On Tue, 11 May 2010 03:02:35 -0700 (PDT), David BL
<davidbl (AT) iinet (DOT) net.au> wrote:

[snip]

Well, I certainly am invoking it. Welcome to my killfile.

Sincerely,

Gene Wirchenko

On May 11, 10:27 pm, Keith H Duggar <dug... (AT) alum (DOT) mit.edu> wrote:
I never said otherwise

No, I was asking what point you are trying to make. You appear to be
foolishly or intentionally misinterpreting me. You previously said
my objection was "lame". I was only trying to understand what we were
actually arguing about.


It is a matter of definition. I prefer to consider variables to
"exist at run time". I agree that it's common and reasonable to also
call symbols in the source code "variables". Obviously there are
important differences.

I used to prefer the latter terminology, but after coming to this
newsgroup / reading C.Date's book I can see that the latter is more
useful for database theory discussions (which normally doesn't care
about how symbols are used in the source code written in some
imperative language).

I once brought up the following C++ example on this newsgroup.

int* p = new int;

A C++ programmer would only call p a variable because a variable is by
definition a symbol in the source code. Indeed I was told that the C+
+ standard is quite specific on this matter. In any case I was flamed
by Bob and his friends by taking this position.

Bob's said that actually there are two variables involved. A pointer
on the frame, and an int variable allocated on the heap. In his eyes
any other point of view was stupid. Since that time I have generally
used Bob's (i.e. Date's) definition of a variable: A variable exists
in time and space and at a given time holds a particular value.


You appear very confused. There are three different uses of the term
"variable" that have been used:
- FOL variables which are used to express quantification in logic
- symbols which are called variables in source code
- variables in computational machines that hold values

I suggest we henceforth only discuss FOL variables to avoid further
mistakes.


Do you really want to start a long discussion on what "is a" means?


I'm not redefining it at all. I'm pointing out that you read too much
into "is a".

I was hoping not to get into a discussion about "is a". I'll assume
you claim a variable is a kind of symbol and nothing more than a kind
of symbol. [Compare this to CIRCLE is-a ELLIPSE where the analogy
holds and "downcasts" can make sense versus COLOURED-RECTANGLE is-a
RECTANGLE where it doesn't. We cannot treat a rectangle as a
coloured rectangle because we don't know what the colour is].

So here's a set of symbols

{0,1,a,b,foo,x,u}

which ones are variables? What is the defining characteristic? I
suggest it is only a matter of convenience to say, in some context,
that {0,1,a,b,foo} shall designate a set of symbols to be used as
function symbols, and {x,u} shall designate a set of symbols to be
used as variables. Within the context of the expression {x,u},
these aren't and cannot be variables. Otherwise that wouldn't be a
ground term and have an interpretation as a particular set. If you
only comment on one point in this post, please make it that one!

Would you agree there isn't some absolute and universal determination
of what symbols must be used for variables? In other words, do you
agree that the designation of whether a symbol happens to represent a
variable depends on a *context*?


<quote>
"A variable is a symbol on whose value a function, polynomial, etc.,
depends."
</quote>

Q: If a variable is a kind of symbol and nothing but a symbol, how
can it have a value (c.f. "... whose value ...").


<quote>
"A variable is a symbol that stands for a value that may vary;"
....
"Varying, in the context of mathematical variables, does not mean
change in the course of time, but rather dependence on the context in
which the variable is used."
</quote>

Q: If a variable is a kind of symbol and nothing but a symbol, how
can it "stand for a value"?

Q: If a variable is a kind of symbol and nothing but a symbol, what
is meant by *the* context in which it is used?


<quote>
.... the variable x is bound ...

.... a detailed example involving quantified variables will prove to be
instructive.
</quote>

Q: If a variable is a symbol and nothing but a symbol, what does it
mean to say the variable is "bound"?

Q: If a variable is a symbol and nothing but a symbol, what is a
"quantified variable"?


I agree there is no shame and I often make mistakes. You're claim
that I "cannot emotionally bear to admit a simple mistake" is pure
guesswork on your part. In actual fact I believe I'm correct.
Comments like that reveal more about yourself than me (i.e. that you
state supposition as fact). You also spend a lot of time appealing
to authority without presenting or even outlining a convincing
argument. Indeed in your first post you even revealed confusion
between variables and function symbols of arity 0, which leaves me
wondering whether you understand the Stanford material you reference.

On May 11, 10:27 pm, Keith H Duggar <dug... (AT) alum (DOT) mit.edu> wrote:

[snip]

Sorry, just in case you're intending to write a long response to my
last post, I thought I'd let you know I'm calling it a day.

Thanks anyway for a spirited debate,

David

On May 10, 5:54 pm, David BL <davi... (AT) iinet (DOT) net.au> wrote:
I've been reading the following Stanford articles:

http://plato.stanford.edu/entries/types-tokens/

(note well section 8 on occurrences), and

http://plato.stanford.edu/entries/logic-classical/

I'm going to eat my words. I see now that I was wrong. I was
associating the term "variable" with occurrences of symbols, whereas
the Stanford articles go to the trouble to distinguish between a
variable and an occurrence of a variable.

Therefore assuming this terminology it is indeed valid to have a set
of variables.

However it is very curious that if one says:

Let {x,y,z} be a set of variables

then what we appear to have is an expression {x,y,z} containing free
variables. According to Section 4 (Semantics) in the SEP article on
classical logic, an interpretation M = <d,I> assigns denotations to
constants. E.g. For constant c, I(c) is an element of d, whereas a
variable-assignment function s on M is required to assign a denotation
to a free variable. The denotation of variable v is s(v) which is an
element of d, not the variable itself. It seems that although one can
have sets of variables, it is rather difficult to denote them!


I was correct there.

I will qualify that. An interpretation function I doesn't map a
variable to anything. Rather a variable assignment function s defined
on an interpretation M is used to assign denotations to free
variables.

Keith's comment was incorrect. A variable assignment function s is
not part of an interpretation M, and therefore it is incorrect to say
that an interpretation M assigns a denotation to a free variable.

On May 17, 10:57 pm, David BL <davi... (AT) iinet (DOT) net.au> wrote:
Good. We've come full circle jerk in yet another extravagant DBL
pose fest. You should study how your profound ignorance and lame
attraction to fallacies (context shifts, strawmen, etc) required
nearly 30 posts across multiple days and posters to correct.

"not the variable itself" and "it is rather difficult to denote
them!" are just more nonsense meaningless drivel.

No, you were and remain wrong because the context was not FOL and
never has been! These ignorant context shifts you keep trying to
impose on the discussion are plain stupid.

The context of my statements was and continues to be mathematics
and formal languages in general and formal semantics in general.
In that broader context variable assignment functions are simply
a "part" of an interpretation. Read section 1 of the following:

http://plato.stanford.edu/entries/model-theory/

Do you understand now? An "interpretation" is the totality of the
"added information". Or as wikipedia concisely puts it

http://en.wikipedia.org/wiki/Interpretation_(logic)

"an interpretation is an assignment of meaning to the symbols of
a language." Across a variety of formal languages and semantics
this is extra information is formalized as a /relation/. Sometimes
that relation is thought of in parts (for various reasons) such as
the "denotation assigment function" and the "variable assignment
function" etc.

But of course, you are near totally ignorant of this broader
context. As evidenced by this post

http://groups.google.com/group/comp....4d854934?hl=en

you were even ignorant of the field of formal semantics until
I told you about it a month ago. Now, after a month, you think
you are qualified to pronounce yourself right and your teacher
wrong?? This has got to be one of the clearest examples of an
idiotic vociferous ignorant poser we've seen in a long while.

That what the rest of formal semantics calls a "model" (which
is exactly why it is commonly represented by the letter M even
in FOL) is often called the "interpretation" in classic first
order interpretation, is completely irrelevant to the more
general context of model theory applied to mathematics and
formal languages as a whole.

As already demonstrated you were nearly ignorant of all this
even just days ago. Had you been aware of variable assignment
functions you would have understood that my general point made
in a more general context, applied equally well to FOL because
a function (the variable assignment function) is a relation!

Obviously the above is flat wrong because free variables are
not used to express quantification. This is part of the Dense
Bullshit and Lies (DBL) that is so time consuming to respond to.

Also, we see yet another example of you trying to impose a context
shift (from languages in general to FOL only). A dishonest "tactic"
that is so blatantly easy to spot for those trained to do so and
yet so annoying and time consuming to repeatedly correct.

Wrong. See above. In the general context of formal semantics and
model theory the variable assignment functions discussed in FOL
are just one part of what formal semantics calls "interpretation".

The problem was and remains that DBL is nearly completely ignorant
of formal semantics. He's never sat in a class for it, never worked
through examples of interpretation, never heard a professor warn you
of some common ambiguities and overloaded terminology and to explain
the history behind them. In other words, DBL is ignorant of the whole
and worse is vociferously arrogant in that ignorance.

KHD

On May 23, 3:53 am, Keith H Duggar <dug... (AT) alum (DOT) mit.edu> wrote:

I'm pointing out that s(v) isn't necessarily equal to v. That's not
meaningless.


I've made it clear in other posts that one should distinguish between
FOL variables and assignable variables.

When Bob introduced the set {a,b,c,rosie} he was claiming that
virtually anything can appear in a set (such as a dog). I thought it
would be interesting to talk about FOL variables (instead of
assignable ones).


You guess incorrectly.


So you were using "interpretation" in a less specific sense. It's
amazing that something like that could trigger such a barrage of
insults. You seem childish.