[FOM] Simmons' denotation paradoxes

[Sandy Hodges]

The example:

Peter Abelard makes the two utterances only:
(1)    "17."
(2)    "The sum of the numbers referred to attributively by Heloise,
               in her utterances about which there is no choice
                 as to whether they are attributive or not."
and Heloise says only:
 (3)    "62."
 (4)   "The sum of the numbers referred to attributively by Peter
Abelard,
               in his utterances about which there is no choice
                 as to whether they are attributive or not."
Alberic of Rheims says only
 (5)   "The sum of the numbers referred to attributively by Peter
Abelard,
               in his utterances about which there is no choice
                 as to whether they are attributive or not."
Hartley Slater says:
 (6)   "There is a choice as to whether Peter Abelard's second utterance
refers attributively or not."

Suppose Hartley were to say:
(7)    "The sum of the numbers referred to attributively by Peter
Abelard,
               in his utterances about which there is no choice
                 as to whether they are attributive or not."

Harvey Slater's response:
"Hence the two 'sum' expressions [e.g. (2) and (4)] are not both
attributive with no choice about them being attributive.  But that still
allows them, even both, to be attributive by choice, and then to refer
to 62 and 17 respectively."

I seem to be having difficulty getting an answer about the status of
Alberic's utterance; this is the third time I have asked.

I hope sentence (6) correctly states Slater's position.   If it does,
then I think (7) must refer to 17.    But the most important question
is, does (7) refer to 17 attributively without any choice?

If the answer is that (7) refers attributively without any choice, then
will Slater agree that the same words were used by him and by Heloise,
but that when she used them it was a matter of choice as to whether they
referred attributively, but when he used them it was not a matter of
choice?

-----
Harvey Slater says:
"But what is the novelty?"

this, plus the fact that he keeps answering about the status of (2) and
(4), and ignores the more interesting case of (5), contributes to my
feeling that we are talking at cross purposes.

When an expression refers directly or indirectly to itself, it can be
such that if the references are handled in the normal way, the result is
triviality.   Such expressions have been characterized in many ways: as
paradoxes, as meaningless, as neither true nor false; there must be
dozens or hundreds of different descriptions.    There is a general view
that we need to justify or explain the fact that we do not handle the
references in these expressions in the ways that work for ordinary
expressions.    Most of the huge literature on the semantic paradoxes
consists of attempts to provide such a justification.

But justification does not interest me.

Suppose we thought a particular one of the dozens or hundreds of
justification proposals was the one right answer.     We can take the
language used in that one right answer, and use it to construct an
example containing three key expressions: two that refer to each other
in a loop, and one which has the status of an observer of the loop.
This can be done so the "observer" expression states our own position
about one of the two "loop" expressions, and also the "observer"
expression is the exact same words as one of the "loop" expressions.

When we have done that, we have two choices: we can say the observer
expression has different status that the loop expression, in spite of
being the same formula.   This is the token-relative option.   Or we can
say that the observer expression has the same status as the loop
expression, but we don't mind asserting an expression having this
status, when we state our position.   Graham Priest's dialetheism is an
example of this.   We can call this the "Liar-asserting" option, since
proponents are willing to assert "The Liar sentence is true."

Into which of these categories, token-relative or Liar-asserting,
Hartley Slater's system falls, or if it manages to escape them both, is
what I am attempting to discover.

------- -- ---- - --- -- --------- -----
Sandy Hodges / Alameda,  California,   USA
mail to SandyHodges at attbi.com will reach me.