On Oct 7, 1:16 pm, "1Z" <peterdjo....domain.name.hidden> wrote:
Numbers that haven't been reified in any sense,
> don't exist in any way and therefore don't behave in any
> way.
Forgive me for butting in again, but is there not some way to stop this
particular disagreement from going round in circles interminably,
entertaining though it may be? For what it's worth, it seems to me that
Bruno has been saying that you get a number of interesting (and
unexpected) results when you start from a certain minimum set of
assumptions involving numbers and their relations. As he often
reiterates, this is a 'modest' view, making no claim to exclusive
explanatory truth, and - dealing as it does in 'machine psychology' -
limiting its claims to the consequences of 'interviewing' such machines
and discovering their povs. In achieving these results, AFAICS, no
claims need be made about the fundamental 'ontic realism' of numbers:
rather one is doing logic or mathematics from an axiomatic basis in the
normal way.
The question of which set of 'ontic prejudices' we in fact employ as we
go about our daily affairs is of course another issue. It may of course
eventually turn out that theoretical or, preferably empirically
disconfirmable, results derived from comp become so compelling as to
force fundamental re-consideration of even such quotidian assumptions -
e.g. the notorious 'yes doctor' proposition. But as Bruno is again at
pains to point out, this won't be based on 'sure knowledge'. It will
always entail some 'act of faith'.
To establish what is in some ultimate sense 'real' - as opposed to
knowable or communicable - is extraordinarily difficult, and perhaps at
root incoherent. The debate, for example, over whether the
computational supervenes on the physical doesn't hinge on the 'ontic
reality' of the fundamental assumptions of physicalism or
computationalism. Rather, it's about resolving the explanatory
commensurability (or otherwise) of the sets of observables and
relations characteristic of these theoretical perspectives. Indeed what
else could it possibly be for humans (or machines) with only such data
at our disposal?
David
> Bruno Marchal wrote:
> > There is no need to reify the numbers.[...]
>
> > I don't think so. Once you accept that the number theoretical truth is
> > independent of you (which I take as a form of humility), then it can be
> > explained quite precisely why "numbers" (in a third person view-view)
> > are bounded to believe in a physical (third person sharable) reality
> > and in a unnameable first person reality etc.Numbers that haven't been reified in any sense,
> don't exist in any way and therefore don't behave in any
> way.
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Received on Sat Oct 07 2006 - 09:39:11 PDT