Howard,
This is where "collateral acquaintance with the object domain" comes in.
We use this or that species of diagrams to represent some of the properties,
hardly ever all of the properties, of the objects in some object domain. The
diagrams that Peirce devised to represent propositions about relations are quite
handy so long as one grasps the conventions of representation, manipulation, and
interpretation. They are not all that different in kind from Feynman's diagrams
or Penrose's twistor diagrams. Iconicity is nice when you can get it but one
has to keep in mind that the map is not the territory, as the saying goes.
What do I see in a picture like this?
```````s``
``````/```
o---<R````
``````\```
```````i``
The "R" brings to mind a triadic relation R, which collateral knowledge tells me
is a set of 3-tuples. What sort of 3-tuples? The picture sets a place for them
by means the place-names "o", "s", "i", in no particular order. Without loss of
generality I can take them up in the ordered triple (o, s, i). All of this is
just mnemonic machination meant to say that a typical element is (o, s, i) in R.
It's up to me to remember that R is a subset of O x S x I, with o in O, s in
S, and i in I. The diagram is just a mnemonic catalyst. You have to know the
codebook to decode it.
Pictures can victimize people, as Wittgenstein stated and as often exemplified.
One way that people fall victim to pictures like the one depicted above is
when they confuse a relation with a single one of its tuples. That would
represents a misunderstanding of what the picture is intended to represent.
Regards,
Jon
Howard Pattee wrote:
At 10:58 PM 12/16/2014, Jon Awbrey wrote:
Howard,
It's hard for someone trained as a graph theorist to make sense of
that question, since graphs, strictly speaking, are just dyadic (or
binary) relations.
HP: So if it makes any sense, you would say the answer to my question
is, No, by definition.
JA: If we are more loosely speaking about the sorts of diagrams that
Peirce called "graphs" and used to represent propositions about
arbitrary k-place relations, then we'll have to take some time to say
what those are exactly and what they represent and how exactly to
interpret them.
I might very hazily hazard a guess that are talking about a picture
like this:
```````s``
``````/```
o---<R````
``````\```
```````i``
And maybe what you call a "dyadic subgraph" is some 2-part piece of that?
HP: That's too hazy. So I wonder: Is it possible to faithfully represent
Peirce's triadic concept of a sign by a diagram or picture of any type?
Frederik discusses
<http://www.digitalpeirce.fee.unicamp.br/hoffmann/p-sighof.htm>Hoffmann
(p. 279) but his diagrams are not graphs and the meaning of the lines
joined at the center is totally occult.
Howard
Howard
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