If no event is random, then is it possible to test for causal connections?

[PseuTonym]

If no event is random, then there could be a pre-established harmony that causes both an action and a reaction. In that case, the action does not necessarily cause the reaction.

For example, if I enter 48 + 27 into a calculator, then perhaps the display of the number 75 was not a response to my action. What caused me to enter 48 + 27? Whatever caused me to enter those numbers might have also directly caused the calculator to display the number 75. If that happened, then the calculator appeared to be responding to the pressing of the keys, but the calculator was actually responding to something else.

Of course, that point of view ignores the mechanism of the calculator. It also fails to explain why the calculator displayed the number 75. It suggests that a malfunctioning calculator might be impossible to repair because of a problem of pre-established disharmony.

 

[john330]

:hypno:

 

[john330]

:whacky:

 

[PseuTonym]

:whacky:

It might seem odd taken in isolation, but there is some context. In a sense this thread is a very delayed response to blase6.

For example, you can see the following thread:

How people make choices and then act upon them
forums.catholic-questions.org/showthread.php?t=947467

That is only the most recent of many threads, including the following:
(I have given the titles only, and not links for these)

Problem with free will
Problems with free will, possibility, and causality
Is this a good understanding of free will?
The Cosmic Slot Machine: a metaphor of free will
Why does God’s nature require freedom?

The more immediate stimulus for this thread was the following statement that I took to be a serious claim and not an attempt at comedy:

“Most atheists don’t consider evolution, or any other thing that happens in the Universe random.”

Link to post:
forums.catholic-questions.org/showpost.php?p=12819809&postcount=22

Link to thread:
forums.catholic-questions.org/showthread.php?t=950636

 

[Oreoracle]

What exactly do you mean by “random”? I suspect you mean something stronger than random in the probabilistic sense.

In probability theory, “random” just means that every possible outcome in the sample space has equal probability. So if we take a strictly deterministic view of the universe, every event only has 1 possible outcome, thus “all” outcomes are equally likely. The events are technically random.

 

[Gorgias]

What exactly do you mean by “random”? I suspect you mean something stronger than random in the probabilistic sense.

That was my first reaction to the OP, too.

In probability theory, “random” just means that every possible outcome in the sample space has equal probability. So if we take a strictly deterministic view of the universe, every event only has 1 possible outcome, thus “all” outcomes are equally likely. The events are technically random.

No, that’s not a good definition of random. A strictly deterministic view of the universe does not restrict the domain to one result; it simply asserts that among all potential outcomes, only one has P>0, and in fact, this one has P=1 (the rest have P=0).

 

[PseuTonym]

What exactly do you mean by “random”?

That’s a good question. I’ll have to give it some thought before I can say anything more than this placeholder for a reply.

In probability theory, “random” just means that every possible outcome in the sample space has equal probability.

A possible counter-example to that claim comes to mind:
Suppose that there are two possible events, and one has probability 1/3 and the other has probability 2/3. We could have a sequence of trials and see what sequence of events occurs. Do you use some word other than “random” in such a situation?

 

[Oreoracle]

A possible counter-example to that claim comes to mind:
Suppose that there are two possible events, and one has probability 1/3 and the other has probability 2/3. We could have a sequence of trials and see what sequence of events occurs. Do you use some word other than “random” in such a situation?

Sometimes such a variable is called “random” but that clashes with the more common definition of randomness. “Stochastic” is less ambiguous.

 

[PseuTonym]

Sometimes such a variable is called “random” but that clashes with the more common definition of randomness. “Stochastic” is less ambiguous.

What if there are three possible events, one having probability zero and each of the other two having probability 1/2? In this case, all the events that have non-zero probability do have the same probability, but there happen to be some events that have zero probability, and some observers do not necessarily have any way to guess which of the events have zero probability and which of the events have non-zero probability.

This is a variation of the Monty Hall 3-door problem. If we always open the door that had probability 0 of having a prize behind it, then this problem seems to have the answer that some experts gave to the original problem.

Link:
marilynvossavant.com/game-show-problem/

 

[Oreoracle]

What if there are three possible events, one having probability zero and each of the other two having probability 1/2?

Such an outcome cannot be called “random” under my definition.

I don’t see this as problematic, either. Consider the interval (-1,1) of the real line. The sample space is the set of numbers on this interval. I pick a number from this interval in such a way that the density function is uniform. This is what “random” typically means.

Now suppose I adjust the sample space. I partition the interval into positive numbers, negative numbers, and 0. The probabilities of landing in these intervals after a real number is randomly selected is 1/2, 1/2, and 0, respectively. I don’t think most people would have any qualms with me saying that such a trial does not have a random outcome. You would never bet your money that 0 would be selected.

Sometimes there are real-life situations where we approximate a non-random event with a random model. For example, the outcome of a coin flip will never be precisely random since there will always be non-zero probability that the coin lands upright. But models are never perfect anyway.

If you insist on defining “random” as “stochastic”, then frankly you’re just being difficult. That is not the usual meaning of the word. Most people would not say that variables such as life expectancy, a person’s height, the weather, etc., are randomly distributed, but we could agree that they are stochastic, i.e., they have some distribution.

 

[PseuTonym]

If you insist on defining “random” as “stochastic”, then frankly you’re just being difficult. That is not the usual meaning of the word.

I have not proposed any definition, and I am not insisting on any definition.

Question:
“What’s the difference between stochastic and random? I’ve read in the Portuguese Wikipedia that there’s a difference, but I still didn’t see this point on English Wikipedia.”

The top answer is now:
“A variable is ‘random’. A process is ‘stochastic’. Apart from this difference the two words are synonyms.”

Link:
math.stackexchange.com/questions/114373/whats-the-difference-between-stochastic-and-random

The first thing that comes to mind is to ask whether an event is a variable or a process. Perhaps an event is neither.

It now occurs to me that the probability half, half, and zero approach to the 3-door problem does not work, because if the contestant chooses the 0 probability door, then it is opened and the contestant has the option of choosing another door. That would change the rules of the game. As originally given, it is very clearly specified that what is opened is a door that satisfies two criteria: first, it was not chosen by the contestant; and second, it has no prize behind it.

 

[inocente]

I have not proposed any definition, and I am not insisting on any definition.

How about:

*‘A random number is a number chosen as if by chance from some specified distribution such that selection of a large set of these numbers reproduces the underlying distribution. [etc.]’ - mathworld.wolfram.com/RandomNumber.html

‘Stochastic is synonymous with “random.” The word is of Greek origin and means “pertaining to chance” (Parzen 1962, p. 7). It is used to indicate that a particular subject is seen from point of view of randomness. Stochastic is often used as counterpart of the word “deterministic,” which means that random phenomena are not involved. Therefore, stochastic models are based on random trials, while deterministic models always produce the same output for a given starting condition.’ - mathworld.wolfram.com/Stochastic.html*

 

[Oreoracle]

There are two definitions of the word “random”, yes. I never said there wasn’t. But there is only one definition of “stochastic”, and that definition coincides with one of the definitions of “random”. So it baffles me that you would deliberately choose the ambiguous usage of “random” when there is already a perfectly good word that captures that meaning unambiguously. You’re just being difficult.

And you never got back to me on what you meant by “random” in the OP.

 

[PseuTonym]

Such an outcome cannot be called “random” under my definition.

I don’t see this as problematic, either.

I think that you are correct on both points. However, did you read my example of the 3 door problem? I think that I failed to formulate what I had in mind, but the example that I gave makes it clear to me now.

Here is my attempt to formulate the idea:

Suppose that there are three descriptions of conceivable events, and one description is of an impossible event, but at least one observer has no way of knowing which description is of an impossible event. Suppose that the other two descriptions are of different events that have equal probability, each probability being 1/2.

Now, in that case we seem to have satisfied your conditions:
“In probability theory, ‘random’ just means that every possible outcome in the sample space has equal probability.”

And you never got back to me on what you meant by “random” in the OP.

Is there a deadline? You didn’t get back to Gorgias, who made a contribution to this thread, and that contribution was on the particular sub-topic that you are interested in.

It might be possible for me to create a new thread with a similar idea and not using the word “random.” I am sure that you are aware that it is too late for me to edit the title and original post of this thread, unless I add to the workload of the people who volunteer to help out here at Catholic Answers.

 

[PseuTonym]

So it baffles me that you would deliberately choose the ambiguous usage of “random” when there is already a perfectly good word that captures that meaning unambiguously.

I write my thread titles for a very general audience, and for that reason I prefer to use words that are familiar to a general audience. Any clarification can be done in the body of the first message, because the amount of space in the body is practically unlimited in comparison to the amount of space available in the title.

In this case, you have touched upon something where I simply had not given the matter any thought, so I did not use the opportunity to provide clarification in the body of the first message. If and when this thread again seems interesting to me, I will attempt to answer questions in it.