PARADOXES AND STATES OF AFFAIRS

It is commonly held that an expression X succeeds to express a
proposition according to a particular linguistic code L iff X depicts a
well defined state of affairs according to L.

Most logicians think that not all sentences express propositions, for
example the Liar-like sentences do not.

Nevertheless, the meta-paradox with the Strengthened Liar seems to show
that a same sentence can sometimes express a proposition while it
cannot do it in other occasions. Let me remind you of the well known
argument on this. Consider the sentence-token:

(1) (1) expresses no true proposition

No classical truth-value can be consistently assigned to (1); so we
have to conclude that (1) expresses no proposition and in particular no
true one, so that we are entitled to state the following
sentence-token:

(2) (1) expresses no true proposition

Different tokens of one and the same sentence seem to possess different
logical values. The usual tokenist approach does not go much farther
this way. And a consequence is that one still remains wondering why (1)
is unable to assert the state of affairs that (1) expresses no true
proposition, precisely what (2) is entitled to assert.

The question can be reformulated this way: why is the state of affairs
that (1) expresses no true proposition available for (2) to state but
not for (1)?

Intuitively one sees that (2) avoids the circularity that affects (1):
once (1) and (2) are distinguished as different logical objects, (1)
but not (2) is (or 'tries to be') self-referential. If we examine
the mental events resulting on the assertion of (2), as depicted above,
we see that when we are prepared to assert (2) we are able to make a
reference to (1) and its truth-value that we wouldn't be able while
uttering (1), i. e. before we've had the chance of performing an
assessment of (1). So, it appears that the thought undelying (2) could
never underlie (1).

The phenomenological approach (in Hussserl's sense) I want to propose
accounts, I think, for this all. The mental act A that accomplishes the
assertion of a proposition p is an 'intentional act', that is, a
mental act referring to some object called the 'intentional object'
of A. This object is precisely p.

It seems to me that it is a general or 'eidetic' feature of
intentional acts that no act can be its own intentional object or a
part of it; no thought can think itself, so to say. I will call this
the 'principle of no self-reference' (PNS) A thought underlying (1)
would have to break PNS and, consequently, would be phenomenologically
impossible. This is why there can be no thought behind (1) and this
explains the difference between it and (2).

Now it seems to be a sensible claim that whatever cannot be an
intentional object for an act of thinking cannot be an available state
of affairs for it to assert. This would in turn explain why the state
of affairs that (1) expresses no true proposition is available for the
one who asserts (2) but not for whoever utters (1).

This proposal also fits cases of indirect self-reference. You may
remember the example proposed by Daryl McCullough on the thread
'Halting Problem for Humans' at
http://groups.google.com/group/sci.logic/browse_frm/thread/25164bcecd12ec30
..
Peter and Daryl are trying to correctly answer respectively the
questions 'Will Daryl answer "yes"?', 'Will Peter answer
"no"?'. Each knows what the other is trying to do but no
interaction between them is allowed. Under these conditions there is no
possibility of both working out the correct answer.

Daryl McCullough defended that the questions were well defined, i. e.
that they proposed well defined states of affairs, for Peter will
either answer "no" or he will not do so and correspondingly for
Daryl and "yes". I think he was right but I think too that the
(eventual) state of affairs 'Peter will answer "no"' is not
available for Daryl and the (eventual) state of affairs 'Daryl will
answer "yes"' is not available for Peter. That is why they get
trapped in vicious circularity when trying to answer correctly. Daryl
McCullough's case is a version of the Card Paradox and an example of
indirect self-reference. Peter, for instance, will confront the
situation 'Daryl answers "yes" iff I answer "no"', so Peter
must take into account how his own calculation will behave in order to
perform it. Out of PNS, Peter's reasoning is not an available state
of affairs for Peter while he is still accomplishing it.

Here I found a difference between humans and Turing machines, namely
that a behavior of a Turing machine is always in principle an available
state of affairs for every human while this is not the case for human
mental behaviors.

The phenomenological approach to the state-of-affairs problem in
paradoxes does not apply to all of them, it is only meant for paradoxes
where direct or indirect self-reference is involved. Abo pointed out on
the thread 'Incompatibility of Computationalism and Classical
Logic' at
http://groups.google.com/group/sci.logic/browse_frm/thread/866ad885e012fd13/aca261aa6e66f2e4?hl=en#aca261aa6e66f2e4
that this approach does not apply to the paradoxes of the kind of the
Infinite Liars introduced by Yablo; for example, everyone in an
infinite queue says 'everyone behind me says an untruth' or 'the
next token is not true'.

However, there is no reason to require that the solution to all
sentential paradoxes be exactly the same. I think that the reason why
'everyone behind me says an untruth' is not an available state of
affairs for each queuer can perfectly be quite different from the
reason applicable to the usual Liar, without this disproving the said
above.

Regards

Laureano

.

Relevant Pages

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