Inductive reasoning

===Enumerative induction===
Enumerative induction is an inductive method in which a generalization is constructed based on the ''number'' of instances that support it. The more supporting instances, the stronger the conclusion.<ref name="dan" /><ref name="jm" />

The most basic form of enumerative induction reasons from particular instances to all instances and is thus an unrestricted generalization.<ref>{{cite book|last=Churchill|first=Robert Paul|title=Logic: An Introduction|publisher=St. Martin's Press|year=1990|isbn=978-0-312-02353-9|edition=2nd|location=New York|page=355|oclc=21216829|quote=In a typical enumerative induction, the premises list the individuals observed to have a common property, and the conclusion claims that all individuals of the same population have that property.}}</ref>  If one observes 100 swans, and all 100 were white, one might infer a probable universal [[categorical proposition]] of the form ''All swans are white''. As this [[argument form|reasoning form]]'s premises, even if true, do not entail the conclusion's truth, this is a form of inductive inference.  The conclusion might be true, and might be thought probably true, yet it can be false. Questions regarding the justification and form of enumerative inductions have been central in [[philosophy of science]], as enumerative induction has a pivotal role in the traditional model of the [[scientific method]].

:All life forms so far discovered are composed of cells.
:Therefore, all life forms are composed of cells.

This is ''enumerative induction'', also known as ''simple induction'' or ''simple predictive induction''. It is a subcategory of inductive generalization. In everyday practice, this is perhaps the most common form of induction. For the preceding argument, the conclusion is tempting but makes a prediction well in excess of the evidence. First, it assumes that life forms observed until now can tell us how future cases will be: an appeal to uniformity. Second, the conclusion ''All'' is a bold assertion. A single contrary instance foils the argument. And last, quantifying the level of probability in any mathematical form is problematic.<ref>Schaum's Outlines, Logic, pp. 243–35</ref> By what standard do we measure our Earthly sample of known life against all (possible) life? Suppose we do discover some new organism—such as some microorganism floating in the mesosphere or an asteroid—and it is cellular. Does the addition of this corroborating evidence oblige us to raise our probability assessment for the subject proposition? It is generally deemed reasonable to answer this question "yes", and for a good many this "yes" is not only reasonable but incontrovertible. So then just ''how much'' should this new data change our probability assessment? Here, consensus melts away, and in its place arises a question about whether we can talk of probability coherently at all with or without numerical quantification.

:All life forms so far discovered have been composed of cells.
:Therefore, the ''next'' life form discovered will be composed of cells.

This is enumerative induction in its ''weak form''. It truncates "all" to a mere single instance and, by making a far weaker claim, considerably strengthens the probability of its conclusion. Otherwise, it has the same shortcomings as the strong form: its sample population is non-random, and quantification methods are elusive.