I am looking to find the difference between possible and plausible.
Here is what Apple's dictionary gives for each word:
Possible: Able to be done; within the power or capacity of someone or something
Plausible: (of an argument or statement) seeming reasonable or probable
I mean, other than these definitions, are there any connotative differences?
You can define something possible in mathematical terms as having a non-zero probability of being true.
As for plausible, the concept does not draw on mathematics but rather on mere common sense. The etymology is the same as applause. Something is plausible if it's acceptable (loosely: if it deserves applause). That is to say if its probability is reasonable.
If you add probable and likely in the equation, you can order theses adjectives by ascending probability as follows:
possible => plausible => probable = likely.
I think the easiest way to think about the difference is this: if something is possible it might be true; if it is plausible it sounds like it might be true.
To me, plausible is something that is explainable, while things that are possible but implausible would surprise me.
I wouldn't be surprised if a plausible event occurred, but I could take notice if a possible event happened that was implausible because it was caused by an absurd chain of events.
(Your mileage may vary on the threshold level of reason or probability that goes into either word. For example, my physics friends could say that due to quantum weirdness, anything is possible – it just may take trillions of years before you'd expect to see it happen. But most people would object to this and argue that the scope of possible should be limited to Newtonian physics.)
Plausible is referred to an explanation, an argument, or a statement, while possible is referred to a fact, or an event.
For example, my explanation on how in future time traveling will be possible could be plausible, but that doesn't mean traveling through time will be possible.
