John C., Gary F.,
Well, clearly I'm not familiar enough with Putnam's argument.
As regards different directions of determination as 'constraint', it
might be sufficient to distinguish level from meta-level. If a given
object always has a certain index accompanying it, by which people
usually interpret there to be the object, then at a theoretical (meta)
level, the object is itself an index (for the theorist) of an object
that is the index at the primary level. Might the cases that you're
alluding to come down to that sort of thing? - semioses about semioses?
and that at the primary level, the same two objects might be object,
index for one mind, and index, object, for the other mind.
Too many generals? That's like saying too many relations. We tend to
confine our attention to those that are nontrivial, or have some novelty
of aspect, or have what Peirce called verisimilitude, or have
plausibility (if inference generally lacked all those characters it
would be worthless) as well as something like testability,
explorability, etc., at least testability in principle. I don't worry
about an excess of generals or relations because I don't think of them
as existing like atoms in a finite space. Mathematical possibilities are
endless, what's wrong with that?
What I've said about numbers doesn't involve any particular view as to
set theory versus ordinals. You're talking about how to define numbers,
I'm talking about when one works with them, and how one can refer to
them whether one regards them as sets of units or as sets of sets or as
ordinals.
Best, Ben
On 1/31/2015 12:57 PM, John Collier wrote:
Comments intertwined. Thanks for the effort, but it doesn’t really
help with what is worrying me.
*From:*Benjamin Udell [mailto:[email protected]]
*Sent:* January 31, 2015 7:08 PM
*To:* [email protected]; [email protected]
*Subject:* [PEIRCE-L] Re: [biosemiotics:8047] Re: Triadic Relations
John C., Gary F.,
John, you wrote,
[JC] As far as the process goes, since we have no way to grasp an
object except through signs, it seems very strange to me to say
that the object determines the sign or its parts through a process
of any sort. This is especially true when the object is a general,
which is an abstraction (however real). That would be rather like
saying that the number twelve determines the number of eggs I
bought today.
[End quote]
The number twelve doesn't determine or compel you to buy twelve rather
than eleven eggs. But the number twelve does determine (in Peirce's
sense of 'determine') the twelve eggs as a representative instance of
twelve in general - rather than of eleven or thirteen in general - to
an interpreting mind. If a cloud reminds you of a certain person's
face, that person's face does not determine or compel the cloud to
physically shape itself into the appearance of that person's face.
Instead that person's face determines the cloud, in the happenstance
shape that it already has, into being an iconic representamen of the
person's face for you. The person's face achieves this through your
individual collateral experience of the person's face. That's where
the "line," as it were, of triadic causation or determination or
influence runs. That cloud is an icon to you but not the kind that
comes already physically attached to an index designating or pointing
to the person's face; your collateral experience supplies the index in
your individual mind.
Quite, Ben. But it doesn’t get at what worries me. Your cloud example
suggests that there could be any number of generals. As I said to Gary
in my recent reply to him, if there are any numbers of generals then
we might as well be nominalists. My approach to cardinal numbers,
which is not that odd historically, says that it is all the twelve
numbered sets that determine the number twelve, not the other way
around. The way you put it is too Platonic for my taste.
You wrote,
[JC] As far as Peirce€™s definition of a sign in terms of
determination goes, it certainly doesn€™t preclude determination
also going in other ways. So we could accept the definition, and
interpret determination as €˜being relevant to€™ or something like
that, and still have determination in all directions. [....]
[End quote]
I'm not sure what you're saying. Do you mean, for example, that each
of two physical objects reacting with each other may be an index of
the other? That's true, though it may be hard to separate out what is
representative of one object and what is representative of the other.
It seems easier to think of both objects as indices of their composite
system; anyway the total object of a representamen is the object's
universe of discourse. Suppose a situation with a mind confined to
observations of only one of the objects, and another mind, a mind
confined to observations of only the other object. Each mind will
need, at some level, to take its observed index as index not
exclusively of the unobserved part, but as an index of the physical
system, the object of which the two separately observed objects are
parts in a complexus, of which the given observed part, the given
index, is a part. Likewise a sample is an index of the totality from
which it is drawn. The lines of object-index determination can run in
various ways and one just needs to keep track of them.
No, I was just saying that determination in one direction does not
preclude determination in another, in the sense of ‘being relevant
to’, or ‘constraining’.
You wrote,
[JC] [....] It seems to me that this is necessary unless there are
multiple mappings (degeneracies) of interpretation and object to
representamen (not sign in my current usage), since there is only
one thing whenever we are talking about a particular sign, which
determines its particular parts. Being a part of the sign is then
determined. By part, of course, I mean the relata of the sign. I
was assuming that we could have the same interpretant and
representamen and object across different signs. If not then
determination of one part by another is trivial by identity and
the part-whole relationship. Which is what I have been worried
about all along.
I guess you're taking 'sign' to mean the triad of representamen,
object, interpretant, or as Edwina prefers to think of it, the triad
of their relations.
As an irreducible triadic relation among object, representamen and
interpretant.
Looking at it that way, I can't see how to see the same triad members
across different signs without just as well being able to say that one
has different cases of the same triad members across different cases
of the same sign.
Neither can I, actually. But this makes determination in all
directions in virtue of being parts of the same thing. In Particular
it seems to me intuitive that the interpretant determines the object,
though I am willing to allow that they are mutually determining. I see
the interpretant as acting like a sort of filter that constrains what
the object could be. The object can be taken easily to have the same
effect on the interpretant, as you and Gary have argued.
You wrote,
[JC] There are some cases in which the object determines the
representamen in the same way as it determines the interpretant. A
weather vane points a particular way. That is caused by the
direction of the wind, so it is so determined. The pointing of the
weather vane is interpreted as the direction of the wind, the
object of the sign in this case. No problem. Where I have trouble
is when we are dealing with not instances of objects, but
generals, as I have mentioned several times now. The nature of
the €œdetermination€ in this case seems very obscure to me, and I
would not call it determination, since that leads far too easily
to what Putnam called €œthe magical theory of reference€ popular
among metaphysical realists. I have been concerned about this
issue since I wrote my thesis on incommensurability, through my
work against Putnam€™s rejection of metaphysical realism, up to
today, right now. I don€™t think things are nearly as clear as you
and Ben seem to think they are.
[End quote]
As far as I can tell, and correct me if I'm wrong about this, what
makes reference magical in Hilary Putnam's scenario of the brain in a
vat is simply that the person claiming to be a (mostly) deluded brain
in a vat has, _/even in principle/_, no way to discover through
sufficient investigation the vat (or some analogue) that the person is
supposedly in and to which therefore the person can refer only
magically. This impossibility of discovery is by Putnam's own magical
fiat. Anyway, in the scenario, one has no way to discover which vat,
or what kind of vat-like thing, what actual analogue to the delusive
mere 'vat-images' to which the brain-in-a-vat is confined to
cognizing, what kind of computer program or computer hologram, what is
this absolutely hidden container's identity, character, measure,
location or path, etc. So the person can't meaningfully make the
claim, can at best offer the proposition as an idle, amusing reverie
including an appeal to incognizability-in-principle.
No, you are wrong. He invokes the magical theory of reference as one
held by metaphysical realists whether brains in vats or not. The idea
is that we can sort of triangulate the reference of our terms by
constraining what the external world is like. Putnam argues we can’t
do that. That is the intended function of his brain in the vat
argument and his models and reality argument. A similar argument to
the latter was made to Russell’s structuralism in the early 30s by MAH
Newman. It works against views that attribute more to reality than
structure, but not Russell’s view. Russell never replied.
Now, one's experience includes actually imagining various instantial
embodiments of the number twelve, where one found that the number
insistently follows certain rules, and so on, and found that in those
cases one could see that those rules would always hold as long as one
holds to certain general rules - the terms and conditions of a
contract - a mathematically nontrivial one - made by the imagination.
The number twelve has no single concrete embodiment, no single sensory
character, etc.. Still, one refers through such experiences to the
number twelve. Anybody of sufficient intelligence can have such
experiences and people generally converge quickly to agreement about
12+12=24, and so on. The natural numbers can serve as a systematic
index (or indexical legisign) of any denumerable well-ordered set. Any
living, actual mind will need to refer such indexical legisigns to
individual actual (or actually imagined) examples in that mind's
experience. One cannot imagine the whole denumerable set distinctly,
but one can refer oneself to experiences of proofs that the rules
would apply throughout, and even to experiences that seeming failures
with, say, very large numbers, turned out to result from calculational
error or the like.
Yeh, as I said I don’t have the same view of numbers. I put
cardinality first rather than the more common ordinality (a set of
ordered indexes).
Best,
John
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