NOTESNote I. The whole ofPart II, i.e.Chapters VtoVII, suffers from a vagueness of expression due to the fact that the implications of my ideas had not shaped themselves with sufficient emphasis in my mind. In the first place every entity is an abstraction and presupposes certain systematic types of relatedness to other things. There is no such thing as an entity which could be real on its own, though it happens to be related to other things. Again the development of these chapters presupposes that philosophy, even modern philosophy, has been unduly influenced by the Aristotelian categories, in particular those of substance, quantity, quality, despite the criticism to which these categories have been subjected. A detailed analysis of the complex notions which are concealed in the terms quantity and quality is required, but it cannot be given in a note. It was for this reason that I avoided terms such as 'Universal' which presuppose an outlook which is here repudiated. But in many respects the statement that an object is a universal does explain what I mean. Particularity attaches to events and to historical routes among events. But there is a flux of things transcending that of nature—in the narrow sense in which nature is here construed. Accordingly particularity cannot be confined to natural events. The whole subject requires fuller and more systematic treatment which I hope in the immediate future to undertake. The main point hinges onto the ingression[10]of objects into social entities, and onto the analysis of the process of the realisation of social entities.In the list of objects in§ 13.2, I was distinguishing the percipient object, which roughly speaking is an individual, as mental, from a percipient event which is the flux of experience of a living organism. But the percipient object is shadowy in this book and is clearly outside 'nature.'[10]Cf. myConcept of Naturefor a short introduction to the meaning of this term.Note II. The book is dominated by the idea [cf.§ 14.1] that the relation of extension has a unique preeminence and that everything can be got out of it. During the development of the theme, it gradually became evident that this is not the case, and cogredience [cf.§ 16.4] had to be introduced. But the true doctrine, that 'process' is the fundamental idea, was not in my mind with sufficient emphasis. Extension is derivative from process, and is required by it.This failure to insist properly on 'process' is the reason for the paradoxical air attaching to the statement that 'objects are only derivatively in space and time by reason of their relations to events' [cf.§ 15.2]. Objects are of course essential for process, as appears clearly enough in the course of any analysis of process. But it is evident that particular times cannot result from the mere relations between objects which are at all times; and analogously for space. Accordingly space and time must result from something in process which transcends objects.But natural objects require space and time, so that space and time belong to their relational essence without which they cannot be themselves.In§ 15.4it is pointed out that it is viâ objects that the concept of possibility has application. This suggestion requires further elaboration which cannot be attempted here. Similarly in§ 15.8, it is pointed out that continuity is derived from events, and atomicity from objects. This also requires development. It must suffice for the moment to suggest that a scientific object is an atomic structure imposed upon the continuity of events.Part IIshould be read in connection withPart IVat the end of the book.Note III.Chapter VIis made clearer by noting that the present duration [cf.§ 16.2] is primarily marked out by the significance of an interconnected display of sensa and of other associated objects immediately apparent. The duration is the realisation of a social entity in which the sense-objects and perceptual objects [cf.§ 23.9] are ingredient.The antecedent physical objects [cf.§ 24.5] and scientific objects [cf.§ 25] which occasion the duration to be what it is are another story, and the persistent habit of muddling the two sets of entities in philosophy—following the lead of language—is the origin of much confusion. For example there are four distinct meanings according to which you can speak of a chair; you may mean (i) a collection of sense-data, or (ii) a perceptual object, or (iii) a physical object, or (iv) a collection of scientific objects, such as molecules or electrons.It will be noted that I now make a distinction between perceptual objects and physical objects, contrary to§ 24.5. Thus a physical object is a social entity resulting from scientific objects, and halfway towards a perceptual object.Physical objects and scientific objects are causal characters which are discussed inChapter XVI. Also sense-objects and perceptual objects are the apparent characters discussed in that chapter. But the separation between the apparent and the causal must not be over stressed: it is relative to a deliberately limited point of view.The whole of§ 23would be made clearer by the use of the term 'ingression' for the complex relation of a sense-object to the other factors of nature which make up a social entity in process of realisation. The over-simplification involved in the Aristotelian concept of 'quality-subject' has obscured the analysis of ingression.Also§ 24is confused by a wavering between the 'class-theory' of perceptual objects and the 'control-theory' of physical objects, and by the confusion between perceptual and physical objects. I do not hold the class-theory now in any form, and was endeavouring in this book to get away from it. InChapter XVIthe 'causal character' is identical with the perceptual object so far as immediate perception is concerned, with the physical object so far as further discrimination of the significance of immediate appearance is concerned, and with scientific objects so far as more detailed analysis is concerned.Note IV. The attempt in§ 33to define a duration merely by means of its unlimitedness is a failure. In a note to theConcept of Nature, I point out that there is an analogous unlimitedness through time, corresponding to the spatial unlimitedness of a duration. Both unlimitednesses arise from the uniform significance of spatial extension for one, and of temporal extension for the other. Thus there is a temporal unlimitedness arising from a stationary event [cf.§ 41] in a definite space-time system. A point-track is the outcome of such an unlimitedness deprived of all spatial extension. But of course a point-track is a mere limit arrived at by the method of extensive abstraction. But I still hold to§ 35.4.Note V. In§ 47the concept of normality is explained with unnecessary elaboration. Letandbe two intersecting moments belonging to diverse space-time systemsand. Thus intersection ofandis an instantaneous planewhich lies in the instantaneous three-dimensional momentsand.fig20Letbe an event-particle [i.e. an instantaneous point] in it. Then there is a point-trackthrough, belonging to the space-time system, and an analogous point-trackbelonging to.This conception is diagrammatically illustrated [but not exactly represented] by the annexed diagram in which two dimensions have been lost. Thus the three-dimensional regionsandare represented by two straight lines. These lines also represent [with full dimensions] two rectsandinandrespectively: the genesis of these rects will be explained below. The two-dimensional 'level'is represented by the single event-particlewhich lies in it:is the-point-track through, andthe-point-track through; these are represented by dotted lines.The plane of the paper is the two-dimensional matrix containing all the-point-tracks through event-particles on, and all the-point-tracks through event-particles on. This matrix intersectsin the rect, andin the rect.Then the rectis perpendicular to the level, or instantaneous plane it, where bothandlie in the three-dimensional instantaneous space; also analogously for the rectand the levelin. Thus the system of levels parallel toinis a system of instantaneous planes inperpendicular to the system of rects inparallel to. This pair of systems reflects inthe relation between the system of-moments to the system of-point-tracks. Thus the geometry of an instantaneous moment expresses the relations of the event-particles of the moment to the whole bundle of alternative time-systems.In this connection it may be well to expand the substance of a paragraph [pp. 89, 90] in theConcept of Nature:—An instantaneous point is an event-particle. It has two aspects. In one aspect it is there, where it is, in relation to the moments of the various space-time systems of the whole bundle of such systems. This aspect is expressed by the definition of a punct, which is determined by the individual moments (one from each space-time system) which contain it. The indivisibility of a point is expressed by the fact that any moment either contains the whole punct or contains nothing of the punct: the three-dimensionality of space, with time as a fourth dimension, is expressed by the fact that a punct is defined by four moments [not exceptionally related]: the position of the punct is expressed by those moments which do contain it. In another aspect a point is got at as a limit by indefinitely diminishing the dimensions of circumambient space-time. This aspect of absence of dimensions is expressed by the definition of an event-particle by means of abstractive sets with a certain quality of primeness in relation to puncts.The intimate connection of geometry with the properties of the bundle of space-time systems is thus illustrated by the characters of instantaneous points, planes, and lines, and by the origin of parallelism and normality. Geometry expresses in three-dimensions these qualities of the four-dimensional space-time continuum.Note VI.The deductions in§ 50.3and§ 51.1are over condensed. They can be expanded as follows:Substituting from (ii) and (iii) of§ 50.3in (iii) of49.7, we findThusHence by (iii) of50.1CAMBRIDGE: PRINTED BY W. LEWIS AT THE UNIVERSITY PRESS
Note I. The whole ofPart II, i.e.Chapters VtoVII, suffers from a vagueness of expression due to the fact that the implications of my ideas had not shaped themselves with sufficient emphasis in my mind. In the first place every entity is an abstraction and presupposes certain systematic types of relatedness to other things. There is no such thing as an entity which could be real on its own, though it happens to be related to other things. Again the development of these chapters presupposes that philosophy, even modern philosophy, has been unduly influenced by the Aristotelian categories, in particular those of substance, quantity, quality, despite the criticism to which these categories have been subjected. A detailed analysis of the complex notions which are concealed in the terms quantity and quality is required, but it cannot be given in a note. It was for this reason that I avoided terms such as 'Universal' which presuppose an outlook which is here repudiated. But in many respects the statement that an object is a universal does explain what I mean. Particularity attaches to events and to historical routes among events. But there is a flux of things transcending that of nature—in the narrow sense in which nature is here construed. Accordingly particularity cannot be confined to natural events. The whole subject requires fuller and more systematic treatment which I hope in the immediate future to undertake. The main point hinges onto the ingression[10]of objects into social entities, and onto the analysis of the process of the realisation of social entities.
In the list of objects in§ 13.2, I was distinguishing the percipient object, which roughly speaking is an individual, as mental, from a percipient event which is the flux of experience of a living organism. But the percipient object is shadowy in this book and is clearly outside 'nature.'
[10]Cf. myConcept of Naturefor a short introduction to the meaning of this term.
[10]Cf. myConcept of Naturefor a short introduction to the meaning of this term.
Note II. The book is dominated by the idea [cf.§ 14.1] that the relation of extension has a unique preeminence and that everything can be got out of it. During the development of the theme, it gradually became evident that this is not the case, and cogredience [cf.§ 16.4] had to be introduced. But the true doctrine, that 'process' is the fundamental idea, was not in my mind with sufficient emphasis. Extension is derivative from process, and is required by it.
This failure to insist properly on 'process' is the reason for the paradoxical air attaching to the statement that 'objects are only derivatively in space and time by reason of their relations to events' [cf.§ 15.2]. Objects are of course essential for process, as appears clearly enough in the course of any analysis of process. But it is evident that particular times cannot result from the mere relations between objects which are at all times; and analogously for space. Accordingly space and time must result from something in process which transcends objects.
But natural objects require space and time, so that space and time belong to their relational essence without which they cannot be themselves.
In§ 15.4it is pointed out that it is viâ objects that the concept of possibility has application. This suggestion requires further elaboration which cannot be attempted here. Similarly in§ 15.8, it is pointed out that continuity is derived from events, and atomicity from objects. This also requires development. It must suffice for the moment to suggest that a scientific object is an atomic structure imposed upon the continuity of events.
Part IIshould be read in connection withPart IVat the end of the book.
Note III.Chapter VIis made clearer by noting that the present duration [cf.§ 16.2] is primarily marked out by the significance of an interconnected display of sensa and of other associated objects immediately apparent. The duration is the realisation of a social entity in which the sense-objects and perceptual objects [cf.§ 23.9] are ingredient.
The antecedent physical objects [cf.§ 24.5] and scientific objects [cf.§ 25] which occasion the duration to be what it is are another story, and the persistent habit of muddling the two sets of entities in philosophy—following the lead of language—is the origin of much confusion. For example there are four distinct meanings according to which you can speak of a chair; you may mean (i) a collection of sense-data, or (ii) a perceptual object, or (iii) a physical object, or (iv) a collection of scientific objects, such as molecules or electrons.
It will be noted that I now make a distinction between perceptual objects and physical objects, contrary to§ 24.5. Thus a physical object is a social entity resulting from scientific objects, and halfway towards a perceptual object.
Physical objects and scientific objects are causal characters which are discussed inChapter XVI. Also sense-objects and perceptual objects are the apparent characters discussed in that chapter. But the separation between the apparent and the causal must not be over stressed: it is relative to a deliberately limited point of view.
The whole of§ 23would be made clearer by the use of the term 'ingression' for the complex relation of a sense-object to the other factors of nature which make up a social entity in process of realisation. The over-simplification involved in the Aristotelian concept of 'quality-subject' has obscured the analysis of ingression.
Also§ 24is confused by a wavering between the 'class-theory' of perceptual objects and the 'control-theory' of physical objects, and by the confusion between perceptual and physical objects. I do not hold the class-theory now in any form, and was endeavouring in this book to get away from it. InChapter XVIthe 'causal character' is identical with the perceptual object so far as immediate perception is concerned, with the physical object so far as further discrimination of the significance of immediate appearance is concerned, and with scientific objects so far as more detailed analysis is concerned.
Note IV. The attempt in§ 33to define a duration merely by means of its unlimitedness is a failure. In a note to theConcept of Nature, I point out that there is an analogous unlimitedness through time, corresponding to the spatial unlimitedness of a duration. Both unlimitednesses arise from the uniform significance of spatial extension for one, and of temporal extension for the other. Thus there is a temporal unlimitedness arising from a stationary event [cf.§ 41] in a definite space-time system. A point-track is the outcome of such an unlimitedness deprived of all spatial extension. But of course a point-track is a mere limit arrived at by the method of extensive abstraction. But I still hold to§ 35.4.
Note V. In§ 47the concept of normality is explained with unnecessary elaboration. Letandbe two intersecting moments belonging to diverse space-time systemsand. Thus intersection ofandis an instantaneous planewhich lies in the instantaneous three-dimensional momentsand.
fig20
Letbe an event-particle [i.e. an instantaneous point] in it. Then there is a point-trackthrough, belonging to the space-time system, and an analogous point-trackbelonging to.
This conception is diagrammatically illustrated [but not exactly represented] by the annexed diagram in which two dimensions have been lost. Thus the three-dimensional regionsandare represented by two straight lines. These lines also represent [with full dimensions] two rectsandinandrespectively: the genesis of these rects will be explained below. The two-dimensional 'level'is represented by the single event-particlewhich lies in it:is the-point-track through, andthe-point-track through; these are represented by dotted lines.
The plane of the paper is the two-dimensional matrix containing all the-point-tracks through event-particles on, and all the-point-tracks through event-particles on. This matrix intersectsin the rect, andin the rect.
Then the rectis perpendicular to the level, or instantaneous plane it, where bothandlie in the three-dimensional instantaneous space; also analogously for the rectand the levelin. Thus the system of levels parallel toinis a system of instantaneous planes inperpendicular to the system of rects inparallel to. This pair of systems reflects inthe relation between the system of-moments to the system of-point-tracks. Thus the geometry of an instantaneous moment expresses the relations of the event-particles of the moment to the whole bundle of alternative time-systems.
In this connection it may be well to expand the substance of a paragraph [pp. 89, 90] in theConcept of Nature:—An instantaneous point is an event-particle. It has two aspects. In one aspect it is there, where it is, in relation to the moments of the various space-time systems of the whole bundle of such systems. This aspect is expressed by the definition of a punct, which is determined by the individual moments (one from each space-time system) which contain it. The indivisibility of a point is expressed by the fact that any moment either contains the whole punct or contains nothing of the punct: the three-dimensionality of space, with time as a fourth dimension, is expressed by the fact that a punct is defined by four moments [not exceptionally related]: the position of the punct is expressed by those moments which do contain it. In another aspect a point is got at as a limit by indefinitely diminishing the dimensions of circumambient space-time. This aspect of absence of dimensions is expressed by the definition of an event-particle by means of abstractive sets with a certain quality of primeness in relation to puncts.
The intimate connection of geometry with the properties of the bundle of space-time systems is thus illustrated by the characters of instantaneous points, planes, and lines, and by the origin of parallelism and normality. Geometry expresses in three-dimensions these qualities of the four-dimensional space-time continuum.
Note VI.The deductions in§ 50.3and§ 51.1are over condensed. They can be expanded as follows:
Substituting from (ii) and (iii) of§ 50.3in (iii) of49.7, we find
Thus
Hence by (iii) of50.1
CAMBRIDGE: PRINTED BY W. LEWIS AT THE UNIVERSITY PRESS