[JLSblogs] [The Grice Club] "Heterological": the implicature

[jlsperanza at aol.com (J. L. Speranza)]

---

There's an item on Russell and 'heterologicality' in the Grice archive
-- Carton 9, folder 8.

>From wiki's entry:

"The Grelling?Nelson paradox is a semantic self-referential paradox
formulated in 1908 by K. Grelling and L. Nelson and sometimes
mistakenly attributed to the German philosopher and mathematician
Hermann Weyl."

"It is thus occasionally called Weyl's paradox as well as Grelling's
paradox."

"Suppose one interprets the adjectives "autological"
and "heterological" as follows."

1. An adjective is autological (sometimes homological) iff it describes
itself.

(For example "short" is autological, since the word "short" is
short. "English," "unhyphenated" and "pentasyllabic" are also
autological).

2. An adjective is heterological if it does not describe itself.
Hence "long" is a heterological word, as are "abbreviated"
and "monosyllabic."

---

All adjectives, it would seem, must be either autological or
heterological, for each adjective either describes itself, or it
doesn't.

The Grelling?Nelson paradox arises when we consider the
adjective "heterological".

To test if the (imaginary) word "'foo" is autological one can ask:

Is "foo" a foo word?

If the answer is 'yes', "foo" is autological.

If the answer is 'no', "foo" is heterological.

By comparison, one can ask:

Is "heterological" a heterological word?

If the answer is 'yes', "heterological" is autological (leading to a
contradiction).

If the answer is 'no', "heterological" is heterological (again leading
to a contradiction, because if it describes itself, it is autological).

----

"The paradox can be eliminated, without changing the meaning
of "heterological" where it was previously well-defined, by modifying
the definition of "heterological" slightly to hold of all
nonautological words except "heterological.""

But "nonautological" is subject to the same paradox, for which this
evasion is not applicable because the rules of English uniquely
determine its meaning from that of "autological."

A similar slight modification to the definition of "autological" (such
as declaring it false of "nonautological" and its synonyms) might seem
to fix that, but the paradox still obtains for synonyms
of "autological" and "heterological" such as "selfdescriptive"
and "nonselfdescriptive," whose meanings also would need adjusting, and
the consequences of those adjustments would then need to be pursued,
and so on.

"Freeing English of the Grelling?Nelson paradox entails considerably
more modification to the language than mere refinements of the
definitions of "autological" and "heterological," which need not even
be in the language for the paradox to arise."

"The scope of these obstacles for English is comparable to that of
Russell's paradox for mathematics founded on sets, argued as follows.

Is "autological" autological?

One may also ask if "autological" is autological. It can be chosen
consistently to be either:

if we say that "autological" is autological, and then ask if it applies
to itself, then yes, it does, and thus is autological;

if we say that "autological" is not autological, and then ask if it
applies to itself, then no, it does not, and thus is not autological.

This is the opposite of the situation for heterological:
while "heterological" logically cannot be autological or
heterological, "autological" can be either.

(It cannot be both, as the category of autological and heterological
cannot overlap.)

In logical terms, the situation for "autological" is:

"autological" is autological if and only if "autological" is autological

A if and only if A, a tautology

while the situation for "heterological" is:

"heterological" is heterological if and only if "heterological" is
autological
A if and only if not A, a contradiction.

----- Grice's point

"The Grelling?Nelson paradox can be translated into Bertrand Russell's
famous paradox in the following way."

"First, one must identify each adjective with the set of objects to
which that adjective applies. So, for example, the adjective "red" is
equated with the set of all red objects. In this way, the
adjective "pronounceable" is equated with the set of all pronounceable
things, one of which is the word "pronounceable" itself. Thus, an
autological word is understood as a set, one of whose elements is the
set itself. Second, then, the question of whether the
word "heterological" is heterological becomes the question of whether
the set of all sets not containing themselves contains itself as an
element."

--
Posted By J. L. Speranza to The Grice Club at 4/25/2010 09:53:00 PM
-------------- next part --------------
An HTML attachment was scrubbed...
URL: 
<http://rbjones.com/pipermail/jlsblogs_rbjones.com/attachments/20100425/67b2ed31/attachment.html>