Now the whole point of the procedure is that the quantitative expressions of these natural properties do converge to limits though the abstractive set does not converge to any limiting duration.

The laws relating these quantitative limits are the laws of nature 'at an instant,' although in truth there is no nature at an instant and there is only the abstractive set.

Thus an abstractive set is effectively the entity meant when we consider an instant of time without temporal extension.

It subserves all the necessary purposes of giving a definite meaning to the concept of the properties of nature at an instant.

I fully agree that this concept is fundamental in the expression of physical science.