The Metaphysical Possibility of Randomness

[AquinasD]

Before I begin our analysis of the concept of “randomness� and its metaphysical possibility, we must first come to terms with what ‘randomness’ means.

When the term “random� is used to describe some event, this is in opposition to its being determined or even explainable in terms of what came before it. So randomness would cover any event for which the antecedent is allowed to have two or more consequents, where the occurrence of either over the other possible consequent is not explainable by the antecedent cause. Therefore, when we speak of “randomness� in the context of causation, we mean something like

randomness: when something occurs for no reason

Now for our question; is randomness metaphysically possible? Before I delve into the strictly metaphysical argument, I want to defuse a possible argument that comes from quantum mechanics. This argument states that randomness must be possible, for it is utilized in certain interpretations of quantum mechanics, viz. M-Theory and the Copenhagen interpretation.

However, I think what is important to note is that randomness is scientifically unfalsifiable. We must remember that science operates under a method that is of the form “If x were true then we would see y under conditions z.� Randomness is not observably distinguishable from events that occur in which we are simply unable to observe the antecedent causes of the consequent. If it is not observably distinguishable, then it is not scientifically unfalsifiable. This means that garnering support from science-qua-scientific-method in favor of the possibility of randomness is to beg the question. What is actually the case is that these interpretations of quantum mechanics are presenting a metaphysical explanation (more properly, non-explanation) for what happens, not a scientific one. This means that no substantial help will come from science in answering this question. It is a purely metaphysical exercise.

I think that randomness, defined like above (based on how it is typically used in the context of causality), is meaningless. What I mean is that the proposition “Things can happen for no reason� is void of semantic content. Let us break it down to see what it would mean, and in this way we will see that the only possible, and therefore necessarily true, proposition is that “Things happen for a reason.�

Causality is linked to being. If something were to cause another thing, then it must be the case that between objects they share an aspect in their forms that makes them capable of interacting directly with each other, and their respective forms will inform the ontology of the causation as it occurs. In other words, it is in the essence of (at least) two beings that determines how the inputs (the motion, or change, of the antecedent efficiently causal being) shall be, as it were, translated to outputs; a sort of instantaneous calculation is performed by both of the objects that yields its result.

To break this down concretely, take the event of a billiards ball striking another. We know that when one strikes the other, the other will be pushed off in the direction it is struck from. What causes just this type of event to occur, and none other, is the essences of the two billiards balls themselves, such that the first’s form informs the other of what it will do in reference to its own form (in this case, they both happen to be spherical).

Now what we must note is that, insofar as the beings involved determine what shall happen in any event, that definite beings give definite conclusions. It is the very definiteness of the beings that allows the transference of energy to occur as it does, for otherwise there must pertain an indefiniteness of just what occurs, for definition cannot follow from indefinition. But what occurs is, in fact, definite, and it must be definite, for otherwise it would not be. This is because any being that is at all a being must be a certain particular being, a definite being, for otherwise it should fail to be a being at all. But then, if there is no room for indefiniteness in a being, then we must conclude that there is no room for indefiniteness in cause.

Concretely, what we mean by this is that it cannot be a being’s final cause that it will cause A or B, and that it causes either A or B shall be for no reason. It simply wouldn’t mean anything to state that it is a thing’s nature to not be naturally disposed towards one consequent over another under certain conditions; we’d be saying it’s nature is to be without nature. But if a thing has a nature, it has a nature, and if a thing didn’t have a nature, it wouldn’t be a thing. Therefore, we must conclude that, if a being is a being, it’s efficient causes can only be of a particular and explainable sort. This precludes the metaphysical possibility of randomness, because randomness requires a being to not have a nature, which is a contradiction in terms. Thus I say “randomness� is meaningless.

*What is a nature? A nature is simply what it is in the being's being to do; or, what Aristotle calls "final cause."

That there are final causes in the world is not difficult to demonstrate. Typically, we like to describe complex processes in terms of what its constituent parts do. However, this mode of explanation falters when it comes to theoretical fundamental particles, which would have no constituent parts to explain their behavior. Yet these fundamental particles would have a definite range of behaviors, and while this behavior is informed by the effective environment of that particle, it remains the case that we can only explain the particle's normative tendency by positing that it is just the nature of the particle to do what it does, and that it has the nature to do what it does is not caused by any underlying constituent parts. In other words, final causes constitute a real aspect in nature.

A practical example of final cause is any given natural law. Take Boyle's law:

"For a fixed amount of an ideal gas kept at a fixed temperature, P [pressure] and V [volume] are inversely proportional (while one doubles, the other halves)."

What is being described here is the nature, of final cause, of gaseous matter. We would say it is just the nature of gas for its pressure and volume to be inversely proportional.

Just to show I'm not being illicit in my utilization of "natures" as an aspect of beings.

[AdHoc]

I've been thinking about this question alot and I can only think of three ways of answering this question:
1) Intuition. Intuitively randomness does not make sense because of the cause and effect that we experience in life. But eternity and infinitity don't sit well with intuition either and they are both generally accepted as true.
2) Observation. Impossible to prove through observation unless we could see everything at once, which I don't believe is possible.
3) Mathematics. I can't imagine that its possible to create a random result with mathematics.
4) Is there another way?

[spoirier]

"the cause and effect that we experience in life" is the naive viewpoint. Go learn quantum physics and you will see how randomness comes.

"I can't imagine that its possible to create a random result with mathematics" Go see the work of G. Chaitin.

[AdHoc]

"the cause and effect that we experience in life" is the naive viewpoint. Go learn quantum physics and you will see how randomness comes.

I followed this link but it led to a document on religion and metaphysics. Yes I am naive when it comes to Quantum physics but I'm curious how anyone could ever make a confident statement that something is completely random. Even if you could precisely identify all the initial locations and velocities of every particle the very act of observing the particles changes their state. To look at it another way you might suppose that all the grains of sand on your beach are random but how could you truly know that for a fact.

"I can't imagine that its possible to create a random result with mathematics" Go see the work of G. Chaitin.

Is there an equation that will produce a different sum if none of the parts are changed?

[spoirier]

I followed this link but it led to a document on religion and metaphysics.

My text starts with notes on metaphysics (and metamathematics in the other page, if you follow the link) but this is just to give preliminaries after which the quantum theory concepts will seem more natural and intuitive (make more metaphysical sense). You may as well directly jump to the presentation of quantum theory itself by starting with the title "Classical probabilities". The problem in this case is that it might make you wonder the usual problem for anyone learning quantum theory: "what is this ? where is reality supposed to be represented there ?" which would not seem so obscure if you started with the metaphysical preliminaries.

Yes I am naive when it comes to Quantum physics but I'm curious how anyone could ever make a confident statement that something is completely random.

Well if you want to be serious about being curious then it's up to you to make the effort to learn the theory and articles on the question, instead of just lazily putting forward your complaints that you did not learn those things yet. Following the other link I gave you could have found that article where this physicist explains that we have a theorem stating some alternative we must make between different metaphysical hypothesis for compatibility with the experimental verifications of quantum physics, and his personal choice is that we have pure randomness because the available alternatives seem less plausible to him. If you want to reject randomness then you must choose an alternative, and be warned that it may make things worse than you are currently expecting.

Even if you could precisely identify all the initial locations and velocities of every particle

which we cannot do because the very concept of "all the initial locations and velocities of every particle" does not mathematically exist in the first place, given the established quantum structure of the world.

Is there an equation that will produce a different sum if none of the parts are changed?

Of course not. But here you are restricting your consideration to primary-school level mathematics. What Chaitin proved is that some sort of randomness can be found on some high-level sort of mathematics. But what sort of randomness it really is, cannot be simply explained in a few words. If you are seriously interested about it, it's up to you to try understanding his work.

[AdHoc]

I followed this link but it led to a document on religion and metaphysics.

My text starts with notes on metaphysics (and metamathematics in the other page, if you follow the link) but this is just to give preliminaries after which the quantum theory concepts will seem more natural and intuitive (make more metaphysical sense). You may as well directly jump to the presentation of quantum theory itself by starting with the title "Classical probabilities". The problem in this case is that it might make you wonder the usual problem for anyone learning quantum theory: "what is this ? where is reality supposed to be represented there ?" which would not seem so obscure if you started with the metaphysical preliminaries.

Yes I am naive when it comes to Quantum physics but I'm curious how anyone could ever make a confident statement that something is completely random.

Well if you want to be serious about being curious then it's up to you to make the effort to learn the theory and articles on the question, instead of just lazily putting forward your complaints that you did not learn those things yet. Following the other link I gave you could have found that article where this physicist explains that we have a theorem stating some alternative we must make between different metaphysical hypothesis for compatibility with the experimental verifications of quantum physics, and his personal choice is that we have pure randomness because the available alternatives seem less plausible to him. If you want to reject randomness then you must choose an alternative, and be warned that it may make things worse than you are currently expecting.

Even if you could precisely identify all the initial locations and velocities of every particle

which we cannot do because the very concept of "all the initial locations and velocities of every particle" does not mathematically exist in the first place, given the established quantum structure of the world.

Is there an equation that will produce a different sum if none of the parts are changed?

Of course not. But here you are restricting your consideration to primary-school level mathematics. What Chaitin proved is that some sort of randomness can be found on some high-level sort of mathematics. But what sort of randomness it really is, cannot be simply explained in a few words. If you are seriously interested about it, it's up to you to try understanding his work.

I will admit I'm definitely lazy about this and was hoping for a grade six summary but I'll do my homework on this.

One question though before I go, does probability describe the known quantum world? I have heard that the position of an electron cannot be described in any way other than by using a probability distribution curve. If this is true for the entire quantum world then would that not suggest determinism?

[spoirier]

Okay if you want some simple remarks about randomness in mathematics, I can give:
- The sequence of decimals of pi somehow behaves as a random sequence, although it is calculable by an algorithm
- It is possible to mathematically define a sequence depending on properties of infinity (namely, depending on the set of natural numbers) but that does not coincide with the output of any algorithm.
- I already mentioned the theorem by Chaitin that the randomness (uncompressibility) of any large amount of data is necessarily unprovable. Thus for most possible sequences, there is "no reason" why it is random, or why eventually it is not random (but it might instead be the final output of a small algorithm running for zillions of years in a cosmic computer).

If you read my work on the foundations of math (til the end of part 1), you will see how some indetermination emerges in mathematics, on questions such as the question whether some given formula is provable, despite the fact that we have a complete and well-established system of rules of proof. (Namely, we cannot know if a given formula is provable but its proof would be too big to be found).

[Goat]

"the cause and effect that we experience in life" is the naive viewpoint. Go learn quantum physics and you will see how randomness comes.

I followed this link but it led to a document on religion and metaphysics. Yes I am naive when it comes to Quantum physics but I'm curious how anyone could ever make a confident statement that something is completely random. Even if you could precisely identify all the initial locations and velocities of every particle the very act of observing the particles changes their state. To look at it another way you might suppose that all the grains of sand on your beach are random but how could you truly know that for a fact.

Ah, and there the Heisenberg uncertainly principle comes into play, which specifically states you can't know precisely a particles velocity, and it's location at the same time.

[AdHoc]

Okay if you want some simple remarks about randomness in mathematics, I can give:
- The sequence of decimals of pi somehow behaves as a random sequence, although it is calculable by an algorithm
- It is possible to mathematically define a sequence depending on properties of infinity (namely, depending on the set of natural numbers) but that does not coincide with the output of any algorithm.
- I already mentioned the theorem by Chaitin that the randomness (uncompressibility) of any large amount of data is necessarily unprovable. Thus for most possible sequences, there is "no reason" why it is random, or why eventually it is not random (but it might instead be the final output of a small algorithm running for zillions of years in a cosmic computer).

If you read my work on the foundations of math (til the end of part 1), you will see how some indetermination emerges in mathematics, on questions such as the question whether some given formula is provable, despite the fact that we have a complete and well-established system of rules of proof. (Namely, we cannot know if a given formula is provable but its proof would be too big to be found).

I read the link and it definitely piqued my interest.

Here's an anecdote from my work last week where I discovered by using even grade school math I can produce random results, namely 4+5 = 8.
I had to produce a one page report for a meeting that involved reporting a certain KPI. The KPI was derived from an index that was based on a very simple algorithim (M x 2 + R x 6 + L x 10)/12.

I meticulously checked this report and all the excel links prior to the meeting and imagine my frustration when one person pointed out what they thought was a error... I had reported one region as having a result = to 4 and another as having a result = to 5, when added together the combined department result was 8!

After the meeting I quickly rechecked my figures and when I reformatted the cells to report to the 2nd decimal place the equation read like this 3.67+4.67 = 8.33.

I took it to the 14th decimal place and I was never able to get the "correct" answer for this simple equation.

[sickles]

Your requirement makes no sense. I'm not the one making any bold new claim, so I'm not responsible to justify it. I just report to you what the current state of science is. I have no duty to re-prove science for you. If someone claims that the Earth should be flat because it would be absurd to imagine people living upside down, and he is absolutely convinced that there could never have been any evidence to see it round, what I can I do ? I can just tell him that there is well-known evidence it is round, and that he needs to go and get informed from the world around him to check that information. If he wants a "proof" to his satisfaction avoiding any "appeal to authority", well, sorry I cannot invite him to the international space station to let him see the shape of the Earth by his own eyes.
So if you don't want to trust me about what science actually discovered, well, that's not my problem; it does not change what the scientific findings actually were. I have more important things to do in life than to dedicate it to people with that attitude.

sorry for the delayed response. Just so we are clear, I want to ask you a question. What, exactly, from your viewpoint, is my 'bold new claim'. I really just want to know how you see it. I think your response would help me understand this conversation better.

On another note, I accept what science has discovered. I do not accept some scientists interpretation of the evidence. It is not the consensus of science that the universe is founded on 'truly random' phenomenon. I do not see how you can qoute 2 or 3 scientists and say this is the consensus. Show me the peer reviewed stuff, sir. I dont want a quantum physicist's philisophical ramblings. I have my own philisophical ramblings to deal with.

[spoirier]

what I meant is that I did not make any bold new claim, contrary to the way you seemed to see my claims, that is you seemed to find intolerable that I dared to make claims without enough justification, while all I did was report the information on the scientific situation without bothering myself to give a "full proof" for the satisfaction of your lazy eyes. Sorry if my sentence was ambiguous. I did not mean that you made any bold new claim either. Rather, I'd say your claims are quite naive and outdated as compared to the current science, and your unability to consider the possibility that they may be so and that there are important things you need to update yourself to for being up to the debate (your a priori unquestionable confidence in the ultimateness of your ideas), is what is bold and finally wrong.

"I accept what science has discovered"
I already explained but you seem to have problem to get it, so I repeat:
You are doing the contrary of what you think you do.
In fact you do not accept what science has really discovered but only what you believe it did, because you have wrong beliefs about what science has or has not discovered.
Well things are uneasy to explain because they are complicated and subtle (just like all science which requires important studies to be grasped) not just simplistically black or white.
What science has established is that the idea of a hidden determination between quantum randomness would be VERY far-fetched. There are some precise scientific reasons that show that this is far-fetched.
However I'm aware that this claim will make no sense to you because this report is just an approximation of some much more complicated stuff that cannot be easily summed up. And as an approximative claim (deprived of the effective complex contents it refers to) it seems to make no sense.
The point is just because things are not as simplistically black or white as would be convenient to sum up for an easy, unscientific discussion, does not mean the sort of total absence of any effective, important scientific findings supporting randomness, that you are assuming here all along.

Otherwise it would be easy to deny science while pretending to accept its findings, by claiming there is "no consensus" on anything just because you focus on a question that does not make meaningful sense and it is possible to either just ignore existing knowledge for pretending that this question makes more sense and remains unsettled, or find some implausible way of distorting the interpretation of observations to make them compatible with the distorted idea, such as to doubt the reality of global warming or of natural unguided evolution.

For example if you ask a biologist why he thinks that evolution happens naturally without divine guidance, first this question makes little sense to him because what he knows is thousands of particular observations of how things happen to be and how this is coherent with natural evolution. However he cannot specifically say that this shows absence of intelligent design because, for example, the idea of intelligent design requires to define some hierarchy of values, criteria how something can be considered better designed than by chance, and such criteria are lacking (the easy ones do not work but it is always possible to argue that God has other criteria that we cannot grasp).

So sorry I deviate here from the subject, but I just mean that you need to learn more carefully of quantum physics if you wish to understand what I mean. And what you really need to be explained, cannot hold in just a few paragraphs.
It's about some diverse considerations on the properties of quantum systems and the mathematical form and properties of quantum theory. An important clue among that is the violation of the Bell inequalities. I guess you heard about these inequalities because they are well-known. However you seem to not have noticed the importance of those things. But however scientifically solid and important, anyway it's easy for you to dismiss that by unfairly accusing scientists who express that, of only telling their philosophical interpretation away from scientific facts (or what you believe them to be).
And because what you are asking is a quite philosophical question that does not make much operational (verifiable) sense. Not that science has nothing to say about this as you wrongly assumed that it would be beyond its scope, but that there are good reasons for scientists to not focus on this precise question and dismiss it as less relevant, compared to the other more effective clues they have about how things work.
Scientific knowledge has no pity for the lazy-minded people who require the answers to their naively favorite questions (which they wrongly assume to be the most essential) to be convincingly explained in a few paragraphs without caring to learn the rest first.
Sorry.