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Re: distinguishability  in context, according to definitions
Posted:
Feb 15, 2013 12:57 AM


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 method with a strategy used by Frege in "Function and Concept":
"My startingpoint is what is called a function in mathematics. [...] So we must go back to the time when higher Analysis was discovered, if we want to know how the word 'function' was originally understood. The answer we are likely to get to this question is: 'A function of x was taken to be a mathematical expression containing x, a formula containing the letter x.'
"Thus, e.g., the expression
(2x^3)+x
would be a function of x, and
(2*2^3)+2
would be a function of 2. This answer cannot satisfy us, for here no distinction is made between form and content, sign and thing signified;..."
So, what I did was to examine certain related syntactic forms normally conjoined as justification for a "trivial" decision involving a use for the sign of equality. Sadly, the attempt to illustrate a context failed. It had been formulated to consider an alphabet of two letters whose infinite concatenation would be a necessary requirement for asserting the meaningful interpretation of identity attached to that decision.
Since I found the term "distinguishability" in a book on automata, I analyzed the situation as best I could relative to the subject matter in which the cited definition appeared.
It would make no sense to treat the presentation of the "math trick" and its corresponding algebraic variant in any semantically meaningful way since that particular proof was not the subject of analysis. The phrase "pattern matching" seemed reasonable.



