The Art of Logical Thinking; Or, The Laws of ReasoningAtkinson, William Walker
Philosophy
The Art of Logical Thinking; Or, The Laws of Reasoning
Atkinson, William Walker
Logic; Reasoning
VIII. _That if one premise is Particular, the Conclusion must be
particular also._ This because only a universal conclusion can be drawn
from two universal premises.
The principles involved in these two Derivative Rules may be tested by
stating Syllogisms violating them. They contain the essence of the other
rules, and every syllogism which breaks them will be found to also break
one or more of the other rules given.
CHAPTER XVII.
VARIETIES OF SYLLOGISMS
The authorities in Logic hold that with the four kinds of propositions
grouped in every possible order of arrangement, it is possible to form
nineteen different kinds of valid arguments, which are called the
_nineteen moods of the syllogism_. These are classified by division into
what are called _the four figures_, each of which figures may be known
by the position of the middle term in the premises. Logicians have
arranged elaborate and curious tables constructed to show what kinds of
propositions when joined in a particular order of arrangement will make
sound and valid syllogisms. We shall not set forth these tables here, as
they are too technical for a popular presentation of the subject before
us, and because they are not necessary to the student who will
thoroughly familiarize himself with the above stated Laws of the
Syllogism and who will therefore be able to determine in every case
whether any given argument is a correct syllogism, or otherwise.
In many instances of ordinary thought and expression the _complete_
syllogistic form is omitted, or not stated at full length. It is common
usage to omit one premise of a syllogism, in ordinary expression, the
missing premise being inferred by the speaker and hearer. A syllogism
with one premise unexpressed is sometimes called an _Enthymene_, the
term meaning "in the mind." For instance, the following: "We are a free
people, therefore we are happy," the major premise "All free people are
happy" being omitted or unexpressed. Also in "Poets are imaginative,
therefore Byron was imaginative," the minor premise "Byron was a poet"
is omitted or unexpressed. Jevons says regarding this phase of the
subject: "Thus in the Sermon on the Mount, the verses known as the
Beatitudes consist each of one premise and a conclusion, and the
conclusion is put first. 'Blessed are the merciful: for they shall
obtain mercy.' The subject and the predicate of the conclusion are here
inverted, so that the proposition is really 'The merciful are blessed.'
It is evidently _understood_ that 'All who shall obtain mercy are
blessed,' so that the syllogism, when stated at full length, becomes:
'All who shall obtain mercy are blessed; All who are merciful shall
obtain mercy; Therefore, all who are merciful are blessed.' This is a
perfectly good syllogism."
Whenever we find any of the words: "_because_, _for_, _therefore_,
_since_," or similar terms, we may know that there is an argument, and
usually a syllogism.
Public-domain text, read in full here on John Shaqi.
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