Latin word for "decided dichotomous possibility"

Question

Suppose you have a fair coin. Then tossing it has two possible outcomes: heads and tails. These are equally likely.

One of these possibilities must occur (assuming that the coin doesn't land on its side)

Before you flip the coin, these possibilities are undecided. If you flip the coin without looking at the result, then the outcome is decided, but which of the two possibilities has occurred is still unknown.

Thus one type of possibility is present or decided, while another is future or undecided.

The result of the coin toss is also such that exactly one outcome must be the case. In other words, one of the outcomes must occur (assuming the coin doesn't land on its side), but both of them cannot occur. It can therefore be said that the possibilities are dichotomous.

Is there a Latin word or phrase meaning decided dichotomous possibility (such as the result of a coin toss before you look at it)?

Answer 1

My initial, extremely rough idea is an adaptation of a phrase from Cicero's Pro Marcello 15:

ex quo nemo erit tam iniustus rerum existimator qui dubitet quae Caesaris de bello voluntas fuerit, cum pacis auctores conservandos statim censuerit, ceteris fuerit iratior. Atque id minus mirum fortasse tum cum esset incertus exitus et anceps fortuna belli: qui vero victor pacis auctores diligit, is profecto declarat maluisse se non dimicare quam vincere.

Here, Cicero says that the actual outcome (of war) isn't decided (incertus exitus) and the side that fortune favors is either one or the other of two but still up in the air (fortuna anceps). In the case that he describes, those two circumstances are broadly equivalent or coextensive. In your case, though, the outcome is decided but the side that fortune favors is still up in the air. So we could say certus exitus sed anceps fortuna.

Or perhaps the two ideas could be combined into a single noun phrase such as certus exitus ancipitis fortunae – or maybe that should be anceps fortuna certi exitus? or maybe anceps fortuna in certo exitu or certus exitus in ancipiti fortuna? Or maybe use an ablative absolute for one of the ideas?

Thoughts?

Answer 2

Latin does indeed have the adjective dichotomos, but the meaning is different from English. It means "split in two" or "halved". It is quite common that concrete things in Greek and Latin have been borrowed to other languages as abstract concepts, and as a consequence distinguishing levels of abstraction is harder in Latin than in English. For example, you might have hard time articulating the difference between "pulling away" and "abstracting" in Latin.

The best adjective I could think of to communicate the dichotomous nature here is binarius, meaning roughly "consisting of two". The Greek loan dichotomos is also possible, but I find myself preferring binarius, perhaps for being more Latin.

Latin has the word possibilitas, but it means "ability or power to do something", not "chance of something happening". While it is an obvious etymological predecessor of "possibility", it looks like a bad translation. The word probabilitas is much closer, although it does have the flavor of "credibility" as well. This noun comes from probare ("to probe", if you will) and can be seen "examinability". This sounds reasonable for your purposes, especially since it is about the revelation of a decided random event.

For "decided" I would use some variant of the participle factum, meaning "done", "that which has happened", or similar.

With these ingredients, I suggest probabilitas binaria facti, roughly "two-pieced probability of what has happened". Of course no translation can exactly capture the naturalness (or lack thereof) of the Latin phrase, but I hope my explanation gives you an idea.