Analysis of Mr. Mill's System of Logic. W. Stebbing
is, that there are three chief kinds of nameable things:—1. Feelings distinct from the objects exciting and the organs supposed to convey them, and divisible into four classes, perceptions being only a particular case of belief, which is itself a sort of thought, while actions are only volitions followed by an effect. 2. Substances, i.e. the unknown cause and the unknown recipient of our sensations. 3. Attributes, subdivisible into Quality, Relation, Quantity. Of these α ([Greek: a]) qualities, like substances, are known only by the states of consciousness which they excite, and on which they are based, and by which alone, though they are treated as a distinct class, they can be described. β ([Greek: b]) Relations also, with four exceptions, are based on some fact, i.e. a series of states of consciousness. γ ([Greek: g]) Quantity is, in the same way, based on our sensations. In short, all attributes are only our sensations and other feelings, or something involved in them. We may, then, classify nameable things thus:—1, Feelings; 2, Minds; 3, Bodies, together with the properties whereby they are popularly (though the evidence is very deficient) supposed to excite sensations; 4, the relations of Succession and Coexistence, Likeness and Unlikeness, which subsist really only between states of consciousness.
These four classes are a substitute for Aristotle's abortive Categories. As they comprise all nameable things, every fact is made up of them or some of them; those that are called subjective facts being composed wholly of feelings as such, and the objective facts, though composed wholly or partly of substances and attributes, being grounded on corresponding subjective facts.
CHAPTER IV.
PROPOSITIONS.
The copula is a mere sign of predication, though it is often confounded with to be, the verb of existence (and that not merely by Greeks, but even by moderns, whose larger experience how one word in one language often answers to several in another, should have saved them from thinking that things with a common name must have a common nature). The first division of propositions is into Affirmative and Negative, the copula in the latter being is not. Hobbes and others, by joining the not to the predicate, made the latter what they call a negative name. But as a negative name is one expressing the absence of an attribute, we thus in fact merely deny its presence, and therefore the affirmative guise these thinkers give to negative propositions is only a fiction. Again, modal propositions cannot be reduced to the common form by joining the modality to the predicate, and turning, e.g. The sun did rise, into, The sun is a thing having risen; for the past time is not a particular kind of rising, and it affects not the predicate, but the predication, i.e. the applicability of the predicate to the subject. There are, however, certain cases in which the qualification may be detached from the copula; e.g. in such expressions as, may be, is perhaps; for, then we really do not mean to assert anything about the fact, but only about the state of our mind about it, so that it is not the predication which is affected: e.g. Cæsar may be dead, may properly be rendered, I am not sure that he is alive.
The second division is into Simple and Complex. Several propositions joined by a conjunction do not make a complex proposition. The conjunction, so far from making the two one, adds another, as being an abbreviation generally of an additional proposition: e.g. and is an abbreviation of one additional proposition, viz. We must think of the two together; while but is an abbreviation of two additional propositions, viz. We must think of them together, and we must recollect there is a contrast between them. But hypothetical propositions, i.e. both disjunctives and conditionals, are true complex propositions, since with several terms they contain but a single assertion. Thus, in, If the Koran comes from God, Mahomet is God's prophet, we do not assert the truth of either of the simple propositions therein contained (viz. the Koran comes from God, and Mahomet is God's prophet), but only the inferribility of one from the other. The only difference, then, between a hypothetical and a categorical proposition, is that the former is always an assertion about an assertion (though some categoricals are so likewise; e.g. That the whole is greater than its parts, is an axiom). Their conspicuous place in treatises on Logic arises from this attribute which they predicate of a proposition (for a proposition, like other things, has attributes), viz. its being an inference from something else, being, with reference to Logic, its chief attribute.
The third common division is into Universal, Particular, Indefinite, and Singular. A proposition whose subject is an individual name, even if not a proper name, is singular, e.g. The founder of Rome was killed. In particular propositions, if the part of the class meant by the some were specified, the proposition would become either singular, or universal with a different subject including all the part. Indefinite in Logic is a solecism like doubtful gender in grammar, for the speaker must mean to make either a particular or a universal assertion.
CHAPTER V.
THE IMPORT OF PROPOSITIONS.
The object of an inquiry into the nature of propositions must be to analyse, either, 1, the state of mind called belief, or 2, what is believed. Philosophers have usually, but wrongly, thought the former, i.e. an analysis of the act of judgment, the chief duty of Logic, considering a proposition to consist in the denying or affirming one idea of another. True, we must have the two ideas in the mind together, in order to believe the assertion about the two things; but so we must also in order to disbelieve it. True also, that besides the putting the ideas together, there may be a mental process; but this has nothing to do with the import of propositions, since they are assertions about things, i.e. facts of external nature, not about the ideas of them, i.e. facts in our mental history. Logic has suffered from stress being laid on the relation between the ideas rather than the phenomena, nature thus coming to be studied by logicians second-hand, that is to say, as represented in our minds. Our present object, therefore, must be to investigate judgments, not judgment, and to inquire what it is which we assert when we make a proposition.
Hobbes (though he certainly often shows his belief that all propositions are not merely about the meaning of words, and that general names are given to things on account of their attributes) declares that what we assert, is our belief that the subject and predicate are names of the same thing. This is, indeed, a property of all true propositions, and the only one true of all. But it is not the scientific definition of propositions; for though the mere collocation which makes a proposition a proposition, signifies only this, yet that form, combined with other matter, conveys much more meaning. Hobbes's principle accounts fully only for propositions where both terms are proper names. He applied it to others, through attending, like all nominalists, to the denotation, and not the connotation of words, holding them to be, like proper names, mere marks put upon individuals. But when saying that, e.g. Socrates is wise, is a true proposition, because of the conformity of import between the terms, he should have asked himself why Socrates and wise are names of the same person. He ought to have seen that they are given to the same person, not because of the intention of the maker of each word, but from the resemblance of their connotation, since a word means properly certain attributes, and, only secondarily, objects denoted by it. What we really assert, therefore, in a proposition, is, that where we find certain attributes, we shall find a certain other one, which is a question not of the meaning of names, but of the laws of nature.
Another theory virtually identical with Hobbes's, is that commonly received, which makes predication consist in referring things to a class; that is (since a class is only an indefinite number of individuals denoted by a general name), in viewing them as some of those to be called