Chris, (01)
You say: (02)
'...there are properties
whose extensions are utterly random sets of natural numbers, ones
whose members cannot be picked out by any finite expression or any
computable process. If ever there were a definition of a
"meaningless" property or relation in the sense that Rob seems to be
groping for, that would be it.' (03)
The connection with randomness is well spotted. But why would you
characterize "properties whose extensions are ... random" as
meaningless, necessarily? (04)
"Random" things don't obey rules, sure, but that need not mean devoid
of content, rather the contrary. (05)
Actually, instead of defining a sense for "meaningless", you might
take what I am saying here as exactly the suggestion that we need to
consider properties with extensions which are "random", by one or
other definition, in our representations of meaning. (06)
Talking about growing evidence of a need for randomness in our
representations of the world (evidence from physics, Category Theory,
and not least natural language) was the other way I pursued this
thread earlier in the conversation (other than "many-body" or set
theory.) (07)
-Rob (08)
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