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 method

with a strategy used by Frege in "Function

and Concept":

"My starting-point 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.