⁂ This Tract contains no more than the author has found, from
experience, to be much wanted by students who are commencing with
Euclid. It will ultimately form an Appendix to his Treatise on
Arithmetic.
The author would not, by any means, in presenting the minimum necessary
for a particular purpose, be held to imply that he has given enough of
the subject for all the ends of education. He has long regretted the
neglect of logic; a science, the study of which would shew many of its
opponents that the light esteem in which they hold it arises from those
habits of inference which thrive best in its absence. He strongly
recommends any student to whom this tract may be the first introduction
of the subject, to pursue it to a much greater extent.
_University College, Jan, 8, 1839._
LONDON:—PRINTED BY JAMES MOYES,
Castle Street, Leicester Square.
FIRST NOTIONS
OF
LOGIC.
What we here mean by Logic is the examination of that part of reasoning
which depends upon the manner in which inferences are formed, and the
investigation of general maxims and rules for constructing arguments, so
that the conclusion may contain no inaccuracy which was not previously
asserted in the premises. It has nothing to do with the truth of the
facts, opinions, or presumptions, from which an inference is derived;
but simply takes care that the inference shall certainly be true, if the
premises be true. Thus, when we say that all men will die, and that all
men are rational beings, and thence infer that some rational beings will
die, the _logical_ truth of this sentence is the same whether it be true
or false that men are mortal and rational. This logical truth depends
upon the structure of the sentence, and not on the particular matters
spoken of. Thus,
Instead of, Write,
All men will die. Every A is B.
All men are rational beings. Every A is C.
Therefore some rational beings will die. Therefore some Cs are Bs.
The second of these is the same proposition, logically considered, as
the first; the consequence in both is virtually contained in, and
rightly inferred from, the premises. Whether the premises be true or
false, is not a question of logic, but of morals, philosophy, history,
or any other knowledge to which their subject-matter belongs: the
question of logic is, does the conclusion certainly follow if the
premises be true?
Every act of reasoning must mainly consist in comparing together
different things, and either finding out, or recalling from previous
knowledge, the points in which they resemble or differ from each other.
That particular part of reasoning which is called _inference_, consists
in the comparison of several and different things with one and the same
other thing; and ascertaining the resemblances, or differences, of the
several things, by means of the points in which they resemble, or differ
from, the thing with which all are compared.
There must then be some propositions already obtained before any
inference can be drawn. All propositions are either assertions or
denials, and are thus divided into _affirmative_ and _negative_. Thus, A
is B, and A is not B, are the two forms to which all propositions may be
reduced. These are, for our present purpose, the most simple forms;
though it will frequently happen that much circumlocution is needed to
reduce propositions to them. Thus, suppose the following assertion, ‘If
he should come to-morrow, he will probably stay till Monday’; how is
this to be reduced to the form A is B? There is evidently something
spoken of, something said of it, and an affirmative connexion between
them. Something, if it happen, that is, the happening of something,
makes the happening of another something probable; or is one of the
things which render the happening of the second thing probable.