Dear Ben,
 
Just a side note on Mendaleev's talbe which I googled.  Mendaleev's periodic table was published 1869  -- Peirce New list in 1867.  So I don't think it could have been the pyramidism of Mendaleev's table that inspired Peirce. Plus Mendeleev's original table didn't look like much the pyramid we remember from chemistry class  -- and he called it a matrix. 
 
But you got me thinking about this notion of pyamidism being an inspiration to Peirce.  The triangle is a fascinating structure or form for sure but I think it was more the semantic form of the triad than its physical form that inspired Peirce.  Just as location can be in semantic as well as physical space.   Although as you know I think that physical space (even if it is itself a crude representation of some other reality) does underlie our notions of semantic space and that location and mass are not just semanticly related in common speech but are in fact related in the abstract theories of Enstein in which mass actually bends or creates the shape of space.    So when we denote or point to an object its hard to say whether it is its mass or location we referencing.   No doubt in our minds we probably think of ourselves as pointing to the object's form as well.  But, I still maintain that in theory all object have a set of qualities (constituting their forms or firstness) which are distinct from their mass/location (otherness or secondness),   In fact I don't think Peirce equated secondness with either mass or location.  He seems to have seen the continuity of space and time as being part of what constituted the mediation of thirdness.  But I think a specific place is a matter of secondness.  And I don't think he included mass as a quality.  I think he equated mass (as a force) with secondness though he does not say this explicitely.  I think mass is more or less the at the philosophers pole of substance with form at the other pole and continutity (representation or thought) being what mediates between them. 
 
Didn't mean to go off in this direction but I suppose this is my lst attempt at responding to some of your recent critiques of my discussions of connotation and denotation.  Which, as usual I find very interesting, helpful  -- and valid.   
 
Cheers,
Jim Piat
 
 
 
I would _not_ bet that his first inspiration was the periodic table or something like it, or the chemical symbolisms that were developing before it.
 
 
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