Reading Notes: April 26th, 2022

“Upon examination, the causal law is found to have a most intimate connection with the temporal and spatial notions, so intimate in fact that at first sight it may seem that this law can have no real meaning when separated from action in space and occurrence in time….[The] formula: Every change has its cause…requires that between every case and its effect a certain interval of time shall have elapsed; otherwise we have an effect contemporaneous with the cause and no change has resulted. Yet here a difficulty for thought arises, for a cause which is separated from its effect from the smallest conceivable time is not properly the cause of the given effect. If between the cause A and the effect B a given time interval exists, reason will attempt to fill up the gap, as for example A, a, b, B; in which series a is the effect of A and the cause of b, which in turn becomes the cause of B. But again the same difficulty repeats itself, for between each member of the time series in the second formula a certain time is likewise supposed to have elapsed. Other members must be introduced and the process must be carried on ad infinitum. Thus reason at this point finds the temporal notion of causality inadequate.” (Colvin, Schopenhauer’s Doctrine of the Thing-in-itself and His Attempt to Relate it to the World of Phenomena, 12) 

“For us, the problem is not by what precise steps the mind comes to “feign” a unity in its objects which is not really there, but whether this conception of a feigned or subjective unity imposed by the mind upon a number of actually disconnected qualities is itself ultimately intelligible. Thus, the metaphysical issue may be narrowed down to the following question: Can we intelligibly hold that a thing is in reality simply a number of qualities, not in their own nature connected, which arbitrarily regard for our own purposes as one? In other words, can we say the thing is simply identical with its qualities considered as a mere sum or collection, and any further unity of the kind the old Metaphysics denotes by “substance,” a mental addition of our own to the facts? Now there are two considerations—both ultimately reducible in principle to one—which seem fatal to the identification of a thing with its qualities, considered as merely discrete. (I) There can be no doubt that it is largely true to say that a given group of qualities appear to us to be the qualities of one thing because we attend to them as one. And again, attention is undoubtedly determined by, or, to put it in a better way, is an expression of our own subjective interests. But these considerations do not in the least show that attention is purely arbitrary. If we take any group of qualities to form one thing because we attend to it as one, it is equally true that we attend to it as one because it affects our subjective purposes or interests as one. That group of qualities is “one thing” for us which functions as one in its bearing upon our subjective interests. What particular interest we consider in pronouncing such a group one, in what interest we attend to it, may be largely independent of the qualities of the group, but the fact that the group does function as one in respect to this interest is no “fiction” or creation of our own thought; it is the expression of the nature of the group itself, and is independent of “our mind” in precisely the same sense in which the existence and character of any single member of the group of qualities is independent. There is no sense in assigning the single quality to “the given,” and the union of the qualities into a single group to “the work of the mind,”; in one sense both are the “work of the mind,” in another both are the expression of the nature of the “given.” (II) Again, the insufficiency of the simple identification of the thing with its qualities, considered as a mere collection, may be illustrated by considering what the group of qualities must contain. The group of qualities is obviously never present in its entirety at any moment of experience. For the majority of what we call qualities of a thing are simply the ways in which the “thing” behaves in the presence of various other things, its modes of reaction upon a number of stimuli. Now, at any moment of the “thing’s” existence it is only actually reacting upon a few of the possible stimuli, and thus only exhibiting a few of its qualities. The vast majority of its qualities are at any moment what Locke calls “powers,” i.e., ways in which it would behave if certain absent conditions were fulfilled. Thus, the thing to which we ascribe a number of predicates as its qualities is never the actual group of predicates themselves….Most of a thing’s qualities thus are mere possibilities; the nature of a thing is to act in this or that way under certain definite conditions which may or may not be realized in actual existence. Thus, the collection of qualities with which Phenomenalism identifies a thing has itself no real existence as a collection. The collection is just as much a “fiction of the mind” as the unity which we attribute to it. Yet the fact that the thing’s qualities are mainly mere possibilities does not destroy the existence of the thing. It actually is, and is somehow qualified by these possibilities. And for that very reason its existence cannot be identified with the actual realization of these possibilities in a group or collection of events. We might add as a further consideration, that the number of such possibilities is indefinite, including not only the ways in which the thing has behaved or will behave on the occurrence of conditions at present non-existent, but also all the ways in which it would behave on the occurrence of conditions which are never realized in actual existence….The being of the things must be sought not in the actual existence of the group of sensible qualities, but in the law or laws stating the qualities which would be exhibited in response to varying sets of conditions. This is just as true of the so-called primary qualities of things as of any others. Thus, the mass and again the kinetic energy of a conservative material system are properly names for the way in which the system will behave under determinate conditions, not of modes of behavior which are necessarily actually exhibited throughout its existence. The laws of motion, again, are statements of the same hypothetical kind about the way in which, as we believe, particles move if certain conditions are fulfilled. The doctrine according to which all events in the physical world are actual motions, rests on no more than a metaphysical blunder of a peculiarly barbarous kind.” (Taylor, Elements of Metaphysics, 135-137)

“Considerations of this kind compel us to forego the attempt to find the substance or being of a thing in the mere sequence of its different states considered as an aggregate. To make Phenomenalism workable, we are forced to say at least that the thing or substance to which the various attributes are assigned is the “law of its states,” or again is “the mode of relation of its various qualities.” Such a definition has obviously a great advantage over either of the who we have just rejected. It is superior to the conception of the thing as an unknown substratum of qualities, since it explicitly excludes the absurd notion of a world of things which first are, without being in any determinate way, and then subsequently set up determinate ways of existing among themselves. For a law, while not the same thing as the mere collection of occurrences in which it is realized, has no existence of its own apart from the series of occurrences which conform to it. Again, every law is a statement of possibilities, a formula describing the lines which the course of events will follow if certain conditions are operative; no law is a mere register of actually observed sequences. Hence, in defining the thing as the “law of its states,” we avoid the difficulty dealt with in the last paragraph, that the collection of the thing’s states never actually exists as a “given” collection. Thus, for ordinary practical purposes the definition is probably a satisfactory one. Yet it should be evident that in calling the thing the “law” of its states, we merely repeat the metaphysical problem of the unity of substance without offering any solution of it. For, not to dwell on the minor difficulty that we might find it impossible to formulate a single law connecting all the ways in which one thing reacts upon others, and thus ought more properly to speak in the plural of the laws of the states, we are not left with two distinct elements or aspects of the being of the thing, namely, the successive states and the law of their succession, and how these two aspects are united the theory fails to explain. We have the variety and multiplicity on the one hand in the states or qualities of the thing, its unity on the other in the form of the law connecting these states, but how the variety belongs to or is possessed by the unity we know no better than before. Thus, the old problem of substance returns upon us; the many qualities must somehow be the qualities of a single thing, but precisely how are we to conceive this union of the one and the many? At this point, light seems to be thrown on the puzzle by the doctrine of Leibnitz, that the only way in which a unity can, without ceasing to be such, contain and indefinite multiplicity is by “representation.” Experience, in fact, presents us with only one example of a unity which remains indubitably one while embracing an indefinite multiplicity of detail, namely the structure of our experience itself. For the single experience regularly consists of a multiplicity of mental states, both “focal” and “marginal,” simultaneous and successive, which are nevertheless felt as one single whole because they form the expression of a coherent purpose or interest. And this conscious unity of feeling, determined by reference to a unique interest, is the only instance to which we can point when we desire to show by an actual illustration how what is many can at the same time be one. If we can think of the thing’s qualities and the law of their connection as standing to one another in the same way as the detailed series of acts embodying a subjective interest of our own, and the interest itself which by its unity confers a felt unity on the series, we can in principle comprehend how the many qualities belong to the one thing. In that case the thing will be one “substance” as the embodiment of an individual experience, determined by a unique subjective interest, and therefore possessing the unity of immediate feeling. Its many qualities will “belong” to it in the same sense in which the various constituents of an experience thus unified by immediate feeling are said to “belong” to the single experience they constitute. And thus, our idealistic interpretation of the general nature of Reality will be found to contain the solution of the problem of Substance and Quality.” (Taylor, Elements of Metaphysics, 137-139)

“Continuity is, strictly speaking, a property of a certain series, and may be defined for purposes of references much as follows. A series is continuous when any term divides the whole series unambiguously into two mutually exclusive parts which between them comprise all the terms of the series, and when every term which so divides the series is itself a term of that series. From this second condition it obviously follows that a number of intermediate terms can always be inserted between any two terms whatever of a continuous series; no term of the series has a next term. This is the peculiarity of the continuous with which we shall be specially concerned. Thus, the series of points on a straight line is continuous because (I) any point P on the line divides it into two collections of points in such a way that every point of the one is to the left of every point of the other, and every point of the second to the right of every point of the former; and (II) every point which divides the line in this way is a point on the line. Again, the whole series of real numbers is continuous for the same reason. Every member of the number-series divides it into two classes, so that every number of one is less than every number of the other, and every number which thus divides the series itself is a term of the number series….From the continuity of the series of real numbers it follows that any other series which corresponds point for point with the terms of the number series will be continuous. Now one such series is that of the successive parts of time. Every moment of time divides the whole series of moments into two mutually exclusive classes, the moments before itself and the moments which are not before itself. And whatever thus divides the time series is itself a moment in that series. Hence from the continuity of the time-series it follows that any puzzles created by this property of continuousness will apply to the case of Causation….We may state the difficulty thus: (I) Causation cannot possibly be thought of as discontinuous, i.e., as the sequence of one distinct event upon an assemblage of other events without gross contradiction. To think of it as discontinuous, we must conceive the cause A to exist first in its completeness, and then to be suddenly followed by the effect B. (That the cause A consists of a number of conditions, a, b, c, … which themselves come into existence successively, and that A is not there until the last of these conditions have been realized, makes no difference to the principle.) Now this seems to be what is actually implied by the language…that in all Causation the cause must precede the effect. But what can such precedence mean? It can only mean that after the complete realization of the conditions included in the cause A, there must intervene a space of empty time before the effect B enters on the scene. However brief and “momentary” you take this gap in the stream of events to be, the gap must be there if your language about the cause as being before the effect is to have any meaning. For if there is no such gap, and the entrance of B is simultaneous with the complete realization of its conditions A, it is no longer true to say that the cause A is before the effect B. A does not exist as A until a, b, c … are all present, and as soon as they are present B is present too. And thus, the relation between A and B is not that of the sequence of a later event on an earlier. They are actually together. In fact, the doctrine that the cause precedes the effect rests upon the notion that the time-series is one in which each member has a next term. And this seems inconceivable. For not only can you subdivide any finite time, however small, into two mutually exclusive parts, but the point at which the division is effected is itself a moment in the time-series lying between the beginning and the end of the original interval. Time therefore must be continuous, if causation is not equally continuous, we must suppose that gaps of empty time are what separate the first event, the cause, from the subsequent event, the effect. Yet if this could be regarded as a defensible doctrine on other groups, it would then follow that the assemblage of events A is not the totality of conditions requisite for the occurrence of B. The “totality of conditions,” i.e., the cause as previously defined would be the events A plus a certain lapse of empty time. And so the cause would once more turn out not to precede the effect, or we should have to suppose the end of the interval of empty time included in it as separated from the beginning of B by a second lapse, and so on indefinitely.” (Taylor, Elements of Metaphysics, 171-173) 

“The defects of the causal postulate as a principle of explanation may also be exhibited by showing the double way in which it leads to the indefinite regress. The indefinite regress in the causal series is an inevitable consequence of the structure of time, and, as we please, may be detected both outside and inside any causal relation of two events, or two stages of a continuous process. For it follows from the structure of the time-series (I) that there are an indefinite number of terms of the series between any two members, between which there is a finite interval, and (II) that there is also an indefinite number of terms before or after any given member of the series. Like the series of real numbers, the time-series, because it satisfies the definition of a continuous infinite series, can have neither a first nor a last term, nor can any member of it have a next term. Applying this to the case of Causation, we may reason as follows: The same reasons which lead us to demand a cause A for any event B, and to find that cause in an assemblage of antecedent events, require that A should be similarly determined by another assemblage of antecedent events, and that this cause of A should itself have its own antecedent cause, and so on indefinitely. Thus, the causal principle, logically applied, never yields an intelligible explanation of any event Instead of exhibiting the transition A—B as the logical expression of a coherent principle, it refers us for the explanation of this transition to a previous instance of the same kind of transition, and then to another, and so forth without end. But it is impossible that what is not intelligible in one instance should become intelligible by the mere multiplication of similar unintelligibilities. (II) Similarly, if we look within the transition A—B. This transition, being continuous, must have its intermediate stages. A becomes B because it has already become C, and the transition A—C—B is again “explained” by showing that A became D which became C which became E which became B. And each of these stages, A—D, D—C, C—E, E—B can be once more submitted to the same sort of analysis. But in all this interpolation of immediate stages there is nothing to show the nature of the common principle in virtue of which the stages form a single process. We are, in fact, trying to do what we try to do wherever we establish a relation between terms, to answer a question by repeating it.” (Taylor, Elements of Metaphysics, 177-178) 

“The mechanical theory of the universe undertakes to account for all physical phenomenal by describing them as variances in the structure or configuration of material systems. It strives to apprehend all phenomenal diversities in the material world as varieties in the grouping of primordial units of mass, to recognize all phenomenal changes as movements of unchangeable elements, and thus to exhibit all apparent qualitative heterogeneity as mere quantitative difference. In the light of this theory the ultimates of scientific analysis are mass and motion, which are assumed to be essentially disparate. Mass, it is said, exists independently of motion and is indifferent to it. It is the same whether it be in motion or at rest. Motion may be transferred from one mas to another without destroying the identity of either. The prime postulate of all science is that there is some constant amid all phenomenal variations. Science is possible only on the hypothesis that all change is in its nature transformation. Without this hypothesis it could discharge neither of its two great functions—those of determining, from the present state of things, the past on the one hand and the future on the other, by exhibiting the one as its necessary antecedent, and the other as its equally necessary consequent. It is evident that the computations of science would be utterly frustrated by the sudden disappearance of one or more of its elements, or the unbidden intrusion of new elements. If, therefore, scientific analysis yields mass and motion as its absolutely irreducible elementary terms—if these terms underlie all possible transformations—it follows that both are quantitatively invariable. Accordingly, the mechanical theory of the universe postulates the conservation of both mass and motion. Mass may be transformed by an aggregation or segregation of parts; but amid all these transformations it persistently remains the same. Similarly, motion may be distributed among a greater or less number of units of mass; it may be transferred from one unit of mass to any number of units, its velocity being reduced in proportion to the number of units to which the transference takes place; nevertheless the sum of motions of the several units is always equal to the motion of the single unit. It may be changed in direction and form; rectilinear motion may become curvilinear, translator motion may be broken up into vibratory motion, molar motion may be converted into molecular agitation; yet, during all these changes, it is never increased, diminished, or lost.” (Stallo, The Concepts and Theories of Modern Physics, 25-26) 

“Now, in any discussion of the operations of thought, it is of the utmost importance to bear in mind the following irrefragable truths, some of which—although all of them seem to be obvious—have not been clearly apprehended until very recent times. (1) Thought deals, not with things as they are, or are supposed to be, in themselves, but with our mental representations of them. Its elements are, not pure objects, but their intellectual counterparts. What is present in the mind in the act of thought is never a thing, but always a state or states of consciousness. However much, and in whatever sense , it may be contended that the intellect and its object are both real and distinct entities, it cannot for a moment be denied that the object, of which the intellect has cognizance, is a synthesis of objective and subjective elements, and is thus primarily, in the very act of its apprehension and to the full extent of its cognizable existence, affected by the determinations of the cognizing faculty. Whenever, therefore, we speak of a thing, or a property of a thing, it must be understood that we mean a product of two factors neither of which is capable of being apprehended by itself. In this sense all knowledge is said to be relative. (2) Objects are known only through their relations to other objects. They have, and can have, no properties, and their concepts can include no attributes, save these relations, or rather, our mental representations of them. Indeed, an object cannot be known or conceived otherwise than as a complex of such relations. In mathematical phrase: things and their properties are known only as functions of other things and properties. In this sense, also, relativity is a necessary predicate of all objects of cognition.” (Stallo, The Concepts and Theories of Modern Physics, 133-134) 

“First, as to the assertion of Riemann and Helmholtz: if space is a physically real object, it certainly is not a thing outside of, coordinate with, and different from, other physical objects. When we say that all things are in space, we do not mean that they are contained in it as water is contained in a vessel, but we mean that there is no objectively real thing which is not spatially extended, or, according to the usual form of expression, that spatial extension is a primary property of all varieties of objective existence. This fact is so obvious that Descartes was led by it to maintain that spatial extension was the only true essence of objective reality. In what way, then, and by what means, do we distinguish between space and physical things ordinarily so called? Certainly not, or at least not directly, by sensation. Different acts of sensation may present different properties of the same object, and these properties may thus be dissociated. But no act of sensation dissociates the extension of a body from all its other properties and presents the property of extension alone. The sensationalists, however, content that, although there are no physical objects without spatial extension, and although such extension is in a sense a common property of all physical objects, nevertheless these objects do not fill all space, there being pure space between them. The reply to this is that this assertion, if true, does not help the sensationalists. For acts of sensation are possible only when and where there is objective difference and change; we have direct sensation of different and variable physical qualities ordinarily so called, and not of that which is absolutely homogenous and invariable….It is precisely the fact of its homogeneity and unchangeableness, in addition to that of its invariable presence in all physical objects, which distinguishes the property of spatial extension from all other properties characteristic of a real thing, and enables the sensationalist to speak of the existence of space at all.” (Stallo, The Concepts and Theories of Modern Physics, 228-229) 

“Space is not, and cannot be, an object of sensation. The attribution of space of relations and sensible interactions of the kind reflected in sensations is impossible without the assumption of diversities among its constituent parts, the denial of which is the basis of every notion or concept of space, whatever may be the logical or psychological doctrine to which that notion is referred.” (Stallo, The Concepts and Theories of Modern Physics, 232) 

“Let us call something, X, “relatively” unknown when some but not all people fail to know propositional truths about X. Furthermore, we will call X “absolutely” unknown if, and only if, nobody knows any propositional truths concerning X. Now, it is clear that relative unknowns exist. Most people know nothing about the Cynic philosopher Hipparchia, but those who study ancient Greek philosophy surely know of her. Thus, Hipparchia is unknown relative to certain people at certain times. Suppose someone, A, does not know about Hipparchia at a time T. Given this, Hipparchia is unknown relative to A at T. It would, then, be a contradiction for A to know of Hipparchia at T. Hence, once it is admitted that Hipparchia is not known by A at T, it follows that she cannot be known by A at T. So, we can reasonably support the following epistemic theorem: whatever is unknown relative to someone at a certain time, is unknowable relative to her at that time. But, suppose that instead of being relatively unknown, Hipparchia is absolutely unknown. In other words, let us consider that Hipparchia is not known by anyone at any time. We might observe that this can be restated as the following: Hipparchia is unknown relative to any person at any given time. When combined with our discovered theorem, we can infer from this that Hipparchia is unknowable relative to any person at any time. Thus, we have reached a second epistemic theorem: whatever is absolutely unknown, is unknowable by anyone whatsoever.” (Thomas-Brown, Idealism and the Known Unknown, 2) 

“Granted our two theorems, we can move to demonstrate that nothing absolutely unknown ever exists. We know as certainly as we can that any given entity is either square or not square, for this is an instance of the law of excluded middle. In grasping this universal truth, we know a truth concerning all things past, present, or future. If an absolute unknown existed, we would have some knowledge of it by way of such universal truths. But, it is a contradiction for an absolute unknown to be known by someone or other. Hence, if we are to have knowledge of universal truths at any time, there can never exist absolute unknowns. Yet, we do, of course, possess such knowledge; and, thus, no absolute unknowns exist, past, present, or future. Whatever exists or comes to exist is, therefore, known by someone or other at some time or other. In other words, to be is to be known and existence implies knowledge. Once we understand that something’s existence entails its being known, we can further see that its existence depends on its being known. However, the presence of knowledge presupposes that of a knower. Hence, the existence of a given object depends on there being an intelligent self or selves.” (Thomas-Brown, Idealism and the Known Unknown, 3-4)