Deductive Logic | Page 4

first case we study the human frame in order that we may
understand its structure; in the second that we may assist its needs.
Whether logic is a speculative or a practical science depends entirely
upon the way in which it is treated. If we study the laws of thought
merely that we may know what they are, we are making it a speculative
science; if we study the same laws with a view to deducing rules for the
guidance of thought, we are making it a practical science.
§ 24. Hence logic may be declared to be both the science and the art of
thinking. It is the art of thinking in the same sense in which grammar is
the art of speaking. Grammar is not in itself the right use of words, but
a knowledge of it enables men to use words correctly. In the same way
a knowledge of logic enables men to think correctly, or at least to avoid
incorrect thoughts. As an art logic may be called the navigation of the
sea of thought.
§ 25. The laws of thought are all reducible to the three following
axioms, which are known as The Three Fundamental Laws of Thought.
(1) The Law of Identity--
Whatever is, is;
or, in a more precise form,
Every A is A.
(2) The Law of Contradiction--
Nothing can both be and not be; Nothing can be A and not A.
(3) The Law of Excluded Middle--
Everything must either be or not be; Everything is either A or not A.

§ 26. Each of these principles is independent and self-evident.
§ 27. If it were possible for the law of identity to be violated, no
violation of the law of contradiction would necessarily ensue: for a
thing might then be something else, without being itself at the same
time, which latter is what the law of contradiction militates against.
Neither would the law of excluded middle be infringed. For, on the
supposition, a thing would be something else, whereas all that the law
of excluded middle demands is that it should either be itself or not. A
would in this case adopt the alternative of being not A.
§ 28. Again, the violation of the law of contradiction does not involve
any violation of the law of identity: for a thing might in that case be
still itself, so that the law of identity would be observed, even though,
owing to the law of contradiction not holding, it were not itself at the
same time. Neither would the law of excluded middle be infringed. For
a thing would, on the supposition, be both itself and not itself, which is
the very reverse of being neither.
§ 29. Lastly, the law of excluded middle might be violated without a
violation of the law of contradiction: for we should then have a thing
which was neither A nor not A, but not a thing which was both at the
same time. Neither would the law of identity be infringed. For we
should in this case have a thing which neither was nor was not, so that
the conditions of the law of identity could not exist to be broken. That
law postulates that whatever is, is: here we have a thing which never
was to begin with.
§ 30. These principles are of so simple a character that the discussion of
them is apt to be regarded as puerile. Especially is this the case with
regard to the law of identity. This principle in fact is one of those things
which are more honoured in the breach than in the observance. Suppose
for a moment that this law did not hold--then what would become of all
our reasoning? Where would be the use of establishing conclusions
about things, if they were liable to evade us by a Protean change of
identity?
§ 31. The remaining two laws supplement each other in the following

way. The law of contradiction enables us to affirm of two exhaustive
and mutually exclusive alternatives, that it is impossible for both to be
true; the law of excluded middle entitles us to add, that it is equally
impossible for both to be false. Or, to put the same thing in a different
form, the law of contradiction lays down that one of two such
alternatives must be false; the law of excluded middle adds that one
must be true.
§32. There are three processes of thought
(1) Conception.
(2) Judgement.
(3) Inference or Reasoning.
§ 33. Conception, which is otherwise known as Simple Apprehension,
is the act of forming in the mind the idea of anything, e.g. when we
form in the mind the idea of a cup, we are performing the process of
conception.
§ 34. Judgement, in the