```Date: Oct 25, 2013 4:47 PM
Author: fom
Subject: Purport is not instantiation

In this link:http://en.wikipedia.org/wiki/Original_proof_of_G%C3%B6del%27s_completeness_theorem#Extension_to_first-order_predicate_calculus_with_equalityit is made clear that the completeness offirst-order logic with identity is, in fact,completeness up to equivalence.The formulas used describe an equivalence relation.In this link:http://en.wikipedia.org/wiki/Incidence_algebra#Examplesone must scroll down a little bit.  What onewill find is that partition lattices are describedby incidence algebras.Note that partition lattices are precisely the latticesof equivalence relations.Now, ask yourself what "singular term" is supposedto represent.  Next, ask yourself how Tarski's semanticsdiffers from Goedel's completeness theorem.The syntactic purport of singular reference can neverbe the same as the instantiation of a referent.Tarski's semantics only makes reference to a singleelement of a partiton lattice -- the node in whichthe individual elements of the domain are to be foundpartitioned into singletons.The purport of identity in the logic makes referenceto any such partition.Now, in the link:https://groups.google.com/forum/#!original/sci.logic/Zc2egCgC9Nw/Q9u7tmEqrJ4JI prove that the terms of a language for a consistenttheory have the structure of a matroid.Matroids have their origins in the consideration ofindependent sets of vectors in linear algebra.In the link:http://rutcor.rutgers.edu/pub/rrr/reports2002/35_2002.pdfone can find a discussion of incidence algebras and matrixalgebra.  So, it should not be surprising that the languageterms of a consistent theory have the structure of amatroid.There is an axiom for infintary matroids introduced here:http://arxiv.org/pdf/1003.3919v3.pdfWell, one can make up one's own mind.  But there are reasonswhy I look at the foundations of mathematics in the way thatI do.Purport is not instantiation.
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