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SUPPLEMENTS
§ I.
Of Space and Time[1]
| The theme; what are the attributes of space? | |
| 1. I do not admit perfectly continuous extension of matter; I consider it to be made up of perfectly indivisible points, which are non-extended, set apart from one another by a certain interval, & connected together by certain forces that are at one time attractive & at another time repulsive, depending on their mutual distances. Here it is to be seen, with this theory, what is my idea of space, & of time, how each of them may be said to be continuous, infinitely divisible, eternal, immense, immovable, necessary, although neither of them, as I have shown in a note, have a real nature of their own that is possessed of these properties. | |
| Real local and temporal modes of existence must of necessity be admitted by every one. | |
| 2. First of all it seems clear to me that not only those who admit absolute space, which is of its own real nature continuous, eternal & immense, but also those who, following Leibniz & Descartes, consider space itself to be the relative arrangement which exists amongst necessity things that exist, over and above these existent things ; it seems to me, I say, that all must admit some mode of existence that is real & not purely imaginary ; through which they are where they are, & this mode exists when they are there, & perishes when they cease to be where they were. For, such a space being admitted in the first theory, if the fact that there is some thing in that part of space depends on the thing & space alone ; then, as often as the thing existed, & space, we should have the fact that that thing was situated in that part of space. Again, if, in the second theory, the arrangement, which constitutes position, depended only on the things themselves that have that arrangement ; then, as often as these things should exist, they would exist in the same arrangement, & could never change their position. What I have said with regard to space applies equally to time. | |
| The name by which this modes is known is immaterial. | |
| 3. Therefore it needs must be admitted that there is some real mode of existence, due to which a thing is where it is, & exists then, when it does exist. Whether this mode is called the thing, or the mode of the thing, or something or nothing, it is bound to be beyond our imagination; & the thing may change this kind of mode, having one mode at one time & another at another time. | |
| Real modes; what real space & real time may be. | |
| 4. Hence, for each of the points of matter (to consider these, from which all I say what can be easily transferred to immaterial things), I admit two real kinds of modes of existence, of which some pertain to space & others to time; & these will be called local & temporal modes respectively. Any point has a real mode of existence, through which it is where it is; & another, due to which it exists at the time when it does exist. These real modes of existence are to me real time & space; the possibility of these modes, hazily apprehended by us, is, to my mind, empty space & again empty time, so to speak; in other words, imaginary space & imaginary time. | |
| Their nature & relations. | |
| 5. These several real modes are produced & perish, and are in my opinion quite indivisible, non-extended, immovable & unvarying in their order. They, as well as the positions & times of them, & of the points to which they belong, are real. They afford the foundation of a real relation of distance, which is either a local relation between two points, or a temporal relation between two events. Nor is the fact that those two points of matter have that determinated distance anything essentially different from the fact that they have those determinated modes of existence, which necessarily alter when they change the distance. Those modes which are descriptive of position I call real points of position; & those that are descriptive of time I call instants; & they are without parts, & the former lack any kind of extension, while the latter lack duration; both are indivisible. | |
| Contiguity of points of space is impossible. | |
| 6. Further, a point of matter that is perfectly indivisible & non-extended cannot be contiguous to any other point of matter; if they have no distance from one another, they coincide completely; if they do not coincide completely, they have some distance between |
- ↑ This & the following section are to be found in the Philosophiæ Recentior, by Benedict Stay, Vol. I, 6, 7.
