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Hence, it is not clear why the correct description of relations among abstract (mathematical) entities is even relevant to understand the behavior of concrete objects in the physical world involved in the application of mathematics.
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But the child operates only when in the presence of concrete objects that can be manipulated.
He called these "combinations of concrete objects," recurring in time, "involutes," a term he borrowed from conchology.
Since sums of spatiotemporally related objects are sums of concrete objects, and sums of concrete objects are concrete objects, Lewisian possible worlds are concrete objects.[25], [26] Another theory of possible worlds has been developed by David Armstrong.
However, even this modal claim appears to talk about collections of concrete objects and relations on these objects.
In the case of concrete objects, however, things seem to stand differently.
Rigidity is most straightforwardly applied to proper names of concrete objects.
For instance, if it could be proven that positing a plurality of concrete objects (or a plurality of anything, or even a single concrete object) led irrevocably to contradiction, this should turn the tide.
It could be argued that certain sets encapsulate the instantiation model, since a set of concrete objects can be instantiated by such objects.
On the contrary, they face it squarely and attempt to make do entirely with an ontology of concrete objects, finitely many such objects in fact.
This can be done for numbers and sets, but probably not for any kind of concrete objects.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com