Re: Triadic Relations

Preceding Discussion:
ET:http://permalink.gmane.org/gmane.science.philosophy.peirce/15125
JD:http://permalink.gmane.org/gmane.science.philosophy.peirce/15126
ET:http://permalink.gmane.org/gmane.science.philosophy.peirce/15127
GR:http://permalink.gmane.org/gmane.science.philosophy.peirce/15128
ET:http://permalink.gmane.org/gmane.science.philosophy.peirce/15129
GF:http://permalink.gmane.org/gmane.science.philosophy.peirce/15130
Place Where I Came In:
HP:http://permalink.gmane.org/gmane.science.philosophy.peirce/15155
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15160
HP:http://permalink.gmane.org/gmane.science.philosophy.peirce/15161
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15162
HP:http://permalink.gmane.org/gmane.science.philosophy.peirce/15163

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 represent
a misunderstanding of what the picture is intended to represent.

Regards,

Jon

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