Re: (OT) Re: Object identity


Stefan Ram wrote:
"David Barrett-Lennard" <davidbl@xxxxxxxxxxxx> writes:
I use the rule : if it's self consistent then it exists. That's my
definition of "exists". Now by Godel's theorem this definition won't
get you far. However this is where I blame formalism rather than
platonism.

We use designations (noun phrases) to refer to objects.

We say "... exists" if "..." is a designation that refers to
an object and that object is an entity of a model, which is
given explicitly or by context.

The existence of an entity within a model is a question of
agreement (declaration). The notion "agreement" here includes
consistency: An agreement must be consistent, because
otherwise one will not know /what/ is agreed upon.

For an examble look at set theory, where an axiom (in ZF) is:

»The empty set exists.«

This means that the noun phrase »empty set« shall refer to an
entity and that whenever someone agrees to use the ZF system
of axioms, he agrees to the existence of this entity.

The most prominent consequence of existence is that
existing objects can carry attributes, i.e., one can
speak about them. One can speak about unicorns, for
example, because there are models (tales) wherein they exist.

Consistency alone is not sufficient, as there exist models
that, for example, do /not/ contain an empty set. Within
those models the empty set does /not/ exist, although it
might be possible to declare their existence consistently.

Thus, existence is a question of agreement and defined
in relation to a model.

Agreed. The moment you mention "empty set" there is implicit agreement
to use the ZF axioms. There is furthermore an implicit assumption that
ZF is self consistent.

However there is no implicit assumption that you limit yourself to the
ZF axioms!

For example, in regard to programming languages we have two
important models: The source code model and the run-time
model. Statements are entities of the source code model, but
often not of the run-time model, while a numeric value is a
run-time entity (represented by a numeric literal [a
source-code entity] within the source code).

Agreed


Cheers,
David Barrett-Lennard

.

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