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While pursuing the analogies between some branches of mathematics and some fields of linguistics, I have recently come across the idea of intermediate trace, which, in the framework of the study of language (particularly, of syntax) is supposed to mean a trace which has to be erased at some further point of the derivation, in order not to block the whole, which would result in no real output. The technical reasons for this are a little dull for people not familiar with the field, so I ignore them for the time being. I know that in maths a trace is basically the constant value of the sum of the diagonal entries of a square matrix, irrespective of changes of basis. It can also be extended to tensors and the like, it appears. My question is then quite simple: Do you know of intermediate traces in mathematics (preferably in matrix and / or tensor domains)? If so, which are their main features? Thanks in advance.

PS: These 2 links might be helpful for you: http://en.wikipedia.org/wiki/Empty_category_principle http://en.wikipedia.org/wiki/Trace_%28linguistics%29

Javier Arias
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  • What is your definition of intermediate trace, exactly? – Travis Willse Apr 29 '15 at 15:36
  • In government and binding theory, traces are subject to the empty category principle (ECP), which states that all traces must be "properly governed". Proper government is either theta-government or antecedent-government:

    Who did John say that Mary saw t? (The verb "see" both governs and theta-marks the trace, so the trace is theta-governed.) Who t said that? (The wh-word governs the trace and is coindexed with it, so the trace is antecedent-governed.) However, intermediate traces are not subject to the ECP because they are deleted at LF (Logical Form).

     – Javier Arias Apr 29 '15 at 15:38
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    As far as I can judge from your Wiki links, there's absolutely no relation between the concepts of "trace" in mathematics and in linguistics, so this question seems rather meaningless to me... – Hans Lundmark Apr 29 '15 at 16:36
  • @Javier: Hans is correct: there is no connection whatsoever between the linguistic and mathematical concepts. – Brian M. Scott Apr 29 '15 at 20:31
  • @BrianM.Scott. I really believe there is such a connection. It may be arguable with regard to Chomsky, but it is certainly traceable (no pun intended) when looking at Harris. Just have a look at his Mathematical Structures in Language (the concept index will tell you which pages to llok at). – Javier Arias Apr 30 '15 at 10:47
  • @Javier: I'm not talking about connections between linguistics and mathematics in general; I'm talking specifically about the meanings of trace in mathematics and in theories of syntax. Between those there is no connection. – Brian M. Scott Apr 30 '15 at 10:52
  • @BrianM Scott. Yes, I know you are talking about that, and so do I. And I am telling you there is indeed connection. Just check Harris, where he defines the trace the same way as Kronecker defined the abstract group.........And as some people in this forum have instructed me, there is a smooth transition from that Kronecker group to tensors, matrices, and their traces...... – Javier Arias Apr 30 '15 at 11:05

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