The importance of the statistical syllogism was urged by Henry E. Kyburg, Jr., who argued that all statements of probability could be traced to a direct inference.
The widespread use of confidence intervals in statistics is often justified using a statistical syllogism, in such words as "Were this procedure to be repeated on multiple samples, the calculated confidence interval (which would differ for each sample) would encompass the true population parameter 90% of the time.
"[4][5] The ancient Jewish law of the Talmud used a "follow the majority" rule to resolve cases of doubt.
He writes, “It is obvious that every single thing or event has an indefinite number of properties or attributes observable in it, and might therefore be considered as belonging to an indefinite number of different classes of things”, leading to problems with how to assign probabilities to a single case, for example the probability that John Smith, a consumptive Englishman aged fifty, will live to sixty-one.
The statistical syllogism was used by Donald Cary Williams and David Stove in their attempt to give a logical solution to the problem of induction.
For example, in L. Jonathan Cohen's "gatecrasher paradox", 499 tickets to a rodeo have been sold and 1000 people are observed in the stands.