An enquiry concerning the principles of natural knowledge

by Alfred North Whitehead

with its peculiar properties really means that the space-units and time-units are comparable; namely, there is a natural relation between them to be expressed by taking

to be unity. Either the time-unit would then be inconveniently small or the space-unit inconveniently large; but this inconvenience does not alter the fact that congruence between time and space is definable. Always when a possible definition of congruence is omitted, such absolute physical quantities occur. The fact that, so far as time and space are concerned, the existence of a congruence theory seems paradoxical is due to absence of any phenomena depending on that theory except in very exceptional circumstances produced by refined observations.

[PART IV]
THE THEORY OF OBJECTS

[CHAPTER XIV]
THE LOCATION OF OBJECTS

[53. Location]. 53.1 We conceive objects as located in space. This conception of location in space is distinct from that of being situated in an event, though the two concepts are closely allied by a determinate connection. The notion of the situation of an object is logically indefinable being one of the ultimate data of science; the notion of the location of an object is definable in terms of the notion of its situation.

An object is said to be 'located' in an abstractive element if there is a simple abstractive class 'converging' to the element and such that each of its members is a situation of the object.

In general when an object is located in an abstractive element there will be many simple abstractive classes converging to the element and such that each of their members is a situation of the object. In any specific case of location usually all abstractive classes of a certain type will possess the required property.

It follows from this definition that, in the primary signification of location, an object is located in an element of instantaneous space. The notion of location in an element of time-less space follows derivatively by correlating the elements of instantaneous space to the elements of time-less space in the way already described. In our immediate thoughts which follow perception we make a jump from the situation of an object within the short specious present to its location in instantaneous space, and thence by further reflexion to its location in time-less space. Thus location in space is always an ideal of thought and never a fact of perception. An object may be located in a volume, an area, a route, or an event-particle of instantaneous space, and thence derivatively it will be located in a volume, or an area, or a segment, or a point of timeless space.