[V]ague terms like “probably” and “likely” make it impossible to judge forecasts. When a forecaster says something could or might or may happening, she could or might or may be saying almost anything.

[T]here is a connection between the supervaluational approach to vague probability […] and Pascal’s own argument. For Pascal was doing something analogous to supervaluating: the conclusion that one should believe that God exists is supposed to come out true for every probability function (except of course the strict atheistic ones that assign zero to God’s existence) It is presumably in the spirit of Pascal to think of these as different sharp probability functions belonging to different people; but we might equally think of them as different precisifications of the vague opinion of a single person. And just as the strict atheistic probability functions pose a problem for Pascal, so too do the strict atheistic precisifications of a vague opinion concerning God.

If the word ‘liberty’ has any definite sense attached to it, and if it is consistently used in this sense, it is almost impossible to make any true general assertion whatever about it, and quite impossible to regard it either as a good thing or a bad one. If, on the other hand, the word is used merely in a general popular way without attaching any distinct signification to it, it is easy to make almost any general assertion you please about it; but these assertions will be incapable of either proof or disproof as they will have no definite meaning. Thus the word is either a misleading appeal to passion, or else it embodies or rather hints at an exceedingly complicated assertion, the truth of which can be proved only by elaborate historical investigations.

The law of excluded middle is true when precise symbols are employed, but it is not true when symbols are vague, as, in fact, all symbols are.