Jaroslav Císař

“ A world independent of mind in general would be a world common to all possible types of mind; but as minds constructed diversely from ours are not only unknown to us, but even impossible for us to imagine in respect of all possibilities of their type, such an absolute external world is not only unknowable, but a concept devoid of content. ”

“ In the first place it seems to me that space as conceived by this theory—in fact every conception of space as a quantity consisting of points, and for that reason also the current definition of space of pure geometry—degenerates into a logical circle and is therefore worthless as a definition—through failing to realise that nothing can be a relation and a relatum at the same time. ”

“ As far as our definition goes up to the present, we can already reject as devoid of meaning any view which would affirm any deformation or discontinuity of time. Time is not a continuum or aggregate of which we could possibly predicate these properties; time is a mode of ordering a given totality of our perceptions, and it is this totality which may be discontinuous, or may have certain metrical properties. Time of itself cannot have metrical properties ”

“ Extension we shall define as the possibility of inclusiveness: a given entity will be said to possess extension, to be extended, if taken by itself it admits of the relation of inclusiveness, i.e., if it is divisible into parts. The relation of extension is implied in the relation of inclusiveness, and is therefore as purely formal a concept as the latter; but although, being void of all spatial and temporal content, it possesses the characteristics necessary for the purposes of our definition, it is not adequate to define space and time. ”

“ If, within the world of our perceptions, we try to order parts of our perceptual data under any ordinal characteristic arbitrarily chosen from among those which we immediately apprehend, we find that we can order (that is, correlate with one or more series of natural numbers) under this characteristic a determinate part of the totality of events into which the mind divides its Experience; but we can as a general rule expect that in a given Experience we shall always be able to find events which remain outside the ordering, that is, outside the system of co-ordinates which we have chosen. ”

“ In perception the external world is presented to the mind as a phenomenon, a something of which the first quality distinguishable by the mind is variety, manifoldness, or, in other words, divisibility into parts. Consciousness of this manifoldness results from the recognition that in perception, as it is found in the mind, there is more than the mind is immediately aware of; and it arises, we may suppose, from the limitation of the mind, from its inability to comprehend totality, to seize the whole of being as such, in its entirety. ”

“ That an element of experience has not parts can be proved as follows: Let us suppose that an element of experience R has parts A and B; then it is possible to find a spherical event X which does not contain the whole of R, but only one of its parts. Since a co-intersection of n spherical events is, by definition, contained in each one of these events, the event X is not a member of the class of events, the co-intersection of which is the element of experience R; but since an element is a co-intersection common to all spherical events which mutually intersect, such an event X cannot exist ”

“ If we divide the content of the mind into the perceptual and non-perceptual, and, contenting ourselves with the “social” criterion of the difference between the two, say that the former is received by the mind from the external world, from nature, and that the latter is produced out of the mind itself, then nature appears to us in our perceptions as a process, as a swarm or succession of events, each of which is marked by this characteristic of its being. ”

“ Finally, geometry once more approaches physics when, to facilitate its work, it borrows from physics its aids: the perceptual representation of its concepts; but here must be kept in mind that this representation is but an approximation to the ideal concepts of geometry, just as (if I may be allowed to present the fact of physical simplification of phenomena in this reverse order) actual empirical physical experience is but a rough approximation to the ideal Experience of physical theory. ”

“ Out of the past and the future there emerge only those swarms of perceptions which remain “the same” in a finite section of the time series of Experience, which, in other words, endure. The mind, we may say, has a special preference for permanence, for what in the ever changing stream of Experience remains the same ”

“ The postulate of the existence of points of empty space has meaning in the pre-Einsteinian space of classical mechanics, where every eternal point is a possible recipient of a particle of matter; the moment, however, we amalgamate space and time into one continuum, as it is amalgamated in Einstein’s theory, empty space becomes a superfluous multiplication of entities, a useless fiction, satisfying perhaps the requirements of æesthetics (not even transcendental) but not of logics and physics. ”

“ If we call the progressive one-dimensional figure of elements of experience, which carries an enduring group of attributes, a perceptual particle—we can define a material particle as a perceptual particle composed of impenetrable elements of experience, where impenetrable elements of experience signify those elements of experience which cannot form a common ingredient of two different material particles. ”

“ We speak of the parts of a given Experience, which come within the same moment, as being co-momentary. Between two co-momentary events there exists no relation of temporal sequence; a moment is thus nature as it would appear to a given mind in an instant, a section of nature in which there is no temporality. Such a section is, indeed, an abstraction which the mind can explore only in idea; reflexion upon it occupies a finite section of the inner time series, whereas the moment itself occupies no such finite section. ”

“ Here, I think, the sensationalist theory of space shares the error of Kant: empty space cannot be imagined, much less examined physically. But it is necessary to distinguish here clearly between the space (point-space) which in accordance with our nomenclature can be called momentary, (therefore an aggregate of points in a given moment) , and the space, which in accordance with the conventional terminology we have called permanent space (therefore the aggregate of permanent points, i.e., routes, consisting of points of the various momentary spaces) . ”

“ It may be, indeed, and it most probably is so, that, even apart from the imperfection of our senses, the mind is more limited in perception than in thought, and that there is inherent in Experience itself a certain characteristic, which uniquely divides Experience, or a given section of it, into a finite number of delimited events, which the mind can further divide in thought but not in perception. ”

“ The answer given by the first class—the Kantian idealists—is in the negative; space and time, they say, are “forms of our intuition,” independent of the external world, and pre-existing to all perception, and they can be only such as are given us; it is not possible for our intuition of the properties of space to be dependent upon our physical theories. ”

“ Even if it were ascertained by exact perceptual analysis that Experience is atomic, it will nevertheless suit us better, from the point of view of facilitating mathematical analysis, to regard it as continuous, with the understanding, of course, that results based on this hypothesis are only approximately valid, like statistical averages within aggregates of great numbers of elements, the individual significance of which in relation to the whole is infinitesimally small. ”

“ Perception presupposes the existence of a percipient, of a mind; the necessity of distinguishing the perceptual contents of the mind from its unperceptual contents then leads to the postulate of a greater number of percipients—of minds—and thus to the pre-supposition of the so-called “external world”: the denial of this external world leads to a denial also of plurality of minds—solipsism, which philosophy endeavours to avoid for reasons mainly ethical, and which physics cannot accept if it does not wish to deprive itself of the most useful criterion of perceptuality. ”

“ In a moment everything is at rest; to speak of change of position in a moment is meaningless, since the position of a given event in a given moment is the sum of its relations to the remaining parts of this moment and is given once for all. Matter also cannot be defined in momentary space. ”

“ Such a view of the external world as a source and cause of percepts, I think, actually predominates with the majority of physicists, perhaps implicitly with the majority of them; from the point of view of physics it cannot be erroneous, while from the point of view of natural philosophy it means a certain facilitation of the processes of thought by fixing a symbol for a comparatively concrete concept. ”

“ If we accept the postulate of the existence of the external world as something which is common to all minds, but independent of each individual one, then perceptions are the result of contact between the mind and this external world, and the bodily senses, themselves parts of the external world, enlarged both in the scope and the precision of their powers by physical instruments, are the media through which the contact is effected. ”

“ Neither shall we make it a part of our present task to study the equally interesting and more important problem of measurement, which is concerned with quantitative determinations of the variation of the ordinal characteristic; it will here suffice if we say that the possibility of measurement of a given continuous aggregate is dependent upon the existence of a certain relation between every two elements of the continuum, which relation it is possible to express numerically, and to compare as to equality or inequality between various pairs of elements ”

“ Empty space, as empty time, is an empty word, with no meaning save that of a possibility of ordering relations: if we say that between the particle A and the particle B there is an empty space, it means that there exists the possibility of placing a particle X between them ”

“ Even if objects changed, which we imagine unaffected by time, it would not be the change which would matter so much as our collective judgment; a red patch of colour will be red as long as everyone calls it red, even though some higher being may see it as changing its colour with time. ↑ I do not know whether of Kant himself; my criticisms are aimed at those Kantians who hold that geometry is determined by the properties of space, or, better, that geometrical postulates determine or express these properties, and that they, together with the intuition of space, are given us a priori. ”

“ Physics, as we have already said above, is concerned only with percepts, and not with the manner in which they enter the mind, or arise within the mind; and the view to which we give the preference in this matter is a matter of personal predilection; as far as physics is concerned, our choice will remain without consequences. ”

“ The first fundamental and undefinable, although generally and unambiguously intelligible relation, which we shall place at the basis of our investigation, is the relation of whole to part, which we shall briefly denote as the relation of inclusiveness. ”

“ The space-time of Einstein is a kind of medium, which by its heterogeneity acquires the properties of matter, becoming superfluous if we wish to describe the phenomena in terms of matter, and useless, if we wish to describe them in terms of something else. ”