Reading Notes: June 15th, 2022

“That error occurs is undeniable, points out Royce, for if we deny it we commit at least to the erroneous belief that it does. But what is error? Error occurs when the thing we refer to is other than we say it is, when our judgement fails to agree with its intended object. It implies that there is a gap between what we judge about the world and what is actually the case. If they are to be in error ideas call for something other than themselves about which they err….How can our judgement fail to agree with its object if the only object it has it that which it describes? A paradox appears. By definition we are in error about what we don’t know, but how can we even speak about or refer to the unknown? “About a really Unknowable [writes Royce] nobody could make any sincere and self-consistent assertions that could be errors. For self-consistent assertions about the Unknowable would of necessity be meaningless. And being meaningless, they could not well be false.” He proposes an ingenious solution. If all reality is present to a single infinite thought in which, in our very limited and incomplete ways, we participate, then error may be explained as the phenomena in which, in our imperfect consciousness, we partially intend that which a wider thought successfully articulates. Our object of reference is given in the perfectly organized experience that completes it and which characterises the reality we meant, for if there is reference beyond our ideas there is no reference beyond ideas themselves. Reality just is ‘perfectly organised experience.’ But Royce’s point is not merely that another sees fully what I grasp only in part, rather he is suggesting that the divine perspective fixes that which I intend but erroneously put, for it is a view in which I actually participate.” (Mander, On Arguing for the Existence of God as a Synthesis Between Realism and Anti-Realism, 103) 

“The [Neo-Realist’s] argument is that it is implied in the very nature of knowing qua knowing that the object of knowledge is independent of the cognitive relation in question. But, since the “independence” alleged must mean, if it is to prove the point, that the fact of knowing as such implies nothing in the object, we have the curious paradox that knowing qua knowing implies that nothing in the object is implied by knowing qua knowing. Or, in other words, it follows from the very nature of knowing that the object of knowledge has a quality by virtue of which no quality which it has follows from knowing. Is this not perilously near self-contradiction? Yet, unless we say that this “independence” is implied in the nature of knowing, the ground for making the relation external seems to disappear. It is indeed true that knowledge of anything is essentially knowledge of it as it is and not as different from what it is, but I do not see at present any way in which an argument based on this fact can be worded so as to prove that the knowing relation is not internal. To say that we know A as it is and not as different from what it is, is not the same as saying that A is not different from what it would be if we had never known it.” (Ewing, The Relation between Knowing and its Object (II), 309) 

“In article (I), I use the argument that the verification principle is on its own showing meaningless since it cannot be verified by sense-experience. The reply has been made that the verification principle is not itself a factual statement and the conditions as to meaningfulness laid down by it were intended to apply only to factual statements. I accept this reply but almost all the argument of the article still stands, for even non-factual statements cannot be asserted without justification, and the verification principle excludes any possibility of its own justification. It cannot even be justified by its results in solving philosophical problems, for we can never tell whether a solution of a philosophical problem (or a scientific problem for that matter) is right or wrong simply by sense-experience….Those who say they are using the verification principle only as a methodological assumption must remember that, unless a proposition can be put forward not merely as an assumption but as true, one is not entitled to infer anything from it.” (Ewing, Non-Linguistic Philosophy, 12-13) 

“Here it is required to prove that the Categories are necessary for the determination of objects. The aim is to show that they are objective as well as a priori. (1) Kant proceeds to prove at the outset that, unless all objects were related to one self, there would be no knowledge. If there be no permanent ego which remains unchanged throughout the passing flux of experience, then sensation cannot be arrested, much less worked up into the elaborate complexities of knowledge. Or, to employ Kant’s own technical language, objects cannot be characterized as such except by the synthesis of their manifold in relation to an identical self. By this he means that all the varied sensations connected with an object must necessarily be held together and united by a single self that remains unchanged throughout the entire course of their rapid alterations. (2) Having thus pointed out that, even to the mere naming of an object as such, an active, synthetic self is necessary, Kant next proceeds to show that the forms under which this unifying activity takes place are the Categories; that, in fact, the Categories are objective, because through them the permanent self characterizes objects as objects. From what has immediately preceded we are aware that knowledge is possible only because an identical self performs the operation of binding together passing sensations. The characteristic of this ego lies in its synthetic office. How, then, is this synthesis brought about? As we have already seen, by the faculty of judgment. But Kant, following the tradition of Formal Logic, supposed that the Categories exhaust the channels through which this faculty exhausts its possibilities of action. Hence, they are the forms whereby this synthesis is executed, and so they are objective in their primary nature.” (Wenley, An Outline Introductory to Kant’s “Critique of Pure Reason”, 47-48) 

“In conceptual space and time, there is no principle by which to distinguish different directions. In perception they can be distinguished as right and left, up and down, and so forth. But since what is right to one percipient is left to another, in conceptual space, where complete abstraction is made from the presence of an individual percipient, there is neither right nor left, up nor down, nor any other qualitative difference between one direction and another, all such differences being relative to the individual percipient. When we wish to introduce into conceptual space distinctions between directions, we always have to begin by arbitrarily assigning some standard direction as our point of departure. Thus we take, e.g., an arbitrarily selected line A______B as such a standard for a given plane, and proceed to distinguish all other directions by the angle they make with AB and the sense in which they are estimated (whether as from B to A or from A to B). But both the line AB and the difference of sense between AB and BA can only be defined by similar reference to some other standard direction, and so on through the endless regress….In conceptual time, there is absolutely no means of distinguishing before from after, past from future. For the past means the direction of our memories, the direction qualified by the feeling of “no longer”; the future is the direction of anticipation and purposive adaptation, the direction of “not yet.” And, apart from the reference given by immediate feeling to the purposive life of an individual subject, these directions cannot be discriminated. In short, conceptual time and space are essentially relative, because they are systems of relations which have no meaning apart from qualitative differences in the terms of which they relate; while yet again…the terms have to be taken as having no character but that which they possess in right of the relations.” (Taylor, Elements of Metaphysics, 252-253) 

“(1) Matter is that which moves and is moved by other matter. (2) Motion of matter is change of spatial relation to some other matter. (3) Change of spatial relation between matters can only be measured by some unchanging spatial relation between matters. (4) No two matters can be known to have unchanging spatial relations unless they are free from dynamical relations to each other and to other matter. (5) But [dynamical] relations constitute the definition of matter. Therefore, (a) No change of spatial relation can be measured. (b) No motion, and therefore no matter and no force can be measured. (c) Dynamics is rendered dialectically untenable by the contradiction arising from the essential relativity of matter. (d) Matter and motion cannot form a self-subsistent world, and cannot constitute Reality.” (Russell, On the Idea of a Dialectic of the Sciences, 49-50) 

“(I) Space is continuous and infinitely divisible; the zero of extension, is called a Point. All points are qualitatively similar, and distinguished by the mere fact that they lie outside one another. (II) Any two points determine a unique figure, the straight line; two straight lines, like two points, are qualitatively similar, and distinguished by the mere fact that they are mutually external. (III) Three points not in one straight line determine a unique figure, the plane, and four points not in one plane determine a figure of three dimensions.” (Russell, An Essay on the Foundations of Geometry, 52) 

“Moreover, the judgment of quantity is the result of comparison, and therefore presupposes the possibility of comparison. To know whether, or by what means, comparison is possible, we must know the qualities of the things compared and of the medium in which comparison in effected; while to know that quantitative comparison is possible, we must know that there is a qualitative identity between the things compared, which again involves a previous qualitative knowledge. When spatial figures have once been reduced to quantity, their quality has already been neglected, as known and similar to the quality of other figures. To hope, therefore, for the qualities of space, from a comparison of its expression as pure quantity with other pure quantities, is an error natural to the analytical geometer, but an error none the less, from which there is no return to the qualitative basis of spatial quantity.” (Russell, An Essay on the Foundations of Geometry, 64-65) 

“Does a quantum of color mean a single line in the spectrum, or a band of finite thickness? In either case, what are the magnitudes to be compared? And how is superposition necessary or even possible? A color is fixed by its position in the spectrum…or even, roughly, their immediate sense-quality. We do not require superposition to measure quantities corresponding to different tones or colors; these can be discovered by analysis of single tones or colors. With space, on the other hand, if we seek for elements, we can find none except points, and no analysis of a point will find magnitudes inherent in it—such magnitudes are a fiction of coordinate Geometry. The magnitudes which space deals with…are relations between points, and it is for this reason that superposition is essential to space-measurement. There is no inherent quality in a single point, as there is in a single colour, by which it can be quantitatively distinguished from another.” (Russell, An Essay on the Foundations of Geometry, 66-67)