st fruitful source of error.

[Footnote 1: Bain's _Logic_, bk. vi. chap. iii. Bacon intended
his _Idola_ to bear the same relation to his _Novum Organum_
that Aristotle's Fallacies or Sophistical Tricks bore to the
old Organum. But in truth, as I have already indicated, what
Bacon classifies is our inbred tendencies to form _idola_ or
false images, and it is these same tendencies that make
us liable to the fallacies named by Aristotle. Some of
Aristotle's, as we shall see, are fallacies of Induction.]

[Footnote 2: Bagehot's _Literary Studies_, ii. 427.]

III.--THE AXIOMS OF DIALECTIC AND OF SYLLOGISM.

There are certain principles known as the Laws of Thought or the
Maxims of Consistency. They are variously expressed, variously
demonstrated, and variously interpreted, but in one form or another
they are often said to be the foundation of all Logic. It is even said
that all the doctrines of Deductive or Syllogistic Logic may be educed
from them. Let us take the most abstract expression of them, and see
how they originated. Three laws are commonly given, named respectively
the Law of Identity, the Law of Contradiction and the Law of Excluded
Middle.

1. _The Law of Identity._ A is A. Socrates is Socrates. Guilt is
guilt.

2. _The Law of Contradiction._ A is not not-A. Socrates is not other
than Socrates. Guilt is not other than guilt. Or A is not at once _b_
and not-_b_. Socrates is not at once good and not-good. Guilt is not
at once punishable and not-punishable.

3. _The Law of Excluded Middle._ Everything is either A or not-A;
or, A is either _b_ or not-_b_. A given thing is either Socrates
or not-Socrates, either guilty or not-guilty. It must be one or the
other: no middle is possible.

Why lay down principles so obvious, in some interpretations, and so
manifestly sophistical in others? The bare forms of modern Logic have
been reached by a process of attenuation from a passage in Aristotle's
_Metaphysics_[1] (iii. 3, 4, 1005_b_ - 1008). He is there laying down
the first principle of demonstration, which he takes to be that "it is
impossible that the same predicate can both belong, and not belong,
to the same subject, at the same time, and in the same sense".[2]
That Socrates knows grammar, and does not know grammar--these two
propositions cannot both be true at the same time, and in the same
sense. Two contraries cannot exist together in the same subject. The
double an