Date: Wed, 23 Jul 2008 22:56:33 -0400
"David BL" <davidbl_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.
> 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 1ís and 0ís 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. 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. Received on Wed Jul 23 2008 - 21:56:33 CDT