Editing Statistical syllogism (section)

==Introduction==

[[Statistics|Statistical]] syllogisms may use [[Grammatical modifier|qualifying]] words like "most", "frequently", "almost never", "rarely", etc., or may have a statistical generalization as one or both of their premises.

''For example:''

#Almost all people are taller than 26&nbsp;inches
#Gareth is a person
#Therefore, Gareth is taller than 26&nbsp;inches

Premise 1 (the major premise) is a [[generalization]], and the argument attempts to draw a conclusion from that generalization. In contrast to a deductive syllogism, the premises logically support or confirm the conclusion rather than strictly implying it: it is possible for the premises to be true and the conclusion false, but it is not likely.

''General form:''

#X proportion of F are G
#I is an F
#I is a G

In the abstract form above, F is called the "reference class" and G is the "attribute class" and I is the individual object. So, in the earlier example, "(things that are) taller than 26 inches" is the attribute class and "people" is the reference class.

Unlike many other forms of syllogism, a statistical syllogism is [[inductive reasoning|inductive]], so when evaluating this kind of argument it is important to consider how [[Inductive reasoning#Strong and weak induction|strong or weak]] it is, along with the other rules of induction (as opposed to [[Deductive reasoning|deduction]]). In the above example, if 99% of people are taller than 26 inches, then the probability of the conclusion being true is 99%.

Two ''[[dicto simpliciter]]'' fallacies can occur in statistical syllogisms. They are "[[accident (fallacy)|accident]]" and "[[converse accident]]". [[Faulty generalization]] fallacies can also affect any argument premise that uses a generalization. A problem with applying the statistical syllogism in real cases is the [[reference class problem]]: given that a particular case I is a member of very many reference classes F, in which the proportion of attribute G may differ widely, how should one decide which class to use in applying the statistical syllogism?

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. For example, when taking off in an airplane, our confidence (but not certainty) that we will land safely is based on our knowledge that the vast majority of flights do land safely. 
 
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."''<ref>Cox DR, Hinkley DV. (1974) Theoretical Statistics, Chapman & Hall, pp. 49, 209</ref> The inference from what would mostly happen in multiple samples to the confidence we should have in the particular sample involves a statistical syllogism.<ref>{{cite journal |last1=Franklin |first1=James |author-link1=James Franklin (philosopher) |date=1994 |title=Resurrecting logical probability |url=https://web.maths.unsw.edu.au/~jim/erkenntnis.pdf |journal=Erkenntnis |volume=55 |issue= 2|pages=277–305 |doi= 10.1023/A:1012918016159|s2cid=130621 |access-date=30 June 2021}}</ref> One person who argues that statistical syllogism is more of a probability is Donald Williams.<ref>{{Cite journal|last=Oliver|first=James Willard|date=December 1953|title=Deduction and the Statistical Syllogism|url=https://www.pdcnet.org/jphil/content/jphil_1953_0050_0026_0805_0807|journal=Journal of Philosophy|volume=50|issue=26 |pages=805–806|doi=10.2307/2020767 |jstor=2020767 |url-access=subscription}}</ref>