The phrase 'live possibility' is correct and can be used in written English.
It is often used to describe an event or possibility that is still possible, such as something that may happen in the future. For example: "The chance of winning the lottery is still a live possibility."
"That is a live possibility," Mr. Capra said.
It is a live possibility, but let's see what the data shows".
Core inflation near zero, or even negative, is a live possibility for 2010 or 2011.
"You have the live possibility that this accident was inevitable and foreseeable," Mr. Brodsky said.
The second option seemed relatively unlikely a week ago, but now — in the House especially — it looks like a live possibility.
"If the incoming information supports that expectation, then our statement indicates that December would be a live possibility, but, importantly, that we have made no decisions about it".
For indicative conditionals, antecedents are typically live possibilities, and we focus on that case.
Stalnaker calls the set of worlds which are not ruled out — the live possibilities — the context set.
Then, The parameter \(X\) in the above definitions is intended to represent the set of strategy profiles that the player \(i\) take to be "live possibilities".
But these are very early days yet, so results should be taken only as illustrative of the space of live possibilities rather than as indicative of what pleasure is.
For instance, in asserting 'It'll be very cold today' to a group of Melburnians, I exploit background knowledge of local weather conditions in June to get my audience to accept that the temperature outside is somewhere between 5 10° C, ruling out live possibilities that it might be in the 15 20° C range.
