Peter Jones wrote:
> On 17 Aug, 11:17, Bruno Marchal <> wrote:
> > On 17 Aug 2009, at 11:11, 1Z wrote:
> >
> > > Without Platonism, there is no UD since it is not observable within
> > > physical space. So the UDA is based on Plat., not the other way
> > > round.
> >
> > Are you saying that without platonism, the square root of 2 does not
> > exist?
> Yes, the square root of two has no ontological existence.
> > Prime number does not exist?
> Yes, prime numbers have no ontological existence

What do you mean by "ontological existence"? The modern perspective among 
analytic philosophers is to tie ontology to the notion of objective truth--if 
we imagine a book containing an exhaustive set of *all* objective truths about 
reality, then the minimal set of entities that we would need to refer to in 
such a book, in such a way that we could not remove all reference to them by 
coming up with a "paraphrase" of all statements involving them, would be the 
ones that must be part of our ontology. This idea goes back to Quine, it's 
discussed at and there's 
also a discussion in the introduction to the book "The Oxford Handbook of 
Metaphysics", which says:
"Quine's criterion of ontological commitment is understood to be something like 
this: If one affirms a statement using a name or other singular term, or an 
initial phrase of 'existential quantification', like 'There are some 
so-and-sos', then one must either (1) admit that one is committed to the 
existence of things answering to the singular term or satisfying the 
description, or (2) provide a 'paraphrase' of the statement that eschews 
singular terms and quantifications over so-and-sos. So interpreted, Quine's 
criterion can be seen as a logical development of the methods of Russell and 
Moore, who assumed that one must accept the existence of entities corresponding 
to the singular terms used in statements one accepts, unless and until one 
finds systematic methods of paraphrase that eliminate these terms. .... Most 
philosophers today who identify themselves as metaphysicians are in basic 
agreement with the Quinean approach to systematic metaphysics"
The "paraphrase" condition means, for example, that instead of adopting a 
statement like "unicorns have one horn" as a true statement about reality and 
thus being forced to accept the existence of unicorns, you could instead 
paraphrase this in terms of what images and concepts are in people's mind when 
they use the word "unicorn"; and if you're an eliminative materialist who wants 
to avoid accepting mental images and concepts as a basic element of your 
ontology, it might seem plausible that you could *in principle* paraphrase all 
statements about human concepts using statements about physical processes in 
human brains, although we may lack the understanding to do that now.
As the quote says, most philosophers (analytic philosophers anyway) adopt this 
point of view when dealing with metaphysical questions. For instance, if you 
believe there are objective truths about mathematics which cannot be reduced to 
statements about the physical world using an appropriate "paraphrase", then in 
Quine's scheme you'd have committed yourself to some form of mathematical 
platonism. Likewise, if you believe there is an objective truth about what it 
is like for a human to experience the color blue which could not be deduced 
from an exhaustive set of facts about their physical brain, as suggested by the 
"Mary's room" thought-experiment (see's_room 
), then you've committed yourself to an ontology where qualia have some sort of 
nonmaterial existence (even if they are entirely determined by the physical 
arrangements of matter and the physical world is 'causally closed', as proposed 
by David Chalmers).
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