I tend to think of objectivity as a portmanteau that combines object and
activity—a mode of engagement where things are treated as if they were
objects, as if there was nothing more to them than some presentation. Some
instances might be:

1. Treating matter without speculation or ambition.
2. Defining the terms of a given structure such as the real numbers.

In my view, objectivity is a special kind of activity undertaken by one or
more subjects—a constrained subjectivity. When I hear Nick or EricC speak
of Peirce's notion of object, I am tempted to regard the idea as a kind of
interobjective limit, where Glen's skepticism continues to apply.

Granting skepticism and other needed generosity, I understand
intersubjectivity as a colimit of subjectivity, objectivity as a limit of
interobjectivity. That is, I imagine intersubjectivity as the universal
construction one gets by gluing together all participating subjective
stances, respecting their relations, identifications, and interconnections.
Dually, objectivity becomes not an *absolute* thing, but a limiting
construction—what remains invariant or universal after "factoring through"
all participating interobjective standpoints. In both cases, subjects are
engaging in some consensus process that in its own right is doing the work
of identifying a relevant ambient category to ground each construction.

In sympathy with EricC's skepticism of any super-underlying-everything
metaphysical monism, I resist the idea of anything like a superset of any
real things in any real sense (including the above categorical framing).
Perhaps there is shared agreement that all objectivism is at best a bound
and scoped objectivism—a convenience.
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