W. E. Johnson, Logic: Part I (1921)
§ 1 A systematic treatment of logic must begin by regarding the proposition as the unit from which the whole body of logical principles may be developed. A proposition is that of which truth and falsity can be significantly predicated. Some logicians have taken the judgment as their central topic, and it will be necessary to examine the distinction between what I have called a proposition and what appears to be meant by a judgment. It has been very generally held that the proposition is the verbal expression of the judgment; this, however, seems to be an error, because such characterisations as true or false cannot be predicated of a mere verbal expression, for which appropriate adjectives would be 'obscure,' ' ungrammatical,' 'ambiguous,' etc. There appear then to be three notions which, though intimately connected, must be clearly distinguished: namely
The sentence may be summarily defined as the verbal expression of a judgment or of a proposition; it remains, therefore, to distinguish and interrelate the proposition and the judgment.
- what may be called the sentence;
- the proposition; and
- the judgment.
The natural use of the term judgment is to denote an act or attitude or process which may constitute an incident in the mental history of an individual. As so conceived, we should have further to distinguish the changing phases of a process (which might alternately involve interrogation, doubt, tentative affirmation or negation) from the terminus of such process in which a final decision replaces the variations undergone during what is commonly called suspense of judgment. It would thus be more natural to speak of passing judgment upon a proposition proposed in thought than to identify judgment as such with the proposition. This more natural usage (which is that which I shall adopt) entails the necessity of recognising the distinction between various attitudes of thought on the one hand, and the object towards which that thought may be directed on the other; and even further, when necessary, of recognising the adoption of any of these alterable attitudes of thought as a datable occurrence within the total experience of some one individual thinker. There will thus be many fundamental attributes that must be predicated of the judgment upon a proposition different from, and often diametrically opposed to, those attributes that are to be predicated of the proposition itself.
In this account the judgment is the more comprehensive or concrete term, since when seriously treated it involves the two terms thinker and proposition and, in addition, the occurrent and alterable relation that may subsist between them. In thus drawing attention to mental process in my exposition of logical doctrine, I am taking what has been unfortunately termed a 'subjective' point of view. For the term 'subjective' should be substituted 'epistemic'; and in discarding the familiar antithesis subjective and objective, it is better for the purposes of Logic to substitute the antithesis epistemic and constitutive. The epistemic side of logical doctrine points to the quite universally acknowledged kinship of Logic with Epistemology, and, in using this term in preference to subjective, we can avoid any confusion between what belongs to Psychology as opposed to what belongs to Logic. As to the term constitutive -- a term for which philosophers are indebted to Kant -- it has the force of 'objective' inasmuch as it points to the constitution of such an object of thought-construction as the proposition when treated independently of this or that thinker. I may anticipate what will be treated fully in the later part of logical doctrine, by pointing out that the distinction and connection between the epistemic and constitutive sides of logical problems plays an important part in the theory of Probability; and, in my view, it ought to assume the same importance throughout the whole of the study of Logic.
Now, as regards the relation of the proposition to any such act as may be called judgment, my special contention is that the proposition cannot be usefully defined in isolation, but only in connection with some such attitude or act of thought; and I prefer to take the notion of asserting as central amongst these variations of attitude -- which will therefore be spoken of as variations in the assertive attitude. I shall also maintain that the fundamental adjectives true and false which are (perhaps universally) predicated of mere propositions as such, derive their significance from the fact that the proposition is not so to speak a self-subsistent entity, but only a factor in the concrete act of judgment. Thus, though we may predicate of a certain proposition -- say 'matter exists' -- that it is true or that it is false, what this ultimately means is, that any and every thinker who might at any time assert the proposition would be either exempt or not exempt from error. In other words, the criticism which reason may offer is directed -- not to the proposition -- but to the asserting of the proposition; and hence the customary expression that such and such a proposition is false merely means that anyone's assertion of the proposition would be erroneous. The equivalence of these two forms of criticism follows from the fundamental principle that an attitude of assertion is to be approved or condemned in total independence of the person asserting or of the time of his assertion, and in exclusive dependence upon the content of his assertion. This fundamental principle of Logic will come up for detailed treatment when the so-called Laws of Thought are explicitly discussed. In order to mark the important distinction, and at the same time the close connection, between the proposition and the act of assertion, I propose to take the term 'assertum' as a synonym for 'proposition' when such terminology may seem convenient. Thus, the assertum will coincide, not exactly with what has been asserted, but with what is in its nature assemble.
§ 2. Many philosophers have used the term belief in its various phases as a substitute either for judgment or for assertion; in fact, when the mental aspect of any problem assumes special prominence, the term belief as applied to the proposition is more naturally suggested than any other. While the object of belief is always a proposition, the proposition may be merely entertained in thought for future consideration, either without being believed, or in a more or less specific attitude opposed to belief, such as disbelief or doubt. To doubt a proposition implies that we neither believe nor disbelieve it, while belief and disbelief as opposed to doubt have in common the mental characteristic of assurance. Thus there are three opposed attitudes towards a proposition, included in the distinction between assurance and doubt; -- the former of which may be either (assured) belief or (assured) disbelief, and the latter of which appears further to be susceptible of varying felt degrees. The close association amongst all the terms here introduced brings into obvious prominence the mental side, which such terms as judgment or assertion seem hardly to emphasise. It would however, I think, be found that there is in reality no relevant distinction between the implications of the two terms 'judgment' and 'belief.' Those logicians who have spoken exclusively of judgment, conception, reasoning, etc., have had in view more complicated processes, the products of which have been explicitly formulated; while those who have used belief and cognate terms have included more primitive and simple processes, the products of which may not have been explicitly formulated. Since the traditional logic has treated only the more developed processes, the term judgment and its associates is perhaps preferable for this somewhat limited view of the scope of Logic, while the use of the term belief -- which must certainly be understood to include the higher as well as the lower processes -- points to a wider conception of the province of Logic. To put the matter shortly, I hold it to be of fundamental importance to insist that there is some factor common to the lower and higher stages, and that this common factor, to which the name belief has been given, is necessarily directed to what in Logic is called a proposition1. Assertion, in the sense here adopted, is to be understood to involve belief, and may be defined as equivalent to conscious belief. This definition restricts the term in two ways: in that, firstly, to assert does not merely mean to utter (without belief); and secondly, merely to believe unconsciously is not to assert.
§ 3. In speaking of variations of attitude towards the proposition, an assumption is involved that there is a single entity called the proposition that is the same whatever may be the attitude adopted towards it. Ordinary language supplies us with names for such different attitudes along with cognate names for the proposition: thus we associate 'to assume' with 'an assumption '; 'to suppose' with 'a supposition'; 'to propose' with 'a proposition'; 'to postulate' with 'a postulate'; 'to presume' with 'a presumption'; etc.2 Consider the two verbs 'to assume' and 'to presume.' It will be acknowledged that these denote attitudes between which some subtle distinction may be understood; and thus it might appear that in correspondence with this distinction there must be a similar subtle distinction between an assumption and a presumption. Unfortunately substantival words such as these are apt to suggest a difference in nature between that which in the one case is presumed and in the other assumed; but this suggestion must be rejected, and it must be maintained on the contrary that the content of a proposition preserves its identity unmodified, independently of all variations of assertive attitude and of personal and temporal reference. This independence holds also in regard to what has been termed 'logical' in contrast with 'psychological' assertion. The phrase logically asserted, applied to this or that proposition, is only metaphorically legitimate, and literally equivalent to 'asserted on purely rational grounds by any or all rational persons.' In other words, the predicate 'asserted ' conveys no meaning when taken apart from a person asserting.
Adopting as we do the general view that no logical treatment is finally sound which does not take account of the mental attitude in thought, it follows that the fundamental terms 'true' and 'false' can only derive their meanjng from the point of view of criticising a certain possible mental attitude. We are thus bound to distinguish the object of this attitude (the assertum) from the attitude itself which may vary independently of the object; but we can only avoid contradiction or vagueness if, while permitting ourselves to distinguish between the attitude and its object, we at the same time refuse to separate them. We may further explain the adjectives 'true' and 'false' so as to bring out what characterises logic in contrast with -- or rather in its relation to -- psychology: namely that logic formulates standards or imperatives which as such have no significance except as imposed upon mental acts. Thus we may say that the application of the adjectives true and false coincides with the application of the imperatives 'to be accepted' and 'to be rejected' respectively. We may add that these imperatives are imposed by the thinker -- in the exercise of his reason -- upon himself. In maintaining this coincidence between the two imperatives on the one hand and the two adjectives (true and false) on the other, it must not be taken that we are able thus to define the adjectives true and false. On the contrary, we are forced to insist that they are indefinable. We are only indicating that a reference to mental attitude is presupposed when Logic recognises the distinction between true and false in its formulation of standards for testing the correctness of a judgment or assertion.
§ 4. So far we have taken the proposition as a unit of which the adjectives true and false may be predicated. Before proceeding to analyse the proposition into its component parts, a word must be said in regard to the relation of logic to universal grammar, and in particular the relation between grammatical and logical analysis. Properly speaking, grammatical analysis cannot be regarded as dealing merely with words and their combinations. The understanding of the grammatical structure of a sentence -- which includes such relations as those of subject to predicate, and of subordinate to co-ordinate clauses -- requires us to penetrate below the mere verbal construction and to consider the formal structure of thought. Hence, on the one hand, grammar cannot be intelligently studied unless it is treated as a department of logic; and, on the other hand, logic cannot proceed without such a preliminary account of linguistic structure as is commonly relegated to grammar. In short, universal grammar (as it is called) must be subsumed under Logic. On this view, a slight alteration in grammatical nomenclature will be required, whereby, for the usual names of the parts of speech, we substitute substantive-word or substantive-phrase, adjective-word or adjective-phrase, preposition-word or phrase, etc., reserving the terms substantive, adjective, preposition, etc., for the different kinds of entity to which the several parts of speech correspond.
§ 5. To turn now to the analysis of the proposition. We find that in every proposition we are determining in thought the character of an object presented to thought to be thus determined. In the most fundamental sense, then, we may speak of a determinandum and a determinans: the determinandum is defined as what is presented to be determined or characterised by thought or cognition; the determinans as what does characterise or determine in thought that which is given to be determined. We shall regard the substantive (used in its widest grammatical sense) as the determinandum and the adjective as the determinans. Neither of these terms can be defined except in their relation to one another as each functions in a possible proposition. As it has frequently been said, the proposition is par excellence the unit of thought. This dictum means that the logical nature of any components into which we may analyse the proposition can only be defined by the mode in which they enter into relation within it. For example, when I use determinandum for the substantive and determinans for the adjective, I am only defining the one in terms of the other, inasmuch as the common factor 'determine' is contained in both. This account goes beyond that which has become commonplace among many philosophers, namely, that the subject of a proposition is ultimately something which cannot be defined in the way in which a predicate or adjective can be defined; for to this we have to add that the predicate of a proposition is ultimately something which cannot be defined in the way in which a subject or substantive can be defined. These two statements present the natures of subject and predicate purely negatively, the positive element being supplied by the terms 'determinans' and 'determinandum.'
We have now to examine the nature of the connection involved in every case where adjective and substantive are joined; for example 'a cold sensation,' 'a tall man.' In order to understand the verbal juxtaposition of substantive and adjective, we must recognise a latent element of form in this construct, which differentiates it from other constructs -- which also are necessarily expressed by a juxtaposition of words. This element of form constitutes what I shall call the characterising tie. The general term 'tie' is used to denote what is not a component of a construct, but is involved in understanding the specific form of unity that gives significance to the construct; and the specific term 'characterising tie' denotes what is involved in understanding the junction of substantive with adjective. The invariable verbal expression for the characterising tie is the verb 'to be' in one or other of its different modes. To think of 'a tall man' or of 'a cold sensation' is to think of 'a man as being tall,' 'a sensation as being cold.' Here the word 'being' expresses the characterising tie, and the fact that in some cases the word may be omitted is further evidence that the tie is not an additional component in the construct, but a mere formal element, indicating the connection of substantive to adjective. This is its peculiar and sole function; and, as the expression of the unique connection that subsists between substantive and adjective, it is entirely unmodifiable.
The distinction and connection between substantive and adjective correspond to -- and, in my view, explain -- the distinction and connection between particular and universal3. Ultimately a universal means an adjective that may characterise a particular, and a particular means a substantive that may be characterised by a universal. The terms particular (or substantive) and universal (or adjective) cannot be defined as functioning in isolation, but only as they enter into union with one another. There is some danger of confusing two different uses of the verb 'to characterise,' which may be partly responsible for the historical dispute concerning the relation of particular to universal. Primarily the term 'characterise' should be used to connect substantive with adjective in the form 'such and such a quality or adjective characterises such and such an object or substantive.' On the other hand, in the phrase 'the thinker characterises such or such an object,' characterises means 'cognitively determines the character of.' Owing to this elliptical use of the term, the particular has been conceived of as 'an uncharacterised object,' and this would mean literally 'an object without any character'; but since actually every object must have character, the only proper meaning for the phrase 'uncharacterised object' is 'an object whose character has not been cognitively determined.' If then the term 'exist' may be predicated equally of a universal as of a particular, then we may agree with the Aristotelian dictum that the universal exists, not apart from, but in the particular; and by this is meant that the adjective exists, not apart from, but as characterising its substantive; to which must be added that the substantive exists, not apart from, but as characterised by its adjective. Now in thought the substantive and the adjective may be said to be separately and independently represented; hence thinking effects a severance between the adjective and the substantive, these being reunited in the asserted proposition -- not only by the characterising tie, but also by what we may call the assertive tie. The blending of the assertive with the characterising tie is expressed in language by the transition from the participial, subordinate, or relative clause, to the finite or declaratory form of the principal verb. Thus in passing from 'a child fearing a dog' to 'a child fears a dog,' the characterising tie joins the same elements, in the same way, in both cases; but is, in the latter, blended with the assertive tie. That the ties are thus blended is further shown by the modifications 'is-not,' 'may be,' 'must be,' by which the verb 'to be' is inflected in order to indicate variations in the assertive attitude while the characterising relation remains unchanged. The copula 'is' of traditional logic is thus seen to be a blend of the characterising with the assertive tie.
§ 6. We must now criticise a view, explicitly opposed to our own, as to the nature of the copula is. There has been for a long period an assumption that the proposition in some way or other asserts the relation of identity. This relation of identity, it is admitted, is not one of complete or absolute identity, but involves also a relation of difference: thus the proposition 'Socrates is mortal' is transformed into 'Socrates is a mortal being' -- where 'Socrates' and 'a mortal being' are affirmed to be identical in denotation but different in connotation. Have logicians quite recognised the extreme elaborateness of this verbal transformation? The adjective 'mortal' has first to be turned into a substantive in using the word 'a mortal being'; secondly, the indefinite article has to be introduced, since it is clear that Socrates is not identical with every mortal; thirdly, the indefinite article has to be carefully defined as meaning one or other; fourthly, the relation of the adjective 'mortal' to the substantive 'being' which it characterises still remains to be elucidated; fifthly, another adjective (a relational adjective) namely identical is introduced in the compound phrase 'is identical with.' The proposition finally becomes: 'Socrates is identical with one or other being that is mortal.' Here the two adjectives 'mortal' and 'identical with' are each introduced after is. Now, if 'is identical with' is to be substituted for is in each case, then we shall arrive at an infinite regress. Thus, in the first place, 'Socrates is identical with X' (say) must be rendered 'Socrates is identical with a being that is identical with X' where the force of is still remains unexplained. And in the second place 'one or other being that is mortal' must be rendered 'one or other being that is identical with a mortal,' where again is still remains to be explained. In each case, if an infinite regress is to be avoided, the word is that remains must be interpreted as representing the unique mode in which the fundamentally distinct categories substantive and adjective are joined.
§ 7. Having so far considered the proposition in its mental or subjective aspect, we have next to examine it in what may be called its objective aspect. Whereas a proposition is related subjectively to assertion, we shall find that it is related objectively to fact4. Our conclusion, briefly expressed, is that any proposition characterises some fact, so that the relation of proposition to fact is the same as that of adjective to substantive. Bradley has represented a proposition as ultimately an adjective characterising Reality, and Bosanquet as an adjective characterising that fragment of Reality with which we are in immediate contact. In adopting the principle that a proposition may be said, in general, to characterise a fact, I am including with some modification what is common to these two points of view.
One parallel that can be drawn between the relation of an adjective to a substantive and that of a proposition to a fact is that, corresponding to a single given substantive, there are an indefinite number of adjectives which are truly predicable of it, just as there are many different propositions which truly characterise any given fact. Thus we do not say that corresponding to a single fact there is a single proposition, but on the contrary, corresponding to a single fact there is an indefinite number of distinct propositions. Again, just as amongst the adjectives which can be truly predicated as characterising a given substantive, some are related to others as relatively more determinate; so, amongst the several propositions which truly characterise a single fact, some characterise it more determinately and thus imply those which characterise the same fact less determinately. We may therefore regard the process of development in thought as starting from a fact given to be characterised, and proceeding from a less to a continually more determinate characterisation.
Again there is an exact parallel between the relation of contradiction or contrariety amongst adjectives that could be predicated of a given substantive, and amongst propositions which could be formulated as characterising a given fact. Thus the impossibility of predicating certain pairs of adjectives of the same substantive involves the same principle as the impossibility of characterising the same fact by certain pairs of propositions: such pairs of adjectives and propositions are incompatible, and this relation of incompatibility lies at the root of the notion of contradiction. We may illustrate the relation of incompatibility amongst adjectives by red and green regarded as characterising the same patch. It is upon this relation of incompatibility that the idea of the contradictory not-red depends; for not-red means some adjective incompatible with red, and predicates indeterminately what is predicated determinately by green, or by blue, or by yellow, etc. Amongst propositions the relation of incompatibility may be illustrated by 'Every p is qu' and 'Every pv is non-q,' which are more determinate forms of the pair of contradictory propositions 'Every p is q' and 'Some p is non-q.' These latter derive their significance as mutually contradictory from the principle that the actual fact must be such that it could be characterised either by such a relatively determinate proposition as 'Every p is qu' or by such a relatively determinate proposition as 'Every pv is non-q.'
This account of the relation of contradiction as ultimately derived from that of incompatibility or contrariety (whether applied to adjectives regarded as characterising substantives or to propositions regarded as characterising facts) brings out in another aspect the principle that any given substantive or any given fact may be truly characterised by a more or by a less determinate adjective or proposition: a topic which will be further developed in later chapters.
The above logical exposition of the nature of a proposition leads to a consideration of the philosophical problem of the relation of thought to reality in one of its aspects. It is at the present day agreed that this relation cannot be taken to be identity, and the notion of correspondence has been put forward in its place. The above account enables us to give a more definite exposition of what more precisely this so-called correspondence entails: the truth of a judgment (expressed in a proposition) may be said to mean that the proposition is in accordance with a certain fact, while any proposition whose falsity would necessarily follow from the truth of the former is in discordance with that fact. In this way the somewhat vague conception of the correspondence between thought and reality is replaced by the relation of accordance with a certain fact attributed to the true proposition, and of discordance with the same fact attributed to the associated false proposition.
1 Readers of Psychology should be warned that, when psychologists contrast 'imagination' with 'belief,' each term indicates an attitude to a proposition; while, when they contrast 'imagination' with 'perception,' the processes to which they refer do not involve any attitude towards a proposition. There is no common element of meaning in these two applications of the word 'imagination.'
2 In further illustration of this point we may select certain prominent logical terms such as hypothesis, postulate, axiom. Each of these terms indicates the peculiar attitude to be assumed towards the proposition in question by any thinker: thus a hypothesis stands for a proposition which awaits further scientific investigation before being finally accepted or rejected; a postulate stands for a proposition which cannot be brought to the test of experience, but the truth of which is demanded by the thinker; and an axiom is a proposition the truth of which is self-evident to the thinker.
3 Here the terms particular and universal are used in the sense current in philosophy, and not in their familiar application in elementary logic, where they stand for sub-divisions of the proposition.
4 Otherwise expressed: The proposition, subjectively regarded, is an assertibile; objectively regarded, a possible.