Bibliography

On the Natural Classification of Arguments

The formula of analogy is as follows:-

S’, S”, and S”’ are taken at random from such a class that their characters at random are such as P’, P”, P”’.
t is P’, P”, and P”’.
S’, S”, and S”’ are q;
.·. t is q.

Such an argument is double. It combines the two following:-

1

S’, S”, S”’ are taken as being P’, P”, P”’.
S’, S”, S”’ are q.
.·. (By induction) P’, P”, P”’ is q.

t is P’, P”, P”’.
.·. (Deductively) t is q.

2

S’, S”, S”’ are, for instance, P’, P”, P”’.
t is P’, P”, P”’;
.·. (By hypothesis) t has the common characters of S’, S”, S”’.

S’, S”, S”’ are q.
.·. (Deductively) t is q.

Owing to its double character, analogy is very strong with only a moderate number of instances.

…every argument has, as portion of its leading principle, a certain principle which cannot be eliminated from its leading principle. Such a principle may be termed a logical principle.

An argument whose leading principle contains nothing which can be eliminated is termed a complete, in opposition to an incomplete, rhetorical, or enthymematic argument.

Hence the formulæ are [—]

Hypothesis

Any M is, for instance, P’ P” P”’, &c.,
S is P’ P” P”’, &c.;
.·. S is probably M.

Hence the formulæ are

Induction
S’ S” S”’, &c. are taken at random as M’s,
S’ S” S”’, &c. are P;
.·. Any M is probably P.

Induction may, therefore, be defined as argument which assumes that a whole collection, from which a number of instances have been taken at random, has all the common characters of those instances …

…every argument has, as portion of its leading principle, a certain principle which cannot be eliminated from its leading principle. Such a principle may be termed a logical principle.

An argument whose leading principle contains nothing which can be eliminated is termed a complete, in opposition to an incomplete, rhetorical, or enthymematic argument.

Since it can never be requisite that a fact stated should also be implied in order to justify a conclusion, every logical principle considered as a proposition will be found to be quite empty. Considered as regulating the procedure of inference, it is determinate; but considered as expressing truth, it is nothing.