Reading Notes: August 12th, 2024

 “To be finite is to be some one among others, some one which is not others. One finite ends where the other finite beings; it is bounded from the outside, and can not go beyond itself without becoming something else, and thereby perishing. We have not to dwell on the inherent contradiction of the finite. Its being is to fall wholly within itself; and yet, so far as it is finite, so far is it determined wholly by the outside….What does infinite mean? There are two wrongs views on the subject, which we will take one at a time. (1) Infinite is not-finite, and that means ‘end-less’. What does endless mean? Not the mere negation of end, because a mere negation is nothing at all, and infinite would thus equal 0. The endless is something positive, it means a positive quantity which has no end. Any given number of units is finite; but a series of units, which is produced indefinitely, is infinite….It is however clear that this infinite is a perpetual self-contradiction, and, so far as it is Real, is only finite. Any Real quantity has ends, beyond which it does not go. ‘Increase the quantity’ merely says ‘Put the end further off’; but in saying that, it does say ‘Put the end’. ‘Increase the quantity forever’ means, ‘Have forever a finite quantity, and forever say that it is not finite’. In other words, ‘Remove the end’ does imply, by that very removal and the production of the series, the making of a fresh end; so that we still have a finite quantity. Here, so far as the infinite exists, it is finite; so far as it is told to exist, it is told again to be nothing but finite. (2) Or, secondly, the infinite is not the finite, no longer in the sense of being something else, which is different in quantity. The infinite is not in the world of limited things; it exists in a sphere of its own. The mind (e.g.) is something beside the aggregate of its states. God is something beside the things of this world….But here once more, against its will, infinite comes to mean merely finite. The infinite is a something over against, beside, and outside the finite; and hence is itself also finite, because limited by something else….What then is the true sense of infinite? As before, it is the negation of the finite; it is not-finite. But, unlike both the false infinites, it does not leave the finite as it is. It neither, with (1), says ‘the finite is to be not-finite, nor, with (2), tries to get rid of it by doubling it. It does Really negate the finite, so that the finite disappears, not by having a negative set over against it, but by being taken up into a higher unity, in which becoming an element, it ceases to have its original character, and is both suppressed and preserved. The infinite is thus ‘the unity of the finite and infinite’. The finite was determined from the outside, so that everywhere to characterize and distinguish it was in fact to divide it. Wherever you defined anything you were at once carried beyond to something else and something else, and this because the negative, required for distinction, was an outside other. In the infinite you can distinguish without dividing; for this is a unity holding within itself subordinated factors which are negative of, and so distinguishable from, each other; while at the same time the whole is so present in each, that each has its own being in its opposite, and depends on that relation for its own life. The negative is also its affirmation. Thus the infinite has a distinction, and so a negation, in itself, but is distinct from and negated by nothing but itself. Far from being one something which is not another something, it is a whole in which both one and the other are mere elements. This whole is hence ‘relative’ utterly and through and through, but the relation does not fall outside it; the relatives are moments in which it is the relation of itself to itself, and so is above the relation, and is absolute Reality. The finite is relative to something else; the infinite is self-related. It is this sort of infinite which the mind is. The simplest symbol of it is the circle, the line which returns into itself, not the straight line produced indefinitely.” (Bradley, Ethical Studies, 70-71)

“The Real is self-existent. And we may put this otherwise by saying, The Real is what is individual….It is a mistake to suppose that “The Real is individual” means either that the Real is abstractly simple, or is merely particular. Internal diversity does not exclude individuality, and still less is a thing made self-existent by standing in a relation of exclusion to others.” (Bradley, The Principles of Logic, Vol. I, 44)

“If space and time are continuous, and if all appearance must occupy some time or space—and it is not hard to support both of these theses—we can at once proceed to the conclusion, no mere particular exists. Every phenomenon will exist in more times or spaces than one; and against that diversity will be itself a universal.” (Bradley, The Principles of Logic, Vol. I, 44)

“We naturally think that the Real, at least as we know it, must be present. Unless I come into contact with it directly, I can never be sure of it. Nothing in the end but what I feel can be Real, and I can not feel anything unless it touches me. But nothing again can immediately encounter me save that which is present. If I have it not here and now, I do not have it at all. “The present is Real;” this seems indubitable. And are we to say that the momentary appearance is therefore Real? This indeed would be mistaken. If we take the Real as that which is confined to a single “here” or a single “now” (in this sense making it particular), we shall have questions on our hands we shall fail to dispose of. For, besides the difficulties as to the truth of all universal judgments, we are threatened with the loss of every proposition which extends beyond the single instant. Synthetic judgments must at once be banished if the Real is only the phenomenon of a moment. Nothing either past or future in time, nor any space I do not directly perceive, can be predicated as adjectives of our one “now” and “here.” All such judgments would be false, for they would attribute to the existent qualities which confessedly are non-existent, or would place the Real as one member in a series of utter unrealities.” (Bradley, The Principles of Logic, Vol. I, 50-51)

“But perhaps we feel we may escape this consequence; or at all events feel so sure of our premise that we can not give it up. “The Real is confined to one here or one now.” But supposing this true, are we sure we know what it is we understand by our “now” and “here”? For time and extension seem continuous elements: the here is one space with the other heres round it; and the now flows ceaselessly and passes forever from the present to the past.” (Bradley, The Principles of Logic, Vol. I, 51)

“We may avoid this difficulty, we may isolate the time we call the present, and fix our now as the moment which is, and has neither past, nor future, nor transition in itself. But here we fall into a hopeless dilemma. This moment which we take either has no duration, and in that case it turns out to be no time at all: or, if it has duration, it is a part of time, and is found to have transition in itself. If the now in which the Real appears is purely discrete, then first we may say that, as characterized by exclusion, the phenomenon, if apparent, is not self-subsistent, and so not Real. But apart from that objection, and to return to our dilemma, the now and the here must have some extension. For no part of space or time is a final element. We find that every here is made up of heres, and every now is resolvable into nows. And thus the appearance of an atomic now could not show itself as any one part of time. But, if so, it could never show itself at all. Or, on the other hand, if we say the appearance has duration, then, like all Real time, it has succession in itself, and it would not be the appearance of our single now.” (Bradley, The Principles of Logic, Vol. I, 51-52)

“It is a mistake to suppose that the present is a part of time, indivisible and stationary, and that the here and now can be solid and atomic. In one sense of the word the present is no time. Itself no part of the process, it is a point we take within the flow of change. It is the line that we draw across the stream, to fix in our mind the relations of one successive event to another event. “Now,” in this sense, stands for “simultaneous with:” it signifies not existence but bare position in the series of time. The Reality is not present in the sense of given in one atomic moment.” (Bradley, The Principles of Logic, Vol. I, 52)

“If time consists of discrete parts, it is hard to see how the fact of succession can possibly be explained, unless time be taken between these parts of time. And that would lead to untenable conclusions. But it is the fact of change which shows that time is continuous. The rate of change, the number of events in every part of time, may, so far as we know, be increased indefinitely: and this means that in every part of time more than one event may be taking place. If the parts be discrete, then not only will motion imply that a thing is in several places in one time (and this is a fact), but also (which is absurd) that throughout all these places no time elapses, that they are strictly contemporaneous.” (Bradley, The Principles of Logic, Vol. I, 52)

“What we mean, when we identify presence with Reality, is something different. The Real is that which I come into immediate contact, and the content of any part of time, any section of the continuous flow of change, is present to me if I directly encounter it. What is given in perception, though it change in my hands, is now and here if only I perceive it. And within that perception any aspect or part, which I specially attend to, is specially present, is now and here in another sense than the rest of that content. The present is the filling of that duration in which the Reality appears to me directly: and there can be no part of the succession of events so small or so great, that conceivably it might not appear as present. In passing we may repeat and may trace the connection of those shades of meaning we have found in “presence.” (i) Two events in time are now to one another, if both are given simultaneously in my series. (ii) Since the Real appears in the series of time, the effort to find it both present and existing within that series, creates the fiction of the atomic now. (iii) If the Real can never exist in time, but only appear there, then that part of the series in which it touches me is my present. (iv) And this suggests the reflection that presence is Really the negation of time, and never can properly be given in the series. It is not the time that can ever be present, but only the content.” (Bradley, The Principles of Logic, Vol. I, 52-53)

“We must be satisfied with knowing that the Real, which (we say) appears in perception, does not appear in one single moment. And if we will pause and reflect for a little, we shall see how hardened we are in superstitions. When we ask for Reality, we at once encounter it in space and time. We find opposed to us a continuous element of perceptual change. We begin to observe and to make distinctions, and this element becomes a series of events. And here we are tempted to deceive ourselves grossly. We allow ourselves to talk as if there existed an actual chain of Real events, and as if this chain were somehow moved past us, or we moved along it, and as if, whenever we came to a link, the machinery stopped and we welcomed each new link with our “here” and our “now.” Still we do not believe that the rest of the links, which are not here and now, do all equally exist, and, if so, we can hardly be quite sure of our chain. And the link, if we must call it so, which is now and here, is no solid substance. If we would but observe it, we should see it itself to be a fluid sequence whose parts offer no resistance to division, and which is both now, and itself without end made up of nows.” (Bradley, The Principles of Logic, Vol. I, 53)

“Or we seem to think that we sit in a boat, and are carried down the stream of time, and that on the bank there is a row of houses with numbers on the doors. And we get out of the boat, and knock at the door of number 19, and, re-entering the boat, then suddenly find ourselves opposite 20, and having there done the same, we go on to 21. And, all this while, the firm fixed row of the past and future stretches in a block behind us and before us.” (Bradley, The Principles of Logic, Vol. I, 53-54)

“Let us fancy ourselves in total darkness hung over a stream and looking down on it. The stream has no banks, and its current is covered and filled continuously with floating things. Right under our faces is a bright illuminated spot on the water, which ceaselessly widens and narrows its area, and shows us what passes away on the current. And this spot that is light is our now, our present. We may go still further and anticipate a little. We have not only an illuminated place, and the rest of the stream in total darkness. There is a paler light which, both up and down stream, is shed on what comes before and after our now. And this paler light is the offspring of the present. Behind our heads there is something perhaps which reflects the rays from the lit-up now, and throws them more dimly upon the past and future. Outside this reflection is utter darkness; within it is gradual increase of brightness, until we reach the illumination immediately below us. In this image we shall mark two things, if we are wise. It is possible, in the first place, that the light of the present may come from behind us, and what reflects the light may also bestow it. We can not tell that, but what we know is, that our know is the source of the light that falls on the past and future. Through it alone do we know there exists a stream of floating things, and without its reflection past and future would vanish. And there is another point we must not lose sight of. There is a difference between the brightness of the now, and the paler revelation of past and future. But, despite this difference, we see the stream and what floats in it as one. We overcome the difference. And we do so by seeing the continuity of the element in past present and future. It is because, through the different illuminations, there are points of connection offered by what floats, in other words, a sameness of content, that the stream and its freightage becomes all one thing to us, and we even forget that most of what we see is not self-subsistent but borrowed and adjectival. We shall perceive hereafter that time and space beyond here and now are not strictly existent in the sense in which the present is. They are not given directly but are inferred from the present. And they are so inferred because the now and here, on which the light falls, are the appearance of a Reality which forever transcends them, and, resting upon which, we go beyond them.” (Bradley, The Principles of Logic, Vol. I, 54-55)

“[The] now and here, in which the Real appears, are not confined within simply discrete and resting moments. They are any portion of that continuous content with which we come into direct relation. Examination shows that not only at their edges they dissolve themselves over into there and then, but that, even within their limits as first given, they know no repose. Within the here is both here and there; and in the ceaseless process of change in time you may narrow your scrutiny to the smallest focus, but you will find no rest. The appearance is always a process of disappearing, and the duration of the process which we call our present has no fixed length.” (Bradley, The Principles of Logic, Vol. I, 55)

“We must get rid of the erroneous notion (if we have it) that space and time are “principles of individuation,” in the sense that a temporal or spatial exclusion will confer uniqueness upon any content. It is an illusion to suppose that, by speaking of “events,” we get down to Real and solid particulars, and leave the airy region of universal adjectives. For the question arises, What space and time do we Really mean, and how can we express it so as not to express what is as much something else? It is true that, in the idea of a series of time or complex of space, uniqueness is in one sense involved; for the parts exclude one another reciprocally. But they do not exclude, unless the series is taken as one continuous whole, and the relations between its members are thus fixed by the unity of the series. Apart from this unity, a point on its recurrence could not be distinguished from the point as first given.” (Bradley, The Principles of Logic, Vol. I, 63)

“The Real we divined to be self-existent, substantial, and individual: but, as it appears within a presentation, it is none of these. The content throughout is infected with relativity, and, adjectival itself, the whole of its elements are also adjectival. Though given as fact every part is given as existing by reference to something else. The mere perpetual disappearance in time of the given appearance is itself the negation of its claim to self-existence. And again, if we take it while it appears, its limits, so to speak, are never secured from the inroads of unreality. In space or in time its outside is made fact solely by relation to what is beyond. Living by relation to what it excludes, it transcends its limits to join another element, and invites that element within its own boundaries. But with edges ragged and wavering, that flow outward and inward unstably, it already is lost. It is adjectival on what is beyond itself. Nor within itself has it any stability. There is no solid point of either time or space. Each atom is merely a collection of atoms, and those atoms again are not things but relations of elements that vanish. And when asked what is ultimate, and can stand as an individual, you can answer nothing. The Real cannot be identical with the content that appears in presentation. It forever transcends it, and gives us a title to make search elsewhere….If the Reality is self-existent, self-contained, and complete, it needs, one would think, no great effort of reason to perceive that this character is not to be found in a mere series of phenomena. It is one thing to seek the Reality in that series: it is quite another thing to try to find as the series. A completed series in time or space cannot possibly exist. It is the well-known phantasm of the spurious infinite, a useful fiction, it may be, for certain purposes and at certain levels of thought, but none the less a phantasm which, until it is recognized, stops the way of all true philosophic thought.” (Bradley, The Principles of Logic, Vol. I, 70-71)

“If we mean by phenomena the things we perceive, or the facts or appearances that are given to us, then the whole of England below our horizon (to say nothing at all of America and Asia), and every event that is past or future are not phenomena. They are not perceived facts. They exist in our minds are mere ideas, as the meaning of symbols. A phenomenon, I repeat, that is past or future is a sheer self-contradiction. It is time we thought of giving up our habit of talking about the “series of phenomena,” or “thread of perceptions,” or Heaven knows what else, as though we held these facts in our hands. One thing or the other. Either a phenomenon may be idea, the content of a symbol and not even predicated directly of the present perception, or there is no phenomenon but what I here and now perceive….If a fact or event is what is felt or perceived, then a fact that is past is simple nonsense (cf. Book II. Part II. Chap. I.). Of course, I know, it is easy to say that past events are all Really there, and, being there, are remembered; as I presume the future, being all there, is anticipated. But suppose that there is a series of facts, both past and future, outside our minds, the question remains How can they get in?....Events past and future, and all things not perceived, exist for us only as ideal constructions connected, by an inference through identity of quality, with the Real that appears in present perception.” (Bradley, The Principles of Logic, Vol. I, 73-74)

“[The] continuity of the element of time strictly excludes a mere serial character.” (Bradley, The Principles of Logic, Vol. I, 80)

“We maintain, on the other hand, that analytic judgments of sense are all false. There are more ways than one of saying the thing that is not true. It is not always necessary to go beyond the facts. It is often more than enough to come short of them. And it is precisely this coming short of the fact, and statin a part as if it were the whole, which makes the falseness of the analytic judgment. The fact, which is given us, is the total complex of qualities and relations which appear to sense. But what we assert of this given fact is, and can be, nothing but an ideal content. And it is evident at once that the idea we use can not possibly exhaust the full particulars of what we have before us. A description, we all know, cannot ever reach to a complete account of the manifold shades, and the sensuous wealth of one entire moment of direct presentation. As soon as we judge, we are forced to analyze, and forced to distinguish. We must separate some elements of the given from others. We sunder and divide what appears to us as a sensible whole. It is never more than an arbitrary selection which goes into the judgment. We say “There is a wolf,” or “This tree is green:” but such poor abstractions, such mere bare meanings, are much less than the wolf and the tree which we see; and they fall even more short of the full particulars, the mass of inward and outward setting, from which we separate the wolf and the tree. If the Real as it appears is X = a b c d e f g h, then our judgment is nothing but X = a, or X = a—b. But a—b by itself has never been given, and is not what appears. It was in the fact and we have taken it out. It was of the fact and we have given it independence. We have separated, divided, abridged, dissected, we have mutilated the given….Now I am not urging that the analytic judgment is in no sense true. I am saying that, if you take it as asserting the existence of its content as given fact, your procedure is unwarranted. And I ask, on what principle do you claim the right of selecting what you please from the presented whole and treating that fragment as an actual quality? It certainly does not exist by itself, and how do you know that, when put by itself, it could be a quality of this Reality? The sensible phenomenon is what it is, and is all that it is; and anything less than itself must surely be something else. A fraction of the truth, here as often elsewhere, becomes entire falsehood because it is used to qualify the whole.” (Bradley, The Principles of Logic, Vol. I, 94-97)

“The analytic judgment is not true per se. It cannot stand by itself. Asserting, as it does, of the particular presentation, it must always suppose a further content, which falls outside that fraction it affirms. What it says is true, if true at all, because of something else. The fact it states is Really fact only in relation to the rest of the context, and only because of the rest of that context. It is not true except under that condition. So we have a judgment which is Really conditioned, and which is false if you take it as categorical. To make it categorical and true, you must get the condition inside the judgment. You must take up the given as it Really appears, without omission, unaltered, and unmutilated. And this is impossible. For ideas are not adequate to sensible perception, and, beyond this obstacle, there are further difficulties. The Real, which appears within the given, cannot possibly be confined to it. Within the limit of its outer edges its character gives rise to the infinite process in space and time. Seeking there for the simple, at the end of our search we still are confronted by the composite and relative. And the outer edges themselves are fluent. They pass forever in time and space into that which is outside them. It is true that the actual light we see falls only upon a limited area; but the continuity of the element, the integrity of the context, forbids us to say that this illuminated section by itself is Real. The reference of the content to something other than itself lies deep within its internal nature. It proclaims itself to be adjectival, to be relative to the outside; and we violate its essence if we try to assert it as having existence entirely in its own right. Space and time have been said to be “principles of individuation.” It would be truer to say they are principles of relativity. They extend the Real just as much as they confine it. I do not mean that past and future are actually given, and that they come within the circle of presentation. I mean that, although they cannot be given, the given would be destroyed by their absence. If Real with them, it would not be given; and, given without them, it is forever incomplete and therefore unreal. The presented content is, in short, not compatible with its own presentation. It involves a contradiction, and might at once on that ground be declared to be unreal.” (Bradley, The Principles of Logic, Vol. I, 98-99)

“We saw that you cannot ascribe to the Real one part of what is given in present perception. And now we must go further. Even if you could predicate the whole present content, yet you still would fail unless you asserted also both the past and the future. You cannot assume (or I, at least, do not know your right to assume) that the present exists independent of the past, and that, taking up one fragment of the whole extension, you may treat this part as self-subsistent, as something that owes nothing to its connection with the rest. If your judgment is to be true as well as categorical, you must get the conditions entirely within it. And here the conditions are the whole extent of spaces and times which are required to make the given complete. The difficulty is insuperable. It is not merely that ideas cannot copy facts of sense. It is not merely that our understandings are limited, that we do not know the whole of the series, and that our powers are inadequate to apprehend so large an object. No possible mind could represent to itself the completed series of space and time; since, for that to happen, the infinite process must have come to an end, and be Realized in a finite result. And this cannot be. It is not merely inconceivable psychologically; it is metaphysically impossible. Our analytic judgments are hence all either false or conditioned….We are fastened to a chain, and we wish to know if we are Really secure. What ought we to do? Is it much use to say, “This link we are tied to is certainly solid, and it is fast to the next, which seems very strong and holds firmly to the next: beyond this we cannot see more than a certain moderate distance, but, so far as we know, it all holds together”? The practical man would first of all ask, “Where can I find the last link of my chain? When I know that it is fast, and not hung in the air, it is time enough to inspect the connection.” But the chain is such that every link begets, so soon as we come to it, a new one; and, ascending in our search, at each remove we are still no nearer the last link of all, on which everything depends. The series of phenomena is so infected with relativity, that, while it is itself, it can never be made absolute. Its existence refers itself to what is beyond, and, did it not do so, it would cease to exist. A last fact, a final link, is not merely a thing which we cannot know, but a thing which could not possibly be Real. Our chain by its nature cannot have a support. Its essence excludes a fastening at the end. We do not merely fear that it hangs in the air, but we know it must do so. And when the end is unsupported, all the rest is unsupported. Hence our “conditioned” truth is only “conditional.” It avowedly depends on what is not fact, and it is not categorically true. Not standing by itself, it hangs from a supposition; or perhaps still worse destiny awaits it, it hangs from nothing and falls altogether….Are the presented phenomenon, and series of phenomena, actual Realities? And, we have seen, they are not so. The given in sense, if we could seize it in judgment, would still disappoint us. It is not self-existent and is therefore unreal, and the Reality transcends it, first in the infinite process of phenomena, and then altogether. The Real, which (as we say) appears in perception, is neither a phenomenon nor a series of phenomena.” (Bradley, The Principles of Logic, Vol. I, 100-101)

“The units themselves can only be determined relatively to each other, and there is no sense in asking how big anything is unless we measure it by a presupposed standard.” (Lotze, Logic, Bk. II, 338)

“A circular movement will only appear circular to a spectator, whose standpoint is somewhere in the line drawn through the centre of the circle at right angles to its plane; to an eye situated anywhere outside this axis and this plane it will appear an oval; while if one views it from any point in the plane of the circle but outside its circumference, it will appear as an oscillation in a straight line. The synthesis of the times traversed by the moving point and the loci corresponding to the times will form a separate series for each point of view, and each such series will be regular in its formation, though one of them will have much more value than another as an indication of what Really takes place.” (Lotze, Logic, Bk. II, 339)

“To put it quite simply, a man who never observes a place of public resort but once every seven days and that on a Sunday afternoon, has no right to suppose because it is crowded then, that it is as crowded on a week-day. A man who never looks at the moon but through a chink which only allows him to see it at its full height, cannot guess the path it pursues through the heavens for the rest of its time.” (Lotze, Logic, Bk. II, 343)

“The apprehending consciousness is no resisting surface, curved or plane, smooth or rough, nor would it gain anything by reflecting rays of light no matter in what direction; it is in itself and in its own coordinating unity, which is not a space, and not a surface, but an activity, that it has to combine the separate ideas excited in it into the perception of a spatial arrangement, which perception again is not itself an order in space but only the idea of that order.” (Lotze, Logic, Bk. III, 459)

“It is not permissible to speak of points of space, as if they constituted the positive element of space, since space, on account of its lack of difference, is only the possibility and not the actual positedness of being-outside-of-one-another and of the negative, and is therefore absolutely continuous; the point, the being-for-self, is consequently rather the negation of space, a negation which is posited in space….The point has meaning only in so far as it is spatial, and so external both to itself and to others….Something which was not external in its own self but only to an Other, would be a point….But the Other of the point is just as much a self-externality as the point is, and therefore the two are undistinguished and unseparated. Beyond its limit, as its otherness, space is still in community with itself, and this unity in asunderness is continuity.” (Hegel, The Philosophy of Nature, §254)

“The point is “immediate differenceless self-externality.” (Hegel, The Philosophy of Nature, §256)

“I perceived that it is impossible to find the principles of a true unity in matter alone, or in what is only passive, since everything in it is only a collection or aggregation of parts to infinity. Now, a multitude can derive its reality only from true unities, which have some other origin and are considerably different from [mathematical] points [which are only the extremities and modifications of extension,] which all agree cannot make up the continuum.” (Leibniz, A New System of Nature, 139)

“Thus physical points are indivisible only in appearance; mathematical points are exact, but they are merely modalities.” (Leibniz, A New System of Nature, 142)

“Extension or space and the surfaces, lines, and points one can conceive in it are only relations of order or orders of coexistence, both of the actually existing thing and for the possible thing one can put in its place. Thus they have no bases for composition, any more than does number. A number divided, ½ for example, can be further divided into two fourths or four eighths, etc. to infinity, without our being able to arrive at any smallest fractions or to conceive of the number as a whole that is formed by the coming together of ultimate elements. It is the same for the line, which can be divided just as this number can. Also, properly speaking, the number ½ in the abstract is an entirely simple ratio, in no way formed through the composition of other fractions, though in things numbered two fourths equal one half. And one can say that same thing for the abstract lines. And it is in this way that mathematical points have their place; they are only modalities, that is, extremities.” (Leibniz, Note on Foucher’s Objection, 142)

“I don’t think that substance consists of extension alone, since the concept of extension is incomplete. And I don’t think that extension can be conceived through itself, but I think it is a notion that is resolvable and relative. For it is resolvable into plurality, continuity, and coexistence, that is, the existence of parts at one and the same time. Plurality is also found in number, and continuity is also found in time and motion, but coexistence is really present alone in an extended thing. But from this it appears that a something must always be assumed which is either continued or diffused, as whiteness is in milk, color, ductility and weight are in gold, and resistance is in matter. For continuity taken by itself (for extension is nothing but simultaneous continuity) no more constitutes a complete substance than does multitude or number, where there must be something numbered, repeated, and continued….I think that the unity of an extended thing lies only in its having been abstracted, namely, when we withdraw the mind from the internal motion of the parts, by virtue of which each and every part of matter is, in turn, actually subdivided into different parts, something that plentitude [i.e., the fact that all place is occupied] does not prevent. The parts of matter don’t differ only modally if they are sprinkled with souls and entelechies, things which always exist.” (Leibniz, From the Letters to de Volder, 171-172)

“Indeed, a mathematical line is like the arithmetical unity [i.e., the number 1]: for both, the parts are only possible and completely indefinite. A line is no more an aggregate of the lines into which it can be divided than the number 1 is an aggregate of the fractions into which it can be broken up….If by the mathematical body you mean space, it must be compared with time; if you mean extension, it must be compared to duration. Indeed, space is only the order of existing for possibles that exist simultaneously, just as time is the order of existing for possibles that exist successively. And the state or series of things relates to time just as to physical body relates to space. Body and the series of things add motion to space and to time, that is, they add action and passion and their source [principium]. Indeed, as I have often reminded you (although you seem not to have noticed), extension is an abstraction from the extended thing, and it is no more a substance than number or multitude can be considered to be a substance; it represents only a certain nonsuccessive ([unlike] duration) and simultaneous diffusion or repetition of a certain nature, or what comes to the same thing, it represents certain order among themselves. It is this nature, I say, that is extended or diffused. And so the notion of extension is relative, that is, extension is the extension of something or the duration of something. Furthermore, the nature which is supposed to be diffused, repeated, continued, is that which constitutes the physical body…” (Leibniz, From the Letters to de Volder, 178-179)

“The diffusion that I conceive of in extension…is, I claim, nothing but the continuity [continuatio] in which a part is similar to a whole, as, for example, we conceive of whiteness as diffused in milk, the same direction as diffused everywhere in a straight line, and equal curvedness as diffused in the circumference of a circle.” (Leibniz, From the Letters to de Volder, 183)