The lack of evidence that something is impossible does not constitute evidence that it is possible. This also means that it is incorrect to consider something possible just because there is a lack of evidence that it's impossible.

The argument is presented in the form of a fun little dialogue (credit to Tracie Harris). I invite you to read along, imagining that you are one of the parties (doesn't matter which one).

A: I hold in my hand a standard & normal six-sided die. Have you ever seen or used dice like this before?

B: Yes, I am familiar with six-sided dice. You roll it and the number showing on top once it stops moving is the number you get, or "rolled".

A: Good. Based on what you know about such dice, is it possible to roll a 4?

B: Yes.

A: How do you know that?

B: Because we know that there are six sides, and that any of them could possibly come up when the die is rolled. I've rolled and seen others roll a 4 in the past.

A: Alright. Is it possible to roll a 5?

B: Yes, for the same reasons.

A: Sure, and it's possible to roll a 7 too, right?

B: No.

A: Why is that not possible?

B: Because there are only 6 sides, labelled 1-6, a roll of 7 would require rolling more than one six-sided dice.

A: Ok, well then let's try this another way. I have here this small coin purse/bag. Do you know or can you see what's in the bag?

B: No, I don't. You just pulled it out of your pocket.

A: Good. Now watch, as I take the six-sided die and put it in the bag. You are now unable to see the die, and the contents of the bag remain hidden.

B: Ok.

A: Now, is it possible to roll an 18 with whatever is in this bag?

B: I don't know.

A: Well, if you don't know, then it must be possible.

B: No, not necessarily.

A: Why not?

B: Because for all I know it could just be the one die in the bag, and the possible outcomes for a single die are only 1-6.

A: But this bag is big enough to hold at least 3 dice, in which case a roll of 18 is possible. So is it possible to roll an 18 with what's in this bag?

B: Well, I don't know what's in the bag apart from the 1 die I saw you put in, so I can't say that it's possible to roll an 18 with what's in the bag. What I could say is that if there were 3 dice in the bag, then it would be possible to roll an 18 with what's in the bag.

A: Ok, so not knowing doesn't mean that it's possible?

B: Correct. Not knowing also means that I can't say it's impossible.

A: Oh? Well, if it's not impossible, then surely it must be possible.

B: Again, not necessarily. While it might make sense to someone with the same information to say that since the bag is big enough to hold at least 3 dice, that it's possible to roll an 18 with the contents of the bag, they wouldn't be justified in believing or claiming that it's actually possible to roll an 18, because they don't know whether there are 3 dice in the bag.

A: But if you don't know whether there are 3 dice in the bag, how can you say that there aren't 3 dice in the bag?

B: I'm not claiming that there aren't 3 dice in bag, just that there's no reason to think that there are.

A: Ok. So, since you don't know how many dice are in the bag, there could be tons of them - hundreds even, right?

B: Uhh no, there couldn't be hundreds of dice in the bag.

A: But you just admitted you don't know how many are in there, so how can you say it's not possible for there to be hundreds?

B: Well, assuming we're talking about dice of the size you showed me, and judging by the size of the bag, then I can still estimate that you couldn't fit hundreds of them in that bag.

A: And you base that on what you know about the apparent volume of the bag and the approximate volume required to fit hundreds of dice?

B: Yes.

A: Ok. So somebody might say that it's possible to roll an 18 with the contents of the bag because we don't know what's in the bag, but you're saying they're not justified in claiming that.

B: Yes.

A: Alright, let me just open the bag and dump the entire contents out onto the table here. There, now the bag is empty, and we can see that 2 dice have dropped out of the bag onto the table.

B: Yes, I see just two dice have dropped from the bag.

A: So if somebody would say that it's possible to roll and 18 with the contents of the bag, they would, in fact, be wrong?

B: Yes. And it's not just a matter of them possibly being wrong when they said that, it's a matter of them actually having been wrong when they said it was possible, because it was actually impossible already when they said it?

A: Right, so it seems that what they were doing is calling something which is impossible, possible, is that right?

B: It would seem that's what they did, yes.

A: But you didn't do that. You said that it wasn't possible, but you also said that it wasn't impossible, even though we know that it was impossible.

B: That's right. Since I didn't have enough information at the time to determine whether it was possible or impossible, the logically correct choice for me was to conclude that I didn't know whether it was possible or impossible, and reject your claim that it was possible. To make such a claim is to commit an argument from ignorance fallacy, which is a situation where someone doesn't have information about something, but they say that because there's no reason to think it's false, they go ahead and claim it's true. But as we just learned, that can lead to incorrect conclusions.

A: But I didn't say it was true, I said it was possible.

B: Oh sure, but that just means you're claiming it's true that it is possible.

A: Okay, but what if there turned out to be 3 dice in the bag? Then it would be correct to say that it's possible to roll an 18, right?

B: It would be correct to say so only after you have the information, not before. Just happening to be right after the fact doesn't make it rational to claim something before the facts are known.

So that's it. I'm interested in hearing your thoughts. I think it's is a great exercise for teaching youngsters how to correctly apply rational skepticism, and can be modified for various apparatus (socks & marbles, pockets & cards).

If anyone would like to argue that since something hasn't been proven to be impossible it therefore is or even just should be considered possible, I'll gladly discuss the matter in the context of the above scenario, but only after you correctly identify each separate instance of the argument from ignorance within the dialogue.

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