mark : 'Astor and I are worth millions.' 'Three and five' make eight, not severally but conjointly, while three and five' are odd numbers severally and not conjointly. 'They all' lifted a log conjointly (cuncti), and they all' told about it severally (omnes). The mosquitoes in Alaska

are so large that many of them weigh a pound.' The terms severally and conjointly are often used in legal documents to indicate the distinction we are discussing. The most usual terms in logic are distributively and collectively.*

The danger.

When we take any of these ambiguous words collectively at one stage of an argument and distributively at another, it is possible to draw conclusions which a fair and unambiguous interpretation of the words would. not warrant, e.g., All the angles of a plane triangle are equal to two right angles; this is one of them; therefore this angle is equal to two right angles.' 'All the feathers in a bed are extremely light; the bed is made up of all the feathers; therefore the bed is extremely light. In the first of these examples the word 'all' is taken collectively when the premise is admitted, but distributively when it is used to prove the conclusion, and the fallacy is called one of Division. In the second example the word 'all' is taken distributively in the ambiguous premise when it is admitted, but collectively when the premise is used to prove the conclusion, and the fallacy is called one of Composition.†

* Both Jevons and Minto contrast Collective terms with General terms. Jevons says "We must carefully avoid any confusion between general and collective terms" (p. 19); and Minto speaks of Collective names as distinguished from general names (Logic, p. 58). In each case,

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however, it seems to be an oversight, for in the exercise at the end of the chapter Jevons says the reader is to determine whether a term is "collective or distributive", not collective or general. So with Minto, most collective names fall under his definition of general names (see p. 44).

A collective term may be either singular or general, e.g.: The Smiths have a new house (singular); he was attacked by a mob (general).

A good many fallacies, such as the stock argument for protective tariffs, are credited by Whately, Jevons, and others to this confusion,

A more serious danger than that just mentioned is that when we use collective terms we shall forget that the individuals in the group are not a real unit, but can be considered as one for certain purposes only. I give one example of this fallacy here.

chapter.

There will be others in a later

"During the last ten years I have read a great many books and articles, especially by German writers, in which an attempt has been made to set up the State' as an entity having conscience, power, and will, sublimated above human limitations, and as constituting a tutelary genius over us all. I have never been able to find in history or experience anything to fit this conception. . . . My notion of the State has dwindled with growing experience of life. As an abstraction, the State is to me only All-of-us. In practicethat is, when it exercises will or adopts a line of action-it is only a little group of men chosen in a very haphazard way by the majority of us to perform certain services for all of us. The majority do not go about their selection very rationally, and they are almost always disappointed by the results of their own operation. Hence the State', instead of offering resources of wisdom, right reason, and pure moral sense beyond what the average of us possess, generally offers much less of all those things."'*

From another standpoint terms are divided into Abstract (such as 'redness', 'anger', 'kindness') and Concrete (such as 'red', 'angry man', 'kind'). Ab- Abstract stract terms are nouns used to indicate the quali- and ties, states, acts, or other relations of things. They are 'Abstract' because, unlike adjectives and verbs, they can be used grammatically without any mention of the thing to which the qualities and so forth belong and without

concrete.

when, so far as I can see, they have absolutely nothing to do with it. I have treated of them elsewhere.

* Sumner, "What Social Classes Owe to Each Other ", pp. 9, 10.

which these latter could not exist. We can say, 'Anger is foolish', or 'A man is foolish to be angry', but not 'Angry is foolish'. Abstract terms thus seem to 'abstract' or draw away one's thought from things.

Every term which is not abstract is called Concrete. Concrete terms are therefore (1) the names of things, or (2) adjectives or verbs, that is to say, names of relations which cannot be used grammatically without any mention of the thing to which they belong.*

The value of abstract terms lies in the fact that through their use attention can be called more briefly and more effectively than in any other way to certain features of things which we wish to discuss without any special reference to the things themselves. It is easier, and on the whole more effective, to say 'Self-sacrifice deserves gratitude' than to say 'When a person acts in such a way as to injure himself because he wishes to benefit some one else, the person whom he meant to benefit ought to feel grateful, no matter who the persons may be'. But in spite of the great value of abstract terms, there is no more important practical rule in logic than that which says Beware of abstractions!

The danger involved in the use of abstract terms is due to the fact that such terms are always nouns and that nouns are usually the names of things. We are therefore very prone to regard the quality or relation referred to by an abstract term as a sort of thing

Hypostatising abstractions.

In

with a certain independent existence, possessing attributes and playing an active part in the world as things alone can. this way 'life', 'natural laws', 'motion', 'force', 'ideas', 'justice', 'evil', 'the Zeitgeist', 'Public Opinion', and a host of other abstractions are liable "to play the part of shamessences, and cheat their way into recognition as realities."†

* The word 'thing' is intended here and is usually intended elsewhere in this book to refer to whatever possesses substantial reality. It therefore includes persons.

† Jas. Martineau, "Study of Spinoza ”, p. 12.

for abstractions.

Nothing exists in the whole universe but a vast number of persons and things acting in various ways. It has no place To say that a person has an idea means that he thinks. To say that a speaker conveys an idea to his hearers means that he makes them know what he thinks. To say that a smile spread through the company means that several persons smiled at once, or that some smiled and then others smiled because they saw them do it. To say that energy is stored up means that a thing is not acting, but is in a condition to act, upon occasion. To say that motion is transmitted means that one thing stops moving and another begins. Imagine a smile spreading through a company like water through a sponge, or energy stored up like grain in the inner recesses of a thing, or motion being carried from its resting-place in one thing to a quiet nook in another! Public opinion is only what is similar in everybody's way of thinking about a question. A law is nothing

but a statement of how people must act if they wish not to be punished by the law-maker, or a statement of how things as a matter of fact do act under certain circumstances. It is not some shadowy reality existing before or apart from all things and compelling their obedience by its own strength. A law is never imposed on things. To say that two chemicals (have an affinity for each other does not explain why they combine or act in conjunction; it merely states the fact that they do.—And so of all the rest.

The habit of defining abstract nouns rather than their corresponding verbs and adjectives helps to entrap us in this "snare of abstractions". We have been taught to say that attraction is the principle or power in virtue of which one body approaches another, or that beneficence is the trait of character manifested in acts of general kindness. It would be better to say that one thing attracts another when it makes it come nearer, and that a person is beneficent when he is kind to everybody. "The snare of abstractions concealing itself chiefly in common nouns, we shall best guard against it

by admitting to our definition no substantive where an adjective [or verb] ought to serve as well." *

It is often said that the tendency to take abstractions for things is particularly characteristic of philosophers. This is probably not true. And yet the philosopher must take special care to overcome it; for the nature of his work is such that a very few blunders of this kind can spoil it. Hence the advice contained in the following quotation is excellent, and the criticism implied in the last sentence is not altogether unjust: "If the student of philosophy would always, or at least in cases of importance, adopt the rule of throwing the abstract language in which it is so frequently couched into a concrete form, he would find it a powerful aid in dealing with the obscurities and perplexities of metaphysical speculation. He would then see clearly the character of the immense mass of nothings which constitute what passes for philosophy."'*

Philosophy, however, is not the only subject that suffers by this tendency to take abstractions for things, as can be shown by the following passages from Langlois and Seignobos' beautiful "Introduction to the Study of History", already quoted.

"The facts of society are of an elusive nature, and for the purpose of seizing and expressing them, fixed and precise language is an indispensable instrument; no historian is complete without good language. It will be well to make the greatest possible use of concrete and descriptive terms: their meaning is always clear. It will be prudent to designate collective groups only by collective, not by abstract names (Royalty, State, Democracy, Reformation, Revolution), and to avoid personifying abstractions. We think we are simply using metaphors, and then we are carried away by the force. of the words. Certainly abstract terms have something very

* Martineau, loc. cit. p. 124. Lotze somewhere says about the same thing. See also the introduction to Berkeley's "Principles of Human Knowledge".

Bailey's "Letters on the Mind", vol. II, p. 159, quoted by Bain, "Logic ", p. 53.