[ulbu]

You are right.

How Aristotle illustrated abstraction – by extracting the definition of triangle. Reversible abstraction would mean the possibility of taking a triangle in the Cartesian space and reconstructing the actual object that includes an instance of this triangle. We’d have to be able to reconstruct its material properties.

It is precisely this impossibility that is essential to abstraction. It involves the removal of properties of a particular to arrive at the abstract – the common, the universal.

Now, it is possible to arrive at a poor, incomplete abstraction. Imagine if we dealt with red triangles and green triangles, as opposed to just triangles. If we wished to operate on the its underlying triangle, we would have to remove the colour at each operation. It would be an unused variable. We don’t want that – so we remove the property of colour from our triangle operations entirely. And thatbis the only way to deal with triangles.

Reversibility is simply a different property that can’t be attached to abstraction is if we wish precision at all.