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 <>, 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


would be a function of x, and


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.