What is precisely a "heterogeneous continuum"? Let me explain :
On face value a "heterogeneous continuum" seems to be a contradiction, and in a mathematical context it is.
We we are doing, however, not Mathematics, but Metaphysics.
When we consider a heterogeneous continuum, then we think about ONE individual Substance having different qualities at different locations in that Substance. These qualities are actually present, and at first sight seem to make this Substance heterogeneous, and, when these qualities are abruptly exchanged for other qualities when we go from one locality within such a Substance to another, (they seem to make this Substance) even discontinuous. These differently qualified locations could even represent (qualitatively) different parts of that Substance. If we want to interpret such a Substance as a continuum nevertheless, then we must resort to metaphysical considerations, namely the "per se" and the "per accidens".
We could then interpret the heterogeneity of that Substance, not as a distribution of parts, but as a distribution of properties -- in metaphysical terms, Accidents, i.e. as per accidens determinations of different locations within that Substance. These properties could be interpreted as "virtual parts" in so far as they relate to those different locations.
Even when we have to do with moving parts of that Substance, we can interpret these as an alternation -- in the time dimension -- of the distribution of the heterogeneity.
So a Substance can be substantially (i.e. within the substantial order) homogeneous, but accidentally (i.e. within the accidental order) heterogeneous.
Because a Substance is what it is, in every location within it, i.e. its Essence pervades the whole Substance, we can say that it is a continuum, while in an accidental sense (i.e. per accidens) it is heterogeneous.
In this way we have a heterogeneous continuum.
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