Jeff, List -
Thank you Jeff for your May 31 comments on Smyth and Peirce, directing
attention to 8.123, and for fleshing out that text with your remarks
on W8 selection 6 as well as other textual material. I'm afraid I
haven't done the homework on Peirce's mathematics that you have.
However, even confining myself to your post, I share your sense that
the projection metaphors may help with Peirce's "logical conception of
the self and other key [logical] conceptions". Commenting on W8,
25-9, you wrote:
"What we have is the idea of a set of rays that radiate out from a
point of perspectivity to some thing that is located in the object
plane. A representation of the object is constructed on the image
plane by determining where the rays from the object intersect to form
an image. Quite literally, the representation is a mathematical image
of the object. Peirce's suggestion is that a particular manifestation
of the self is analogous to some particular image plane that cuts
through the rays that radiate out from the point of perspectivity.
There are a continuum of possible image planes that could cut through
these rays, and the many different particular manifestations of self
are related to one another in a manner that is analogous to this
continuum. Each of these possible image planes will give rise to
different images of the objects in the object plane--depending upon
the orientation of the image plane with respect to the point of
perspectivity and the object plane."
You go on to allude to a "projection" which is "the cone of rays that
radiate down from the point of perspectivity and just touch the
surface of the spherical [object plane] as a continuous series of
tangents. The image plane can be oriented to cut through that cone at
different angles."
You suggest what the projection represents on the side of Peirce's
theory of the self: the "I" we refer to when we speak, e.g., of
"something that 'I' have in mind", the "logical self", or "the self
that has the aim of seeking the truth and that is committed to acting
on the basis of the the requirements of reasonable inquiry". You
suggest what the image planes represent: "particular manifestations of
the self" or "[t]he particular self that looks out on the world from a
given perspective". You suggest, I think, that the former self
recognizes certain ones of the latter sort as that self's own, and
recognizes an obligation to act so as to relate these to others
consistently with the requirements of reasonable inquiry.
On this analogy, then, there are analogues for two sorts of self on
the side of Peirce's theory. My first response is that Peirce's
remarks about the self suggest a need for more than two. First, there
is what Kees calls the supra-individual institution, which if
construed as the community of inquiry is also a candidate for the
analogue of the projection. Then there is the individual considered
in accordance with 5.421 as what Kees might call a tightly compacted
institution, what Smyth calls a vague particular. Third there are
"phases" of this latter self: what you quote Peirce from 8.123 as
calling "the better self", etc. Then there is the individual
considered most narrowly, individuated by actions. After re-reading
Gary R's note from February 16, 2014 3:44:32 PM, citing 5.223 and
6.111, I am reminded of complexities here as well, and of my
uncertainty whether these are selves at an instant or at a moment.
Somewhere in all this is what we ordinarily think of as the finite
person, performing a very limited number of scientific acts over the
course of a lifetime.
I imagine I will be unable to follow the geometrical example if it is
complicated sufficiently to provide the requisite company of
analogues. Nevertheless I would invite you to say more about it
toward that end.
My second response has to do with what you say about the recognition
by the "logical" self of obligations with regards to its "particular
manifestations". There are several questions here. First, what in
the geometric analogy might enlighten us regarding how the logical
self recognizes its particular manifestations? In Peirce's discussion
of the map(s) he says "what ... makes my ideas mine is that they
appeal to me, and are, or tend to become, represented in my general
consciousness as representations" 8.124. I am trying without success
to make sense of this in terms of the indexical relationships which
bundle the self in his Consequences essay.
Or, putting the question more specifically, having in mind the
uncertainties I mention in my first response just above, what compares
with the finite inquirer's recognition of, say, how his obligations of
one moment compare with the obligations of another moment?
A related question is this: how does the geometry example, in which
the bearer of obligations of inquiry is analogous to the _projection_,
match up with what I just said (which seems natural enough) about the
obligations of a "particular manifestation" of a self?
Finally I have a question about what logical issue(s) the geometry
example is supposed to illuminate. From what you say, especially
about the variant of the example involving the projective absolute, I
take it that your concern is with how the self deals with the aim to
reach the truth. I would like to bring this into closer relation to
Peirce's 1877-78 series. Would it be reasonable to say that the
example will help us understand why the laws of logic are valid?
Would it help us understand why you or I should adopt the laws of
logic as normative for our behavior? As I'm sure you will recognize,
I am thinking here of Smyth's stress on distinguishing the role of
examples in relation to these two questions (RPR, 195; PNSR, 303).
All best,
Charles
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