[FRIAM] The danger of a single story

[Jon Zingale]

"""
For lack of a better (or more ironic, since Euler went blind) dichotomy
lever, the operational conception might be called Lagrangian and the
latter Eulerian. From a Lagrangian perspective any point in an open ball
is infinitely far from the outer bound as long as our operations are
functions of that outer bound. But from an Eulerian perspective, it's
trivial to see the boundary is just fuzzy and all we need do is take
constant steps to leave the ball. That renders the koan a simple fallacy
of ambiguity, hinged on the conception of "center".
"""

I am unsure that I can address everything here, and I feel like my
reasoning has been sh!t lately, but here is an attempt to work out your
suggestion of a "fallacy of ambiguity"[⊬]:
  a) the term shared by the two premisses
  b) the subject of the conclusion
  c) the predicate of the conclusion

a) Perhaps here you are talking about *center of a ball* as the shared
concept between a Lagrangian and an Eulerian perspective? Or maybe the
*center of a ball* as shared between the p-adic and euclidean conceptions
of space? In this last case, maybe the "missing premise" is that we are
making an analogy to balls and centers when we move to non-archimedean
norms? The fallacy might then appear as:

"All Euclidean balls have a single center. x is the center of a p-adic
ball. Thus x is the single center of the p-adic ball."

b) I am not sure how to finagle this one a wholes and parts argument,
but let me try. Maybe it is that centers are things that balls have but
are not properties of points? That attributing center to a point becomes
a category error?

c) Perhaps you feel that *center of a ball* fails operationally, that
centers of balls are singular by their very nature, privileging insights
of Archimedean experiences? I haven't worked it out, but I (perhaps
falsely) assume that any one of these centers can be handled as a center
of mass, a barycenter, maximally situated away from the ball's closure.
Here, I suppose, is where your Gordian step is apt? From each "center"
it takes the same number of constant steps to leave.

All of this is to say that I would like to better understand the *fallacy*.
In terms of the larger metaphor, I like the image of many individuals,
all within the scope of one another, granted the center of their shared
milieux.

[⊬] https://www2.palomar.edu/users/bthompson/Fallacies%20of%20Ambiguity.html
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://redfish.com/pipermail/friam_redfish.com/attachments/20211110/a5f04570/attachment.html>