Re: they mention various metaphors and ramble about various concerns (Re: Kuratowski Ordered Pair)

On Dec 22, 1:21 am, galathaea <galath...@xxxxxxxxx> wrote:
On Dec 22, 12:29 am, Marshall <marshall.spi...@xxxxxxxxx> wrote:
On Dec 21, 9:10 pm, galathaea <galath...@xxxxxxxxx> wrote:
On Dec 21, 2:55 pm, Marshall <marshall.spi...@xxxxxxxxx> wrote:
On Dec 21, 1:22 pm, galathaea <galath...@xxxxxxxxx> wrote:
it is regularly pointed out in the foundations of math
that the concept of 2 cannot be defined
without some presumption that the parser already has some bivalence

whether in two neighboring symbols
or two different symbols
or some other embedding of the concept innately

pairs

this is not true of higher naturals

This is just syntax again. This is not "the foundations"
of math; this is the syntax of math. We could as well
"write" expression in trees, assembling them via something
like tinker toys, where we have spokes and edges.
Or any of a variety of other ways. Linear strings
of symbols are convenient; don't mistake convenience
for semantics.

there is no mistake

definitions are syntactical

one tries to make the syntax
obtain the desired semantic properties

Huh who what? Syntax has semantic properties?

"Syntax is syntax and semantics is semantics and never the twain shall
meet."

Hmmm. Doesn't have quite the poetic ring to it one might wish.
Still, the point is, syntax doesn't have semantic properties.
So I can't imagine what you mean.

do you have familiarity with formal semantics?
have you read tarski?
do you know any model theory?
interpretations?

Haven't read Tarski. Have read Pierce. Familiar
with operational semantics. Not familiar with denotational
semantics. Have studied parsing. Have studied a variety
programming languages. I know what "interpretations"
and "valuations" are in the context of predicate logic,
say. Am in the market for an intro model theory book.


i can't imagine what you mean by
"never the twain will meet"

Here's a syntax:

eq ::= product ('=' product)*;
product ::= sum ('*' sum)*;
sum ::= name ('+' name)*;
name ::= [a-z]+;

With this syntax, what does

a+b=b+a

evaluate to? True? False? The name of a Swedish music
sensation ("abba"?) Is * associative? Does * distribute
over +?

Or is it the case that the answers depend on the semantics,
independent of the syntax?


Marshall
.

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