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Extract from A TREATISE OF HUMAN NATURE:

We shall afterwards see many instances of this tendency of relation to make us ascribe an identity to different objects; but shall here confine ourselves to the present subject.
We find by experience, that there is such a constancy in almost all the impressions of the senses, that their interruption produces no alteration on them, and hinders them not from returning the same in appearance and in situation as at their first existence.
I survey the furniture of my chamber; I shut my eyes, and afterwards open them; and find the new perceptions to resemble perfectly those, which formerly struck my senses.
This resemblance is observed in a thousand instances, and naturally connects together our ideas of these interrupted perceptions by the strongest relation.
and conveys the mind with an easy transition from one to another.
An easy transition or passage of the imagination, along the ideas of these different and interrupted perceptions, is almost the same disposition of mind with that in which we consider one constant and uninterrupted perception.
It is therefore very natural for us to mistake the one for the other.
[Footnote 9 This reasoning, it must be confest, is somewhat abstruse, and difficult to be comprehended; but it is remarkable, that this very difficulty may be converted into a proof of the reasoning.
We may observe, that there are two relations, and both of them resemblances, which contribute to our mistaking the succession of our interrupted perceptions for an identical object.
The first is, the resemblance of the perceptions: The second is the resemblance, which the act of the mind in surveying a succession of resembling objects bears to that in surveying an identical object.
Now these resemblances we are apt to confound with each other; and it is natural we shoud, according to this very reasoning.
But let us keep them distinct, and we shall find no difficulty in conceiving the precedent argument.]
The persons, who entertain this opinion concerning the identity of our resembling perceptions, are in general an the unthinking and unphilosophical part of mankind, (that is, all of us, at one time or other) and consequently such as suppose their perceptions to be their only objects, and never think of a double existence internal and external, representing and represented.
The very image, which is present to the senses, is with us the real body; and it is to these interrupted images we ascribe a perfect identity.
But as the interruption of the appearance seems contrary to the identity, and naturally leads us to regard these resembling perceptions as different from each other, we here find ourselves at a loss how to reconcile such opposite opinions.
The smooth passage of the imagination along the ideas of the resembling perceptions makes us ascribe to them a perfect identity.
The interrupted manner of their appearance makes us consider them as so many resembling, but still distinct beings, which appear after certain intervals.
The perplexity arising from this contradiction produces a propension to unite these broken appearances by the fiction of a continued existence, which is the third part of that hypothesis I proposed to explain.
Nothing is more certain from experience, than that any contradiction either to the sentiments or passions gives a sensible uneasiness, whether it proceeds from without or from within; from the opposition of external objects, or from the combat of internal principles.
On the contrary, whatever strikes in with the natural propensities, and either externally forwards their satisfaction, or internally concurs with their movements, is sure to give a sensible pleasure.
Now there being here an opposition betwixt the notion of the identity of resembling perceptions, and the interruption of their appearance, the mind must be uneasy in that situation, and will naturally seek relief from the uneasiness.