First notions of logic (preparatory to the study of geometry)De Morgan, Augustus
Philosophy
First notions of logic (preparatory to the study of geometry)
De Morgan, Augustus
Logic
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.
A │is│ B
The happening of his arrival │ │an event from which it may be
to-morrow │is│ inferred as probable that he
│ │ will stay till Monday.
The forms of language will allow the manner of asserting to be varied in
a great number of ways; but the reduction to the preceding form is
always possible. Thus, ‘so he said’ is an affirmation, reducible as
follows:
What you have just said (or │is│the thing which he said.
whatever else ‘so’ refers to) │ │
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