e, or in a mild form, or in
somewhat similar yet different circumstances, can be considered
logically conclusive. What proofs are conclusive we shall see in the
following chapters.

Sec. 2. To begin with the conditions of direct Induction.--An Induction is
an universal real proposition, based on observation, in reliance on the
uniformity of Nature: when well ascertained, it is called a Law. Thus,
that all life depends on the presence of oxygen is (1) an universal
proposition; (2) a real one, since the 'presence of oxygen' is not
connoted by 'life'; (3) it is based on observation; (4) it relies on the
uniformity of Nature, since all cases of life have not been examined.

Such a proposition is here called 'an induction,' when it is inductively
proved; that is, proved by facts, not merely deduced from more general
premises (except the premise of Nature's uniformity): and by the
'process of induction' is meant the method of inductive proof. The
phrase 'process of induction' is often used in another sense, namely for
the inference or judgment by which such propositions are arrived at. But
it is better to call this 'the process of hypothesis,' and to regard it
as a preliminary to the process of induction (that is, proof), as
furnishing the hypothesis which, if it can stand the proper tests,
becomes an induction or law.

Sec. 3. Inductive proofs are usually classed as Perfect and Imperfect.
They are said to be perfect when all the instances within the scope of
the given proposition have been severally examined, and the proposition
has been found true in each case. But we have seen (chap. xiii. Sec. 2)
that the instances included in universal propositions concerning Causes
and Kinds cannot be exhaustively examined: we do not know all planets,
all heat, all liquids, all life, etc.; and we never can, since a man's
life is never long enough. It is only where the conditions of time,
place, etc., are arbitrarily limited that examination can be exhaustive.
Perfect induction might show (say) that every member of the present
House of Commons has two Christian names. Such an argument is sometimes
exhibited as a Syllogism in Darapti with a Minor premise in U., which
legitimates a Conclusion in A., thus:

A.B. to Z have two Christian names;
A.B. to Z are all the present M.P.'s:
.'. All the present M.P.'s have two Christian names.

But in such an investigation there is no need of logical method to find
the major premi