¹ Some philosophers (Russell, Whitehead, et. al.) have, at various times, preferred to speak of “events” instead of particulars. Since, however, these “events” were taken as the terms for the spatial relations, they would be comprehended within the present notion of a particular.

² Although this dilemma could be stated by using any attribute which particulars might possess, change of place (motion) will alone be considered in keeping with the decision to treat particulars, for the present, simply as spatial entities. The relational properties in question are, for example, “to the left of B”, “to the right of C”. A change in the relation or a change in the term of this relation (B or C) constitutes a change in the relational property. The first horn of this dilemma is largely taken from Gustav Bergmann's “Some Reflections on Time,” reprinted in Meaning and Existence (Madison, Wis.; 1960), pp. 225–263.

³ In this example A and B are contemporaneous. The introduction of special relations (e.g., “temporal overlap,” “extending over in time”) would not alleviate the difficulty since, whatever their relationship in this respect might be, A is still beneath and not beneath B.

⁴ Anyone seriously maintaining this position would, of course, be obliged to tell how, if not literally, such statements are to be interpreted (reconstructed, constructed, etc.) so as to retain their significance.

⁵ Certain refinements in the statement of this definition (e.g., binding the variable “R”) have been neglected in order to preserve what a brief inspection will reveal to be its more or less obvious function. A clause specifying that W ≠ Z has also been omitted because it is not important, for the present purpose, to deny that any reference object endures throughout the period in question. What is important is that this definition can be utilized whether or not this occurs—or, better, is said to occur. I shall assume, however, in the following discussion that W and Z are never the same since this is an essential part of the scheme which is to stand as a counter-example to Strawson's conclusion.

⁶ Not conceptual scheme; I am attempting to show that these two modes of description constitute, in Strawson's sense of the term and in respect of spatial comparison, the same conceptual scheme.

⁷ Complications relating to distance below are being ignored as they were earlier; their consideration would not add anything materially new and would simply the length of our examples.

⁸ The mistake in question is, of course, the divergence between our ordinary description and a description in terms of our definition in (6). Since it is Strawson's contention that the lack of particular reidentification cripples the mechanism for making certain types of common spatial comparisons, the norm by which the present account is being judged is its capacity to duplicate, in these relevant respects, the ordinary idiom. Hereafter, whenever “mistake” or “error” is mentioned, it should be understood in this sense.