Actually, you're wrong. There's a 0.00000000000000000001 percent chance someone invented a time-freezing machine, and decided to "bring" a couple hundred or so people with him into this technically new world of frozen time. And decided to swap out every single die mid-roll with a die that has a number 7 instead of 6. Just to mess with people who go on about probability. Kudos to them. It's unlikely, to say the least. But it's not impossible, so technically, you cannot say never nor always...

To summarize, two words - "never" and "always" - that are about absolute certainty are used to full effect, in complete accordance with their definitions, without the slightest change, in a domain about uncertainty. Paradox? Or is this a case of "this is not even wrong"? — TheMadFool

Never and always only work within a specific framework, because things are inconstant flux in the whole. So, if you define your world as having the only the numbers 1 and 2, then never 3. In the entire mathematical system, this would not apply as Outlanders' example revels.

If you want to get picky, then you can get rid of 2 as well (even in your closed system) as it is fairly easy to make the case that there is no such thing as 2 (all things being unique).

It's thinking, you can do whatever you want.

You’ve set the limitations - ‘never’ and ‘always’ - by using a six-sided die. Take away these imposed limitations, and uncertainty returns.

You’ve set the limitations - ‘never’ and ‘always’ - by using a six-sided die. Take away these imposed limitations, and uncertainty returns. — Possibility

I was just wondering at the way the notion of absolute certainty is part of a subject dedicated to uncertainty. To me, that's like describing theism as a position in atheism. It seems odd that we can describe good as a variety/strain of bad. That's what I mean.

Requesting @Wayfarer to look into this and share his thoughts provided that Wayfarer remembers the discussion we had: Is Quality An Illusion?.

There seems to be something fishy going on here but I can't quite put a finger on it. @Wayfarer@Possibility any luck?

Likewise, what's the probability of getting a number between 1 and 6, inclusive? Why, that would be 100% — TheMadFool

Not quite. There is an extremely small probability the die will end up balanced on an edge. Or that as you toss the die a meteor will crash into your home and blow everything to smithereens. Or any number of other weird things. A bit like Feynman with his path integral where he is tasked with computing a quantity for every possible path between points a and b.

But I didn't mean to interrupt the flow of your argument.

Not quite. There is an extremely small probability the die will end up balanced on an edge. Or that as you toss the die a meteor will crash into your home and blow everything to smithereens. — jgill

If the question were, in a universe with a lot of floating rocks - you throw a six sided dice, what are the odds of getting hit by an asteroid in the moment before it falls, the odds are very small, but if they're not zero, where does it end? A confused Llama escaped from the zoo could run in and swallow the dice! A time traveller from the future could materialise in a ball of light that vaporises the dice. A world war two explosive buried in the foundation of the building could explode - and destroy the dice. And so on and on, and adding a presumably infinite number of infinitesimally small chances together, once one starts down that road, one must eventually conclude that there's almost zero probability of a result between 1 and 6!

We all know what probability is — TheMadFool

I'd dispute that.

Always and never are words/concepts that apply to other concepts that within the ambit of their usage(s) can be always or never. That is, the words are tools in a sense. Probability another word/concept/tool with it's own proper and correct usages. Before using words, it's good to give thought to how each is used, just as in using tools it's good to give thought to which is the right tool for the job. And most of the time in most cases that thinking and checking is done more than adequately for most purposes. But to look at screwdriver and wonder why it's not a wrench is a sign of confusion.

Aristotle covered this:
"Our discussion will be adequate if it has as much clearness as the subject-matter admits of, for precision is not to be sought for alike in all discussions, any more than in all the products of the crafts. Now fine and just actions, which political science investigates, admit of much variety and fluctuation of opinion, so that they may be thought to exist only by convention, and not by nature. And goods also give rise to a similar fluctuation because they bring harm to many people; for before now men have been undone by reason of their wealth, and others by reason of their courage. We must be content, then, in speaking of such subjects and with such premisses to indicate the truth roughly and in outline, and in speaking about things which are only for the most part true and with premisses of the same kind to reach conclusions that are no better. In the same spirit, therefore, should each type of statement be received; for it is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits; it is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician scientific proofs."

Not quite. There is an extremely small probability the die will end up balanced on an edge. Or that as you toss the die a meteor will crash into your home and blow everything to smithereens. Or any number of other weird things. A bit like Feynman with his path integral where he is tasked with computing a quantity for every possible path between points a and b.

But I didn't mean to interrupt the flow of your argument. — jgill

I'm considering the ideal scenario but point noted. Nevertheless, even such outcomes could be included into the possibility space and we could think of a behavior impossible for the die. Can you think of anything? I'm all out.

I'd dispute that. — fishfry

A very basic understanding of probability should suffice for the discussion, no? and that doesn't seem to be beyond the kin of the average person like me.

But to look at screwdriver and wonder why it's not a wrench is a sign of confusion. — tim wood

Are you saying I'm a victim of Moha? How so? Can you tell me more? Is it not true that if I frame atheism as the probability of god's nonexistence, theists would be atheists who think or believe that that probability is 0%. I could be a full-blown case of a religious nut as some theists are referred to but could, without any contradiction, claim myself to be an atheist who believes that god doesn't exist but the probability of that is 0%. Is this a case of mere word play or is there something deeper going on?

You’ve set the limitations - ‘never’ and ‘always’ - by using a six-sided die. Take away these imposed limitations, and uncertainty returns.
— Possibility

I was just wondering at the way the notion of absolute certainty is part of a subject dedicated to uncertainty. To me, that's like describing theism as a position in atheism. It seems odd that we can describe good as a variety/strain of bad. That's what I mean. — TheMadFool

Probability is not really about uncertainty, per se. Potentiality is about uncertainty. Probability is a solution to, or consolidation of, uncertainty - it quantifies and then reduces all potentiality to a single value: between a 0 limit of ‘never’ and a 1 limit of ‘always’. In doing so, it ignores, isolates or excludes qualitative potentiality, or any possibility that cannot be quantified.

I was just wondering at the way the notion of absolute certainty is part of a subject dedicated to uncertainty. To me, that's like describing theism as a position in atheism. It seems odd that we can describe good as a variety/strain of bad. That's what I mean. — TheMadFool

Yeah, but that's not what we have here, really.

To calculate probability, you need two things:

A random variable, and assumptions about its distribution.

A random variable is by it's nature uncertain, but it's only uncertain within the limits of a well-defined distribution. Or differently put, both certainty and uncertainty collaborate probability. Without any certainty you're just left with pure uncertainty - there's no probability, no way to calculate it.

Note that this only applies to the math. Real world (un)certainty is irrelevant for the calculation. You can calculate the likelihood of a known outcome just as well as that of an unknown outcome, as long as you decide which of your variables is random, and how it's distributed.