FOM: Fiction and Mathematics

Dean Buckner Dean.Buckner at
Thu Feb 21 16:16:51 EST 2002

I've downloaded & will need time to digest the very interesting papers you

Readers beware the paper in question lurks in a corner of website and must
be looked for.  A couple of points right now - forgive if I misunderstand.

(i)  I don't really like "ontology" or "metaphysics" for the reasons stated.
Nor fictional objects.  Concerning these, there aren't any.  I don't mean,
they haven't property of existence, but in some sense have "being", I mean
there aren't any at all.  Not for some x fictional(x).  You'll probably
object, if I don't like fictional objects, what are these things I don't
like?  Well, I would like another glass of beer, very much, but there isn't
any in the fridge.  Not for some x, is-glass-of-beer-in-fridge(x).  Hmm.
(For South-East English readers I warmly recommend "Spitfire" Kentish Ale -
am I allowed to say that?)

You quote sympathetically Brentano's  "All mental references refer to things
... in many cases the things to which we refer do not exist".  Precisely the
point of view to which I am opposed.  To reiterate an earlier point, the
truth of the sentence

    (1) There is a unicorn in the cupboard

is "object-dependent".  Some unicorn must exist, for it to be true.  But the
truth of

    (2) Harvey thinks that there is a unicorn in the cupboard.

depends on there being someone such as Harvey, but not on there being any
unicorns.  We don't have to invoke fictional entities in order to explain
the meaning of (1) or the truth of (2).  Ordinary language is very simple,
and is not Meinongian (nor Brentanian, though Brentano changed his mind a
lot on this point).  My point was that "there are no unicorns" really is as
simple as it looks.  We should not have to explain it in may symbols.  That
is precisely what is wrong with F.O.M.  Everywhere I look I see pages and
pages of densely packed formulas in invented language.  Let's put it in

If one man walked home & another man was with him, then *two* men walked
home.  Yes?  Do we need any more?

(B) In CR p. 13, you say that singular reference is essentially similar to
general reference, so we can write "Socrates(x)" e.g.  "Just as the common
name "raven" stands for a sortal concept by which we are able to identify
and refer to one or more ravens, so too a proper name such as "Socrates"
stands for a sortal concept by which we are able to identify and refer to a
single individual."

Here's one brief argument against this idea.  Geach, as you must be aware
has others.  Also Aquinas, Frege &c.  Consider

    (3) I heard of someone called "Socrates".  Socrates was a philosophy

The two sentences as a whole don't identify any person "outside the story".
The first sentence tells us I heard of someone called "Socrates" (without
telling us who this is - there are/were many people  called "Socrates").
The two sentences together tell us that I heard of someone called "Socrates"
& he was a philosophy teacher - still without saying exactly which person
this is.  There could have been many such people.

But to understand what I say, you must be able to infer (if I'm telling
truth) that I heard of someone called "Socrates" who was a philosophy
teacher.  If you understand what I say, you understand the *same* person is
in question.  The use of the same proper name twice always implies numerical
identity, "sameness". But if "Socrates" is a sortal, then in theory another
individual could be Socrates.  For some x, Socrates(x) and Socrates(y) and x
<> y.  The use of a predicate never implies numerical identity.  We must
always be able to say "an F and another F and a third F ...".  The use of a
proper name always identity.  Proper names and predicates are in
fundamentally different categories.  Geach was never more correct (and
Aquinas and Reid and Mill and Frege)

You'll probably object you could put in some axiom so this can't happen but
it's not as simple.  You could say "actually there's only one Socrates".
But you are using "Socrates" as a common noun, not as a proper name.  You
can't even say what you want to say in ordinary language, good.  This is
essentially Frege's Trieste is no Vienna" argument.  Also Aquinas:

"No name signifying an individual is properly common (communicabile) to
many, but only by way of similitude; as for instance a person can be called
Achilles metaphorically, forasmuch as he may possess something of the
properties of Achilles, such as strength.  (Summa q.13 9)"

You probably have many arugments against this, would like to hear please.


PS also:

Saint Bonaventura also argued that the word "God" is a proper, and not  a
common noun.  For "Every noun [nomen], which has a plural, is an appellative
[common] noun; for proper nouns are not plurified, for there is not said:
more Peters and/or Johns; but this noun God is not an appellative noun,
because it does not signify a multiplicable form".  (Saint Bonaventura XXX
Q3).   Compare these to an argument of Geach, who says that we can give a
dog the name "Cerberus" but cannot on that account say of another dog: "here
is another Cerberus". [Mental Acts, p.68].

There was a v. interesting controversy in early Christian church as to
whether "God" is proper or common noun.  People were afraid if "God"
referred directly to God then they might as it were be blown away by awesome
majesty of direct referential contact with supreme omnipotent Being.

Dean Buckner
4 Spencer Walk
London, SW15 1PL

Work 020 7676 1750
Home 020 8788 4273

----- Original Message -----
From: "nino cocchiarella" <cocchiar at>
To: "Dean Buckner" <dean.buckner at>
Sent: Wednesday, February 20, 2002 9:11 PM
Subject: Re: FOM: Fiction and Mathematics

> Dear Dean Buckner,
>    I am very sympathtic to your view that mathematical entities and
> fictional entities are both of the same type; specifically that both are
> intensional objects.
>    I have described just such a view in a number of papers. My general
> framework in this project is a form of conceptual realism that is an
> intensional counterpart to my reconstruction of Frege's logic, where
> intensional objects are the result of nominalizing predicate expressions.
> For Frege, who was an extensionalist, nominalization resulted in a
> representation of the extension of a concept.
>    You can download some of my papers at the Italian website,
>, and do a search on my name. The paper, "Conceptual
> realism as a formal ontology" is a reasonable summary of the framework
> and view in question.
>    I found your objection to the empty set interesting. You might check my
> other paper, "On the logic of classes as many", at that same website.
> Classes as many are the "plural objects" Russell wrote about in his 1903
> _Principles of Math_. Needless to say, but there is no empty class as
> many.
>    If you are interested in a consistent logical reconstruction of Frege's
> and early Russell's frameworks, see my book _Logical Studies in Early
> Analytic Philosophy_ (1987).
>    I am also sympathetic to your interest in Ockham. You might find my
> paper, "A logical reconstruction of medieval terminist logic in conceptual
> realism," (in _Logical Analysis and History of Philosophy_, vol 4, 2001:
> 35-72), of some interest as well.
> -- Nino Cocchiarella
> **********************************************************
> On Wed, 20 Feb 2002, Dean Buckner wrote:
> > I've not had a great take-up on this theme, but I'll persevere!  The
> > background is the work I've been doing on explaining fiction without
> > invoking fictional characters, sets or numbers of such characters, (such
> > e.g the statement  that Jane Austen's Mr Bennett had five daughters).  I
> > believe we can even do without "metaphysical" concepts like meaning and
> > truth.  Ordinary language can cope perfectly well with the meaning of
> > fiction, without being Platonistic.
> >
> > Surely there is some connection between these ideas, and ideas about the
> > foundation of mathematics?
> >
> > I know very little about maths or set theory but I looked at some of the
> > propositions underlying ZF.  A number of them seem to assert existence
> > some sort, the most bizarre being the one about the "empty set".  Here's
> > set theory would explain the brief and elegant sentence  "there are no
> > unicorns".
> >
> > "the number corresponding to the set defined by the property of
> > is equal to the number corresponding to the set defined by the property
> > non-self identicalness"
> >
> > Really?  There are two equal and opposite ways of looking at this.
> > Platonists leap in excitement at the thought of proving the existence of
> > strange entities from minimal conceptual assumptions ("Axiom of
> > Specification").  Radical Ockhamists (me) will be pleased that a long
> > sentence containing apparently existence-invoking expressions ("the
> > of non-self identicalness") can be compacted into short sentence
> > no such expressions.
> >
> > (Note Frege himself abandoned this Platonism late in life.  He writes
> > the use of definite article in language creates the illlusion that an
> > is designated, and adds rather sadly "I myself was under this illusion
> > in attempting to provide a logical foundation for numbers, I tried to
> > construe numbers as sets."  (PW p.269).)
> >
> > It will be argued that ordinary language though simple, may be difficult
> > explain.  The language required to explain the meaning of a simple
> > sentence may be complex and difficult and inelegant. I can't go deep
> > this right now, but would just like to challenge it.
> >
> > Why can't "thought" and "meaning" lie right underneath the surface of
> > language?  If only we could focus on the right place.  This is an
> > that drove logic for 2,000 years until Frege.  Is the foundation of
> > mathematics really as difficult as it looks?
> >
> > In light of the raging debate over intuition vs rigour, admit little
> > (but can supply on demand).  The intuition is:  ordinary language  looks
> > simple, why shouldn't it actually be so?
> >
> >
> >
> > Dean Buckner (research interest: semantics of fiction)
> > 4 Spencer Walk
> > London, SW15 1PL
> >
> > Work 020 7676 1750
> > Home 020 8788 4273
> >
> >
> >
> >

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