measure of our knowledge about E. Thus P(E)= 0 or 1 implies perfect knowledge while P(E) = 1/n where n is the number of possible outcomes (including unknown ones) implies zero knowledge.
Here follows my tediously repetitive caution about too easily sashaying from (Aristotelian, or really any) philosophy to Catholic theology. For instance: a perfectly formed clock, in perfect working order, absent malign outside influence, can do no other than be a good clock. So how could beings perfectly formed by God Himself — angels, and Adam and Eve — in perfect working order, ever even desire to be dis-ordered at all, let alone want to be so titanically dis-ordered as to Fall, let alone be able to do so? They were created with their passions perfectly ordered by God Himself — with God as their Creator, how could it have been otherwise? Their intellects, perfectly formed by God, were not blinded by the Fall, which had not even happened yet. So what — who — caused dis-order to come into the world? Within the impeccable, unbroken chain of causes that is God’s good and holy Law, where does this mysterious ‘free will’ fit in, or even mean? The four hundred year (and counting) dispute de auxiliis, never resolved among Thomists, is only one testimony that things are not straightforward.
Maybe if we knew all the causes of a given situation or all the causes in the world, we would find that some have probabilistic tendencies and that it is part of their nature to have probabilistic tendencies. Then, it would not necessarily be the case that all of probability boiled down to unknown causes, though I think most situations do boil down to unknown causes, leaving us to calculate probabilities which are evidence of our lack of knowledge about unknown causes. Or, imagine a cause working instrumentally through a machine to bring about certain effects but that the machine had probabilistic tendencies, i.e., could give a distribution of results. In both situations, we might end up with a distribution of results that were intended but not intended in detail. Some result was intended but the actual results were determined, in part, by probability because the agent acted probabilistically or had a machine determine the outcomes probabilistically. But is any cause like this, in the last resort? Can there be a machine or type of cause that causes things probabilistically or randomly or in some real sense by chance, where ‘chance’ is not an agent and not really a cause, but factors into the way a result or set of results came about so that there is some sense in mentioning chance, even if it is not a causal agent?
When Einstein said ‘God does not play dice’ was he not talking along these lines?
Some say Einstein was not thinking of God per se, but using the term metaphorically.
Fine.
If we allow for accidents and free secondary causes that are real, then it seems God might have been playing dice, not ultimately in control of everything that happens, contra occasionalism.
But what is the relation of probability to secondary causation and what is its relation to accidents or intersecting causal lines?
If we knew all everything, maybe we would still find the need for probability in the objective sense and not just in the probability is not real but a product of our uncertainty sense.
Could we ever know?
For we might think it is all a matter of probability as a reflection of our uncertainty but not know enough to know that it was not also, in part, a matter of probability built into life in some way. That is, not being able to know all the causes, we cannot know which it is, ultimately. (?)
But from what Briggs is saying I suspect that if probability calculations are not all about our uncertainty or lack of knowledge of causes, that many or most are about just that and not much more.
But I am still not sure if this is always the case or if it is just usually the case.
McChuck,
I am thinking about what you said. Here’s a thought.
It does seem that every effect has to have one or more causes, but would the cause have to lead to the effect non-probabilistically? Could an agent cause y, but do so probabilistically?
If so, we could still know a lot about the world because not all causes would be like this (perhaps) and, in knowing probabilistic causes (?) (causes that cause that way or that can), we would still know a lot, but there would be something left over, something left to be said by probability, though probability is not a force or cause as such and could not cause outside real causal agents.
But, within real causal agents, maybe probability is real (not as as cause or agent) but as a way of causing that is different than other ways of causing.
And, in the intersecting of causes, maybe there is no real cause so that something other than causality might have a role.
It would be like having a bunch of causes acting directly and non-probabilistically and then having some that act probabilistically and then having them intersect one another randomly or by chance or in some way that is not really caused by another cause, even if permitted. Does everything have to be caused, even the intersecting of causes?
Interesting topic, for sure! Hard for me to get my mind around and maybe I am terribly off-track.
If some randomness was really built into this or that aspect of the world, then random would not just mean unknown or unknown cause but something about the cause that was not even knowable or, similarly, that was knowable, but only up to a point. Imagine knowing someone with an internal probability function built into them that truly was random and that one knew the person very well but knew also that the probability function kicked in in certain areas giving certain results, the probability of which could be calculated but one could never get to a cause that explained this because the probability function ‘mechanism’ really was random and so not open to explanation in terms of causes.
But would this be possible? I do not know. It sounds strange and I tend to think that Briggs is right about most situations that we actually encounter after seeing the explanation above.
And, operationally speaking, it seems best to assume probability is a matter of our own uncertainty and then look for causes that might reduce that uncertainty, perhaps to the point of not having to rely on probability any longer, probability being something we rely on when we do not know enough.
If we start with the hypothesis that the world is just probabilistic in its nature (in some of its aspects), why look into causality for answers? But one could, still. For example, one could think that causation explains most everything so that the answer is to find the relevant causes but then also think there will be a few things that are ultimately unknowable and that still have to be discussed probabilistically because of the nature of certain things.
But why think this from the start or why be very confident about it? Why not just assume probability is something we bring in when we do not know the causes and then look for them so that we do not miss any that might prove that in that situation, at least, probability was not real?
So, we might go with Briggs provisionally, on this, because we cannot really prove he is wrong (?) and because there are real advantages to understanding things in terms of causes rather than just probabilities.
Let me add to the last response–particularly the last line: And not just because we cannot prove the thesis wrong or because there are advantages to understanding things in terms of causes rather than probabilities, but also because so many situations do seem to be as Briggs says they are–where if we only knew more, we would not be speaking probabilistically any longer. So, there might be a presumption in favor of that kind of working hypothesis, the kind that says probability is not real.