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the indefinite adjective some for the more particular description, getting,
Some gas is some element,
or, in the still more vague form of common language,
Some gas is an element.
31. The mood Datisi may thus be illustrated :
(1) Some metals are inflammable,
(3) Some elements are inflammable.
C = inflammable,
we may represent the premises in the forms
(1) DB = DBC
A = elements,
B = metals,
Substitution, in the second side of (1), of the description of B given in (2) produces the conclusion
(3) DB = DBCA,
or, in words,
Some metal = some metal element inflammable.
In this and many other instances my method of representation is found to give a far more full and
strict conclusion than the old syllogism; but ellipsis or a substitution of indefinite particles or adjectives easily enables us to pass from the strict form to the vague results of the syllogism: it would be in vain that we should attempt to reach the more strict conclusion by the syllogism alone. But I must beg of the reader not to judge the validity of my forms by any single instance only, but rather by the wide embracing powers of the principle involved. Even common thought must be condemned as loose and imperfect if it should be found in certain cases to be inconsistent with a generalization which holds true throughout the exact sciences as well as the greater part of the ordinary acts of reasoning.
32. Certain forms of so-called immediate inference, chiefly brought into notice in recent times by Dr. Thomson, are readily derived from our principle.
Immediate inference by added determinant1 consists in joining a determining or qualifying adjective, or some equivalent phrase, to each member of a proposition, a new proposition being thus inferred. Dr. Thomson's own example is as follows
A negro is a fellow-creature;
whence we infer immediately,
1 "Outline of the Laws of Thought," § 87.
A negro in suffering is a fellow-creature in suffering.
To explain accurately the mode in which this inference seems to be made according to our principle, let us take
The premise may be represented as
A = AB.
Now it is self-evident that AC is identical with AC, this being a fact which some may think to be somewhat unnecessarily laid down in the first of the primary laws of thought (see § 41).
In the symbolic expression of this fact,
AC = AC,
we can substitute for A in the second member its equivalent AB, getting
AC = ABC.
This may be interpreted in ordinary words as,
A suffering negro is a suffering negro fellow-creature, which differs only from the conclusion as stated by Dr. Thomson by containing the qualification negro in the second member,
33. Immediate inference by complex conception closely resembles the preceding, and is of exceedingly frequent occurrence in common thought and language, although it has never had a properly recognised place in logical doctrine until lately.1
Its nature is best learnt from such an example as the following:
Oxygen is an element,
Therefore a pound weight of oxygen is a
This is a very plain case of substitution; for if we make
0 = oxygen,
P = pound weight,
we may represent the premise as
0 = 0Q.
Now it is self-evident that
P of O = P of O,
and substituting in the second member the description of O we have
P of OP of OQ.
1 Thomson's "Outline," § 88.
34. In an exactly similar manner we may solve a common form of reasoning which the authors of the "Port Royal Logic" described as the Complex Syllogism, remarking how little attention logicians had in their day given to many common forms of reasoning.1 I will employ their example, which is as follows:
(1) The sun is an insensible thing,
(2) The Persians worship the sun,
(3) The Persians, therefore, worship an insensible thing.
we may represent the above by the symbols
A = AB
(2) CCD of A.
Hence, by substitution for A in (2) by means of (1), (3) CCD of AB.
35. I regard hypothetical propositions as only differing from categorical propositions in the acci
1 "Port Royal Logic," translated by Mr. Spencer Baynes, p. 207.