[hist-analytic] A Scientist's Landscape

Roger Bishop Jones rbj at rbjones.com
Fri Jul 31 11:08:54 EDT 2009


I'd like to respond on one point from a message of
Steve's from a few days back.

On Tuesday 28 July 2009 12:20:02 Baynesr at comcast.net wrote:

>You remark:
>
>"But for Russell these are all "logical fictions" and I would
>be inclined to go further and regard ontology in its entirety
>as conventional (with some caveats)."
>
>Well, that would require quite a debate. The way the world is may be just a
> logical construct; but if so the world itself would not exist.

I would not say that the world is a fiction, but that there may
be no single way of carving it up into pieces so that we can
talk about it.
It is not reality which is similar to a logical fiction,
but rather that the ways in which we elect to talk about
it may have that character.

I don't personally think of abstract objects as fictions,
because to talk of something being a fiction is to admit
that it does not in fact exist.
However, explaining the status of abstract objects in
a sentence is not easy, and to go along with Russell's
talk of logical fictions gets you reasonably close.
Unfortunately, one then is construed as denying their
existence.

> I'm inclined
> to believe it is real and that ontology is what these constructs are
> constructed out of. But it's a topic that requires a systematic approach.

Yes, I think I have one of those.

> I'm inclind to think that ontology is the "real deal" and logic is a set of
> conventions about marks on paper, but I'm not sure. I waver on this;
> thinking one thing at one time and another at another time. It's a serious
> question.

I think Logic is the most fundamental "real deal" we have.
i.e. that the notion of logical truth is very important
very fundamental and objective (when properly construed)..
It is, in the underlying metaphysic of "Metaphysical Positivism"
a most fundamental concept.
In this conception of logical truth, abstract ontology is
significant (it plays a role in the explication of logical
truth), but it cannot in my scheme of things be considered
prior to logic.  It is a foundational co-conspirator.

>"It makes no difference to me whether or not abstract objects
>exist, I care only that their supposition is consistent and useful.
>Your denial of their existence has great disutility because it
>makes difficult a discussion of semantics or mathematics
>(and many other topics)."
>
>The existence of abstract entities is not essential. Much depends on what
> you take philosophy of mathematics to be. My view that there are no
> abstract entities required for mathematics, as fleeting as it is from time
> to time, doesn't really impact my view on proof theory; avoiding the
> paradoxes; or the nature of infinity. Others may see it another way, of
> course, but that is where the debate begins not ends.

The main point of this response is to correct an _apparent_
misunderstanding which you seem here to show of my indifference
to the existence of abstract entities.

It is not that I contemplate with equanimity doing without
the assumption that they exist.
I have not the least inclination to engage in nominalistic
reconstructions of mathematics or philosophy.

I am indifferent to the existence of abstract entities,
because I am quite confidence that mathematics would be
just as effective when done under the presumption of
their existence, even if that presumption were false.
If they really were fictions, (i.e. counterfactual
hypotheses or presuppositions), this would not diminish
the coherence and utility of mathematics.
Or even its truth, so long as the propositions of
mathematics are (as I believe they should be) interpreted
in a metaphysically neutral way.

I do care whether the assumptions we make about
abstract objects are consistent, for there would
quite possibly be dire practical consequences of
their not being.

RBJ




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