The different signs on a die are incommensurables (amorphous, or exhaustively mutually exclusive), and as such are not summatable as “6”. In other words, when we calculate the chance of a sign or numeral (“number”) coming up on the throw of a die, then, we are no longer treating the signs as incommensurables - this is because we are using the number “6” as a summation of the signs to help us with the calculation.

But there can be no summation of incommensurables.

So I suggest by way of a “thought experiment” that we find the chances of a sign coming up on the throw of a die but that we do so only in terms of the signs that are already there, and not in terms of an entirely new sign that is a sum and is called “6”.

Such a procedure, if possible, would show, I think, that there are no chances of any sign or numeral coming up on a thrown die that is taken purely from a property of the die. This is not a mathematical hypothesis.

The different signs on a die are incommensurate, but still summatable. This is because all of the signs have in common the property of being a number. All numbers are summatable. (…That’s why we call them “numbers”).

Practically speaking, I’m glad you’re not offering this as a mathmatical hypothesis.
Theoretically speaking, I hope you are not suggesting that different numbers have different ontological statuses—and hence are not summatable.

Hmm this is interesting, are you saying jj, that the numbers on the sides mean nothing, that the only valid realism of the die is that it has 6 sides. Naturally that it does have six sides makes it summatable irrespective of the symbols on each side. Nevertheless, what we denote as numbers 6 or 1 and thence any in-between are meaningless e.g. what side do we begin or end with ~ we have to presume a random side as denoting the sixth or first sides, so as to make calculations apart from random variations of 6.

You could make calculations that by having six sides there would be a probability of the die landing on sides x,y,z, but if the die was a sphere the numbers would mean nothing et al.

Yes, it has no bearing on the probabilities.
We manufacture an entirely new object to calculate a probability. That new object is the die and its orientation to another object, in this case, our eyes or line of vision.

So I repeat. Incommensurables - meaningless marks on a die - are neither summatable (as “6”) nor partake in any calculation of probability.

A revision would be too soon.
The marks on a die are simply that - marks, or numerals. They become a number when they are sequenced. But there is nothing in the die that suggests a sequence.

Yes, the numerals on the side mean nothing (they are not numbers). The die also does not have six sides. This might sound strange, but a die only has six sides if the die is placed in another domain where a count can be made, such as handling or seeing a die.

If the sides are indistinguishable, then how do you count them without imposing some sort of exteriorised mark upon them?

Of course. A numeral is simply a mark that we call “number”.
But a number proper arises through a calculus or calculation of some sort, such as being a member of a sequence.
The distinction is a natural one to make.

A count must be enabled, and to be enabled we must first establish differences. If the sides of a die have different signs then we must be able to see that they are different. To do that we must place the die in a system that can establish differences. This system need not be psychological or needing “someone to count”.

Well, sure - the sides can be plotted on a graph. As long as we can tell one side from another - that is, as long as we can discern their relative location, we can distinguish the sides. We don’t have to actually count them at all.

At some point we have to know when we have finished counting the marks on the sides, for the sides won’t tell us, neither will the marks. Some marks may be doubled or tripled - how would we know?

Ummm…okay. We don’t need the marks. While co-ordinates are numbers, we can discern the sides with co-ordinates alone. The North Pole doesn’t have a big “N” on it.

faust, why are you even trying?
this guy is saying that you can’t calculate the probability of rolling a particular side of a die.
what do you think you can convince him of?
he’s bonkers man.
nuts.
wacko.
beyond redemption.