At the level of our consideration the phenomena of the upper cave are not in fact secondary and derivative at all. They are part and parcel of the shared life of understanding which is for us for the time being the primary phenomenon the explanatory point of absoluteness in the human cave the phenomenon in their bearing on which all other phenomena are viewed and in terms of which they are to be understood. For a long course of antimony has made us cease to think merely in terms of the bodies and spaces and times and embodied intelligent egos of the lower regions of the cave according to one or other of them some sort of ontological priority over the others. Thought that operates in terms of mere foundations existential priorities will never we have decided sustain itself adequately: we must look to some outcome some unifying end in relation to which all these competing priorities can play a part or have a role. That outcome that end we have seen in the rational life of communicating persons. The separateness of persons with its moments of metaphysical anguish and darkness is basically a device that makes this rational communal life possible as the merely material world with its overloaded detail and dizzying mixture of regularity and anomaly provides the stage-scenery and properties among and through which this rational communal life can be conducted. It is ‘for us men’ and our rational education that this complex machinery is there at all though it has not on our view been put there by anyone whether human or superhuman. The radical teleology with which we are now working has we may be sure its own brand of absurdity and incredibility but this will at least be quite different from the older types of absurdity and incredibility that we found so unenlightening. We shall therefore not question our radical teleology till we come to our fifth lecture. What we shall do in the next few lectures will be to explore the peculiarities of the hypostatic activity through which creatures of reason are summoned up for us and come to be built hierarchically on one another. We shall be concerned in successive lectures first with the products of ordinary abstraction next with the special products of value-hypostatization and then lastly with the level of religious projection of theogony the three zones into which the upper reaches of the cave may most conveniently be divided.

The phenomenology of the upper reaches of the cave may best be approached by way of the notion of ‘conscious light’ or ‘angle’. It is as we saw the essence of the conscious life of an ego to be of a thing or class of things or a situation or class of situations which perhaps but not necessarily have a place in the order of things to which we give the preferred status of ‘realities’. All conscious life is referential though the word ‘referential’ must not be given the modern implication of involving an actual referent a circumstance necessary only to the success of a reference which involves matters going beyond the features which make it referential. Confusion would be avoided if we distinguished between the ‘reference’ or ‘referential character’ of a conscious state and the application which constitutes the success of its reference: a reference which applies e.g. to an object is like a bowshot which hits its target whereas a reference that lacks application is like a bowshot that shoots wide of its mark. Quite distinct from the referential dimensions of conscious life are the dimensions to which reference is irrelevant: here as sketched in a previous lecture we have the dimensions of the focally and the marginally given the dimensions of the illustratively ‘seeingly’ and the non-illustratively ‘emptily’ given and finally and for our present purposes most importantly the infinitely diversified dimension of ‘conscious light.’

What we have in mind are the remarkable differences in which it is as much we who approach our object differently as it is our object which impresses us differently which comes before us in a different respect or regard differences which are as readily given a subjective as an objective colouring and attachment being in fact among the differences in which the whole subjective-objective distinction itself first comes to light. An object seen or thought of can be seen as being thus or thus qualified or as being thus or thus knit together or related to other objects it can be seen or thought of as there existent and not replaced by a corresponding gap or absence it can be seen as involving these or those lacks or deficiencies these or those open possibilities these or those elements of fixity and invariance and so on. In each of these cases we see or think of our object or objects or our situation in this or that ‘light’ and the ‘light’ in which we see it floats ambiguously between ourselves and the thing or situation seen or thought of so that it is as much a part of our individual personal life as of the parcelled divided world of things around us while at other times it seems to be broken by what it connects into two wholly diverse if correlated aspects: the seeing or conceiving of something as e.g. a rather washed out red cushion on the one hand and its simply being such a washed out red cushion on the other. What we are here dealing with is the sort of primary abstraction of seeing or thinking of something only qua this or qua that or seeing or thinking of it in Berkeley's phrase so far forth and no further an abstraction which would seem to be part of all conscious reference as opposed to those merely facultative confrontations in which not making anything of what lies before us it is only by courtesy that we can be said to have anything before us at all.

Differences in conscious light of course acquire systematic fixity in language and its forms: it is in language and language alone that we can refer to something as being about to happen the day after tomorrow as reversing a policy that had been pursued over a long period and so on. But it would be gravely misguided to think that there were not many differentiations of ‘light’ which preceded and conditioned linguistic usage: the simple tense-distinctions for example the distinction between presence and absence the distinctions of readiness and unreadiness etc. etc. The basic linguistic differences between sense reference and application have a pre-linguistic basis and the ‘light’ in which things are seen or thought of first provides the sense of an expression which is used to refer and if successfully used to apply to such things. It is further clear that it is part and parcel of conscious experience that the seeing or thinking of things in varying lights should have behind it an ever enriched marginal or dispositional background: what we now see in this light is what we have seen in that light and in that light and what we are again ready to see in all the lights in question. Also part of conscious experience is a vaguer background of open possibilities: what we have seen in certain specified lights is what we shall or may see in countless further unspecified lights. All this is reflected in the subject-predicate structure of language in which there is always an open possibility of further predication as well as an identity of subject or subject-matter that will persist through it.

It is important here to note that through all this variation of conscious light there may be seen to run a vein of deep generality or community: any light in which anything is seen or thought of is a light in which other things could have been seen or thought of and it is also a light in which the same or other things could be seen or thought of on many occasions and by a diversity of persons. In other words while there may be particularity in the objects of our references and particularity in the occasions and performers of such references there is always unfettered generality in the lights in which the references are made. This is the foundation of the perhaps exaggerated Hegelian doctrine of the universal character of all features and factors in thought and discourse even of such as are avowedly demonstrative and tied to the here now and the exclusive personal ‘I’ Obviously a general predicament lurks even in reference to such immediacies and particularities. It is in a sense always we an unboundedly variable subject that is in this unboundedly variable situation and in it here and now even if we think we can give such free variables a not further describable precise value on each occasion of their use. It is also the foundation of the somewhat exaggerated denial of the possibility of a private language: for what this doctrine really amounts to is that nothing in a reference apart from certain necessarily unshared particulars is intrinsically unshareable and incommunicable. If owing to some oddity or defect of sensibility there is a light in which an object is seen by A in which it cannot be seen by B this is plainly an accidental failure in communication. A could have had senses which would have shown him objects just as they appear to B and all ordinary discourse proceeds on the assumption that it is in fact inherently likely or ‘normal’ that this should be the case that while we can understand that it should not be so either normally or at all what we thus understand represents something quite gratuitous something in which we shall never have the slightest reason to believe. This strange mixture of absolutely understanding a possibility that we reject with almost equal certainty is part of the unquestioned phenomenology of the situation. In the same way if there is some posture of the mind which A can take up to an object and which does not fall within B's repertoire this too is given as a merely accidental limitation: every access of clearness illustration and conscious light of which A is capable is also given as one of which B is intrinsically capable. That a thought can be communicated in all but the point of particularity from which it originates or to which it applies is part of what we understand by a thought. And even as we have said the incommunicable individuality of our references is in a general manner communicable since everyone is necessarily this one i.e. an individual and lives through references non-recurrent and particular and which may have points of attachment which are also so. However we look on things in experience and thought and however we look on our own selves and their experiences is therefore intrinsically a common a shareable matter and can accordingly be given a fixed form and currency in the use of some particular expression.

What we are however further maintaining is that to see things in any conscious light is in a sense to rise above one's own personal particularity and the sheer particularities of one's environmental position and to enjoy a life that is in principle common: language with its fixed rules and its fixed points of attachment and ostension merely serves to ensure and regularize the publicity the commonness of intent and import which is the essence of thought as such. Which must not however be distorted into the doctrine that the particular circumstances in which we learn languages and the environmental oddities to which such learning is attached set limits to the range of what can be communicated and built into linguistic usage. Some things e.g. the red and the blue enter into the sphere of discourse because we are shown instances of them other things e.g. mental apartness enter the sphere of discourse even though it is quite impossible to show instances of them and yet other things e.g. certain basic categories enter the sphere of discourse because however much we try it is impossible to find anything which is not an instance of them. The function of ostension is often as much to direct our thought away from what comes before us as to direct our attention to what is there or to direct our attention to what is so all-pervasive that it cannot except in general contrast with what can be as much presented as not presented be brought before us at all.

The common life of thought we have been sketching with the language which gives it content and currency is at the stage at which we (and the ‘phenomena’) have now arrived a more important and logically central feature than the particularities personal and environmental from which it takes its rise. It is as we have said in a sense peculiar and ultimate for the sake of this common thought-life that these particularities can be held to exist or to be there at all. The thought-life in question is however capable of a further impressive performance or endless series of performances in virtue of which its sphere of objects can be indefinitely augmented thereby acquiring a riches which can only through confusion be found embarrassing. The performances we are to deal with are those of hypostasis or of abstraction in the strict sense of the word the passage from something red to redness as such from the situation in which both Jane and Mary are washing to the general possibility of something's being true of both of two things and so on. Such performances plainly involve language; from a non-substantival synsemantic way of talking we proceed in a regular manner to a substantival manner of talking and it is not easy to imagine such a performance being carried out without the help of the thing-like substantival suggestions of separate words and phrases. But it is easy to pass from this admission to a view according to which the step is largely misguided and misleading according to which it only serves to people the world with fictions and springs from the basic confusion of imagining that every expression that helps in reference has also an independent referential function that there is some object or objective feature it brings before us and of which it can rightly be regarded as a name. Whereas it may be argued against all this that the step involved in hypostasis genuinely serves to bring to light phenomena infinitely more varied and interesting than the lowest-order population of the world and that it moreover brings logical power and richness into the phenomena which cannot be discovered by any mere scratching about on the logical ground.

The nature of hypostasis will be best seen by considering one or two examples. Let us imagine that I see someone in the marketplace at Pella and remark ‘There goes the teacher of Alexander’. I shall then have directed my mind to a particular individual present to my senses and shall further have seen him in a particular light as being one who teaches and who exercises this function in regard to the local crown-prince Alexander. The intentionality involved in this relatively simple reference craves a carrying-out and a carrying-further by a vast family of further intentions some of which will also fulfil or illustrate it in various ways as e.g. by presenting us with situations in which Aristotle is shown with Alexander and as actually instructing him. But my reference is limited in the sense that in it I do not refer to Aristotle in every respect in which it would be possible to refer to him—I may not for instance even have heard that he is a pupil of a famous Athenian Professor called Plato—and that while he comes before me as something which can be teased out into dizzying complexity involving much border-line obscurity this yet cannot be teased out into more than a thin excerpt of all that could be asserted of Aristotle the man. My reference in other words has a fairly limited sense or scope even if it leaves room for indefinite additions and to conceive of someone as the teacher of Alexander is to fall vastly short of conceiving him as all that he is or could be.

So far we have a case merely of the angular purblindness essential to all consciousness not anything that properly merits the title of abstraction. It is however possible for us as thinking persons to reflect on our previous act of reference or on the way in which it was directed to its theme of concern and on that theme of concern to the extent that it was made the target of our reference. What this means is that we can achieve a remarkable feat of retractation in which the open becomes the closed the loose rigid the developing frozen and where we deliberately on one pretext or another stay confined in this scope of our previous reference and refuse to budge beyond it thereby achieving that astonishing conceptual death that separation of the essentially inseparable which Hegel describes in the Preface to the Phenomenology and which he sees as the necessary prelude to the highest forms of rational conceptual life. The kind of retractation we are considering can be very various: it can take the form of considering only the scope of the approach represented by the phrase ‘The teacher of Alexander’ or alternatively the objective coverage of this phrase the object intended to the extent that it is so intended. We can consider in other words what precisely it means for someone to think of Aristotle as a teacher of Alexander its cash-value in terms of personal awareness and we can consider what is the same thing seen by a kind of projective turning-inside-out what it means for Aristotle to be thus characterized. We shall leave undetermined which of these senses the subjective or the objective corresponds to the Sinn the sense which fulfils so important a role in Frege's semantic theory. In general our act of retractation or abstraction can bring to light a large number of differing abstracta particularly if different groups of words are selected: we can consider the meaning or sense of the various expressions ‘There goes the teacher of Alexander’ ‘the teacher of Alexander’ ‘teacher of Alexander’ ‘teacher of’ ‘of Alexander’ ‘of’ ‘Alexander’ etc. We can consider what exactly it is for the teacher of Alexander to go by what exactly it is to be the teacher of Alexander or a teacher of Alexander or to teach Alexander or to be the teacher of anyone etc. In talking of ‘meanings’ or ‘senses’ we are on the whole looking at the matter non-objectively as is not the case when we speak of ‘being a teacher of Alexander’ etc. This appears in the fact that it would be somewhat unnatural to say that being a teacher of Alexander was a meaning or sense whereas it would be quite natural to say that it was a property an abstract something possessed by Aristotle and so forth. If the sense of an expression represents the direction of a verbalized intention its ‘intentional object’ represents the object of that intention artificially limited by the direction in question. The notion of limitation of an artificial stopping-short of a cutting adrift is part and parcel of all the entities that are now under consideration. A non-abstract reference has a limited scope but it is also open in its limitation: in thinking of Aristotle as a teacher of Alexander I am at least ready to think of him as a son of a specific person the pupil of a specific person or as born in a specific place etc. But in thinking of such abstracta as the sense of the expression ‘Aristotle was a teacher of Alexander’ as the property of being a teacher of Alexander or the proposition that Aristotle taught Alexander as the intentional object Aristotle the teacher of Alexander etc. all this openness vanishes. While what I have before me may have rough edges and gaps to be filled it is no longer permissible to fill them. The sense of ‘being a pupil of Plato’ falls quite outside of the sense of ‘being a teacher of Alexander’ outside of the scope of what it is to teach Alexander outside of the content of the proposition that Aristotle taught Alexander outside of the intentional object present in my reference when I recognized Aristotle in the market-place. And being thus abstractly cut short the abstracta in question are necessarily new objects separate from the old ones from which they were derived and better describable in separatistic and Platonic than in Aristotelian terms. Locke was moreover perfectly right in seeing the absurdity in some of the abstracta thus constituted and in seeing them in all their absurdity as part of the real phenomenology of the situation. The triangle as such has an incompleteness of specifiable character incompatible with its status as a triangle and even being triangular is absurd in its abstract divorce from context.

That the hypostasis or abstraction just mentioned—the turning of a reference with limited but open scope into a reference which freezes its scope at the previous point of limitation—is a psychologically genuine and epistemologically important process would of course be questioned by many. Many would doubt whether there is or can be a precise specification of inner experience answering the sense of a phrase like ‘being true of both of two objects’ whether anything could correspond to it but the use of more natural phrases which its abstract form travesties. No one however for whom it was a momentous issue whether or not both of two possibilities were realized and who then looking across the room saw that both were can doubt that there is a uniquely specific interior realization of ‘bothness’ or of any other abstract feature however formal and incapable of separate exemplification. Phrases of the form what it is for something to be such and such plainly indicate something of which there may be a vivid interior realization directed precisely to what the phrase covers and nothing beyond and this as much in the most rarefied higher-order formal case as in the case of the separable features of objects which seem ready to drop off like ripe plums into our hand.¹ And that the interior realization is pragmatically fruitful lies in the fact that it permits us to deal unconfusedly with the innumerable lights in which things show themselves and to see these lights in higher-order lights and so on ad infinitum in a manner which would be impossible without reification or hypostatization. It is for example only because likelihood or probability has been reified or hypostatized and not left in the synsemantic state of a merely modal qualification of other verbs (‘It will probably rain’ etc.) that the vast conceptual structures built upon it have become possible at all. True these structures have confused many and have led to a search for probabilities among the first-order characters and relations of objects but for the wise they have made possible the running up and down of the conceptual ladder in which all true science consists. Only empiricism and the dictates of certain works on English usage have made it seem respectable and enlightening to run down the conceptual ladder and never to run up it whereas the rising to an embracing abstraction and the due and solemn naming of it is as essential to understanding as is the constant running down from it to the applications which fall under it.

Here too a much misunderstood dictum attributed to William of Ockham has played its deplorable part making us forget that while certain conceptual multiplications particularly in natural science may well be a dangerous redundancy the very essence of thought is in a sense to multiply entities every light in which things are seen being the foundation for further critical and assessing lights and so on ad infinitum. Such infinity terrifies only because we fail to realize that it is an infinity of intentionality an infinity no more noxious than that of the endless images formed in two mutually confronting mirrors. The meanings propositions universals intentional objects etc. which are thus generated only need enjoy a bracketed intentional inexistence: they need be there only in the sense that there are or may be higher intentions directed upon them which never entails or permits us to make of them genuine subjects of predications. And their merely intentional status permits them to have a summary and an illuminative use which is not nullified by the inherent absurdity involved in the refusal to specify them completely.

The common life of mind consists therefore in seeing the particularities of personal and environmental existence in lights that are universal and common as among objects and likewise universal and common as among thinking persons and it consists further in the use of these lights by way of the words which give them a seeming thinghood for the setting up the hypostasis of an endless hierarchy of abstractions which preside like a panel of magistrates in their public majesty even when what falls under their jurisdiction is variable and altogether lacking. These abstractions are of course of various sorts—types classes characters relations relational properties numbers negations disjunctions truth-values variables tenses modalities etc.—and the setting up of each is the subject-matter of a special study such as is to some extent found in the various writings of Husserl as well as in some fine parts of the Logics of Bradley and Bosanquet where the origins of such things as negations hypotheticals etc. is treated with some care and brilliance. It is not our task in the present lectures to do any of this detailed constitution-theory: suffice it to say in general that the mind is capable of seeing things or thinking of things in a great number of conscious lights simple and complex and that further it is capable through self-retractation of employing these lights to present truncated abstract artificially frozen objects which stay within the precise coverage of the lights in question which need have only an intentional inexistence but which have profound value both in lending precision and distinctness to the coverage of each conscious light and so enabling us better to understand the cases we see in terms of it and also by making the coverage of the light the subject of new higher-order comparisons and predications thus gaining an ever deepening grasp of the whole eidetic territory.

What it is important further to stress is that even at the highest level of abstraction it is always possible to undo whatever damage may have been done by the truncation or freezing involved in all abstraction. We can reintegrate abstractions into abstractions of any degree of interior richness and complexity as when for example we combine separate characters into some highly complex characterization or description and propositions into a complex propositional system or a fictional narrative or even a science. It is here important that we should keep in mind the difference of two modes of procedures which belong to quite different types of discourse: the procedure in which we deal with first-order material in a variety of conscious lights describe an object to ourselves utter or hear a connected narrative study a science which deals with some special field in the real world e.g. the past of man or of the earth's rocks and the second-order procedure which deals with such descriptions narratives sciences as an ordered assemblage of abstract characterizations propositions etc. There are two senses for example of every science every ‘ology’ a sense in which it embraces a field of phenomena in the real world and a sense in which it embraces only a set of propositions definitions concepts etc. which are to be found in books lectures and other modes of communication. There is a geology which embraces the rocks on the ground-floor of the cave and a geology which floats in the upper regions of the cave and consists only of propositions about rocks. One can pass from one geology to the other much in the manner in which one can pass from looking at the world through elaborately coloured engraved spectacles to taking off the spectacles and considering the colours and engravings upon them. Everything however detailed and particular that is present on the lower floor of the cave can in fact be taken up into its upper reaches: even the contents of a trivial day's diary full of nugatory events constitute an eternal meaning all stateable in general terms that all men at all times can understand. Plato in later life was beginning to be worried by the way in which the turbidities of the world of sense could not be kept from filtering through into the world of forms: we on the other hand may be pleased by such infiltration. For provided one has some relatively clear tone-setting members in the conceptual field it does not matter how many turbid ragged squalidly empirical members one also admits.

Here however we have to direct attention to a science which holds sway in the highest reaches of the cave and which holds sway not as some frozen set of propositions (though it can also be presented in this form) but as a science which concerns itself with abstracta and with manipulating and transforming them. This science of second intentions can be given various names but in the present lecture I propose to give it the ancient well-established name of ‘logic’ though perhaps the titles ‘meta-logic’ or ‘philosophical logic’ or ‘philosophy of logic’ might suit it better. I shall now for the remainder of this lecture be concerned to make a few unusual statements about this logic statements which will disturb you only because the true purport and implications of the science have been utterly lost sight of. I shall try to show in this logic properly understood nothing beyond a higher expression of the pervasive rational teleology among all objects in the world and the communicating minds which have to deal with them. Logic is an expression of the existence of everything for a mutually recognizant society of minds which has become for the moment our explanatory absolute.

Logic as I propose to understand it is first of all concerned with the categories of abstracta (and of the conscious lights they abstract from) which we shall admit into our discourse and with the principles which tell us how they could fulfil their role in the propositions which are in some sense the units of understanding and communication. Among these categories there is unquestionably that of the first subjects of discourse the thematic things that can be seen in various conscious lights and at a more sophisticated level brought under corresponding abstractions (e.g. as being red or as being instances of redness). Objections might be made to treating these first subjects of discourse as themselves abstract but from the point of view of understanding and communication this is what they are: they are the mere first termini the points of attachment of discourse the things shown in various communicable lights. It is important to stress that though the mere forms of discourse say nothing about these first subjects they presuppose much regarding them: that they are many and diverse that they are identical and identifiable in many contexts and by many speakers and thinkers that they have unique places in some total order which makes their picking-out possible that they are points of attachment of countless characterizing and relational lights which attach also to other prime subjects that none of these lights quarrel or conflict with one another that the prime subjects are exhaustively characterizable and definite in every respect etc. etc. It is obvious that these prime subjects of discourse are the ordinary population of the bodily world or of some similar first-order system and that in default of some such subjects there could be no abstract category as that of prime subjects at all. Other subjects of discourse will arise in indefinite numbers: things abstract and momentary and subjective and metaphysical and monistically absolute in all their varieties and there is absolutely no reason why some of these may not in a revised deepened form of diction come to occupy the position of prime subjects from which they were originally remote. Characters may arguably end as in Platonism in becoming more substantial than their instances or our original subjects may end as in Spinozism by becoming mere modes of a single absolute prime subject. All these new subjects must stand however in some original relation to those straightforward first subjects of which bodies are the paradigm and the latter can only be demoted from their prime position if they have first held it.

It will be necessary for us to say much regarding the other higher categories and their necessity for understanding and communication. Characters e.g. must not be indefinitely diverse nor belonging in all cases to single individuals if they are to fulfil their role of sorting things out of placing them in an understandable order of kinds. Propositions are further among the particularly important abstracta which thoughtful retractation sets up as new intentional objects: having seen A a logical subject in a certain conscious light and having replaced that conscious light by an abstract character or relation or other determination we can conceive just what it is for A to have that character or to stand in that relation or other determination and are then framing the new and valuable abstraction of the lekton or proposition. Among such propositions no distinction is more important than that of the asserted the given as true on the one hand and the unasserted the not so given on the other whether or not we represent assertion or ‘truth’ by a special sign or merely show it by the non-subordinated occurrence of a sentence the form of its verbs etc. Yet this distinction is not one that is understandable until merely cited subordinated occurrences of propositions can be opposed to independent ones and this in turn can have no meaning if we could not start from the compulsively fulfilling experience of sense-confrontation the same for others as ourselves which by fulfilling all our meanings utterly differentiates the imaginary from the real and unless there were also that widely-ranging systematic interconnection of things whether by space and time or by special links of causality which enables us to admit one propositional unit as ‘fitting in’ with the total pattern of things while another gets bracketed as embodying an illusion or an error and is only as such incorporated in the total picture. In default of the compulsively fulfilling shareable experiences of the senses and in default of the discoverable interconnection just mentioned and the more or less monistic character of the system they generate there could be neither truth nor belief (which is the claim to have truth) nor knowledge (which is the well justified claim to possess the same). Truth belief and knowledge range of course over territories remote from the bodily and the sensuous: they cover the abstract the interior the possible the transcendently metaphysical. Perverse belief is further possible in what is absurd and groundless and unintelligible simply because it has these belief-repellent characters. But such extensions and perversions of the believing attitude all point back to ordinary belief and this presupposes the possibility of compulsive public sensory fulfilment and far-reaching coherence among what is thus compulsively given as well as our unlearnt power to use the notion of intentional bracketing. These notions may be modified beyond all recognition as we deepen our phenomenological insight but such deepened insight always builds upon and incorporates its origins. All these immense phenomenological and ontological commitments with their revisionary extensions lie concealed beyond the simple formal use of p q r in an ordinary prepositional calculus.

A large number of ontological and phenomenological commitments come out in our ordinary approaches though they have not as yet received full acceptance and elaboration in the systems of symbolic logicians. The essence-accident distinction for instance lies deep in ordinary language and in the procedures of science as well as in the logic of Aristotle: there is a vast distinction between the sort of thing something basically is which it could not without absurdity be thought of as not being and the various properties that as a specimen of that sort it may or may not have. In the same way distinctions of tense have a place in the logic of ordinary speech in which having been ill or being about to be ill do not count as cases of being ill at all and in which merely having existed or being about to exist are sufficient to remove a term from among genuine subjects of predication. Ordinary approaches likewise use the notion of existence in such a way that it is possible to say of individual objects—e.g. this table before me—that it exists and might not have existed and they regard existence as something presupposed by but not identical with the possession of properties. It is clear further that the logic of ordinary speech admits the use of sentences and descriptions in oblique contexts thereby making room for all the phenomena of intentionality and it is clear further that ordinary speakers are not all unready in their more detached contemplative moods of talking in terms of ‘deeper identities’ which override or underlie ordinary surface differences and separatenesses and even embrace incompatibilities in a manner which many logicians would condemn as essentially illogical and mystical. Symbolic systems have not until quite recently thought it worth their while to disturb their own artificial smoothness by trying to accommodate all these complicating features.

What we are in general maintaining is that the notion of a quite uncommitted emptily formal wholly topic-neutral logic is entirely inadmissible. By the forms which our thought and our symbolism accept and accept in full seriousness they presuppose the existence of orders and categories of things variously related even if they explicitly assert the existence of none of them. Though the scheme they decide on may ideally represent the only possibility other schemes having merely an abstract feasibility they none the less decide among what are for us and for our imperfectly developed reflection genuine alternatives. And by excluding suitable forms in which certain sorts of objects and states of affairs can be talked of they certainly try to legislate them out of existence. A perverse logic has certainly been employed to prove that there can be no relations that the thought of what is non-existent or false is impossible unless preposterously analysed that what will be tomorrow is as definite as what was yesterday that the notion of a single necessarily existent all-pervasive absolute is senseless etc. etc. What we are here maintaining is that the categories and the forms of propositions that are to be admitted into a satisfactory logic demand a deep-going examination of the requirements which make a world of objects understandable to us both severally and collectively which render possible the emergence of the shared life of rational mind. In every age there is a science which prepares its own downfall by its overweening hubris: physics biology psychology economics have been such sciences in the past but in our own day the supremely hubristic science is symbolic logic. It is our plea that the forms of discourse should not be formulated without a full consideration of what we can understand of all that we can understand. What logic will emerge from the examination in question cannot be specified in advance and is in its higher reaches necessarily and permanently controversial.

The higher ether of the cave not only contains a logic which determines the ultimate categories of our concepts and their possibilities of integration in propositions or unities of sense: it also contains a logic of transformation of legitimate inference resting on formulated or unformulated relations of necessitation exclusion or probabilification. These rules of transformation are of very various sorts some rising to a high ‘formal’ indifference to the sorts of things we are dealing with and that we might encounter in individual experience some depending on specificities e.g. colours that we could only know of through individual cases some only arising out of repeated encounter with specimens of certain natural kinds some lastly depending on our deep understanding and experience of particular individuals. Necessitation exclusion and probabilification do not differ in kind because known formally or intensionally or inductively or by individual understanding: they are always the same notions the most ultimate and important in philosophy. And all these rules of transformation in a sense lead us from the same to the same they illuminate an identical area of existence even if only problematically and so are in a very wide sense tautological. Thus one is entitled to go from conceiving of something as blue and sweet to conceiving it as sweet and blue or as not being either and one is entitled to do so because despite differences in conscious light one is and must be laying hold of the same real items in either case that are items for everyone and with a fixed place in the real world. In the same manner one is entitled to go from conceiving of something as purple to conceiving it as nearer to red and blue than to green in colour because again one is laying hold of the same real items despite all profound differences in conscious light. In the same manner one is entitled to pass from conceiving of something as having a certain molecular constitution to conceiving of it as readily entering certain combinations since one is laying hold of the same substances or sorts of substance in either case. One is even entitled to pass from conceiving of a thing as the morning star to conceiving of it as the evening star because of a deep but discoverable identity underlying the the two manifestations. None of the transformations just considered is however emptily tautological in the manner of ‘There is a blue thing here so there is a blue thing here’. This is obviously true in the cases where the necessitation etc. belongs to the sphere of the a posteriori and it is necessary to encounter things falling under the conscious lights in question in order to establish a connection among such lights. It is true but less obviously true in cases like that regarding the relationships of colours just mentioned where the conscious lights are much closer together and where the leap from one to the other can be made with complete confidence after seeing or imagining a single case or even by merely savouring the senses of words used and not seeing or even imagining cases. But to pass from ‘That is blue and sweet’ to ‘That is sweet and blue’ involves a change in conscious light so minimal and so indifferent to the specific characters it concerns that one is tempted to think that it involves no change in conscious light at all. There is however a genuine change in conscious light even in most purely formal transformations and a blue e.g. to which sweetness has been added is a differently conceived matter from a sweetness to which blue has been added. Strict synonymy we may hold approvedly hardly ever exists: even faithful translation into another language brings subtle changes in conscious light. There is an indefinable difference reflecting the whole spirit and attitude of two cultures between deux mains sales and two dirty hands. Strict tautology is a degenerate useless case of inference and inference is more truly inference the more it departs therefrom. This is plainest where the inference in question is ampliative and problematic as in all cases of analogy and extrapolation whether in science or philosophy.

We may hold finally that the whole of logic is presided over by a number of values and disvalues which are seldom explicitly acknowledged and hardly ever argued about. To do so would be felt to bring a note of emotional persuasion into the serene air of logical conception and reasoning it being forgotten that serenity is nothing if not an emotional attitude. These values have been presupposed in much that has been so far said and like all values they lie in very varied directions so that there are often relations of practical antinomy among them. We have in the first place the familiar value of the definite and the unchanging the goals of most rigorously formulated and controlled thinking to which however may be opposed the less obvious value of the open and changing the sort of value that characterizes a good discussion as opposed to a rigorous demonstration on prearranged lines. We have in the next place the familiar value of the contradiction-and conflict-free a value hedged about with dire warnings quite groundless in practice as to the ruinous consequences of admitting even a single trivial contradiction into one's thought: freedom from contradiction is indeed an ultimate desideratum provided it is not achieved by adopting conceptions of a too one-sided or ground-level type. And what we have said stresses the less familiar dialectical value of a contradiction the sort of value that produced for what they are worth the theory of types or Goedel's theorem. We have in the next place the value of the exhaustiveness of determination wrongly supposed to be implied by the logical law of excluded middle and the violation of this exhaustiveness which characterizes e.g. many illuminating intentional objects including the content of the anticipated future. We have the value of the simply uniform and the value of the diversified and richly complex. We have the value of the luminously necessary and the value of the imaginatively or empirically contingent. There is finally largely unrecognized in logic as usually treated the all-pervasive value of ‘truth’ capable of large number of degrees to the compulsive deliverances of experience in the sense of individual encounter. It is the general possibility of applying one's logical forms to such deliverances of finding material that fits them that gives value to all these logical forms and the whole methodology of enquiry further revolves around the need of adjusting one's theoretical notions and assertions so that they precisely fit the detail of individual encounter and so that the slightest change in that detail would throw them out of gear. All treatments of the crucial instance from Bacon to Popper are here in place even if on our view the lax treatments of earlier thinkers did better justice to the ontology and phenomenology of the situation that the would-be exactitudes of later ones.

To write about logical values is somewhat terrifying: they are childishly limpid and indefeasible yet so long relegated among the indecencies of philosophy. Any sort of nugatory technicality or paradoxical manipulation is discussable in preference to such concepts as those of simplicity harmony and truth to experience. The study of the values of logic is not however merely edifying: we must be able to show how such values stem from the basic endeavour of the mind to burst the springes of its merely personal subjectivity and to achieve understandings with its fellows concerning the common world which compulsively confronts them all. This endeavour is none other than thinking mind itself and all the subordinate goals it involves are simply different aspects of thinking mind. And on the view we are adopting—which we hold to be the secret persuasion of all who engage in science—the world and its objects is geared to satisfy this endeavour and to oppose only such resistance to it as will make of it a brighter more sustained effort. The eternal life of thought is its own end and all its conditions are by teleological seepage made part of itself.