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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