Re: Existence of mathematical entities (Re: Successor Axiom: on what grounds TF?)

From: Paul Holbach (paulholbachSPAMBAN_at_freenet.de)
Date: 02/20/05 

Date: 19 Feb 2005 18:47:28 -0800

> mitch wrote:

> The history of "logicism"--as I understand it thus far--ignores
> "objectification."
> One can verify this in both Dedekind and Frege.
> Moreover, when one turns
> to Russell or Carnap, you see the advent of what Shapiro calls
> "fictionalism."
> Russell clearly refers to classes as "logical fictions."

Itīs important to notice that Field doesnīt hold that mathematical
entities exist fictionally but that they donīt exist *at all*.

To consider mathematical discourse semantically analogous to literary
discourse with regard to fiction does not necessarily commit one
referentially to the existence of a realm of fictional objects.

All singular terms *purport* to refer to something because, seen from
the psycho-linguistic point of view, our intrinsically intentional
minds always aim at objects, often failing to hit one.

- "To exist is to have the simple property of existence, but
non-existence seems to be matter of failed intentionality."
- "The basic truth condition of the negative existential is that there
was only an entertaining of existence."
- "Non-existence is essentially and constitutively failed
intentionality."
- "Non-existence results from the occurrence of a certain kind of
mental act-a pretence or an erroneous postulation of existence.
Assertions of non-existence really are statements about mental acts."
- "The non-existence of Holmes depends upon the occurrence of certain
creative mental acts that have no target in the real world; if you
like, such non-existence is supervenient on mental acts that have no
real world reference."
- "To say that an object does not exist is to allude to mistaken
suppositions or acts of make-believe."
- "Non-existence really does have a lot more to do with misfirings of
the mind than do other kinds of property lack."

[Quoted from: McGinn, C. (2000). /Logical properties: Identity,
existence, predication, necessity, truth/. Oxford: Oxford University
Press.]

So, even if a singular term in fact happens to refer to absolutely
nothing, we are--per intrinsic intentionality--naturally inclined to
behave as if it did refer to something. But here weīre very often led
astray, with natural inclination being a bad adviser.

Regards
PH

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