Words from ‘Iconicity as a Creative Force in Language Use’ an Introduction by Olga Fischer and Max Nanny (the a in Nanny has an umlaut over it)

Sources noted, though admittedly most are from Wikipedia or Dictionary.com (a subscription to the OED was just too expensive).

1. “Moving from a phylogenesis of language development–from its mythical origins in ‘natural language’ to some twentieth-century literary revivals of pristine iconicity–to ontogenesis, we discover that a natural language fantasy is also strongly present in children, as many studies have shown…” (Fischer and Nanny, 17)

phylogenesis: Evolutionary development of a species

Phylogenetics
Field Of Study

In biology, phylogenetics (pron.: /flɵɪˈnɛtɪks/) is the study of evolutionary relationships among groups of organisms  (e.g. species, populations), which are discovered through molecular sequencing data and morphological data matrices. The term phylogenetics derives from the Greek terms phylé (φυλή) and phylon (φῦλον), denoting “tribe”, “clan”, “race”[1] and the adjectival form, genetikós (γενετικός), of the word genesis (γένεσις) “origin”, “source”, “birth”.[2] The result of phylogenetic studies is a hypothesis about the evolutionary history of taxonomic groups: their phylogeny.[3]

ontogenesis: Biology . The development or developmental history of an individual organism.

So, it looks like there is a relationship, a comparison between the many and the one.  Very interesting.

2.“Within structural diagrammatic iconicity two types are usually distinguished: isomorphism and iconicity of motivation…The first one, Haiman claims, is universal, the second is not.  Isomorphism means that there is a one to one relationship between signifier and the object/concept signified. This can be found on the lexical as well as the grammatical level.” (Fischer and Nanny, 24)

“Similarly, in syntax, isomorphism entails that one cannot really have optional differences in surface structure.  In other words, the old generative tenet that several surface structures may have one deep structure, implying that these surface structures all mean the same (because transformations which link deep and surface structures are meaning-preserving) is not really possible.” (24)

isomorphic/isomorphism:

1. Similarity in form, as in organisms of different ancestry.
2. A one-to-one correspondence between the elements of two sets such that the result of an operation on elements of one set corresponds to the result of the analogous operation on their images in the other set.
3. A close similarity in the [crystalline] structure of two or more substances of different chemical composition. Isomorphism is seen, for example, in the group of minerals known as garnets, which can vary in chemical composition but always have the same crystal structure.
Taken from http://www.thefreedictionary.com/isomorphism and marked up by me.
I am looking to understand isomorphism in iconicity a little better.  I think I understand it to be this one to one relationship, but I need it to go a bit further.  I like the last quote, about ‘deep’ and ‘surface’, this makes some sense.  It means (to me?) that no two words actually mean the same thing.  And that is awesome, wonderful, and a bit overwhelming.
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