Analysis of Mr. Mill's System of Logic. W. Stebbing
basis of the dictum de omni et nullo, on which is supposed to rest the validity of all reasoning. Such a theory is an example of ὑστερον πρὁτερον [Greek: hysteron proteron]: it explains the cause by the effect, since the predicate cannot be known for a class name which includes the subject, till several propositions having it for predicate have been first assented to. This doctrine seems to suppose all individuals to have been made into parcels, with the common name outside; so that, to know if a general name can be predicated correctly of the subject, we need only search the roll so entitled. But the truth is, that general names are marks put, not upon definite objects, but upon collections of objects ever fluctuating. We may frame a class without knowing a single individual belonging to it: the individual is placed in the class because the proposition is true; the proposition is not made true by the individual being placed there.
Analysis of different propositions shows what is the real import of propositions not simply verbal. Thus, we find that even a proposition with a proper name for subject, means to assert that an individual thing has the attributes connoted by the predicate, the name being thought of only as means for giving information of a physical fact. This is still more the case in propositions with connotative subjects. In these the denoted objects are indicated by some of their attributes, and the assertion really is, that the predicate's set of attributes constantly accompanies the subject's set. But as every attribute is grounded on some fact or phenomenon, a proposition, when asserting the attendance of one or some attributes on others, really asserts simply the attendance of one phenomenon on another; e.g. When we say Man is mortal, we mean that where certain physical and moral facts called humanity are found, there also will be found the physical and moral facts called death. But analysis shows that propositions assert other things besides (although this is indeed their ordinary import) this coexistence or sequence of two phenomena, viz. two states of consciousness. Assertions in propositions about those unknowable entities (noümena) which are the hidden causes of phenomena, are made, indeed, only in virtue of the knowable phenomena. Still, such propositions do, besides asserting the sequence or coexistence of the phenomena, assert further the existence of the noümena; and, moreover, in affirming the existence of a noümenon, which is an unknowable cause, they assert causation also. Lastly, propositions sometimes assert resemblance between two phenomena. It is not true that, as some contend, every proposition whose predicate is a general name affirms resemblance to the other members of the class; for such propositions generally assert only the possession by the subject of certain common peculiarities; and the assertion would be true though there were no members of the class besides those denoted by the subject. Nevertheless, resemblance alone is sometimes predicated. Thus, when individuals are put into a class as belonging to it, not absolutely, but rather than to any other, the assertion is, not that they have the attributes connoted, but that they resemble those having them more than they do other objects. So, again, only resemblance is predicated, when, though the predicate is a class name, the class is based on general unanalysable resemblance. The classes in question are those of the simple feelings; the names of feelings being, like all concrete general names, connotative, but only of a mere resemblance.
In short, one of five things, viz. Existence, Coexistence (or, to be more particular, Order in Place), Sequence (or, more particularly, Order in Time, which comprises also the mere fact of Coexistence), Causation, and Resemblance, is asserted or denied in every proposition. This division is an exhaustive classification with respect to all things that can be believed. Although only propositions with concrete terms have been spoken of, it is equally the fact that, in propositions with an abstract term or terms, we predicate one of these same five things. There cannot be any difference in the import of these two classes of propositions, since there is none in the import of their terms, for the real signification of a concrete term resides in its connotation (so that in a concrete proposition we really predicate an attribute), and what the concrete term connotes forms the whole sense of the abstract. Thus, all propositions with abstract terms can be turned into equivalent ones with concrete, the new terms being either the names which connote the attributes, or names of the facts which are the fundamenta of the attributes: e.g. Thoughtlessness is danger, is equivalent to, Thoughtless actions (the fundamentum) are dangerous.
Finally, as these five are the only things affirmable, so are they the only things deniable.
CHAPTER VI.
PROPOSITIONS MERELY VERBAL.
The object of Logic is to find how propositions are to be proved. As preliminary to this, it has been already shown that the Conceptualist view of propositions, viz. that they assert a relation between two ideas, and the Nominalist, that they assert agreement or disagreement between the meanings of two names, are both wrong as general theories: for that generally the import of propositions is, to affirm or deny respecting a phenomenon, or its hidden source, one of five kinds of facts. There is, however, a class of propositions which relate not to matter of fact, but to the meaning of names, and which, therefore, as names and their meanings are arbitrary, admit not of truth or falsity, but only of agreement or disagreement with usage. These verbal propositions are not only those in which both terms are proper names, but also some, viz. essential propositions, thought to be more closely related to things than any others. The Aristotelians' belief that objects are made what they are called by the inherence of a certain general substance in the individuals which get from it all their essential properties, prevented even Porphyry (though more reasonable than the mediæval Realists) from seeing that the only difference between altering a non-essential (or accidental) property, which, he says, makes the thing ἁλλοἱον [Greek: alloion], and altering an essential one, which makes it ἁλλο [Greek: allo] (i.e. a different thing), is, that the latter change makes the object change its name. But even when it was no longer believed that there are real entities answering to general terms, the doctrine based upon it, viz. that a thing's essence is that without which the thing could neither be, nor be conceived to be, was still generally held, till Locke convinced most thinkers that the supposed essences of classes are simply the significations of their names. Yet even Locke supposed that, though the essences of classes are nominal, individuals have real essences, which, though unknown, are the causes of their sensible properties.
An accidental proposition (i.e. in which a property not connoted by the subject is predicated of it) tacitly asserts the existence of a thing corresponding to the subject; otherwise, such a proposition, as it does not explain the name, would assert nothing at all. But an essential proposition (i.e. in which a property connoted by the subject is predicated of it) is identical. The only use of such propositions is to define words by unfolding the meaning involved in a name. When, as in mathematics, important consequences seem to follow from them, such really follow from the tacit assumption, through the ambiguity of the copula, of the real existence of the object named.
Accidental propositions include, 1, those with a proper name for subject, since an individual has no essence (although the schoolmen, and rightly, according to their view of genera and species as entities inhering in the individuals, attributed to the individual the essence of his class); and, 2, all general or particular propositions in which the predicate connotes any attribute not connoted by the subject. Accidental propositions may be called real; they add to our knowledge. Their import may be expressed (according as the attention is directed mainly, either to what the proposition means, or to the way in which it is to be used), either, by the formula: The attributes of the subject are always (or never) accompanied by those signified by the predicate; or, by the formula: The attributes of the subject are evidence, or a mark, of the presence of those of the predicate. For the purposes of reasoning, since propositions enter into that, not as ultimate results, but as means for establishing other propositions, the latter formula is preferable.
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