How do you measure the probability of something not known?

Question

The probability of a dice landing on 1 is 1/6. What is the probability of it turning into a butterfly? What is the probability of god existing and him forming the universe? If it makes no sense to calculate it, how should we determine whether or not something that has no independent evidence for it yet may still exist? Should we dismiss them or what?

Answer 1

"The probability of a dice landing on 1 is 1/6"

no, that is a statement about a probability model of a dice. If you were to actually measure the probability of a particular dice landing on 1 it would be statistically significantly different from one if you were to collect sufficient data.

This sort of question has been raised repeatedly on this SE, and illustrates a lack of understanding of probability rather than it being a question of philosophy.

There are broadly two common definitions of a probability. The first one, known as "frequentism" defines probability in terms of long-run frequencies - if you did something a large number of times, what on average would be the result. For instance, if you were to roll a six sided die a large number of times, then you would find roughly 1/6 of rolls were a 1, so it would be reasonably to assign that outcome a probability of 1/6. Note will all measurements, there will be some uncertainty.

The problem with frequentism is that it can't assign a probability to something that doesn't have a long run frequency, such as the truth of a proposition (e.g. "God exists"). Propositions are either true or they are false, so the only "long run frequencies" they could have would be 0 or 1 (but we don't know which). When frequentists answer questions about such events they are probably actually telling you a probability about some unspoken (probably fictional) population of events rather than the specific even that you are talking about, so that they can shoe-horn in a long run frequency somewhere.

However, people have always attached probabilities to things like the truth of a proposition, and in fact that was essentially the initial definition of a probability (the word-stem is the same as that for "aprobation"). However some statisticians didn't like the apparent subjectivity there so they invented frequentism, but at the cost of not being able to give a direct answer to many of the questions we want to ask.

So the other form of probability is "Bayesian" where probability is used as a measure of the state of knowledge regarding some event. This can be subjective, where we are using it to quantify our degree of subjective belief that the proposition is true. This is the most reasonable interpretation when we ask about the probability of God's existence. Note this doesn't require measurment - it just requires that we can order our probability judgements, e.g. the probability that God exists is less than the probability that a fair coin will give a head when it is next flipped, and a few other reasonable requiremnets. Bayes rule can be used to update our "prior belief" when we get "evidence" (according to the "likelihood" of the "evidence" under our model) to give us a "posterrior belief". Frequentists dislike this as they view the prior belief as being inherently subjective.

Bayesian probability can however be objective in the sense that our prior belief can be a reference state of knowledge (rather than what we personally believe), which often is that we know nothing, or we know some facts that everybody would agree with (such that the conclusion should not depend on units of measurement etc.).

"how should we determine whether or not something that has no independent evidence for it yet may still exist?"

we should use reason, which is what philosophers do.

Answer 2

Probability is explicitly intended for measuring the degree to which you don't know things. To say that the die will turn up 3 with probability 1/6 means that you don't know if it will turn up 3, but you think it won't, and the degree of your disbelief is measured by the number 1/6.

We can always assign subjective credences to any statement, including the statement that the die will turn into a butterfly. You can start by trying to quantify your "gut feeling" of how likely the statement seems to you, and you can improve on that number by comparing different ways the statement could be true or false and trying to make the number coherent with other probabilities you assign to different statements.

Think about designing a robot. The robot needs to assign probabilities to different propositions in order to make decisions and achieve its objectives, and for many of these propositions the robot has no clear way to calculate them. If the robot is delivering pizza, what's the probability there's a dangerous pothole around the next corner? The robot might need to estimate this to decide whether to slow down and how much. It's an unknown, unexpected event, but nonetheless a probability must be assigned.

So the robot has some internal algorithms that it uses to assign probabilities to different possible outcomes, allowing it to make decisions. These algorithms aren't necessarily mathematically precise and well-justified; they can be based on heuristics or based on training a neural network. But it needs them. We judge the quality of these algorithms based on how well the robot performs when it uses them. How often was the robot right or wrong, when relying on these algorithms? How often does it successfully deliver the pizza? Is there a different set of algorithms that would make the robot right more often?

It is the same for humans. We have cognitive methods that we use to assign probabilities to different statements, and if the cognitive methods are good in the sense of being more accurate than other methods and helping us to make decisions to achieve our goals effectively, then it is reasonable to accept the probabilities these methods produce, even if their results are not mathematically precise or completely coherent.

We can say, for example, that the chance the die turns into a butterfly is very low. Lower than 1%, for sure. How many dice have been rolled without turning into butterflies? Trillions, probably. So that would suggest the chance the die turns into a butterfly is less than 1 in a trillion.

We can also look at the laws of physics: if the die follows physics, what are the chances it suddenly turns into a butterfly? It's actually possible that it could, due to spontaneous quantum tunneling of the particles into a different arrangement, but the chances of that are unimaginably low, much lower than 1 in 10^(# of subatomic particles in the die). The chance that the die turns into a butterfly because the laws of physics are incorrect (and, perhaps, we live in a simulation and a simulation administrator is playing tricks) is much higher than the chance the die turns into a butterfly following the laws of physics.

So these are some methods we can use to assign a probability to the die turning into a butterfly. Any very small number, less than 1 in 10^12 (maybe a lot less), would be acceptable. And what we can say is good or bad is the cognitive method used to assign the number, rather than just the number itself.

Answer 3

In the absence of odds which can be explicitly calculated, you have to make observations in the course of performing experiments. So for example you collect a billion dice and watch them for several years to see how may of them turn into butterflies during that time. If none do, you have just determined a statistical bound on the probability of any single die converting into a butterfly. The longer you run the experiment, the lower the bound gets set.

Answer 4

Statistically, you count how often something could have happened, and how often it did happen, and based on these two numbers you can mathematically calculate a guess for the probability, and how confident you should be that your guess was correct.

Now if something doesn’t happen at all, you can decide that the probability is not large. Perform an experiment where X had 1,000 chances to happen but didn’t happen at all. You might for example decide that the probability is not less then 0.05 and be quite confident. A probability of 0.000001 is possible but would be difficult to justify.

Answer 5

When you talk about probability and measurement, you are inside mathematical context. Whatever lies outside this context cannot be evaluated as a measurement, at least in an objective way. For example in the dice example - by getting out of this context - the probability cannot be 1/6: since there always exist a possibility that the dice may never land you should account for this too.

Besides that, your question is basically related to causality. For example if in an experiment the result is that if you smoke there is a X% probability to die of cancer, that X is not a fact, or a truth if you like, but a number out of math calculations based on a "constructed" explanation of causality. What in fact is accounted for, in that experiment, is correlations; but the explanation of these correlations lie in our perspectives.

Answer 6

If it makes no sense to calculate it, how should we determine whether or not something that has no independent evidence for it yet may still exist? Should we dismiss them or what?

If a person has faith, and is not inconvened by it, they just keep it. If a person has no faith and is not inconvened by it, they keep the lack.

Since naturalistic science provided strong evidence for a narrative of nature that does not require a peeping grandfatherly type on a cloud punishing or rewarding behaviors, philosophy is not very concerned about gods anymore.

There are infinitely many things and entities that could exist, invisibly, unnoticeably, would you believe in all of them?

For those who still find this an interesting topic, there is plenty of literature pointing one way or the other, but don't expect any of it to be officially declared the ultimate truth by academia or the mainstream.