Reading Notes: February 27th, 2023

“I shall allow myself to speak of an event, and events in the plural, but I shall note raise the problem of the relation between the continuity of events and their plurality. We are told by mathematicians that this problem has been solved by the notion of a compact series, which is at once discrete, because a series, and continuous, because compact. I do not see that this is really so. If, between any two terms of a series, there is still a third term, it appears to me that we are still as far from continuity as ever; for ex hypothesi, the series as actually counted always has gaps between all its terms, and however many terms are interpolated the gaps always remain. We are told that these gaps are filled by uncounted terms; but no evidence is brought that these terms, however numerous, fill the gaps. At most, they will only occur in the gaps, and serve to delimit their extent; and event this is not guaranteed by the definition of a compact series, for that definition does not stipulate that all the gaps between the terms are to be of the same size, or that an interpolated term is to be interpolated at one point in the gap rather than another. The theory of compact series, in a word, does not meet the facts; and it is only advanced in the interests of what I take to be a logical error, namely logical atomism, which in its application does not differ very widely from the sensational atomism of Hume, and is amenable to all the same criticisms.” (Collingwood, Some Perplexities About Time: With an Attempted Solution, 136-137) 

“Suppose, again, we say that time is continuous. What, in saying this, are we denying? Presumably, that time is discrete. If it had been discrete, it would have had gaps in it. But what would the gaps have been made of? Nothing but time: any gap in a series of events must be a gap consisting of time, for if there is no time in the gap there is no gap. Clearly, then, time is continuous.—But this does not seem to follow. That which must be either discrete or continuous must be a quantity. But if time cannot be measured, it is doubtful whether we ought to call it a quantity; it is, in any case, an unmeasurable quantity, and in this phrase it is reasonable to suspect a contradictio in adjecto.” (Collingwood, Some Perplexities About Time: With an Attempted Solution, 140-141) 

“When one event in time is said to be continuous with the next, the statement is either meaningless or false. Meaningless if “the next” is simply “that with which it is continuous”; false, if it is assumed that events in time are really packed side by side with no intervals between them.” (Collingwood, Some Perplexities About Time: With an Attempted Solution, 141) 

“We do not perceive our perceptivity…” (Richardson, Spiritual Pluralism and Recent Philosophy, 33) 

“A review of classical attempts to deal with the notion of substance makes it clear that the problem resolves itself into an endeavour to reconcile the principles of permanence and change. Heraclitus, who was the first to bring out more or less plainly the nature of the difficulties involved, held that only change is permanent; but closer examination shows that, with any significant meaning which can be attached to the term “change,” the truth of the matter is that change implies permanence. For, in the first place, it is apparent on general grounds that if there is a change, there must be a thing which changes, the said thing maintaining its identity throughout the change. Otherwise, there is simply one thing and then another thing, that is, mere succession and not change at all, properly so-called. From the scientific standpoint we certainly do consider mere alteration alone, that is, simply a succession of different presentations. But from the subjective point of view, if I have first A and then B before me, I can in no significant sense be said to have apprehended a process of change; at most there has been a change in myself, and this, since it is I who have perceived both A and B, assumes my permanence.” (Richardson, Spiritual Pluralism and Recent Philosophy, 39-40)