Armchair Philosophy #1 - Not Everything Is Possible

The universe is vast, and our knowledge of it, infinitesimally small. Our intuitions say, "Who are we to claim then, that something isn't possible?" If we know next to nothing, then isn't claiming something is impossible arrogant and small-minded?

My argument hopes to convince you of two things:

1. There are things that are not possible
2. Saying that everything is possible undermines scientific progress

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Definitions

Let's dive into some definitions.

We're going to start with the obvious one:
Possible - able to be done; within the power or capacity of someone or something.

Alright. Easy enough. Now we're going to dive a little deeper into the four different positions related to knowledge and a claim. Hopefully I don't lose anyone here, because this part is very important.

We have two dichotomies - claim (on whether or not something is possible) and claim of knowledge (on whether or not knowledge is claimed about whether or not something is possible).

For those keeping track, this effectively gives us three positions:

1. Claim knowledge that something is possible
2. Claim knowledge that something is impossible
3. Do not claim knowledge on whether or not something is possible

It is important to note that position three does not require a justification. Justifications are needed for claims. Therefore not claiming something, requires no justification.

It is also important to note that saying something is possible is a claim (just as saying something is impossible is a claim). Therefore, these positions require justification.

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Experiments

Alright, now on to some experiments. In these experiments, we'll be using some pretty basic set theory to underpin everything.

Experiment 1: Rolling a die

You have a single, normally-numbered, fair, cubed die which can be represented by the set [1, 2, 3, 4, 5, 6].

Is it possible to roll a 2?

Is it possible to roll a 6?

Is it possible to roll a 7?

No, I'm not trying to trick you. The answers should be very straightforward, and yes the answer to the third question is no. But, hold on. What if we had an infinite number of rolls? Then would it be possible for any single roll to be 7?

Hopefully, you see that this doesn't change anything. The answer will always be that it is impossible. In order for it to become possible, one or more of the setup criteria would have to be false which would result in a different set of possible values.

Experiment #2: Placing a die inside a small, opaque bag

You place the die from the previous experiment inside a bag.

Is it possible (if you emptied the contents of the bag onto a tabletop) to roll a 16?

The answer to this might be a little less obvious. Sure, it's possible, you might think. But what if, I were to empty the contents of the bag, and there was only the single die I had placed in it initially? Was it actually possible?

The answer is no. So if you had claimed that, because the contents of the bag were unknown, it was possible to roll a 16, you would have been wrong.

So what is the answer? Well, it's pretty straightforward. Until more information is known about the contents of the bag, the only honest answer is 'I don't know.'

Notice that doing the experiment an infinite number of times doesn't change the answer to this experiment either.

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Takeaway

So where am I going with all this?

Well, there are topics for which there is a clear scientific consensus where at one point in the past, the scientific consensus was something contradictory. There are numerous examples of this across different fields. One example comes from the major paradigm shifts in physics. First, there was Aristotle's work. This was then supplanted by Newton's work (classical mechanics), which was then supplanted again by Einstein's work (relativity). Since then, we've once again updated the consensus to quantum mechanics.

So is science ever 100% right? No, most likely not. But that's okay. It is often people's intuition that because science does not claim to have 100% correct answers, all answers become valid. This ignores the fact that new models of the world still need to be able to explain the current body of evidence. Therefore, any new theory will simply give a clearer picture of the truth than before.

In other words, just because Newton disproved parts of Aristotle's work, and Einstein disproved parts of Newton's work, that doesn't mean that maybe gravity doesn't exist at all, and we all stay on the surface of the earth because Achmed the Space Dragon gets mad if the ground lets go of our feet for too long.