CHAPTER I.
IMPORT OF JUDGMENTS AND PROPOSITIONS.
46. Judgments and Propositions.—In passing to the next division of our subject we are confronted, first of all, with a question which is partly, but not entirely, a question of phraseology. Shall we speak of the judgment or of the proposition? The usage of logicians differs widely. Some treat almost exclusively of judgments; others almost exclusively of propositions. It will be found that for the most part the former are those who tend to emphasise the psychological or the metaphysical aspects of logic, while the latter are those who are more inclined to develop the symbolic or the material aspects.
To a certain extent it is a matter of little importance which of the alternatives is ostensively adopted. Those who deal with judgments from the logical standpoint must when pressed admit that they can deal with them only as expressed in language, and all their illustrations necessarily consist of judgments expressed in language. But a judgment expressed in language is precisely what is meant by a proposition. Hence in treating of judgments it is impossible not to treat also of propositions. 67
On the other hand, so far as we treat of propositions in logic, we treat of them not as grammatical sentences, but as assertions, as verbal expressions of judgments. The logical proposition is the proposition as understood; and a proposition as understood is a judgment. Hence in treating of propositions in logic we necessarily treat also of judgments.
In a large degree, then, the problem does resolve itself into a merely verbal question. At the same time, reasons and counter-reasons may be adduced in favour of the one alternative and in favour of the other.
On the one side, it is said that the use of the term proposition tends to confuse the sentence as a grammatical combination of words with the proposition as apprehended and intellectually affirmed; and it is urged that in treating of propositions the logician tends to become a mere grammarian.
On the other side, it is submitted that the logician is primarily concerned, not with the process of judgment, the discussion of which belongs to the sphere of psychology, but with judgment as a product, and moreover that he is concerned with this product only in so far as it assumes a fixed and definite form, which it cannot do until it receives verbal expression; and it is urged that if we concentrate our attention on judgments without explicit regard to their expression in language, our treatment tends to become too psychological.
It has been said above that logically we can deal with judgments only as expressed in propositions; and no doubt all judgments can with more or less effort be so expressed. But as a matter of fact we constantly judge in a vague sort of way without the precision that is necessary even in loose modes of expression, and we find that to give expression to our judgments may sometimes require very considerable effort. It must be remembered that logic has in view an ideal. Its object is to determine the conditions to which valid judgments must conform, and it is concerned with the characteristics of actual judgments only in subordination to this end. From this point of view it is specially important that we should deal with judgments in the only form in which it is possible for them to attain precision; and this consideration appears to be conclusive in favour of our 68 treating explicitly of propositions in some part at any rate of a logical course.
No doubt in dealing with propositions we have to raise certain questions that relate to the usage of language. Unfortunately the same propositional form may be understood as expressing very different judgments. It is therefore requisite that in any scientific treatment of logic we should discuss the interpretation of the propositional forms that we recognise. This problem is akin to the problem of definition which has to be faced sooner or later in every science; and, as is also true of a definition, the solution in any particular case is largely of the nature of a convention. But this does not detract from its importance as conducing to clearness of thought.
The question of the interpretation of propositional forms is as a matter of fact one that cannot be altogether avoided on any treatment of logic; and it is of importance to recognise explicitly that in discussing this question we are not dealing with judgments pure and simple. Words are like mathematical symbols, and the meaning of a given form of words is not something inherent either in the words themselves or in the thoughts that they may represent, but is dependent on a convention established by those who employ the words. In the force of a given judgment, however, there can be nothing that is dependent on convention. This distinction is not always remembered by those who confine their attention mainly to judgments, and they are consequently sometimes led to express themselves with an appearance of dogmatism on questions that do not really admit of dogmatic treatment.
But while in certain aspects of logical enquiry it is requisite to deal explicitly with propositions, it must never be forgotten that as logicians we are concerned with propositions only as the expressions of judgments; and there are numerous occasions when we have to go behind propositional forms and ask what are the fundamental characteristics of the judgments that they express.
47. The Abstract Character of Logic.—Reference has been made in the preceding section to the necessity for logical purposes of making our judgments precise. For only if they 69 are precise is it possible to determine with accuracy what are their logical implications considered either individually or in conjunction with one another. It has also been pointed out that we can make our judgments precise only by expressing them in propositional forms, the interpretation of which has been agreed upon.
But this is not without its disadvantages. Sometimes the full force of an actual judgment hardly admits of being expressed in words, and even the force of a proposition as understood may not be found exclusively in the words of which it composed, but may depend partly on the context in which it is placed. Hence the isolated proposition must frequently be regarded as in a sense an abstraction, leaving behind it some portion of the actual judgment for which it stands.
This is indeed much less true of the propositions of science than of those of everyday life; and the more fully a statement is independent of context the more fully may it be regarded as fulfilling its purpose from the scientific standpoint. Still the abstract character of logic must be frankly recognised. “Just as thought is abstract in its dealings with reality, so logic is abstract in its dealings with ordinary thought.”[75]
[75] Hobhouse, Theory of Knowledge, p. 7.
That they are in some degree abstractions is true not only of propositions, but also of inferences, as we have to deal with them in logic. Much of the reasoning of everyday life does not admit of expression in the form of definite premisses and conclusions such as would satisfy the canons of logic. The grounds upon which our conclusions are based are often so complex, and the influence which some of them exert upon our beliefs is so subtle and delicate, that they cannot be completely set forth. This will be realised at once if an attempt is made to apply the rules of logic to any ordinary inference; and an explanation is herein found why the illustrations given in logical text-books frequently appear so artificial and unreal.
It must be admitted that the abstract character of logic detracts to some extent from its utility as an art, though the extent of this drawback may easily be exaggerated. Regarded as a science, however, the value, of logic remains unimpaired. 70 Other sciences besides logic have to proceed by abstractions and separations that do not fully correspond to the complexities of nature; and this often becomes the more true the higher the stage that the science has reached. Its necessary abstractness does not prevent logic from analysing successfully the characteristics of the developed judgment or from determining the principles of valid reasoning. If we were to seek to treat logical problems without abstraction we should be in danger of destroying the scientific character of logic without achieving any valuable result even from the purely utilitarian point of view. It is of little value to criticise received systems without providing any new constructive system in their place.
48. Nature of the Enquiry into the Import of Propositions.—Under the general head of the import of propositions it is usual to include problems that are really very different in character.[76]
[76] Compare Mr W. E. Johnson in Mind, April, 1895, p. 242.
(1) There is, in the first place, the fundamental problem or series of problems as to what are the essential characteristics of judgments, and therefore of propositions as expressing judgments. The discussion of questions of this character must be based directly on psychological or philosophical considerations, and in the solutions nothing arbitrary or conventional can find a place.
Under this head are to be included such problems as the following: Do all judgments contain a reference to reality? In what sense, if any, can all judgments claim to possess universality or necessity? What is the nature of significant denial? Are distinctions of modality subjective or objective?
(2) In the interpretation of propositional forms we have an enquiry of a very different character, an enquiry which relates distinctively to propositions, and not to judgments considered apart from their expression. The problem is indeed to determine what is the precise judgment that a given proposition shall be understood to express; and, in consequence of the uncertainty and ambiguity of ordinary language, the solution of the problem includes an optional or selective element.
71 As a simple illustration of the kind of problem that we here have in view, we may note that in the traditional scheme of propositions, All S is P, No S is P, Some S is P, Some S is not P, the signs of quantity have to be interpreted. The existential and modal import of these propositions is also partly a question of interpretation.
In connexion with the interpretation of propositions, the distinction between meaning and implication has to be considered. What we do in interpreting propositions is to assign to them a meaning; and when the meaning has once been fixed, the implications are determined in accordance with logical principles.
The dividing line between meaning and implication is not in practice always easy to draw, and some writers seek to ignore it by including within the scope of meaning all the implications of a proposition. But this is a fatal error. The assignment of meaning is within certain limits arbitrary and selective. But if element a necessarily involves element b, then a having been assigned as part of the meaning of a given propositional form, it is no question of meaning as to whether the form in question does or does not imply b, and there is nothing arbitrary or selective in the solution of this question.
Sometimes the elements a and b mutually involve one another. It may then be a question of interpretation whether a shall be included in meaning, b thus becoming an implication, or whether b shall be included in meaning, a becoming an implication.
A failure to recognise what is really the point at issue in a case like this has sometimes caused discussions to take a wrong turn. Thus the question is raised whether the import of the proposition All S is P is that the class S is included in the class P, or that the set of attributes S is invariably accompanied by the set of attributes P ; and these are regarded as antagonistic theories. If the implications of a proposition are regarded as part of its import, then the proposition may be said to import both these things. But if by the import of a proposition we intend to signify its meaning only, then we may adopt an interpretation that will make either of them (but not both) part of its import, or our interpretation may be such 72 that the proposition imports neither of them. The question here raised is dealt with in more detail [later on].
(3) A third problem, distinct from both those described above, arises in connexion with the expression of judgments in propositional form.
In ordinary discourse we meet with an infinite variety of forms of statement. To recognise and deal separately with all these forms in our treatment of logical problems would, however, be impracticable. We have, therefore, in some at any rate of our discussions, to limit ourselves to a certain number of selected forms; and in such discussions we have to assume that the judgments with which we are dealing are at the outset expressed in one or other or a combination of these selected forms.
This reduction of a statement to some canonical form has been called by Mr Johnson its formulation.
A given statement, since it involves many different relations which mutually implicate one another, may be formulated in a number of different ways; and it is needless to say that there is no one scheme of formulating propositions that we are bound to accept to the exclusion of others. Different schemes are useful for different purposes, and several schedules of propositions (for example, equational and existential schedules) will presently be considered in addition to the traditional fourfold schedule. It should be added that a given scheme may profess to cover part only of the field. Thus the traditional schedule (All S is P, etc.) professes to be a scheme for categorical judgments only, and (as traditionally interpreted) for assertoric judgments only.
With reference to the reduction of a statement to a form in which it belongs to a given schedule two points call for notice.
(a) There is danger lest some part of the force of the original statement may be lost.
To a certain extent this is inevitable, especially if the original statement contains suggestion or innuendo in addition to what it definitely affirms; and this must be taken in connexion with what has already been said about the abstract character of logic. If, however, there is any substantial loss of 73 import, the scheme stands condemned so far as it professes to be a complete scheme of formulation. It may, as we have seen, not profess to be a complete scheme, but only to formulate statements falling within a certain category, for example, assertoric statements or categorical statements.
It is to be added that a statement which does not admit of being translated into any one of the simple forms included in a given scheme may still be capable of being expressed by a conjunctive or disjunctive combination of such simple forms. Thus, if the statement Some S is P is made with an emphasis on some, implying not all, then the statement cannot be expressed in any one of the forms of the traditional schedule of propositions, but it is equivalent to Some S is P and some S is not P.
(b) In the reduction of a statement to a form in which it belongs to a given schedule there may be involved what must be admitted to be inference. As, for instance, if statements are given in the ordinary predicative form and have to be expressed in an equational scheme.
It may perhaps be urged that this is legitimate, simply on the ground that one of the postulates of logic is that we be allowed to substitute for any given form of words the technical form (and in an equational system this will be an equation) which is equivalent to it. Have we not, however, in reality a vicious circle if a process which involves inference is to be regarded as a postulate of logic?
The difficulty here raised is a serious one only if we suppose ourselves rigidly limited in logic to a single scheme of formulation; and the solution is to be found in our not confining ourselves to any one scheme, but in our recognising several and investigating the logical relations between them. We can then refuse to regard any substitution of one set of words for another as pre-logical except in so far as it consists of a merely verbal transformation: and our postulate will merely be that we are free to make verbal changes as we please; it will not by itself authorise any change of an inferential character. For a change of this kind, appeal must be made to logical principles.
74 We have then in this section distinguished between three problems any or all of which may be involved in discussions concerning the import of propositions. We have
(1) the discussion of the essential nature of judgments and of the fundamental distinctions between judgments;
(2) the interpretation of propositional forms;
(3) the discussion and comparison of logical schedules or schemes of propositions, drawn up with a view to the expression of judgments in a limited number of propositional forms.
These problems are inter-related and do not admit of being discussed in complete isolation. It is clear, for instance, that the drawing up of a schedule of propositions needs to be supplemented by the exact interpretation of the different forms which it is proposed to recognise; and both in the drawing up of the schedule and in the interpretation we shall be guided and controlled by a consideration of fundamental distinctions between judgments.
The problems are, however, in themselves distinct; and some misunderstanding may be avoided if we can make it clear what is the actual problem that we are discussing at any given point.
In particular, it is important to recognise that in the formulation and interpretation of propositions there is an arbitrary and selective element which is absent from the more fundamental problem. Systems of formulation and interpretation, therefore, if only they are intelligible and self-consistent, can hardly be condemned as radically wrong, though they may be rejected as inconvenient or unsuitable. When, however, we are dealing with the fundamental import of judgments, the questions raised do become questions of absolute right or wrong.
It should be added that in the present treatise, since it is concerned with logic in its more formal aspects, questions of interpretation and formulation occupy a position of greater relative importance than they would in a treatment of the science more fully developed on the philosophical side.
49. The Objective Reference in Judgments.—A judgment can be formed or understood only through the occurrence of certain psychical events in the minds of those who form or 75 understand it; and in this sense it may be included amongst subjective states. It is, however, distinguished from all other subjective states by the fact that it claims to be true.
This claim to be true implies an objective reference. For a merely subjective state is not, as such, either true or false; it is simply an occurrence. Thus, the distinction between truth and falsity is inapplicable to an emotion or a volition. An emotion may be pleasurable or painful; it may be strong or weak; it may or may not impel to action; but we cannot describe it as true or false.
And the same applies to a judgment regarded as no more than a subjective connexion of ideas. The claim to truth necessarily involves more than this, namely, a reference to something external to the psychical occurrence involved in the formation of the judgment. Every judgment implies, therefore, on the part of the judging mind, the recognition of an objective system of reality of some sort. The validity that is claimed for judgment is an objective validity.
The word “objective” is always a dangerous word to use, and some further explanation may be given of the meaning to be attached to it here. When we say that a judgment refers to an objective system, we mean a system that subsists independently of the act of judgment itself, and that is not dependent on the passing fancy of the person who forms the judgment. An objective system of reality in this sense may, however, include subjective states, that is, states of consciousness. A body of psychological doctrine consists of judgments relating to states of mind. But such judgments have an external reference (that is, external to the judgments themselves) just as much as a body of judgments relating to material phenomena. Indeed the doctrine of judgment here laid down is not inconsistent with the theory of subjective idealism that resolves all phenomena into states of consciousness.
Even when a judgment relates to purely fictitious objects there is still an external reference,—in this case, to the world of convention.
The particular aspect or portion of the total system of reality referred to in any judgment may sometimes be 76 conveniently spoken of as the universe of discourse. The limits, if any, intended to be placed upon the universe of discourse in any given proposition are usually not explicitly stated; but they must be considered to be implicit in the judgment which the proposition is meant to express, and to be capable of being themselves expressed should there be any danger of misunderstanding. At the same time, it is only fair to add that attempts to define the universe of discourse are likely to raise metaphysical difficulties as to the ultimate nature of reality. What is of main importance from the logical standpoint is the recognition that there is a reference to some system of reality which is to be distinguished from the uncontrolled course of our own ideas. And so far as a distinction can be drawn between different systems of reality, there is need of the assumption that, when we combine judgments or view them in their mutual relations, the universe of discourse is the same throughout.
50. The Universality of Judgments.—The fundamental characteristic then of judgments is their objective reference, their claim to objective validity. It follows that all judgments claim universality, that is to say, they claim to be acknowledged as true not for a given person only, or for a limited number of persons, but for everyone; and again, not for a given time only, or for a limited time, but for all time. In other words, the import of a judgment is not merely to express some connexion of ideas in my own mind; but to express something that claims to be true. And truth is not relative to the individual, nor is it when fully set forth limited by considerations of time.
We shall have subsequently to deal with the ordinary distinction between universal and particular propositions; but it will be clear that the claim to universality which we are now considering is one that must be made on behalf of so-called particular, as well as of so-called universal, propositions. The judgment that some men are six feet in height claims universal acceptance just as much as the judgment that all men are mortal.
Some judgments again contain an explicit or implicit reference to time. But this is really part of the judgment. As 77 soon as the judgment is fully stated it becomes independent of time. It may perhaps be said that the judgment France is under Bourbon rule was true two centuries ago, but is not true now. But the judgment as it stands, without context, is incompletely stated. That France is (or was) under Bourbon rule in the year 1906 A.D. is for all time false; that France is (or was) under Bourbon rule in the year 1706 A.D. is for all time true.
In regard to the nature and significance of the reference to time in judgments, Mr Bosanquet draws a useful distinction between the time of predication and the time in predication.[77] By the time of predication is meant the time at which some thinking being makes the judgment; and this in no way affects the truth of the judgment. But, as Sigwart points out, everything which exists as a particular thing occupies a definite position in time. Hence all judgments relating to particular things, including singular judgments and so-called narrative judgments, relate to some definite time, past, present, or future, with reference to which alone the statements made are valid. This is the time in predication, and the reference to it must be regarded as an intrinsic part of the judgment itself, although it is not always explicitly mentioned.
[77] Logic, I. p. 215. Compare Sigwart, Logic, § 15.
It will be seen that the recognition of the universality of all judgments in the sense here indicated is but the recognition in another aspect of their objective character.
51. The Necessity of Judgments.—A further characteristic that has been ascribed to all judgments, when considered in relation to the judging mind, is necessity. This too is connected with the claim to objective validity. When we judge, we are not free to judge as we will. No doubt by controlling the intellectual influences to which we subject ourselves we may indirectly and in the long run modify within certain limits our beliefs. This is a question belonging to psychology into which we need not now enter. But at any given moment the judgments we form are determined by our mental history and the circumstances in which we are placed. We are bound to judge as we do judge; so far as we feel a question to be an 78 open one our judgment regarding it is suspended. It must be granted that we not unfrequently make statements which do not betray the doubts which as a matter of fact we feel with regard to the point at issue; but such statements do not represent our real judgments. The propositions we utter are the expressions of possible judgments, but not of our judgments.
In any discussion of the modality of judgments, other senses in which the term “necessary” may be applied to judgments have to be considered. In here affirming necessity as a characteristic of all judgments, we are merely declaring over again in another aspect their objective character. The merely subjective sequence of ideas in our minds is more or less under our own control. At any rate we can at will bring given ideas together in our mind. But a judgment is more than a relation between ideas. It claims to be true of some system of reality; and hence it is not so much determined by us, as for us by the knowledge which we have come to possess or think we have come to possess about that system of reality.
EXERCISE.
52. “What is once true is always true.”
“What is true to-day may be false to-morrow.”
Examine these statements. [L.]