Re: [ontolog-forum] Truth

[Chris Menzel <chris.menzel@xxxxxxxxx>]

On Fri, Jul 13, 2012 at 5:11 PM, John F Sowa <sowa@xxxxxxxxxxx> wrote:

On 7/13/2012 2:21 PM, Chris Menzel wrote:
> But, of course, that doesn't mean that a semantical model can't be

> exactly correct as far as it goes. BTW, it would be /great/ if in the

> future you numbered your slides. ;-)

Re slides:  The Adobe reader shows the slide number.  To go to slide N,
just type N into the little box in Adobe.

But not everyone uses Adobe Reader. I looked at your slides by clicking on the link and viewing it in my browser, which doesn't use the Adobe plugin.

 

In any case, slide 23 leaves open the option that the model could
be exactly isomorphic (or even identical) to the subject matter.
But that case is possible *only* for mathematics -- or for
formally defined games like chess.

That is far from obvious. Seems to me that "Human(Sowa)" (and a corresponding model thereof containing you and the property of being human) gets the world exactly right as far as it goes. More complex cases can be understood accordingly. But I don't wish to debate this point.

 

To represent any chunk of the physical world perfectly, we'd need
some notation that could exactly represent every state of every
atom.  

Who said anything about exact representation? My claim is only that models/theories can get the world right as far as they go.

 

That would run into quantum mechanical effects, and an
impossibly large amount of data.  Approximations are the norm.
As engineers say, "All models are wrong, but some are useful."

It's a stupid slogan. Models are useful (typically) because they get the world right to some extent, at some level of granularity. If that weren'tt so, their usefulness would be a complete mystery.

 

> What I meant of course was a predicate whose intended semantics
> is a relation between names and the things they name.

I assumed that was your intention.  But it's common practice in NLP
systems to use surrogates (such as GENSYM in LISP) as URIs for the
named entities.  Computational linguists would normally use some
predicate to link the internal identifiers to the external names.

Of course, but that doesn't really alter the point.

 

> ... through the magic of Gödel coding, any theory containing a bit

> of number theory can construct such a predicate. I am talking about

> languages like that, in which semantical predicates...

I have a very high regard for Gödel's achievement and related methods
in the foundations of mathematics. But very little, if any, of that work is of

any relevance to AI, NLP, cognitive science, or applications of ontology

to the areas that Ontolog Forum addresses.

It was just an example of a language that likes of which you seemed to be saying didn't exist.  Obviously, you wouldn't use Gödel coding to represent naming in a more practical, real-world environment.

 

> you can introduce what you call semantical predicates and pretend
> they have a certain intended meaning, but if those meanings are not

> encoded in axioms and are not reflected in the semantics...

I'm not pretending anything.  I define them.

Then you are belying what I took you to be saying before. I said that languages containing alleged semantic predicates that aren't formalized are like box/arrow diagrams where the intended semantics are only in the minds of the users. And you replied "Absolutely! That is all we can ever have in our computers...." I took that to mean that you can't formalize semantic predicates. But perhaps I misunderstood.

 

> And I recommend R. L. Martin's classic Recent Essays on Truth and
> the Liar Paradox and the recent book Axiomatic Theories of Truth
> by Volker Halbach for understanding the issues I'm referring to.

I read enough about the Liar Paradox, and I find it moderately
interesting.  Those rare cases that occur in NL documents written
by people for the purpose of communicating with other people never
require any features beyond the Tarski hierarchy.

You are really missing the point. The sorts of problems illustrated most simply and dramatically in the Liar Paradox arise in far more practical KR environments.  A good example is in the theory of contexts. Suppose you are in context C1 and you want it to be able to represent, in C1, that something FOO is the case in context C2. Let's use McCarthy's "ist" predicate:

  (ist (C1, ist(FOO, C2)))

This is exactly the kind of thing you want an account of contexts to be able to express. But "ist" is a semantic predicate and it is very easy to generate liar-like paradoxes with it. The question is then critical: Given that we want to implement a theory of contexts in a KR environment, how do we manage this theoretically? Do we restrict the language? How do we do so without robbing ourselves of the very expressive power we looked to a theory of contexts to provide? Do we restrict the logic? How do we do so without robbing ourselves of the ability to make the sorts of inferences we need to be able to make? These are profoundly difficult practical questions of knowledge representation.

 

> But the Tarski hierarchy doesn't solve the problem, it simply avoids
> it by restricting the languages in the hierarchy so that paradoxes
> can't even be expressed.

By treating 'true' as an indexical, you can process English sentences,
including the Liar Paradox, in a way that classifies paradoxical
statements as ill formed because they create cycles in the hierarchy.

Sounds like an interesting sketch of a germ of an idea. Where's the theory?

 

I have never seen any document written by people who are trying to
communicate with other people that requires anything more.

Perhaps when it comes to truth that is the case but, as noted, the problem is much more broad and general.

 

The only exceptions are the 0.000001% of documents written by
philosophers for other philosophers.  I am not against processing
that kind of language.  But there are so many serious problems of NLP,
that I consider those issues to be a frivolous waste of time.

 
> [Tarksi's solution] like avoiding illness by enclosing yourself in a sterile bubble.
> It might keep you healthy but it puts severe limits on what you can do.

 

Comments like that sound like the kind of disease that Wittgenstein
said only philosophers ever succumb to.

I'm disappointed that you are taking the same low road that others in this forum have taken in response to certain theoretical challenges: in place of informed argument, simply a haughty dismissal of "philosophers" in their ivory towers by the wise and experienced real-world practitioner. It also means that reasoned debate is at an end.

-chris

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