Re: On Formal IS-A definition

On May 23, 3:53 am, Keith H Duggar <dug..._at_alum.mit.edu> wrote:
> On May 17, 10:57 pm, David BL <davi..._at_iinet.net.au> wrote:
>
>
>
>
>
> > On May 10, 5:54 pm, David BL <davi..._at_iinet.net.au> wrote:
> > > On May 10, 1:34 pm, Keith H Duggar <dug..._at_alum.mit.edu> wrote:
> > > > On May 9, 9:29 am, David BL <davi..._at_iinet.net.au> wrote:
> > > > > On May 9, 11:38 am, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
>
> > > > > > My set of three variables and a dog fully complies with ZFC.
>
> > > > > Here is a quote from (http://en.wikipedia.org/wiki/Zermelo
> > > > > %E2%80%93Fraenkel_set_theory)
>
> > > > > "ZFC has a single primitive ontological notion, that of a hereditary
> > > > > well-founded set, and a single ontological assumption, namely that all
> > > > > individuals in the universe of discourse are such sets. Thus, ZFC is a
> > > > > set theory without urelements (elements of sets which are not
> > > > > themselves sets)."
>
> > > > > and this (fromhttp://en.wikipedia.org/wiki/Hereditary_set)
>
> > > > > "In set theory, a hereditary set (or pure set) is a set all of whose
> > > > > elements are hereditary sets. That is, all elements of the set are
> > > > > themselves sets, as are all elements of the elements, and so on."
>
> > > > > I wonder whether Bob enjoys putting a leash on a set and taking it for
> > > > > a walk.
>
> > > > I wonder if you know what a variable is? Or more specifically I
> > > > wonder if you can prove that a variable is not a set? Well, that
> > > > is a rhetorical question really because I already know that a
> > > > variable /is/ a set. Or rather, because the word "is" is vacuous
> > > > most of the time, a variable can be represented by a set. Since
> > > > you enjoy wikipedia so much (since when did wikipedia become an
> > > > authoritative source?) try reading this (thoughtfully):
>
> > > > http://en.wikipedia.org/wiki/Variable_(mathematics)
>
> > > > and see if you can figure out how it is that variables can be
> > > > represented by sets. Hint, a variable is a /symbol/.
>
> > > You are using "variable" in the sense that a logician would use it.
> > > This discussion actually began with variables accessed by programs
> > > that support imperative assignment statements. Let's be sure we
> > > don't confuse these.
>
> > > In any case you are still wrong. I believe you are suggesting one
> > > can
>
> > > 1) Have a symbol x
>
> > > 2) Form a set {x}
>
> > > 3) Have a logic formula where symbol x is a variable, such as
>
> > > for all x, x+0 = x
>
> > > 4) Deduce that variables can appear in sets.
>
> > > I accept 1), 2) and 3) but not 4). You make the mistake of thinking
> > > that symbols represent variables outside the context of the formula
> > > they appear in - even when the variable is bound. If that were true
> > > that would be remarkably bad!
>
> > 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.
>
> 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.

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

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

> > > > DBL knows that in formal semantics /variables/ are /interpreted/
>
> > > Wrong (assuming "interpreted" means mapped by an interpretation
> > > function). Only function symbols and predicate symbols are
> > > interpreted.
>
> > I was correct there.
>
> 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.

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).

> 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.databases.theory/msg/05f51dba4d85...
>
> you were even ignorant of the field of formal semantics until
> I told you about it a month ago.

You guess incorrectly.

> 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!
>
> > > > DBL knows that an interpretation is formally a /relation/ mapping
> > > > variables (and all other symbols) to elements of the /domain of
> > > > interpretation/ also sometimes called a "universe"
>
> > > Wrong. FOL variables are not mapped to anything. They are *only*
> > > used to express quantification in logic.
>
> 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.
>
> > > A sentence (i.e. formula where all variables are bound) is interpreted
> > > according to the semantics of existential or universal quantification
> > > on the bound variables that are assumed to range over the universe of
> > > discourse.
>
> > 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.
>
> 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.

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. Received on Sun May 23 2010 - 23:10:21 CEST