Explanation of list reference

[Ian Kelly]

On Sat, Feb 15, 2014 at 10:30 AM, Rustom Mody <rustompmody at gmail.com> wrote:
> Thanks! -- Nice to hear slightly more philosophically astute attempt than
> the naivete going around: "Object?! We all know whats an object!
> Everyone knows whats an object!!"
>
> However I am betting that the problem remains. Youve transfered the identity
> question into the lifetime.
>
> Now define object-lifetime without reference to identity :-)

Fundamentally that's what definitions do.  They transfer the question
of "what is X" to "okay, so what is this thing that defines X".  All
definitions must ultimately be circular, simply because we have only
finitely many words and concepts to work with.

>> "The id() function returns the identity of an object.  The 'is' operator
>> compares the identities of its two operands and returns True if they are
>> the same."
>
> Thats good -- 'is' in terms of 'id' -- better than the obfuscation and
> prevarication of the other way round. Only the name id is misleading -- it
> should be machine-id or some such.
>
> Consider these examples:
>
> Two graphs are the same if they have the same no of vertices and
> there is a mapping f from one vertex set to the other such that
> vw is edge in graph1 iff f(v)f(w) is edge in graph2.
>
> For a mathematician such an identity is unexceptionable

Is it though?  If we were to play the same game with it, I could point
out that you haven't defined graph.  So I'll retrieve a definition
from Wikipedia:

"""
a graph is an ordered pair G = (V, E) comprising a set V of vertices
or nodes together with a set E of edges or lines, which are 2-element
subsets of V
"""

Well, that's great, but it just transfers the definition of graph into
the definition of an ordered pair.  Ordered pairs can be defined in
terms of sets:

"""
In 1921 Kazimierz Kuratowski offered the now-accepted definition of
the ordered pair (a, b):

(a, b) := {{a}, {a, b}}
"""

But what is a set?  Cantor offers this definition:

"""
A set is a gathering together into a whole of definite, distinct
objects of our perception [Anschauung] or of our thought - which are
called elements of the set.
"""

But what precisely are "objects" and how are we to determine their
distinctness?  Cantor above relates them to perception or thought, but
surely my own perception and thought differ from Cantor's.  If
mathematics or philosophy offer us any absolute answer to this
question, I'm unable to find it.