Relations & Their Relatives : 7

Re: Peirce List DiscussionHoward Pattee

We use this or that species of diagrams to represent a fraction of the properties, hardly ever all the properties, of the objects in an object domain.  The diagrams that Peirce developed 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 interaction diagrams or Penrose 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---<L    
        \   
         i  

The ``L" brings to mind a triadic relation L, which collateral knowledge tells me is a set of triples.  What sort of triples?  The picture sets a place for them by means of 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 L.  It’s up to me to remember that L is a subset of O \times S \times 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 remarked and often exemplified.  One way 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.

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This entry was posted in Diagrammatic Reasoning, Diagrams, Logic, Logic of Relatives, Mathematics, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Tertium Quid, Thirdness, Triadic Relations, Triadicity and tagged , , , , , , , , , , , , , . Bookmark the permalink.

3 Responses to Relations & Their Relatives : 7

  1. Pingback: Survey of Relation Theory • 1 | Inquiry Into Inquiry

  2. Pingback: Survey of Relation Theory • 2 | Inquiry Into Inquiry

  3. Pingback: Survey of Relation Theory • 3 | Inquiry Into Inquiry

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