```Date: Feb 15, 2013 12:57 AM
Author: fom
Subject: Re: distinguishability - in context, according to definitions

On 2/14/2013 9:32 AM, Shmuel (Seymour J.) Metz wrote:> In <qImdnYCz5tRmvITMnZ2dnUVZ_oWdnZ2d@giganews.com>, on 02/11/2013 >> ..., then> asking whether "pattern matching" has any relevance.On that count, let me compare my methodwith a strategy used by Frege in "Functionand Concept":"My starting-point is what is called afunction in mathematics. [...] So wemust go back to the time when higherAnalysis was discovered, if we want toknow how the word 'function' was originallyunderstood.  The answer we are likelyto get to this question is: 'A functionof x was taken to be a mathematical expressioncontaining x, a formula containing theletter x.'"Thus, e.g., the expression(2x^3)+xwould be a function of x, and(2*2^3)+2would be a function of 2.  This answercannot satisfy us, for here no distinctionis made between form and content, sign andthing signified;..."So, what I did was to examine certain relatedsyntactic forms normally conjoined as justificationfor a "trivial" decision involving a use for thesign of equality.  Sadly, the attempt to illustratea context failed.  It had been formulated to consider analphabet of two letters whose infinite concatenationwould be a necessary requirement for asserting themeaningful interpretation of identity attachedto that decision.Since I found the term "distinguishability" in abook on automata, I analyzed the situation as bestI could relative to the subject matter in whichthe cited definition appeared.It would make no sense to treat the presentationof the "math trick" and its corresponding algebraicvariant in any semantically meaningful way sincethat particular proof was not the subject of analysis.The phrase "pattern matching" seemed reasonable.
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