Bibliography

On the Algebra of Logic

A cerebral habit of the highest kind, which will determine what we do in fancy as well as what we do in action, is called a belief.

…a leading principle, which contains no fact not implied or observable in the premisses, is termed a logical principle, and the argument it governs is termed a complete, in contradistinction to an incomplete, argument, or enthymeme.

A complete argument, with only one premiss, is called an immediate inference. Example: All crows are black birds; therefore, all crows are birds.

A cerebral habit of the highest kind, which will determine what we do in fancy as well as what we do in action, is called a belief. The representation to ourselves that we have a specified habit of this kind is called a judgment. A belief-habit in its development begins by being vague, special, and meagre; it becomes more precise, general, and full, without limit. The process of this development, so far as it takes place in the imagination, is called thought. A judgment is formed; and under the influence of a belief-habit this gives rise to a new judgment, indicating an addition to belief. Such a process is called an inference; the antecedent judgment is called the premise; the consequent judgment, the conclusion; the habit of thought, which determined the passage from the one to the other (when formulated as a proposition), the leading principle.

A cerebral habit of the highest kind, which will determine what we do in fancy as well as what we do in action, is called a belief. The representation to ourselves that we have a specified habit of this kind is called a judgment.

A cerebral habit of the highest kind, which will determine what we do in fancy as well as what we do in action, is called a belief. The representation to ourselves that we have a specified habit of this kind is called a judgment. A belief-habit in its development begins by being vague, special, and meagre; it becomes more precise, general, and full, without limit. The process of this development, so far as it takes place in the imagination, is called thought. A judgment is formed; and under the influence of a belief-habit this gives rise to a new judgment, indicating an addition to belief. Such a process is called an inference; the antecedent judgment is called the premise; the consequent judgment, the conclusion; the habit of thought, which determined the passage from the one to the other (when formulated as a proposition), the leading principle.

A habit of inference may be formulated in a proposition which shall state that every proposition c, related in a given general way to any true proposition p, is true. Such a proposition is called the leading principle of the class of inferences whose validity it implies. When the inference is first drawn, the leading principle is not present to the mind, but the habit it formulates is active in such a way that, upon contemplating the believed premise, by a sort of perception the conclusion is judged to be true.¹ Afterwards, when the inference is subjected to logical criticism, we make a new inference, of which one premise is that leading principle of the former inference, according to which propositions related to one another in a certain way are fit to be premise and conclusion of a valid inference, while another premise is a fact of observation, namely, that the given relation does subsist between the premise and conclusion of the inference under criticism; whence it is concluded that the inference was valid.

¹Though the leading principle itself is not present to the mind, we are generally conscious of inferring on some general principle.

The term logical leading principle we may take to mean the principle which must be supposed true in order to sustain the logical validity of any argument. Such a principle states that among all the states of things which can be supposed without conflict with logical principles, those in which the premiss of the argument would be true would also be cases of the truth of the conclusion. Nothing more than this would be relevant to the logical leading principle, which is, therefore, perfectly determinate and not vague, as we have seen an extralogical leading principle to be.

…a leading principle, which contains no fact not implied or observable in the premisses, is termed a logical principle, and the argument it governs is termed a complete, in contradistinction to an incomplete, argument, or enthymeme.

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A logical principle is said to be an empty or merely formal proposition, because it can add nothing to the premisses of the argument it governs, although it is relevant; so that it implies no fact except such as is presupposed in all discourse…

…a leading principle, which contains no fact not implied or observable in the premisses, is termed a logical principle, and the argument it governs is termed a complete, in contradistinction to an incomplete, argument, or enthymeme.

[—]

We may here distinguish between logical and extralogical validity; the former being that of a complete, the latter that of an incomplete argument.

A cerebral habit of the highest kind, which will determine what we do in fancy as well as what we do in action, is called a belief. The representation to ourselves that we have a specified habit of this kind is called a judgment. A belief-habit in its development begins by being vague, special, and meagre; it becomes more precise, general, and full, without limit. The process of this development, so far as it takes place in the imagination, is called thought.

De Morgan, in the remarkable memoir with which he opened his discussion of the syllogism (1846, p. 380) has pointed out that we often carry on reasoning under an implied restriction as to what we shall consider as possible, which restriction, applying to the whole of what is said, need not be expressed. The total of all that we consider possible is called the universe of discourse, and may be very limited. One mode of limiting our universe is by considering only what actually occurs, so that everything which does not occur is regarded as impossible.