[FOM] Unrestricted Quantification and Paradox

laureano luna laureanoluna at yahoo.es
Thu Jun 7 08:59:53 EDT 2007

Robert Smith wrote:

>General prohibitions against "self-reference" are
>untenable IMHO.

My claim is that all forbidden self-references stem
from the impossibility of an intentional act to be its
own intentional object. Someone told me Ernst Mally
wrote that no thought can think itself. In other
terms, no thought is about itself.

This principle seems evident to me, since the thought
I'm performing is not yet there to face me while I'm
still performing it. It is easy to see that, if an
intentional act were its own intentional object, there
would be an infinite regress in the determination of
the content of the act:

let 'PSI(x)' be the intentional act whose objetc is x.
Set x = PSI(x). Then you have:

PSI(x)= PSI(PSI(x)) = PSI(PSI(PSI(x))) etc.

Nevertheless, I consider two kinds of only apparent,
non genuine, self-reference:

1. An intentional act refers to an associated physical
act, or similarly, a proposition refers to the
sentence that expresses it.
2. An intentional act refers by means of a general
concept to a class of objects to which the act itself

The first case isn't problematic:

(1) 'I am pronouncing five words'

As for the second, there are considerations for its
possibility, mainly the fact that those cases can be
mostly reduced to expressions of implication between
concepts or concepts and features. When we say:

(2) all propositions are either true or false

we can reformulate as:

(3) the concept of proposition implies the feature of
being either true or false.

Or when I say:

(4) no cat can understand what I'm saying

It can be argued that (4) reduces to 

(5) I am speaking English and the concept of cat
implies inability to understand English

or something alike.

Nevertheless, this second kind of cases seems
problematic to me because of some set theoretic
considerations closely related to the topic of
unrestricted quantification.

This all goes back to infinite regress and
circularity, i.e. to kinds of non well-foundedness.
What I'm claiming is that the attempt to imply a
genuine intentional self-reference is one source of
non well-foundedness. This is, I think, the case for
unbounded recursion in the Liar and the Truth Teller.


Laureano Luna

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