Indians smell not their nest The Swiss and Finn taste best The spices of the East.

So men accustomed to riches are not acutely sensible of their advantages: dwellers in noisy streets cease to be distracted by the din: the watchmaker ceases to hear the multitudinous ticking in his shop: the neighbours of chemical works are not annoyed by the smells like the casual passenger. But we find also that wine-tasters acquire by practice an unusual delicacy of sense; that the eyes once accustomed to a dim light begin to distinguish objects that were at first indistinguishable; and so on. What meanings of "custom" and of "sensibility" will reconcile these apparently conflicting examples?

What are the exact attributes signified by the names? We should probably find that by sensibility is meant emotional sensibility as distinguished from intellectual discrimination, and that by custom is meant familiarity with impressions whose variations are not attended to, or subjection to one unvarying impression.

To verify the meaning of abstract proverbs in this way is to travel over the road by which the Greek dialecticians were led to feel the importance of definition. Of this more will be said presently. If it is contended that such excursions are beyond the bounds of Formal Logic, the answer is that the exercise is a useful one and that it starts naturally and conveniently from the formulae of Logic. It is the practice and discipline that historically preceded the Aristotelian Logic, and in the absence of which the Aristotelian formulae would have a narrowing and cramping effect.

CAN ALL PROPOSITIONS BE REDUCED TO THE SYLLOGISTIC FORM? Probably: but this is a purely scientific inquiry, collateral to Practical Logic.

The concern of Practical Logic is chiefly with forms of proposition that favour inaccuracy or inexactness of thought. When there is no room for ambiguity or other error, there is no virtue in artificial syllogistic form. The attempt so to reduce any and every proposition may lead, however, to the study of what Mr. Bosanquet happily calls the "Morphology" of Judgment, Judgment being the technical name for the mental act that accompanies the utterance of a proposition. Even in such sentences as "How hot it is!" or "It rains," the rudiment of subject and predicate may be detected. When a man says "How hot it is," he conveys the meaning, though there is no definitely formed subject in his mind, that the outer world at the moment of his speaking has a certain quality or attribute. So with "It rains". The study of such examples in their context, however, reveals the fact that the same form of Common speech may cover different subjects and predicates in different connexions. Thus in the argument:--

"Whatever is, is best.

It rains!"--

the Subject is _Rain_ and the Predicate _is now_, "is at the present time," "is in the class of present events".

[Footnote 1: Remember that when we speak of a general name, we do not necessarily mean a single word. A general name, logically viewed, is simply the name of a _genus_, kind, or class: and whether this is single-worded or many-worded is, strictly speaking, a grammatical question. "Man,"

"man-of-ability," "man-of-ability-and-courage,"

"man-of-ability-and-courage-and-gigantic-stature,"

"man-who-fought-at-Marathon"--these are all general names in their logical function. No matter how the constitutive properties of the class are indicated, by one word or in combination, that word or combination is a general name. In actual speech we can seldom indicate by a single word the meaning predicated.]

[Footnote 2: The objection taken to the word "indefinite,"

that the quantity of particular propositions is indefinite, _some_ meaning any quantity less than all, is an example of the misplaced and frivolous subtlety that has done so much to disorder the tradition of Logic. By "indefinite" is simply meant not definitely expressed as either Universal or Particular, Total or Partial. The same objection might be taken to any word used to express the distinction: the degree of quantity in Some S is not "designate" any more than it is "definite" or "dioristic".]

[Footnote 3: _Generally._ In this word we have an instance of the frequent conflict between the words of common speech and logical terminology. How it arises shall be explained in next chapter. A General proposition is a synonym for a Universal proposition (if the forms A and E are so termed): but "generally" in common speech means "for the most part," and is represented by the symbol of particular quantity, _Some_.]

[Footnote 4: With some logicians it is a mechanical rule in reducing to syllogistic form to treat as I or O all sentences in which there is no formal expression of quantity. This is to err on the safe side, but common speakers are not so guarded, and it is to be presumed rather that they have a universal application in their minds when they do not expressly qualify.]

III.--SOME TECHNICAL DIFFICULTIES.

_The formula for_ EXCLUSIVE PROPOSITIONS. "None but the brave deserve the fair": "No admittance except on business": "Only Protestants can sit on the throne of England".

These propositions exemplify different ways in common speech of naming a subject _exclusively_, the predication being made of all outside a certain term. "None that are not brave, etc.;" "none that are not on business, etc.;" "none that are not Protestants, etc.". No not-S is P. It is only about all outside the given term that the universal assertion is made: we say nothing universally about the individuals within the term: we do not say that all Protestants are eligible, nor that all persons on business are admitted, nor that every one of the brave deserves the fair. All that we say is that the possession of the attribute named is an indispensable condition: a person may possess the attribute, and yet on other grounds may not be entitled to the predicate.

The justification for taking special note of this form in Logic is that we are apt by inadvertence to make an inclusive inference from it. Let it be said that None but those who work hard can reasonably expect to pass, and we are apt to take this as meaning that all who work hard may reasonably expect to pass. But what is denied of every Not-S is not necessarily affirmed of every S.

_The expression of_ TENSE or TIME _in the Syllogistic Forms_. Seeing that the Copula in S is P or S is in P does not express time, but only a certain relation between S and P, the question arises Where are we to put time in the analytic formula? "Wheat is dear;" "All had fled;"

time is expressed in these propositions, and our formula should render the whole content of what is given. Are we to include it in the Predicate term or in the Subject term? If it must not be left out altogether, and we cannot put it with the copula, we have a choice between the two terms.

It is a purely scholastic question. The common technical treatment is to view the tense as part of the predicate. "All had fled," All S is P, _i.e._, the whole subject is included in a class constituted on the attributes of flight at a given time. It may be that the Predicate is solely a predicate of time. "The Board met yesterday at noon." S is P, _i.e._, the meeting of the Board is one of the events characterised by having happened at a certain time, agreeing with other events in that respect.

But in some cases the time is more properly regarded as part of the subject. _E.g._, "Wheat is dear". S does not here stand for wheat collectively, but for the wheat now in the market, the wheat of the present time: it is concerning this that the attribute of dearness is predicated; it is this that is in the class of dear things.

_The expression of_ MODALITY _in the Syllogistic Forms_. Propositions in which the predicate is qualified by an expression of necessity, contingency, possibility or impossibility [_i.e._, in English by _must_, _may_, _can_, or _cannot_], were called in Mediaeval Logic _Modal_ Propositions. "Two and two _must_ make four." "Grubs _may_ become butterflies." "Z _can_ paint." "Y _cannot_ fly."

There are two recognised ways of reducing such propositions to the form S is P. One is to distinguish between the _Dictum_ and the _Mode_, the proposition and the qualification of its certainty, and to treat the _Dictum_ as the Subject and the _Mode_ as the Predicate.

Thus: "That two and two make four is necessary"; "That Y can fly is impossible".

The other way is to treat the Mode as part of the predicate.

The propriety of this is not obvious in the case of Necessary propositions, but it is unobjectionable in the case of the other three modes. Thus: "Grubs are things that have the potentiality of becoming butterflies"; "Z has the faculty of painting"; "Y has not the faculty of flying".

The chief risk of error is in determining the quantity of the subject about which the Contingent or Possible predicate is made. When it is said that "Victories may be gained by accident," is the predicate made concerning All victories or Some only? Here we are apt to confuse the meaning of the contingent assertion with the matter of fact on which in common belief it rests. It is true only that some victories have been gained by accident, and it is on this ground that we assert in the absence of certain knowledge concerning any victory that it may have been so gained. The latter is the effect of the contingent assertion: it is made about any victory in the absence of certain knowledge, that is to say, formally about all.

The history of Modals in Logic is a good illustration of intricate confusion arising from disregard of a clear traditional definition.

The treatment of them by Aristotle was simple, and had direct reference to tricks of disputation practised in his time. He specified four "modes," the four that descended to mediaeval logic, and he concerned himself chiefly with the import of contradicting these modals. What is the true contradictory of such propositions as, "It is possible to be" ([Greek: dynaton einai]), "It admits of being"

([Greek: endechetai einai]), "It must be" ([Greek: anankaion einai]), "It is impossible to be" ([Greek: adynaton einai])? What is implied in saying "No" to such propositions put interrogatively? "Is it possible for Socrates to fly?" "No." Does this mean that it is not possible for Socrates to fly, or that it is possible for Socrates not to fly?

A disputant who had trapped a respondent into admitting that it is possible for Socrates not to fly, might have pushed the concession farther in some such way as this: "Is it possible for Socrates not to walk?" "Certainly." "Is it possible for him to walk?" "Yes." "When you say that it is possible for a man to do anything do you not believe that it is possible for him to do it?" "Yes." "But you have admitted that it is possible for Socrates not to fly?"

It was in view of such perplexities as these that Aristotle set forth the true contradictories of his four Modals. We may laugh at such quibbles now and wonder that a grave logician should have thought them worth guarding against. But historically this is the origin of the Modals of Formal Logic, and to divert the names of them to signify other distinctions than those between modes of qualifying the certainty of a statement is to introduce confusion.

Thus we find "Alexander was a great general," given as an example of a Contingent Modal, on the ground that though as a matter of fact Alexander was so he might have been otherwise. It was not _necessary_ that Alexander should be a great general: therefore the proposition is _contingent_. Now the distinction between Necessary truth and Contingent truth may be important philosophically: but it is merely confusing to call the character of propositions as one or the other by the name of Modality. The original Modality is a mode of expression: to apply the name to this character is to shift its meaning.

A more simple and obviously unwarrantable departure from tradition is to extend the name Modality to any grammatical qualification of a single verb in common speech. On this understanding "Alexander conquered Darius" is given by Hamilton as a _Pure_ proposition, and "Alexander conquered Darius honourably" as a _Modal_. This is a merely grammatical distinction, a distinction in the mode of composing the predicate term in common speech. In logical tradition Modality is a mode of qualifying the certainty of an affirmation. "The conquest of Darius by Alexander was honourable," or "Alexander in conquering Darius was an honourable conqueror," is the syllogistic form of the proposition: it is simply assertory, not qualified in any "mode".

There is a similar misunderstanding in Mr. Shedden's treatment of "generally" as constituting a Modal in such sentences, as "Rivers _generally_ flow into the sea". He argues that as _generally_ is not part either of the Subject term or of the Predicate term, it must belong to the Copula, and is therefore a _modal_ qualification of the whole assertion. He overlooked the fact that the word "generally" is an expression of Quantity: it determines the quantity of the Subject term.

Finally it is sometimes held (_e.g._, by Mr. Venn) that the question of Modality belongs properly to Scientific or Inductive Logic, and is out of place in Formal Logic. This is so far accurate that it is for Inductive Logic to expound the conditions of various degrees of certainty. The consideration of Modality is pertinent to Formal Logic only in so far as concerns special perplexities in the expression of it. The treatment of it by Logicians has been rendered intricate by torturing the old tradition to suit different conceptions of the end and aim of Logic.

PART II.

DEFINITION.

CHAPTER I.

IMPERFECT UNDERSTANDING OF WORDS AND THE REMEDIES THEREFOR.--DIALECTIC.--DEFINITION.

We cannot inquire far into the meaning of proverbs or traditional sayings without discovering that the common understanding of general and abstract names is loose and uncertain. Common speech is a quicksand.

Consider how we acquire our vocabulary, how we pick up the words that we use from our neighbours and from books, and why this is so soon becomes apparent. Theoretically we know the full meaning of a name when we know all the attributes that it connotes, and we are not justified in extending it except to objects that possess all the attributes. This is the logical ideal, but between the _ought to be_ of Logic and the _is_ of practical life, there is a vast difference.

How seldom do we conceive words in their full meaning! And who is to instruct us in the full meaning? It is not as in the exact sciences, where we start with a knowledge of the full meaning. In Geometry, for example, we learn the definitions of the words used, _point_, _line_, _parallel_, etc., before we proceed to use them. But in common speech, we learn words first in their application to individual cases. Nobody ever defined _good_ to us, or _fair_, or _kind_, or _highly educated_.

We hear the words applied to individual objects: we utter them in the same connexion: we extend them to other objects that strike us as like without knowing the precise points of likeness that the convention of common speech includes. The more exact meaning we learn by gradual induction from individual cases. _Ugly_, _beautiful_, _good_, _bad_--we learn the words first as applicable to things and persons: gradually there arises a more or less definite sense of what the objects so designated have in common. The individual's extension of the name proceeds upon what in the objects has most impressed him when he caught the word: this may differ in different individuals; the usage of neighbours corrects individual eccentricities. The child in arms shouts _Da_ at the passing stranger who reminds him of his father: for him at first it is a general name applicable to every man: by degrees he learns that for him it is a singular name.

The mode in which words are learnt and extended may be studied most simply in the nursery. A child, say, has learnt to say _mambro_ when it sees its nurse. The nurse works a hand-turned sewing machine, and sings to it as she works. In the street the child sees an organ-grinder singing as he turns his handle: it calls _mambro_: the nurse catches the meaning and the child is overjoyed. The organ-grinder has a monkey: the child has an india-rubber monkey toy: it calls this also _mambro_. The name is extended to a monkey in a picture-book. It has a toy musical box with a handle: this also becomes _mambro_, the word being extended along another line of resemblance. A stroller with a French fiddle comes within the denotation of the word: a towel-rail is also called _mambro_ from some fancied resemblance to the fiddle. A very swarthy hunch-back _mambro_ frightens the child: this leads to the transference of the word to a terrific coalman with a bag of coals on his back. In a short time the word has become a name for a great variety of objects that have nothing whatever common to all of them, though each is strikingly like in some point to a predecessor in the series. When the application becomes too heterogeneous, the word ceases to be of use as a sign and is gradually abandoned, the most impressive meaning being the last to go. In a child's vocabulary where the word _mambro_ had a run of nearly two years, its last use was as an adjective signifying ugly or horrible.

The history of such a word in a child's language is a type of what goes on in the language of men. In the larger history we see similar extensions under similar motives, checked and controlled in the same way by surrounding usage.

It is obvious that to avoid error and confusion, the meaning or connotation of names, the concepts, should somehow be fixed: names cannot otherwise have an identical reference in human intercourse. We may call this ideal fixed concept the LOGICAL CONCEPT: or we may call it the SCIENTIFIC CONCEPT, inasmuch as one of the main objects of the sciences is to attain such ideals in different departments of study.

But in actual speech we have also the PERSONAL CONCEPT, which varies more or less with the individual user, and the POPULAR or VERNACULAR CONCEPT, which, though roughly fixed, varies from social sect to social sect and from generation to generation.

The variations in Popular Concepts may be traced in linguistic history. Words change with things and with the aspects of things, as these change in public interest and importance. As long as the attributes that govern the application of words are simple, sensible attributes, little confusion need arise: the variations are matters of curious research for the philologist, but are logically insignificant.

Murray's Dictionary, or such books as Trench's _English Past and Present_, supply endless examples, as many, indeed as there are words in the language. _Clerk_ has almost as many connotations as our typical _mambro_: clerk in holy orders, church clerk, town clerk, clerk of assize, grocer's clerk. In Early English, the word meant "man in a religious order, cleric, clergyman"; ability to read, write, and keep accounts being a prominent attribute of the class, the word was extended on this simple ground till it has ceased altogether to cover its original field except as a formal designation. But no confusion is caused by the variation, because the property connoted is simple.[1]

So with any common noun: street, carriage, ship, house, merchant, lawyer, professor. We might be puzzled to give an exact definition of such words, to say precisely what they connote in common usage; but the risk of error in the use of them is small.