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
The law may be stated in this wise. Every phenomenon, event or
relation must have a sufficient reason for being what it is. To
illustrate: (1) If Venus is the evening star, there must be a
sufficient reason. (2) If the ground is wet, there must be a cause.
Many logicians argue that this law has no place in logic, its
field being that of the physical sciences. The laws of identity,
contradiction and excluded middle are, however, universally regarded
as the Primary Laws of thought.
=6. UNITY OF PRIMARY LAWS OF THOUGHT ILLUSTRATED BY SYMBOLS.=
(1) Absolute Symbols Relative Symbols.
Excluded middle.
A is either A or not-A. A is either B or not-B.
Contradiction.
A is not not-A. A is not B or A is not not-B.
Identity.
A is A. A is not-B or A is B.
(2) Propositions made to fit symbols.
Excluded middle.
A man is either a man or A man is either honest or
a not-man. not-honest.
Contradiction.
A man is not a not-man. A man is not honest, or a man
is not not-honest.
Identity.
A man is a man. A man is not-honest, or a man
is honest.
The “excluded middle” propositions of the foregoing express
alternatives which are mutually contradictory. There is no middle
ground. The “contradictory propositions” contradict the identity of
the subject with one alternative, while the “identity” propositions
affirm the identity of the subject with the other alternative. This is
made possible because of the principle, “Of two mutually contradictory
terms, if one is true the other must be false.” The foregoing scheme
shows how closely “contradictory” and “identity” propositions are
related to “excluded middle” propositions. Expressed mathematically:
excluded middle = contradiction + identity.
=7. OUTLINE.=
PRIMARY LAWS OF THOUGHT.
(1) Two fundamental laws.
Identity, contradiction.
(2) Law of identity.
Absolute――complete, incomplete.
Relative.
(3) Law of contradiction.
Two uses of _not_.
Contradictory and opposite terms.
(4) Law of excluded middle.
(5) Law of sufficient reason.
(6) Unity of primary laws of thought.
=8. SUMMARY.=
(1) The elemental forms of evolved thought are the affirmative and
negative judgments. This suggests two fundamental laws of thought, the
law of identity and the law of contradiction. The former conditions the
affirmative judgment, the latter the negative.
(2) The law of identity implies a permanency of being. “Everything
remains identical with itself,” is a statement of identity.
Absolute identity may be divided into complete and incomplete identity.
In complete absolute identity the subject is the same as the predicate
in both form and meaning. Truisms illustrate this.
Public-domain text, read in full here on John Shaqi.
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