_Origin of the hypothesis._--In our analysis of the process of judgment, we attempted to show that the predicate arises in case of failure of some line of activity going on in terms of an established habit. When the old habit is checked through failure to deal with new conditions (_i. e._, when the situation is such as to stimulate two habits with distinct aims) the problem is to find a new method of response--that is, to co-ordinate the conflicting tendencies by building up a single aim which will function the existing situation. As we saw that, in case of judgment, habit when checked became ideal, an idea, so the new habit is first formalized as an ideal type of reaction and is the hypothesis by which we attempt to construe new data. In our inquiry as to how this formulation is effected, _i. e._, how the hypothesis is developed, it will be convenient to take some of the currently accepted statements as to their origin, and show how these statements stand in reference to the analysis proposed. _Enumerative induction and allied processes._--It is pointed out by Welton[73] that the various ways in which hypotheses are suggested may be reduced to three classes, viz., enumerative induction, conversion of propositions, and analogy. Under the head of "enumeration" he reminds us that "every observed regularity of connection between phenomena suggests a question as to whether it is universal." There are numerous instances of this in mathematics. For example, it is noticed that 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2, etc.; and one is led to ask whether there is any general principle involved, so that the sum of the first _n_ odd numbers will be _n_^2, where _n_ is any number, however great. In this early form of inductive inference there are two divergent tendencies. One is the tendency to complete enumeration. This _tendency_ is clearly ideal--it transcends the facts as given. To look for all the cases is thus itself an experimental inquiry, based upon a hypothesis which it endeavors to test. But in most cases enumeration can be only incomplete, and we are able to reach nothing better than probability. Hence the other tendency in the direction of an analysis of content in search for a principle of connection in the elements in any _one_ case. For if a characteristic belonging to a number of individuals suggests a class where it belongs to all individuals, it must be that it is found in every individual as such. The hypothesis of complete class involves a hypothesis as to the character of each individual in the class. Thus a hypothesis as to extension transforms itself into one as to intension.