Date: Wed, 23 Jul 2008 22:50:16 -0700 (PDT)
On Jul 24, 10:56 am, "Brian Selzer" <br..._at_selzer-software.com> wrote:
> "David BL" <davi..._at_iinet.net.au> wrote in message
> > On Jul 23, 12:44 pm, "Brian Selzer" <br..._at_selzer-software.com> wrote:
> > > > A symbol is already defined as "something used for or regarded as
> > > > representing something else".
> > > Yet symbols are not values.
> > When one says false is a value, one is referring to the abstract
> > boolean value of false. When one says false is a symbol one is
> > referring to its use as an identifier within a sentence. Both usages
> > are common.
> > Only sentences contain symbols and conversely sentences only contain
> > symbols (ie not the values that they represent). However within a
> > sentence we normally interpret a symbol as standing for the value it
> > is deemed to represent and not the symbol itself.
> > In the RM formalism, relations are defined as abstract sets of tuples,
> > and tuples are formalised as mappings from attribute names to
> > attribute values. Relations are not sentences on some grammar and
> > therefore are not composed from symbols.
> Relation schemata /are/ sentences.
By relation schemata I assume you are referring to relation types. In the above my usage of “relation” means a relation value not a relation type. In any case I wouldn’t think any formalism of a relation type would consider it to be a sentence over some grammar. Type systems ofen formalise a type as a tuple in the manner of an abstract algebra. Eg (G,+) for a group with a binary + operator.
Do you agree there is an important distinction between a mathematical expression and the value it may be deemed to represent? Presumably you do since you say that symbols are not values. So why would you expect composite values (like relation values) to be composed from symbols rather than nested values?
> > In a database encoding there is only a single defined interpretation
> > of the encoded attributes as values in the RM formalism. Therefore
> > there is no distinction between symbol and value that can be made.
> I don't agree. Under the domain closure, unique name and closed world
> assumptions, a database is a proposition that is supposed to be true. How
> the database is physically implemented is irrelevant.
> > For example the integer value 42 may be represented using a little
> > endian encoding in memory where we ultimately need to know how to
> > interpret voltage levels, address lines, data lines and so on. Even
> > though an underlying binary representation can be seen as a symbol
> > composed of 1’s and 0’s in some language it is as irrelevant an
> > implementation detail as the choice of voltage level or address line
> > conventions to the RM formalism.
> What I'm saying is that absent interpretation, 42 is not a value--regardless
> of how it is encoded in the machine.
Well you don’t seem to be saying much at all then! When you say 42 is not a value you must simply be referring to it as a symbol within the context of your containing sentence. So what?
> Axioms are not just /assumed/ to be
> true, they are /accepted/ or /understood/ as being true. That is a critical
> distinction because acceptance and understanding both imply either that
> there is a particular intended interpretation and that under that
> interpretation the axioms are true, or that there is at least one
> interpretation and that under any and every interpretation the axioms are
> true. So it is only because the axioms that underpin arithmetic are
> accepted as being true that 42 can appear as an integer in the universe; it
> is only because those axioms have been assigned a truth value that 42 can be
> a value.
I can’t make any sense of this “critical distinction” or how it is relevant. Received on Thu Jul 24 2008 - 07:50:16 CEST