A Class Room Logic: Deductive and Inductive, with Special Application to the Science and Art of TeachingMcNair, George Hastings
Philosophy
A Class Room Logic: Deductive and Inductive, with Special Application to the Science and Art of Teaching
McNair, George Hastings
Logic
It has been affirmed that a term is distributed when it is referred to
as a definite whole. To put it in another way, a term is distributed
when it is employed in its fullest sense. It is obvious that we should
not employ a term in its fullest sense in the conclusion when it has
been used only in a partial sense in its premise. What is said of the
part cannot necessarily be said of the whole. For example: Because
_some_ men are honest it does not follow that _all_ men are honest. Of
course the converse of this is true, namely, if it could be proved that
all men are honest then surely it would follow that some of the men are
honest. To put it briefly: What is true of _all_ is true of _some_ but
what is true of _some_ is not necessarily true of _all_.
To distribute a term in the conclusion when it is not distributed in
the premise where it occurs is equivalent to saying, “what is true of
some is true of all.” This error which violates rule “4” leads to the
two fallacies of illicit process of the major and minor terms. The
following illustrate the two fallacies.
Syllogism illustrating illicit major:
All trees grow,
No men are trees,
∴ No men grow.
The first premise is an A and consequently its subject is distributed.
The second premise and conclusion being E’s have both subject and
predicate distributed. Thus _grow_, as used in the conclusion, is
distributed, but, as used in the major premise, it is not distributed.
Fallacy shown by circles:
Illustration: FIG. 11.
Here all of the “tree” circle belongs to the “grow” circle and none
of the “men” circle belongs to the “tree” circle, hence the diagram
correctly represents the meaning of the two premises and shows the
fallacy of concluding that _no men grow_. The “men” circle, being
entirely within the “grow” circle, indicates that _all men grow_.
Syllogism illustrating illicit minor:
All true teachers are just,
All true teachers are sympathetic,
∴ All the sympathetic are just.
Each proposition being an A distributes its subject. But the subject of
the conclusion which is “_the sympathetic_” is not distributed in the
minor premise, as an A proposition distributes its subject only. Hence
the fallacy of illicit minor.
Fallacy shown by circles:
Illustration: FIG. 12.
The diagram correctly represents the two premises since all of the
“true teacher” circle belongs to both the “just” and “sympathetic”
circles. But all of the “sympathetic” circle does not belong to the
“just” circle. Hence the fallacy.
(5) _No conclusion can be drawn from two negative premises._
When two terms are both denied of a third term, it is quite impossible
to draw any conclusion relative to the two terms, as the absolute
exclusion of the third term eliminates any possibility of a common link
or standard.
The circles will make this apparent:
No men are immortal,
No trees are immortal,
Illustration: FIG. 13.
“No trees are men” is the conclusion represented by Fig. 13.
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