Reading Notes: February 27th, 2023

“I shall allow myself to speak of an event, and events in the plural, but I shall note raise the problem of the relation between the continuity of events and their plurality. We are told by mathematicians that this problem has been solved by the notion of a compact series, which is at once discrete, because a series, and continuous, because compact. I do not see that this is really so. If, between any two terms of a series, there is still a third term, it appears to me that we are still as far from continuity as ever; for ex hypothesi, the series as actually counted always has gaps between all its terms, and however many terms are interpolated the gaps always remain. We are told that these gaps are filled by uncounted terms; but no evidence is brought that these terms, however numerous, fill the gaps. At most, they will only occur in the gaps, and serve to delimit their extent; and event this is not guaranteed by the definition of a compact series, for that definition does not stipulate that all the gaps between the terms are to be of the same size, or that an interpolated term is to be interpolated at one point in the gap rather than another. The theory of compact series, in a word, does not meet the facts; and it is only advanced in the interests of what I take to be a logical error, namely logical atomism, which in its application does not differ very widely from the sensational atomism of Hume, and is amenable to all the same criticisms.” (Collingwood, Some Perplexities About Time: With an Attempted Solution, 136-137) 

“Suppose, again, we say that time is continuous. What, in saying this, are we denying? Presumably, that time is discrete. If it had been discrete, it would have had gaps in it. But what would the gaps have been made of? Nothing but time: any gap in a series of events must be a gap consisting of time, for if there is no time in the gap there is no gap. Clearly, then, time is continuous.—But this does not seem to follow. That which must be either discrete or continuous must be a quantity. But if time cannot be measured, it is doubtful whether we ought to call it a quantity; it is, in any case, an unmeasurable quantity, and in this phrase it is reasonable to suspect a contradictio in adjecto.” (Collingwood, Some Perplexities About Time: With an Attempted Solution, 140-141) 

“When one event in time is said to be continuous with the next, the statement is either meaningless or false. Meaningless if “the next” is simply “that with which it is continuous”; false, if it is assumed that events in time are really packed side by side with no intervals between them.” (Collingwood, Some Perplexities About Time: With an Attempted Solution, 141) 

“We do not perceive our perceptivity…” (Richardson, Spiritual Pluralism and Recent Philosophy, 33) 

“A review of classical attempts to deal with the notion of substance makes it clear that the problem resolves itself into an endeavour to reconcile the principles of permanence and change. Heraclitus, who was the first to bring out more or less plainly the nature of the difficulties involved, held that only change is permanent; but closer examination shows that, with any significant meaning which can be attached to the term “change,” the truth of the matter is that change implies permanence. For, in the first place, it is apparent on general grounds that if there is a change, there must be a thing which changes, the said thing maintaining its identity throughout the change. Otherwise, there is simply one thing and then another thing, that is, mere succession and not change at all, properly so-called. From the scientific standpoint we certainly do consider mere alteration alone, that is, simply a succession of different presentations. But from the subjective point of view, if I have first A and then B before me, I can in no significant sense be said to have apprehended a process of change; at most there has been a change in myself, and this, since it is I who have perceived both A and B, assumes my permanence.” (Richardson, Spiritual Pluralism and Recent Philosophy, 39-40)

Reading Notes: February 22nd, 2023

“The finitude of space is implied in its very infinity, and conversely.” (Hegel, Science of Logic, §131) 

“Space is not a thing, but rather the pure relation of the outer to the outer.” (Hegel, Encyclopedia of the Philosophical Sciences, §162) 

“To say that anything is a whole is to imply that it is not a mere congeries of disconnected and separable items, nor even just a loose collection. It also implies that it is a unity of coherent parts. Every whole is made up of differences that are combined within it to constitute one totality. A purely blank unity is virtually impossible to conceive. A mathematical point having position but no magnitude is not a whole in any strict sense; yet even that, simply to have position, must imply directions in space and distances from other points. Thus, even so abstract a concept is not altogether devoid of internal differentiation. Mathematical space itself is by no means blank, however empty it may be presumed. It is an order manifold, involving dimensions, distances between points, possible rotations of lines, distinguishable planes, and the like. Even the simplest of wholes, therefore, is a unity of differences.” (Harris, Cosmos and Anthropos, 17) 

“Not only so, but the parts distinguishable within the whole, genuinely to belong to it, must be mutually adjusted and must, in some discernible way, intermesh. This is even true of so primitive a whole as a loose collection, because to be a collection at all its elements must have some sort of togetherness involving some sort of mutual effect or influence. A bundle of sticks is a bundle only so long as the sticks are mutually contiguous and each supports those above it and adjusts itself to the shape and weight of the others. But the word “whole” implies more than this. It implies an interlock between parts that are systematically interrelated (as in a jigsaw), so that their mutual relations are governed by a principle of order or organization that pervades the entire structure. A machine is a good example, or the pattern on a wallpaper, or the design of a work of art. These are wholes of very different kinds and on different levels; they are, however, far from exhaustive. The essential feature is the prevalence of an ordering principle universally determining the interrelations of the elements so that it determines likewise their intrinsic natures, for each must be adapted and adjusted to its neighbors.” (Harris, Cosmos and Anthropos, 17-18) 

“Because a whole must be a unity of differences, the elements into which it differentiates itself are finite, each limited and defined by what it excludes and what negates it. We shall see that this mutual exclusion is not (and cannot be) absolute, for reasons already partly apparent; but, being finite, each element is circumscribed by more or less definite boundaries. Nevertheless (or rather, for this very reason), its specific character is determined by what is other than and opposed to it. The elements are opposed because, in some sense, they confront one another. Although opposition is commonly asserted only of the extremes in a series (for example, white to black in the colour scale; hot to cold in a range of temperatures), even consecutive terms in the series are in mutual opposition to the extent that exclude one another. Yet the opposition is definitive of the contrasted elements, because what anything is in itself depends on that from which it is distinguished, and without such distinction its inner content because so vague as to vanish altogether.” (Harris, Cosmos and Anthropos, 18) 

“A finite entity is therefore in conflict not only with its other, but at the same time with itself, because, while its necessary difference from its other restricts it within its own limits, its very nature is defined by its boundary and by the negating other that it excludes. To assert itself (or to be asserted as itself) within its natural bounds, therefore, it vacillates between denying its other and affirming its inevitable dependence upon it, acknowledging by implication its unity with it. Accordingly, so long as this interdependence and mutual complementarity is ignored or explicitly denied in the assertion of the finite’s own identity, its attempt to maintain its independence is frustrated, and it contradicts itself because it disowns that which defines what it claims to be, at once asserting and denying its distinguishing demarcation. Such self-contradiction is unavoidable, and is ubiquitous among differentiated finites. Yet, while it is endemic, it is not insuperable, because as soon as the mutual implication of the opposites is recognized and their unification in the identity of a more comprehensive whole is admitted, the contradiction is resolved and the opposition reconciled.” (Harris, Cosmos and Anthropos, 18) 

“Nevertheless, the necessity for differentiation within any genuine whole carries with it the inevitability of internal conflict and provisional disunity, which are the more exacerbated the more the finite elements tend to shun one another and to emphasize their respective exclusiveness in order to maintain their self-identities. This is the consequence of the defect in the finite, which is never self-sufficient within itself, because of its dependence on, and definition by, what it lacks and omits. The result of this conflict is relative chaos and contingency in the unfolding of relations among the elements within a complex, which is overcome, and unity reestablished, only when identity in and through differences is acknowledged, so that the effort of the finite to maintain itself and to persist in its own being succeeds only when it reaches out (so to speak) beyond its own limits to embrace its other and unite with it in mutual complementation in a larger and more comprehensive whole.” (Harris, Cosmos and Anthropos, 18-19) 

“Because of their mutual adaptation, interrelated terms within the whole overlap. They all have in common their subjection to the organizing principle, although they must inevitably differ from one another to avoid complete coincidence. Despite this difference, they overlap because of what they share in common, and because of their mutual coordination and interdependence, each for its own specific identity. While they contrast one with another, negate and exclude each other, they are nevertheless defined by their mutual relations and differences, and they are inseparable from one another owning to their mutual implications. This overlap despite difference is what effects their integration into a single whole. For example, the pieces of a jigsaw puzzle are all different, but because their shapes are reciprocally interlocking there is an area of spatial overlap among them, and apart from spatial interlock, the picture or pattern that together they constitute exercises a regulating and coordinating control over their juxtapositions. Overlap together with integration of opposites in a wider whole involves self-enfoldment, because the wider whole includes the more fragmentary parts, each implying the other in its own self-maintenance. As the implications of the more fragmentary parts are explicated, therefore, what was formerly explicit is repeated along with what subsequently becomes explicit (though formerly implicit), with a consequent complexification of self-enfoldments as the process advances.” (Harris, Cosmos and Anthropos, 19) 

“To return to the jigsaw puzzle, each convoluted shape implies the contrasting shapes that fit together with it (convex with concave), and when they are conjoined, the conjunction explicates (as does the picture on the surfaces) what was implicit in the separate pieces. So when the fragments are connected, the new combination includes everything that the parts contain as well as what, in each separately, was only implicit but is now made explicit. In a developing organism, such as a growing embryo, the mutual implication of successive stages is more apparent, as is its explicit realization in subsequent phases of development, and the self-enfoldment of the earlier forms and processes to create emerging complexifications is unmistakable: segmentation of primitive cells continues at the stage of specialization and functional differentiation, which again is repeated and internalized in each limb and organ. What ensues is a continuous succession of provisional realization of the organizing principle (for the embryo, the structure of the mature organism) in a series of whole increasing in complexity and integration.” (Harris, Cosmos and Anthropos, 19-20) 

“Such a series is clearly a system, and every system must be a whole, because the ordering principle is pervasive throughout and integrates all the parts into a single complex. Some wholes, however, are “open” systems, some are self-repetitive, and some are self-representative (like a fractal curve, which repeats itself in every part and on every scale of magnitude). Of this variety and range of systems we shall say more later; what has so far been maintained is that a whole is a concrescent system, united by a governing principle of organization that differentiates the unity, expressing (or exemplifying) itself in the mutual adjustment of diverse parts (or elements), which consequently overlap in their reciprocal definition and interdependent relationships.” (Harris, Cosmos and Anthropos, 20) 

“The overlap of the interrelated elements is double-edged. On the one hand, the identity of each depends on its distinction from the others; on the other hand, its contrast with its correlates is determined by the principle of structure that orders the system and is universal to them all. Adjacent and consecutive elements, therefore, at once exclude each other in mutual opposition, and are complementary each to the other in mutual determination and dependence for their several identities. They are distinct despite overlap, and they are complementary despite contrast and opposition. In each the others are implicit, so each expresses in some degree the universal principle of wholeness; as each requires integration with its neighbors for its own self-maintenance, as it embraces its other in its persistence in its own character (what Spinoza called its conatus in suo esse perseverandi), it develops into a more comprehensive whole that expresses the universal principle in a higher degree. So the elements of the whole are related as opposites, as distincts, as complementaries, and (in successive degrees of adequacy) as exemplifications of the universal principle of order. In this way, progressing by successive steps, from a primitive element up the scale of degrees of more adequate manifestation of the universal principle, the totality that is immanent in every element and every phase of the process develops. A scale of this kind is dialectical because it proceeds through opposition and distinction, which is at the same time complementarity, interdependence, and mutual identity. In it opposites are united and differents are identified in the unity of the whole they constitute. In the graded scale, each form or phase sublates (supersedes, while it includes, preserves, and transforms) the lower degrees, and foreshadows those yet to emerge.” (Harris, Cosmos and Anthropos, 20-21) 

“It will immediately be obvious that a whole of this nature cannot all be present in any one instant or at any one point. Whatever element or part may be at hand, because of its dependence for its own identity and nature on its relations to other elements, but be unstable within the confines of its own limits. The immanence in it of the organizing principle of the system will impel it to evoke its other and to unite with it to form a more stable entity. Accordingly, the universal principle is necessarily a dynamic principle, forbidding any partial element to rest in isolation from the remainder of the tectonic. It is the nisus, the conatus, that drives the finite element to transcend its own limits in order to persist in its own being. The course that it follows traces a scale of forms, the genus of which is the entire complex, explicitly elaborating the principle of organization. Each for is thus a specific exemplification, in its appropriate degree, of that genus. In each the lesser degrees and lower specific forms are all involved, for each is the realization (at least in part) of their potentialities—it is the explication of what, in them, was implicit. The higher degrees are similarly implicit in lower forms, for the universal is immanent in them all, makes each what it is, and causes it to do whatever it does.” (Harris, Cosmos and Anthropos, 21) 

“The universal is, accordingly, the explanatory principle throughout the gamut, and each successive form, being the most satisfactory explication of the ultimate totality, up to the point reached on the scale, will provide the key to the intelligibility to all the prior phases in the scale, as well as the most fruitful clue to the nature of what lies ahead. Each form will sublate its predecessors while it presages its successors, until the ultimate totality is reached, which will encompass and explicate, including (while it transcends) the entire scale of forms.” (Harris, Cosmos and Anthropos, 21) 

“Certain corollaries follow: (1) there can be no ultimately partial whole, or partially systematic complex. Every partial element is at least a provisional whole, because the universal generic principle is immanent in it. Equally, for that reason, the full totality is implied in every partial form, at every stage of development. Because the principle of organization is immanent in each part and constitutes it a part, its very existence as partial must require (as it is itself involved in) the full elaboration of the whole. Without the full circle, if only in presumption, there can be no arc. (2) Again, for the same reason that any partial element, at any stage, implies the whole, no element, however primitive and lowly, equals zero—there is no zero in the scale. (3) The series cannot go on forever. It must reach a conclusion—namely the totality which is implicit at the beginning and is progressively developing itself throughout. Its principle is one of wholeness; and endless progression never achieves fulfilment, so would never satisfy the immanent universal. Consequently, the scale perpetually tends toward completion and must have an end. In short, neither does the scale include zero nor is it doomed to everlasting insufficiency. (4) Because the unity of the whole must be a differentiated oneness, the principle of organization must specify itself in finite forms, related, as we have said, dialectically. Internal oppositions and contradictions, the incidents of defect, are thus inevitably involved. Although the oppositions are reconciled and the contradictions resolved as the scale advances, they are ineliminable at finite levels, and are overcome only in subsequent phases of development. Contingency and ineptitude are therefore always one aspect of the progressive self-determination of the whole in its immature stages, with attendant conflict, confusion, error and evil, varying in degree with position in the scale. In the ultimate outcome they will all be wiped out and resolved, but this consummation is not possible, nor properly conceivable, without the process of self-development through which it is achieved, that is, without the phases of its own self-specification (for the very reason that it is a whole only by virtue of its own self-differentiation). The consummation is finally attained only with the unity and coalescence of process and end in the fulfilment of the comprehensive dynamic system.” (Harris, Cosmos and Anthropos, 21-22) 

“Such is the character of every whole and of all systematicity. Every whole is a system, however primitive; every system is a whole, structured in accordance with a universal principle of order. That, in consequence, specifies itself in a scale of forms that differ consecutively in the degree of their adequacy to its explicit wholeness. Appearances to the contrary, we shall discover as we proceed, are invariably belied. And the scale of forms is characteristic even of the variety of systems as such. They range from loose and merely haphazard collections of items, through simple arrangements of abstract units, to mathematically structured and dynamically ordered systems. These develop into complexes of more intricately related components and of elements more intimately bound together. The scale continues to the emergence of organic wholes and thence to yet more explicit totalities of more transparently interrelated concepts. Some of these wholes are relatively closed systems; that is, relatively self-contained and self-complete. They are only relatively so, because, apart from the final phase in the scale, none is absolutely whole. Others are open systems; that is, they are configurations or Gestalten remaining constant although imposed upon material in perpetual flux. The structure is a relatively closed system although the material basis is fluid. Yet others are self-reproducing and regenerate their own intrinsic pattern either within or outside themselves.” (Harris, Cosmos and Anthropos, 22) 

“The explicit system of an ordered totality is what Hegel and others have called “the concrete universal”…a system or whole that generates its own particulars by specifying itself in and as a scale of overlapping forms, which are mutual opposites while they are also complementary distincts as well as degrees of explicit realization of the generic principle of the system. Consequently, its internal structure is similarly dialectical, so that, under analysis, at every level and in whatever part it is scanned, the same dialectic pattern reemerges. Hence every system is a system of systems, and every system is self-representative. This fractal character is not always, in fact not often, apparent on the surface, and has to be discovered by close, sometimes minute scrutiny, just as, in fractal geometry, the self-representative character of the fractal curve involved in natural forms (for instance, the shapes of coastlines or mountain rangers, vascular branching, or the reticulation of fronds in the leaves of a fern) only becomes apparent under detailed analysis.” (Harris, Cosmos and Anthropos, 23-24) 

“That wholes are complexes of elements in relation must be clear from what has already been maintained. We have already found that the related elements overlap and are mutually determinant. Hence, the relations will be internal to the terms and will determine their intrinsic natures, just as the intrinsic characters of the terms dictate the relations in which they stand. This is so, of course, because the whole is structured by a principle of order that is immanent in all its elements and regulates the relations between them. But relations of any kind, whether they are in this way internal or are external in the sense that they fall between their terms and leave them unaffected (as is usually assumed in symbolic logic), can be apprehended only by a conscious subject, because what stands in relation must be grasped all together and as a whole. No term alone can comprehend its relation to others, and no subject cognizing them can, in consequence, be confined to any one or any limited group of the terms. It follows that elements in relation must either be objects of some consciousness or must, as a complex totality, be conscious of themselves. T.H. Green, in the first two books of his Prolegomena to Ethics, argues that relations and entities constituted by and dependent for their being on relations can exist only as the objects of some consciousness. This is strictly correct, if by existence one means fully actualized being; but, although a relational complex is only explicit at the level of consciousness, there can be lower levels, prior to consciousness and requisite for its emergence in the order of nature, at which the relations are implicit, so that they exist in potency and latent inter-relativity. These are phases in the dialectical scale prior to mind, through which the natural whole brings itself to consciousness by its inherent nisus to self-completion.” (Harris, Cosmos and Anthropos, 25) 

“One the other hand, what I am advocating is not to be confused with the so-called Neural Identity Theory. That, it seems to me, plays fast and loose with the sense of the word identity. It is alleged that there is only one reality but that it is describable, and is described, in two different languages; and that is palpably false. To describe the sensation I experience when a dentist exposes an unanesthetized nerve is quite definitely not to describe the neural reaction he causes. That, the neurophysiologist assures us, when measured by means of an electrode, is barely noticeable, whereas my sensation is one of extreme and excruciating pain. In like manner, when I see and describe a circle drawn on a blackboard, what I see and describe is circular. But the neurophysiologist discovers that the excited area of the brain is divided into two parts, one in each hemisphere, and that neither part is circular nor even semicircular, but that each is an elongated horseshoe shape. Moreover, whereas the circle perceived lies in a plane perpendicular to the line of sight, the affected cerebral areas are aligned parallel to the line of sight, on either side of it, with the open ends of the horseshoes towards the rear. What now is supposed to be identical with what? In what sense are they identical, since neither has properties or qualities like the other? Furthermore, neurophysiologists can find no difference in character, but only, at most, a difference in disposition and pattern between the nerve impulses accompanying sensations of sight and those of hearing, or between either of these and those of smell or taste. Yet the sensations are so different that comparison between them defeats all efforts to express it in words. Again, in what sense of identity can it be said that the sensations are identical with the neural activity, or that the specifically different linguistic expressions describing them are describing an identical reality?” (Harris, Cosmos and Anthropos, 108-109)

A Question Concerning Schopenhauer’s Conception of the Principium Individuationis

“Basically, Schopenhauer holds that the multiplicity that we see is something constructed by our cognition. My question is this: Fair enough—multiplicity as we experience it is a product of our cognition. But how can we rule out that in the “Thing-in-itself” there’s some non-cognitive process that individuates things?”

This is an interesting question. I’ll try to clarify Schopenhauer’s (sometimes inconsistent) views on the issue and provide what I think would be his answer to your question.

For Schopenhauer, all “oneness” and “manyness,” “unity” and “multiplicity,” are features made possible by the principium individuations; and this, Schopenhauer maintained, was Space-Time. Thus, the categories or determinations of “oneness” and “manyness,” “unity” and “multiplicity,” all, in some way or another, invoke Space-Time. Now, Space-Time, as Schopenhauer points out, has its being (i.e., “realizes” or “manifests” itself) in and through its “operations” as spatio-temporal relations (or spatio-temporal “relatings”) holding good of, and within, Substance (i.e., “matter” and its affections—or “causality”). Thus, the principium individuationis has its being only through Substance. Indeed, this principle has no being apart from its manifestation, and this manifestation just is the differentiating of Substance.

  

Schopenhauer held to an idiosyncratic form of an empiricist criterion of meaning—which explains why he believed that the predicates of “oneness” and “manyness,” “unity” and “multiplicity,” could only be sensibly ascribed to Substance (i.e., “matter”).

 

Now, Schopenhauer maintained that Substance (i.e., “matter”) is a function (or correlate) of the Understanding—just as much as the Understanding is a function (or correlate) of Substance. This correlativity entails that Space-Time (i.e., the principium individuationis) is inextricably tied to the Understanding: the two stand and fall together, and the predicates of “oneness” and “manyness,” “unity” and “multiplicity,” cannot be sensibly ascribed to anything that was not itself a mode or modification of matter—the sensible correlative of the Understanding (i.e., cognition). 

Furthermore, since Schopenhauer reserves the features of “oneness” and “manyness,” “unity” and “multiplicity,” for Substance (which itself has no being apart from Space-Time), he would reject the notion that “The Will” or “Thing-in-itself” is a “One” or a “Unity.” Indeed, Schopenhauer mentions (in some place, I can’t remember where exactly) that “oneness” or “unity” cannot be predicated of “The Will” or “Thing-in-itself” in any but a metaphorical sense. “The Will” or “Thing-in-itself” is the ground of “oneness” and “manyness,” “unity” and “multiplicity.” If anything, “The Will” or “Thing-in-itself” ought to be grasped as a “one-in-many” and as a “unity-in-multiplicity” (expressions which Schopenhauer would likely find objectionable because of its “Hegelian” tones).

My Reading Notes

I have decided to start publishing my reading notes to the site. Since I am accustomed to annotating the pages of books and articles, rather than recording my thoughts in a separate document or notebook, the majority of my published reading notes (the entirety of which spans nearly 6,000 pages) will consist of quotations that I transcribed while reading—having considered them to be thought-provoking and worthy of further exploration (While many quotes contain fragments that I sympathize with, one will encounter passages which are radically disparate from my own beliefs and ways of thinking). I hope this archive sparks your interest. Enjoy.

Reading Notes